Four Fours Problem

Compiled by Paul Bourke
Major contributor: Frank Primer

Contributions by Chris Smith, Guido Roach, Dhruv Chand, Jim Millar, Vijay Kailas, David Bevan, Ewald R. de Wit, Martin Olivella, Heiner Marxen, Scott Forschler, Wayne Goode, Jörg Wiegels, Ben Rudiak-Gould, Charles Dillingham, Peter Karsanow, Brad McInnes, Richard Schorn, Ewart Shaw, Rick Hevener, Toufic Batouli, and Sven Peterson.


This classical problem is most commonly formulated as follows:

"Given no more than four instances of the digit 4,
represent all integers using a finite number of
mathematical symbols and operators in common use."

The central issue then is which symbols may one use and which ones may not, the rules that will be applied to the following lists are outlined below. In situations where more than one solution can be found the challenge is to find the simplest, least number of symbols and operators as well as the simplest operators.

  • Acceptable symbols and operators

       +,-   addition subtraction
       *,/   multiplication, division
       sqrt,^   square root, power
       !   factorial, eg: n! = n * (n-1) * (n-2) * ... * 2 * 1
       .   decimal point, eg: .4
       `   repeating decimal, eg: .4` = .444444444...

  • Other Symbols

    Cannot use representations for other numbers, eg: use of [pi] in sin(pi / 4) = 1

  • Infinity

    Cannot use ... to represent an infinite number of operations eg: sqrt(sqrt(sqrt(...4))) = 1

  • Subfactorials

    Many solutions to this problem in the past have relied on an operator called the subfactorial, defined as follows.

    !n = n! (1 - 1/1! + 1/2! - 1/3! + 1/4! - ... +/-1/n!)

    Note that !n is always an integer.
    In particular
       !1 = 0
       !2 = 1
       !3 = 2
       !4 = 9

    Since the subfactorial is not considered a symbol in "common" use it will not be used here.

  • Gamma function

    The gamma function can be used to get an expression of 6 with only one 4.

    gamma(4) = 3! = 6

    Gamma function will not be used here.

  • 0.4th root (Courtesy of Scott Forschler)

    The 0.4th root of a number, normally written as This will be represented in the ASCII form as sqrt.4(x). It gives a shorter solution for 32, namely root.4(4) = 4^(5/2) = 32. Solutions are also listed below for 766, 770, and 772.

  • Arbitrary root (Courtesy of Frank Mrazik)

    An arbitrary root "b" of a number "a" may be written as root(a,b) where, in this context, a and b are made up entirely of the digit 4. This gives a four 4 solution for 657 for example.

  • Percent (Courtesy of Scott Forschler)

    While "%" is not strictly a mathematical symbol it is "in common use". It is shown below as alternative solutions for some numbers but still the primary solution for the problematic 113. This has been extended by Frank Mrazik to the following .4% (.004), .4'% (.00444444....), and even 4!% (0.24).

  • Percent-percent (Courtesy of Frank Mrazik)

    Getting a bit weird, 1%% = 1/10000. So for example 10000 = 4 / 4%%

  • Summation (Courtesy of Scott Forschler)

    A summation can be used to give various solutions, in particular, 303.

    Because solutions based upon summations use additional symbols, namely "i", they will not be used here.

  • Using five 4's

    Some of the gaps in the numbers below (numbers for which a solution with only four 4's hasn't yet been found) have solutions listed that use five 4's. Note that variations of the problem allow 'free' squaring (eg: 4^2 uses only one 4). In this case those five 4 solutions that use sqrt(4) in the rules used here become solutions with four or less fours. For example, 163 = (4^2+4^2+.4'^2)/.4'^2 uses only four 4's but eight if the 2's are replaced by sqrt(4) as required here.

  • 2/9 (First introduced by Richard Schorn for 113)

    This and the next repeating decimals are pushing the limits of what is acceptable. In this case it is written as .(sqrt(4))' = 0.22222222... otherwise known as 2/9.

  • 24/99 (Introduced by Rick Hevener)

    Hardly standard but some of the difficult numbers can be solved with .(4!)' which is supposed to represent 24/99 or 0.2424242424..... For example 99 then can be solved with two 4's as 4! / .(4!)'.

  • Mille (Proposed by Frank Mrazik)

    Frank Mrazik proposed use of the mille notation %o to mean 1/1000. Initially used for the elusive 713.

  • n!! (Proposed by Gerard Schildberger)

    Double factorial !! for even and odd numbers, for example
    8!! = 8 * 6 * 4 * 2
    9!! = 9 * 7 * 5 * 3

    For example, Jim Millar gave the following solution for 113
    113 = (4!! - 4/4)!! + 4!!

    A further list by Frank Mrazik.
         8 = 4!!
        15 = 5!!
        48 = 6!!
       105 = 7!!
       384 = 8!!
       945 = 9!!
      3840 = 10!!
    
    Including a double double !, by Frank Wrazik
       384 = (4!!)!!
       113 = ((4!!)! / (4!!)!!) + 4!!
    
  • !!n (Proposed by Gerard Schildberger)

    !!n = 0! + 1! + 2! + 3! + ... + n!
    For example !!4 = 10

  • Any number with three 4's (Contributed by Ben Rudiak-Gould)

    A cute solution to any number using just 3 fours. By admitting natural logarithms "ln()" then any positive integer n can be represented as

    n = -ln[ ln( sqrt(sqrt(...(sqrt(4))...))) / ln(4) ] / ln(4)

    where the number of nested sqrt() functions is twice n. Or if base 4 logarithms are permitted "log4()" then the expression becomes

    n = -log4(log4(sqrt(sqrt(...(sqrt(4))...))))

  • Any number with two 4's (Contributed by "whetstone")

    Using log10, any number can be represented using two fours and creative use of % as shown below:

       log(srqt(4/(4%)))      = log(sqrt(100))   = log(10)  = 1
       log(sqrt(4/(4%%)))     = log(sqrt(10000)) = log(100) = 2
       log(sqrt(4/(4%%...%)))                               = n
    

  • Any number with one 4 (Contributed by Jim Millar)

    Another cunning idea sees any number created using only one 4 and a lot of nested trigonometric functions (atan and sec). The principle lies in the relationship

    tan2(x)+1 = sec2(x)

    from which

    sec(atan(x)) = sqrt(x2+1)

    Repeated and nested application k times gives

    sec(atan(...(sec(atan(x))...)) = sqrt(x2+k)

    So if x=4 we can get any number (greater than 4) by only using a single 4. For example 5 is represented as

    sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(4))))))))))))))))))

    To get a particular number n requires k = n2-16 nestings. For more information, including how to derive numbers up to 4, see this description by Jim Millar.

  • Primorial (Suggested by Chris Smith)

    The primorial function, often written using the "#" symbol and it is the prime equivalent for factorial. So, for example, 4# is the product of the first 4 primes, 2*3*5*7=210.

    (4+4/4)=3210 and (4+(4+4)/4)=30030.

  • ceiling() and floor() (Suggested by Bruno Curfs)

    An option that provides another solution for the pesky 113, namely the "ceiling(x)" function defined as the smallest integer greater than or equal to x. Written as //x\\, then //.4\\ = 1.

    113 can be written as 4 * (4 + 4!) + //.4\\

    Along the same lines, if floor(x) is the largest integer less than or equal to x, if floor(x) is written as \\x// then

    113 = \\exp(4.4)// + root.4(4)

  • Exactly 4 fours

    A variation to the problems description above is to use exactly 4 fours. A list compiled by Sven Peterson is given here: 4_4_4_4.docx.

The solutions so far


      0      2      4 - 4
      1      2      4 / 4
      2      1      sqrt(4)
      3      2      sqrt(4 / .4`)
             3      4 - 4 / 4
      4      1      4
      5      2      sqrt(4) / .4
      6      2      4 + sqrt(4)
      7      3      (4! + 4) / 4
             4      4 + 4 - 4 / 4
      8      2      4 + 4
      9      2      4 / .4`

     10      2      4 / .4
     11      3      44 / 4
     12      2      4! / sqrt(4)
             3      4 + 4 + 4
     13      3      (4! + sqrt(4)) / sqrt(4)
     14      3      4 * 4 - sqrt(4)
     15      3      (4 + sqrt(4)) / .4
             4      4 * 4 - 4 / 4
             2      sqrt(.4') / 4' %
     16      2      4 * 4
     17      4      4 * 4 + 4/4
             3      (4 - .(sqrt(4))`) / .(sqrt(4))`
             3      sqrt(4) + root(-sqrt(4), .4`%)
     18      3      4 * 4 + sqrt(4)
             2      4 / .(sqrt(4))'
     19      3      4! - sqrt(4) /.4
     20      2      4! - 4
     21      3      4! - sqrt(4) / sqrt(.4`)
     22      2      4! - sqrt(4)
     23      3      4! - 4 / 4
     24      1      4!
     25      3      4! + 4 / 4
             2      .(sqrt(4))^(-sqrt(4))
             2      sqrt(4% ^ -sqrt(4))
     26      2      4! + sqrt(4)
     27      3      4! / (.4` * sqrt(4))
     28      2      4! + 4
     29      3      4! + sqrt(4) / .4
     30      3      4! + 4 + sqrt(4)
             2      sqrt(4) / sqrt(.4' %)
     31      4      4! + (4! + 4) / 4
             3      (sqrt(4) + sqrt(.4' %)) / sqrt(.4' %)
     32      3      4 * (4 + 4)
             2      root.4(4)
     33      3      4! + 4 / .4`
     34      3      4! + 4 / .4
     35      3      (4! - sqrt(.4`)) / sqrt(.4`)
     36      4      4 * (4 + 4) + 4 
             3      4! + 4! / sqrt(4)
             2      4! / sqrt(.4`)
     37      3      (4! + sqrt(.4`)) / sqrt(.4`)
     38      3      4! / sqrt(.4`) + sqrt(4)
     39      3      (sqrt(4) + 4!) / sqrt(.4`)
     40      3      44 - 4
     41      4      (4 * 4 + .4) / .4
             3      (sqrt(4%) / .4`%) - 4
     42      3      44 - sqrt(4)
     43      4      44 - 4/4
             3      (sqrt(4%) / .4`%) - sqrt(4)
     44      2      44
     45      3      (4! - 4) / .4`
             2      sqrt(4) / 4' %
     46      3      44 + sqrt(4)
     47      4      4! + 4! - 4 / 4
             3      sqrt(4) + (sqrt(4%) / .4`%)
     48      2      4! + 4!
     49      4      4! + 4! + 4 / 4
             3      .(sqrt(4))^(-sqrt(4)) + 4!
             3      (sqrt(4) - 4%) / 4%
     50      3      4! + 4! + sqrt(4)
             2      sqrt(4) / 4 %
     51      4      (.4 + 4! - 4) / .4
             3      (sqrt(4) + 4%) / 4%
     52      3      4! + 4! + 4
     53      3      (4! - .4`) / .4`
     54      2      4! /.4`
     55      3      (4! - sqrt(4)) / .4
     56      3      4! / .4 - 4
     57      4      (4! + .4) / .4 - 4
             3      (4 - sqrt(4%)) / sqrt(.4`%)
     58      3      4! / .4 - sqrt(4)
     59      3      (4! - .4) /.4
     60      2      4! / .4
     61      3      (4!+ .4) / .4
     62      3      4! / .4 + sqrt(4)
     63      3      (4! + 4) / .4`
     64      2      sqrt(sqrt(sqrt(4^(4!))))
     65      3      (4! + sqrt(4)) / .4
     66      3      sqrt(sqrt(sqrt(4^(4!)))) + sqrt(4)
             3      44 / sqrt(.4`)
     67      4      sqrt(4) + (4! + sqrt(4)) / .4
     68      3      44 + 4!
     69      4      (4! + 4 - .4) / .4
             3      4! + (sqrt(4%) / .4`%)
     70      3      (4! + 4) / .4
     71      4      (4! + 4.4) / .4
     72      3      4! + 4! + 4!
     73      4      sqrt(sqrt(sqrt(4^(4!)))) + 4 / .4`
     74      4      4! + 4! + 4! + sqrt(4)
             3      (sqrt(4) / 4%) + 4!
     75      4      (4! + 4 + sqrt(4)) / .4
             3      4! / root(.4, 4)%
     76      4      4! + 4! + 4! + 4
             3      4! / .(4!) - 4!
             3      (4 / 4%) - 4!
     77      4      4! / (.4` * sqrt(.4`)) - 4
     78      3      4! + 4! / .4`
     79      4      4! + (4! - sqrt(4)) / .4
     80      3      4 * (4! - 4)
     81      3      (4 / .4')^sqrt(4)
     82      4      4 * (4! - 4) + sqrt(4)
     83      4      4! - (.4 - 4!) / .4
     84      3      4! / .4 + 4!
     85      4      (4! + 4 / .4) / .4
             3      (.4` - sqrt(.4`%)) / .4`%
     86      4      44 * sqrt(4) - sqrt(4)
             3      (.4 / .4`%) - 4
     87      4      4 * 4! - 4 / .4`
     88      3      44 * sqrt(4)
     89      4      (4! + sqrt(4)) / .4 + 4!
             3      (.4 - .4`%) / .4`%
     90      3      4 / (.4` - .4)
             2      .4 / .4`%
     91      4      4 * 4! - sqrt(4) / .4
             3      (.4` - 4%) / .4`%
     92      3      4 * 4! - 4
     93      4      4 * 4! - sqrt(4) / sqrt(.4`)
     94      3      4 * 4! - sqrt(4)
     95      4      4 * 4! - 4/4
             3      (4 - sqrt(4%)) / 4%
     96      2      4 * 4!
     97      4      4 * 4! + 4/4
             3      (sqrt(.4`) - sqrt(4)%) / sqrt(.4`)%
     98      3      4 * 4! + sqrt(4)
     99      3      44 / .4`
             2      4! / .(4!)'

    100      3      4 * 4! + 4                
             2      4! / .(4!)
             2      4 / 4%
    101      4      4 * 4! + sqrt(4) / .4
             3      (4 + 4%) / 4%
    102      4      4 * 4! + 4 + sqrt(4)
             3      4! / .(4!) + sqrt(4)
             3      (4 / 4%) + sqrt(4)
    103      4      44 / .4` + 4
             3      (sqrt(4)% + sqrt(.4`)) / sqrt(.4`)%
    104      3      4 * (4! + sqrt(4))
    105      4      (44 - sqrt(4)) / .4
             3      (4 + sqrt(4%)) / 4%
    106      4      44 / .4 - 4
             3      (4 + 4!%) / 4%
    107      4      (4! + 4! - .4`) / .4`
             3      (4! - .(sqrt(4))`) / .(sqrt(4))`
    108      3      (4! + 4!) / .4`
             2      4!/.(sqrt(4))`
    109      4      (44 - .4) / .4
             3      (4! + .(sqrt(4))`) / .(sqrt(4))`
             3      (4% + .4`) / .4`%
    110      3      44 / .4
    111      4      444/4
    112      3      4 * (4! + 4)
    113      4      4!/.(sqrt(4))` + sqrt(4)/.4
             4      (.4 - .4`%) / .4`% + 4!
             4      ( sqrt(4) / .4' + sqrt(4)% ) / 4%
             4      (sqrt(4) + (sqrt(4) + 4!)%) / (sqrt(4))%
             3      (.(sqrt(4))' / (.(sqrt(4)) % )') + sqrt(4)
    114      4      44 / .4 + 4
             3      4! + (.4 / .4`%)
    115      4      (44 + sqrt(4)) / .4
             3      (.4` + sqrt(.4`%)) / .4`%
    116      3      (sqrt(4) / .4)! - 4
    117      4      (4! + 4! + 4) / .4`
    118      3      (sqrt(4) / .4)! - sqrt(4)
    119      4      (4! + 4! - .4) / .4
             3      (4! - sqrt(4%)) / sqrt(4%)
    120      2      (sqrt(4) / .4)!
    121      4      (44 / 4) ^ sqrt(4)
             3      (4! + sqrt(4%)) / sqrt(4%)
    122      3      (sqrt(4) / .4)! + sqrt(4)
    123      4      44 / .4` + 4!
    124      3      (sqrt(4) / .4)! + 4
    125      4      (4! - 4) / (.4 * .4)
             3      sqrt(sqrt(sqrt((sqrt(4) / .4)^(4!))))
             2      sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!)
    126      4      4^4 / sqrt(4) - sqrt(4)
             3      (4! + 4) / .(sqrt(4))`
             3      (sqrt(.4`) / .4`%) - 4!
    127      4      (4^4 - sqrt(4)) / sqrt(4)
    128      3      4^4 / sqrt(4)
    129      4      (4^4 + sqrt(4)) / sqrt(4) 
    130      4      4^4 / sqrt(4) + sqrt(4)
             3      (sqrt(4) + 4!) / sqrt(4%)
    131      4      4! / (.4 * .4`) - 4
    132      4      4^4 / sqrt(4) + 4
    133      4      4! / (.4 * .4`) - sqrt(4)
    134      4      4! + 44 / .4
    135      3      4! / (.4 * .4`)
    136      4      4 * ( 4! + 4 / .4)
             3      (4!% + sqrt(.4`)) / sqrt(.4`)%
    137      4      4! / (.4 * .4`) + sqrt(4)
    138      4      (4! * 4! - 4!) / 4
    139      4      4! / (.4 * .4`) + 4
    140      4      4 * 4! + 44
             3      (4! + 4) / .(sqrt(4))
             3      (4 + 4!) / sqrt(4%)
    141      4      (4 * 4! - sqrt(4)) / sqrt(.4`)
             3      (sqrt(.4`) - 4%) / .4`%
    142      4      4! * 4! / 4 - sqrt(4)
    143      4      (4! * 4! - 4) / 4
    144      3      4! * 4! / 4
    145      4      (4 + 4! * 4!) / 4
             3      (sqrt(4%) + .4`) / .4`%
    146      4      4! / .4 / .4 - 4
             3      (sqrt(.4`) / .4`%) - 4
    147      4      (4 * 4! + sqrt(4)) / sqrt(.4`)
    148      4      4 + 4! * 4! / 4
             3      (sqrt(.4`) / .4`%) - sqrt(4)
    149      4      (4! / .4 - .4) / .4
             3      (sqrt(.4`) - .4`%) / .4`%
    150      3      4! / (.4 * .4)
             2      sqrt(.4') / .4' %
    151      4      (4! / .4 + .4) / .4
             3      (sqrt(.4`) + .4`%) / .4`%
    152      4      4 * 44 - 4!
             3      sqrt(4) + (sqrt(.4`) / .4`%)
    153      4      (44 + 4!) / .4`
    154      4      4 + 4! / .4 / .4
             3      4 + (sqrt(.4`) / .4`%)
    155      4      (4! / .4 + sqrt(4)) / .4
    156      4      (4! + sqrt(4)) * (4 + sqrt(4))
    157      4      4^4 - 4! / .(4!)'
             4      ((4% + sqrt(.4`)) / .4`%) - sqrt(4)
    158      4      sqrt(sqrt(sqrt(4^4!))) / .4 - sqrt(4)
    159      4      4! / .4 / .4` + 4!
             3      (4% + sqrt(.4`)) / .4`%
    160      3      sqrt(sqrt(sqrt(4^4!))) / .4
    161      4      (sqrt(sqrt(sqrt(4^4!))) + .4) / .4
    162      4      (4! * 4 - 4!) / .4`
             3      4! / sqrt(.4') / .(sqrt(4))'
    163      4      (4! / sqrt(.4`) + .(sqrt(4))`) / .(sqrt(4))`
             4      ((4 + 4!)% + .4`) / .4`%
    164      4      (sqrt(4) / .4)! + 44
    165      4      44 / .4 / sqrt(.4`)
             2      .4 / .(4!)' %
             3      (sqrt(.4`) - sqrt(.4`)%) / .4%
    166      4      4! / (sqrt(.4') * .(sqrt(4))') + 4
             4      (sqrt(.4)^(-4) + sqrt(.4')) * 4!
             3      (sqrt(.4`) / .4%) - sqrt(.4`)
    167      4      (sqrt(.4') / .4 % ) + (sqrt(.4') / sqrt(4))
             5      4! + ((4!)^sqrt(4) - 4) / 4
    168      4      (4! + 4) * (4 + sqrt(4))
    169      4      (4! + sqrt(4))^sqrt(4) / 4
    170      4      (44 + 4!) / .4
    171      4      (.4 / .(4!)' %) + sqrt(4) + 4
             4      ((4 / 4%) - 4!) / .4`
    172      4      4 * 44 - 4
    173      4      ((4!/4)! * .(4!)) + .(sqrt(4))
             4      (4 - (4! / .4`)%) / sqrt(4)%
    174      4      4 * 44 - sqrt(4)
             3      4! + (sqrt(.4`) / .4`%)
    175      4      (4! + 4) / (.4 * .4)
    176      3      4 * 44
    177      4      ((sqrt(4) / .4)! - sqrt(4)) / sqrt(.4`)
    178      4      4 * 44 + sqrt(4)
    179      4      ((4! / 4)! - 4) / 4
    180      3      (4 + sqrt(4))! / 4
             2      .4 / .(sqrt(4))' %
    181      4      ((4! / 4)! + 4) / 4
    182      4      sqrt(4) + (4! / 4)! / 4
    183      4      ((sqrt(4) / .4)! + sqrt(4)) / sqrt(.4`)
    184      4      4 * (sqrt(4) + 44)
    185      4      44.4 / .(4!)
             4      44.4 / 4!%
    186      4      ((4! / 4)! + 4!) / 4
    187      4      (4 - .(4!) - sqrt(4) % ) / sqrt(4) %
             4      (4 - (sqrt(4) + 4!)%) / sqrt(4)%
    188      4      4 * (4! + 4!) - 4
             3      (4 - 4!%) / sqrt(4)%
    189      4      (4! / .4 + 4!) / .4`
    190      4      4! (4 + 4) - sqrt (4)
             3      (.4 + .4`) / .4`%
    191      4      (.4' % + .4 + .4') / .4' %
    192      3      4 * (4! + 4!)
    193      4      (4 + .(sqrt(4))' + sqrt(.4' % ))  /  (sqrt(4) % )'  
             4      sqrt(.4`% ^ -sqrt(4)) - root(.4, 4)
    194      4      4! (4 + 4) + sqrt (4)
    195      4      (4! / .4` + 4!) / .4
             3      (sqrt(4%) + sqrt(.4`)) / .4`%
    196      4      sqrt(4) * (4 * 4! + sqrt(4))
             3      (4 / sqrt(4)%) - 4
    197      4      (44 - .(sqrt(4)')) / .(sqrt(4)')
             4      (4 - (4 + sqrt(4))%) / sqrt(4)%
    198      4      (4! - sqrt(4)) * 4 / .4`
             3      44 / .(sqrt(4)')
             3      (4 / sqrt(4)%) - sqrt(4)
    199      4      (44 + .(sqrt(4)')) / .(sqrt(4)')
             4      4!/.(4!)' + 4!/(4!)
             3      (4 - sqrt(4)%) / sqrt(4)%
    200      4      4 * 44 + 4!
             2      .4' / .(sqrt(4))' %
             2      4 / sqrt(4)%
    201      4      ((4!) - (sqrt(sqrt(sqrt(.4))))^(-4!)) * (4!)
             3      (4 + sqrt(4)%) / sqrt(4)%
    202      4      4^4 - 4! / .4`
             3      (4 / sqrt(4)%) + sqrt(4)
    203      3      (.4' + sqrt(.4') %  /  .(sqrt(4))' %
             4      (4 + (4 + sqrt(4))%) / sqrt(4)%
    204      4      4! + (4! / 4)! / 4
             3      4 + (4 / sqrt(4)%)
    205      4      ((sqrt(4) / 4' %) - 4) / .(sqrt(4))
             4      (4 + (.4 / 4)) / sqrt(4)%
    206      4      (4! / .(4!)' + 4) * sqrt(4)
             4      4 ^ 4 - (sqrt(4) / 4%)
    207      4      (4 * 4! - 4) / .4`
    208      4      4^4 - 4! - 4!
    209      4      ((sqrt(4) / 4 % ) + sqrt(.4'))  /  .(4!)'
             4      (4 / sqrt(4)%) + (4 / .4`)
    210      4      (4! / .4 + 4!) / .4
             3      (4 + sqrt(4%)) / sqrt(4)%
    211      4      ((.4 * 4!) - .sqrt(4))') / 4' %
             4      4 ^ 4 - (sqrt(4%) / .4`%)
    212      4      4^4 - 44
             3      (4 + 4!%) / sqrt(4)%
    213      4      (4! * sqrt(4) - sqrt(.4')) / .(sqrt(4))'  
             4      (4 + (sqrt(4) + 4!)%) / sqrt(4)%
    214      4      4! * 4 / .4` - sqrt(4)
    215      4      (4 * 4! - .4`) / .4`
    216      3      4 * 4! / .4`
    217      4      (4 * 4! + .4') / .4'
    218      4      4! * 4 / .4` + sqrt(4)
    219      4      (root.4(4/.4')) - 4!
    220      4      44 * sqrt(4) / .4
             3      44 / sqrt(4%)
    221      4      (44 + .(sqrt(4))) / .(sqrt(4)
             3      sqrt(.4`% ^ -sqrt(4)) - 4
    222      4      444 / sqrt(4)
    223      4      ((4! / .(4!)) / .4')  -  sqrt(4)
             3      sqrt(.4`% ^ -sqrt(4)) - sqrt(4)
    224      4      (4 + 4) * (4! + 4)
             3      (4 / sqrt(4)%) + 4!
    225      4      ((sqrt(4) + 4) / .4)^sqrt(4)
             2      sqrt(.4`% ^ -sqrt(4))
    226      4      ((4! / .(4!))  + .4') / .4'
             3      sqrt(.4% ^ -sqrt(4)) - 4!
    227      4      ((4! / .(4!)) / .4')  +  sqrt(4)
             3      sqrt(4) + sqrt(.4`% ^ -sqrt(4))
    228      4      4^4 - 4! - 4
    229      4      ((4! / .(4!)) / .4')  + 4
             3      4 + sqrt(.4`% ^ -sqrt(4))
    230      4      (4 * 4! - 4) / .4
    231      4      (sqrt(4) + 4! / .4') / .(4!)'
             4      ((4 / .4`%) + 4!) / 4
    232      3      4^4 - 4!
    233      4      (4! / .(sqrt(4))') + sqrt(sqrt(sqrt(.(sqrt(4)))) ^ (- 4!)
             4      4 + 4 + sqrt(.4`% ^ -sqrt(4))
    234      4      4^4 - 4! + sqrt(4)
    235      4      (4 * 4! - sqrt(4)) / .4
    236      4      4^4 - 4! + 4
    237      4      (4 * 4) - .(sqrt(4)) / sqrt(.4' %)
             4      ((4 * 4) - sqrt(4%)) / sqrt(.4`%)
    238      4      4! * 4 /.4 - sqrt(4)
    239      4      (4 * 4! - .4) / .4
    240      3      4 * 4! / .4
    241      4      (4 * 4! + .4) / .4
    242      4      4! * 4 / .4 + sqrt(4)
    243      4      sqrt(4) * 4! / (.4` * .4`)
             3      root(sqrt(4%), sqrt(4 / .4`))
    244      4      4^4 - 4! / sqrt(4)
    245      4      (4 * 4! + sqrt(4)) / .4
    246      4      4^4 - 4 / .4
             3      sqrt(.4% ^ -sqrt(4)) - 4
    247      4      4^4 - 4 / .4`
    248      4      4^4 - 4 - 4
             3      sqrt(.4% ^ -sqrt(4)) - sqrt(4)
    249      4      ((4!/.4)  - .(4!))  / .(4!)
             3      4! + sqrt(.4`% ^ -sqrt(4))
    250      4      (4 * 4! + 4) / .4
             2      sqrt(.4% ^ -sqrt(4))
    251      4      4^4 - sqrt(4) / .4
    252      3      4^4 - 4
    253      4      4^4 - sqrt(4) / sqrt(.4`)
    254      3      4^4 - sqrt(4)
    255      4      4^4 - 4/4
    256      2      4^4
    257      4      4^4 + 4/4
    258      3      4^4 + sqrt(4)
    259      4      4^4 + sqrt(4) / sqrt(.4`)
    260      3      4^4 + 4
    261      4      4^4 + sqrt(4) / .4
    262      4      4^4 + 4 + sqrt(4)
    263      4      (sqrt(sqrt(sqrt(4^4!))) - .(4!)') / .(4!)'
             4      (sqrt(4) - (4! + sqrt(.4`))%) / sqrt(.4`)%
    264      4      44 * (4 + sqrt(4))
             3      (sqrt(4) - 4!%) / sqrt(.4`)%
    265      4      4^4 + 4 / .4`
    266      4      4^4 + 4 / .4
    267      4      (root.4(4/.4')) + 4!
    268      4      4^4 + 4! / sqrt(4)
    269      4      ((sqrt(4) / .4)! - .4`) / .4`
    270      3      (sqrt(4) / .4)! / .4`
    271      4      ((sqrt(4) / .4)! + .4`) / .4`
    272      4      4^4 + 4 * 4
    273      4      ((4! / .4) + .4') / .(sqrt(4))'
             4      ((sqrt(4) - sqrt(4)%) / sqrt(.4`)%) - 4!
    274      4      (sqrt(4) / .4)! / .4` + 4
             3      4! + sqrt(.4% ^ -sqrt(4))
    275      4      44 / .4 / .4
             2      sqrt(.4') / .(4!)' %
    276      4      4^4 + 4! - 4
             3      (sqrt(4) / sqrt(.4`)%) - 4!
    277      4      ((sqrt(.4') + .(sqrt(4))' % ) / .(sqrt(4))' % )  -  4!
             4      ((sqrt(4) + sqrt(.4`)%) / sqrt(.4`)%) - 4!
    278      4      4^4 + 4! - sqrt(4)
    279      4      ((sqrt(4) / .4)! + 4) / .4`
             4      (((sqrt(sqrt(sqrt(.4))))^(-4!)) - (4)) * (4!)
    280      3      4^4 + 4!
    281      4      .(sqrt(4))^(-sqrt(4)) + 4^4
             4      4 ^ 4 + sqrt(4% ^ -sqrt(4))
    282      4      4^4 + 4! + sqrt(4)
    283      4      (sqrt(.4') - 4 % + .(sqrt(4))' % / .(sqrt(4))' %
    284      4      4^4 + 4! + 4
    285      4      (sqrt(sqrt(sqrt(4^4!))) - .4') / .(sqrt(4))' 
             4      (4! + (.4 / .4`%)) / .4
    286      4      (4! * 4! / sqrt (4)) - sqrt (4)
    287      4      (4! * 4! - sqrt(4)) / sqrt(4)
    288      3      (4 + sqrt(4))! * .4
    289      4      (sqrt(4) + 4! * 4!) / sqrt(4)
    290      4      (4! * 4! / sqrt (4)) + sqrt(4)
             3      (sqrt(4) - sqrt(.4`%)) / sqrt(.4`)%
    291      4      (sqrt(sqrt(sqrt(4^4!))) + .4') / .(sqrt(4))'
             4      (sqrt(4 * .4`) - 4%) / .4`%
    292      4      (4! * 4! / sqrt (4)) + 4
    293      4      ((sqrt(.4') - sqrt(4) % ) / .(sqrt(4))' % )  + sqrt(4)  
             4      ((sqrt(4) - sqrt(4)%) / sqrt(.4`)%) - 4
    294      4      (sqrt(4) / .4)! / .4` + 4!
             3      (sqrt(4) - 4%) / sqrt(.4`)%
    295      4      ((sqrt(4) / .4)! - sqrt(4)) / .4
    296      4      (sqrt(4) / .4)! / .4 - 4
             3      (sqrt(4) / sqrt(.4`)%) - 4
    297      4      4! / .(4!)' * sqrt(4 / .4')
             3      (sqrt(4) - sqrt(4)%) / sqrt(.4`)%
    298      4      (sqrt(4) / .4)! / .4 - sqrt(4)
             3      (sqrt(4) / sqrt(.4`)%) - sqrt(4)
    299      4      ((sqrt(4) / .4)! - .4) / .4
             3      (sqrt(4) - sqrt(.4`)%) / sqrt(.4`)%
    300      3      (sqrt(4) / .4)! / .4
             2      sqrt(.4') / .(sqrt(4))' %
             2      sqrt(4) / sqrt(.4`)%
    301      4      (.4 + (sqrt(4) / .4)!) / .4
             3      (sqrt(4) + sqrt(.4`)%) / sqrt(.4`)%
    302      4      sqrt(4) + (sqrt(4) / .4)! / .4
             3      sqrt(4) + (sqrt(4) / sqrt(.4`)%)
    303      4      ((4! / sqrt(4)) + .(4!)') / .4'%
             3      (sqrt(4) + sqrt(4)%) / sqrt(.4`)%
    304      4      4^4 + 4! + 4!
             3      4 + (sqrt(4) / sqrt(.4`)%)
    305      4      (sqrt(4) + (sqrt(4) / .4)!) / .4
    306      4      (4 + sqrt(sqrt(sqrt(4^4!)) / .(sqrt(4))'
             3      (sqrt(4) + 4%) / sqrt(.4`)%
    307      4      (.(4!) + .4' - .(sqrt(4))' % ) / .(sqrt(4))' %
             4      4 + ((sqrt(4) + sqrt(4)%) / sqrt(.4`)%)
    308      4      (4 + (sqrt(.4') / .4' % )) * sqrt(4)  
    309      4      (sqrt(.4' * 4) + 4 % ) / .4' %
    310      4      (4 + (sqrt(4) / .4)!) / .4
             3      (sqrt(4) + sqrt(.4`%)) / sqrt(.4`)%
    311      4      (sqrt(.4') + (4 % )' - sqrt(4) % )  /  .(sqrt(4))' %
             4      (sqrt(sqrt(4) - 4%) / .4`%) - 4
    312      4      (4 + sqrt(4))! * .4 + 4!
    313      4      (.(sqrt(4)) + (.(sqrt(4)) ^ -(sqrt(sqrt(sqrt((4!)))))  / .4
             4      (sqrt(sqrt(4) - 4%) / .4`%) - sqrt(4)
    314      4      ((sqrt(.4') - sqrt(4)' % ) / .(sqrt(4)' % )  +  4!
             4      4 + ((sqrt(4) + sqrt(.4`%)) / sqrt(.4`)%)
    315      4      (4! / sqrt(.4' %)) - (sqrt(4) / 4' %)
             3      sqrt(sqrt(4) - 4%) / .4`%
    316      4      4^4 + 4! / .4
    317      4      ((sqrt(.4') + 4 % - .(sqrt(4))' % )  /  .(sqrt(4))' %
             4      sqrt(4) + (sqrt(sqrt(4) - 4%) / .4`%)
    318      4      (4 + sqrt(4))! * .4` - sqrt(4)
    319      4      (sqrt(sqrt(sqrt(4 ^ 4!)))) - .(sqrt(4))) / .(sqrt(4))
             4      4 + (sqrt(sqrt(4) - 4%) / .4`%)
    320      3      (4 + sqrt(4))! * .4`
    321      4      (sqrt(sqrt(sqrt(4 ^ 4!) + .(sqrt(4)))  /  .(sqrt(4)
             4      ((sqrt(.4`) / .4%) - 4!) / .4`
    322      4      (4 + sqrt(4))! * .4` + sqrt(4)
    323      4      ((sqrt(.4') - .(sqrt(4))' % ) / .(sqrt(4))' % )  +  4!
             4      ((sqrt(4) - sqrt(.4`)%) / sqrt(.4`)%) + 4!
    324      4      (4 * 4 + sqrt(4))^sqrt(4)
             3      (sqrt(4) / sqrt(.4`)%) + 4!
    325      4      (4! + sqrt(4))! / (4!)! / sqrt(4)
    326      4      (4! - sqrt(4)) / sqrt(.4' %)) - 4
    327      4      ((sqrt(sqrt(sqrt(.4))))^(-4!) - sqrt(4)) * 4!
    328      4      (4! / sqrt(.4' % )) - root.4(4)
    329      4      (4! - (sqrt(4) + sqrt(.4' %)))  / sqrt(.4' %)
    330      4      (root.4(4) / .4)  / .(4!)'
             3      (4! - sqrt(4)) / sqrt(.4`%)
    331      4      (sqrt(.4' %) - sqrt(4) + 4!) / sqrt(.4' %) 
    332      4      (4! / sqrt(.4' %)) - (4 + 4!)
    333      4      (4! - sqrt(4) + .(sqrt(4))) / sqrt(.4' % )
             3      (sqrt(.4`) - sqrt(.4`%)%) / sqrt(4%)%
    334      4      (4! / sqrt(.4' %)) - (sqrt(4) + 4!)
             3      (sqrt(.4`) / sqrt(4%)%) + sqrt(.4`)
    335      4      (4! / sqrt(.4' %)) - .(sqrt(4)) ^ - (sqrt(4))
             4      (4 + sqrt(4)%) / (sqrt(4) / .4)!%%
    336      4      4! * (4! + 4) / sqrt(4)
             3      (4! / sqrt(.4`%)) - 4!
    337      4      ((4! + sqrt(.4' % ))  /  sqrt(.4' % ))  -  4!
    338      4      (4! + sqrt(4))^sqrt(4) / sqrt(4)
    339      4      ((sqrt(.4') / 4' % ) + sqrt(.4' % ))  /  4' %)
    340      4      (4! / sqrt(.4' %)) - (4! - 4) 
    341      4      (sqrt(4) - .4' - 4 % ) / .4' %
    342      4      (root(.(sqrt(4))' ,4) * sqrt(.4'))  +  sqrt(.4')
             4      (4 - sqrt(4%)) * .4 / .4`%
    343      4      sqrt(sqrt(sqrt((sqrt(4) + sqrt(4) / .4))))^4!
    344      4      (4 + sqrt(4))! * .4` + 4!
    345      4      (4! / sqrt(.4' %)) - (sqrt(.4') / 4' %)
    346      4      ((4! - sqrt(.4')) / sqrt(.4' % )) - 4
    347      4      ((4! - sqrt(.4') - .(sqrt(4))) / sqrt(.4' % )
             4      (4! - (sqrt(4%) + sqrt(.4`))) / sqrt(.4`%)
    348      4      ((4! / 4)! - 4!) / sqrt(4)
    349      4      ((4! - sqrt(.4') - sqrt(.4' % )) / sqrt(.4' % )
    350      4      (4! - (4 / .4)) / 4%
             3      (sqrt(4) - .4`) / .4`%
    351      4      4! / sqrt(sqrt(sqrt(.4^(4!)))) - 4!
    352      4      44 * (4 + 4)
    353      4      ((4! - sqrt(.4') + .(sqrt(4))) / sqrt(.4' % )
             4      ((4! - sqrt(4%)) / sqrt(.4`%)) - 4
    354      4      (sqrt(4) / .4' %) - (4 * 4!)
             3      (4! - .4) / sqrt(.4`%)
    355      4      4^4 + 4! / .(4!)'
             4      ((4 * .4`) - sqrt(4%)) / .4`%
    356      4      (4! / 4)! / sqrt(4) - 4
             3      (4! / sqrt(.4`%)) - 4
    357      3      (4! - .(sqrt(4))) / sqrt(.4' %)
             3      (4! - sqrt(4%)) / sqrt(.4`%)
    358      4      ((4! / 4)! - 4) / sqrt(4)
             3      (4! / sqrt(.4`%)) - sqrt(4)
    359      4      ((4! / 4)! - sqrt(4)) / sqrt(4)
             3      (4! - sqrt(.4`%)) / sqrt(.4`%)
    360      3      (sqrt(4) + 4)! / sqrt(4)
             2      4! / sqrt(.4' % )
    361      4      (sqrt(4) + (4! / 4)!) / sqrt(4)
             3      (4! + sqrt(.4`%)) / sqrt(.4`%)
    362      4      ((4! / 4)! + 4) / sqrt (4)
             3      sqrt(4) + (4! / sqrt(.4`%))
    363      4      44 * sqrt(4)  /  .(4!)'
             3      (4! + sqrt(4%)) / sqrt(.4`%)
    364      4      4 + (4! / 4)! / sqrt(4)
             3      4 + (4! / sqrt(.4`%))
    365      4      (4! / sqrt(.4' %)) + (sqrt(4) / .4)
    366      4      (4! / sqrt(.4' %)) + (4! / 4)
             3      (4! + .4) / sqrt(.4`%)
    367      4      (4! + sqrt(.4') - .(sqrt(4))) / sqrt(.4' % )
             4      4 + ((4! + sqrt(4%)) / sqrt(.4`%))
    368      4      4 * (4 * 4! - 4)
    369      4      .(sqrt(4))^(-4)  -  4^4
             4      4% ^ -sqrt(4) - 4 ^ 4
    370      4      (4! / sqrt(.4' %)) + (4 / .4)
             3      (4! + sqrt(.4`)) / sqrt(.4`%)
    371      4      4! / sqrt(sqrt(sqrt(.4^(4!)))) - 4
    372      4      (4! + (4! / 4)!) / sqrt(4)
    373      4      4! / sqrt(sqrt(sqrt(.4^(4!)))) - sqrt(4)
    374      4      (.(sqrt(4)) ^ - (sqrt(4)) - (sqrt(.4' %)) / sqrt(.4' %)
             4      ((sqrt(4) - .4`) / .4`%) + 4!
    375      4      .4 * 4! / .4^4
             3      4! / sqrt(sqrt(sqrt(.4 ^ (4!)))
    376      4      (4! - 4)^sqrt(4) - 4!
    377      4      4! / sqrt(sqrt(sqrt(.4^(4!)))) + sqrt(4)
    378      4      (4^4 - 4) / sqrt(.4`)
    379      4      4! / sqrt(sqrt(sqrt(.4^(4!)))) + 4
    380      4      4 * 4 * 4! - 4
    381      4      (4^4 - sqrt(4)) / sqrt(.4`)
    382      4      4 * 4 * 4! - sqrt(4)
    383      4      (4^4 - sqrt(.4`)) / sqrt(.4`)
    384      3      4 * 4 * 4!
    385      4      (4^4 + sqrt(.4`)) / sqrt(.4`)
    386      4      4 * 4 * 4! + sqrt(4)
    387      4      (4^4 + sqrt(4)) / sqrt(.4`)
    388      4      4 * 4 * 4! + 4
    389      4      (sqrt(4) + 4! - sqrt(.4`%)) / sqrt(.4`%)
    390      4      (4^4 + 4) / sqrt(.4`)
             3      (sqrt(4) + 4!) / sqrt(.4`%)
    391      4      (sqrt(.4' %) + sqrt(4) + 4!) / sqrt(.4' %)
    392      4      4 * (4 * 4! + sqrt(4))
    393      4      (.(sqrt(4)) + sqrt(4) + 4!) / sqrt(.4' %)
             4      (sqrt(4) + 4! + sqrt(4%)) / sqrt(.4`%)
    394      4      ((4*4!) / .(4!)') - sqrt(4)
             4      ((4 * 4) - 4!%) / 4%
    395      4      ((4*4!) - .(4!)') / .(4!)'
             4      ((4 * 4) - sqrt(4%)) / 4%
    396      4      (4! - 4)^sqrt(4) - 4
             3      ((4*4!) / .(4!)')
             3      (sqrt(4) - 4!%) / .4`%
    397      4      ((4*4!) + .(4!)') / .(4!)'
             4      (sqrt(4) - (4! - .4`)%) / .4`%
    398      4      (4! - 4)^sqrt(4) - sqrt(4) 
    399      4      (4! / sqrt(sqrt(sqrt(.4^(4!)))))  +  4!
    400      3      (4! - 4)^sqrt(4)
    401      4      (.(4!) + (4! * 4)) / .(4!)
             4      ((4 * 4) + 4%) / 4%
    402      4      (4! - 4)^sqrt(4) + sqrt(4)
    403      4      ((sqrt(4) - .(sqrt(4))) / .4' % ) - sqrt(4)
             3      (4 + 4)!% - sqrt(4%)
    404      4      (4! - 4)^sqrt(4) + 4
    405      4      (4 + sqrt(4))! / 4 / .4`
             3      (sqrt(4) - sqrt(4%)) / .4`%
    406      4      ((sqrt(4) - .(sqrt(4)) + .4' % ) / .4' %
             4      (sqrt(4) / .4`%) - 44
    407      4      ((sqrt(4) - .(sqrt(4))) / .4' % ) + sqrt(4)
             4      4 + (4 + 4)!% - sqrt(4%)
    408      4      4 * 4 * 4! + 4!
    409      4      ((sqrt(4) - .(sqrt(4))) / .4' % ) + 4
             4      ((4 * .4`) + 4%) / .4`%
    410      4      ((4 * 4) + .4) / 4%
    411      4      ((sqrt(4) - sqrt(.4' % )) / .4' % ) - 4!   
    412      4      ((4! / .(4!)') + 4) * 4
             4      (4 + 4 + 4!%) / sqrt(4)%
    413      4      root(.(sqrt(4))' ,4)  -  (4! / .(4!)')
    414      4      ((4*4!) - 4) / .(sqrt(4)')
             4      (sqrt(4) - (4 * 4)%) / .4`%
    415      4      (sqrt(4) - .(sqrt(4)) + 4' % ) / .4' %
             4      ((4 / 4%) - .4) / 4!%
    416      4      4 * 4 * (4! + sqrt(4))
    417      4      (4 - .(sqrt(4)) + 4!) / sqrt(.4')
             4      ((sqrt(4) - 4%) / .4`%) - 4!
    418      4      (sqrt(4) / .4' %) - root(.4,4)
    419      4      (4 + 4! - sqrt(.4' %)) / sqrt(.4' %)
    420      4      444 - 4!
             3      (4 + 4!) / sqrt(.4`%)
    421      4      (sqrt(.4') + 4 + 4!) / sqrt(.4' %)
    422      4      (sqrt(4) / .4' %) - (4 + 4!)
    423      4      (((sqrt(sqrt(sqrt(.4))))^(-4!)) + (sqrt(4))) * (4!)
    424      4      (4! - 4)^sqrt(4) + 4!
    425      4      ((sqrt(4) - .4' % ) / .4' % ) - 4!
    426      4      4! * (4! - .4^(-sqrt(4)))
             3      (sqrt(4) / .4`%) - 4!
    427      4      ((sqrt(4) + .4' % ) / .4' % ) - 4!
    428      4      (4*4!) / .sqrt(4)' - 4
             4      sqrt(4) + (sqrt(4) / .4`%) - 4!
    429      4      ((4*4!) - .4') / .(sqrt(4))'
             4      (4! + (sqrt(.4`) / .4%)) / .4`
    430      4      (4*4!) / .sqrt(4)' - sqrt(4)
             4      ((4 / .4`) - .4) / sqrt(4)%
    431      4      ((4*4!) - .sqrt(4)') / .sqrt(4)'
             4      ((sqrt(4) - sqrt(.4`%)) / .4`%) - 4
    432      4      4! * (4 * 4 + sqrt(4))
             3      (4*4!) / .sqrt(4)'
    433      4      ((4*4!) + .sqrt(4)') / .sqrt(4)'    
             4      ((sqrt(4) - sqrt(.4`%)) / .4`%) - sqrt(4)
    434      4      (4*4!) / .sqrt(4)' + sqrt(4)  
             4      (sqrt(4) / .4`%) - (4 * 4)
    435      4      ((4*4!) + .4') / .(sqrt(4))'
             3      (sqrt(4) - sqrt(.4`%)) / .4`%
    436      4      (4*4!) / .sqrt(4)' + 4 
             4      4 * (4% + .4`) / .4`%
    437      4      ((sqrt(4) - 4 %) / .4' % ) - 4
    438      4      (sqrt(4) / .4' %) - (4! / sqrt(4))
    439      4      ((sqrt(4) - 4 % ) / .4' % ) - sqrt(4)
    440      4      444 - 4
             3      (sqrt(4) - 4!%) / .4%
    441      4      (4! - sqrt(4) / sqrt(.4`))^sqrt(4)
             3      (sqrt(4) - 4%) / .4`%
    442      4      444 - sqrt(4)
    443      4      ((sqrt(4) - 4 % ) / .4' % ) + sqrt(4)
    444      3      444
    445      4      (sqrt(4) / .4' %) - (sqrt(4) / .4)
    446      4      444 + sqrt(4)
             3      (sqrt(4) / .4`%) - 4
    447      4      ((sqrt(4) / .4'% ) - (sqrt(4 / .4')
    448      4      444 + 4
             3      (sqrt(4) / .4`%) - sqrt(4)
    449      4      (4! / .(sqrt(4))' - .(4!)) / .(4!)
             3      (sqrt(4) - .4`%) / .4`%
    450      4      (4! / 4)! / 4 / .4
             2      sqrt(4) / .4' %
    451      4      (4! / .(sqrt(4)) + .(4!)) / .(4!)
             3      (sqrt(4) + .4`%) / .4`%
    452      4      root(.(sqrt(4))' ,4)  -  (4! / .4)
             3      sqrt(4) + (sqrt(4) / .4`%)
    453      4      ((4! / .(4!)) + sqrt(.4')) / .(sqrt(4))'
             4      4 + ((sqrt(4) - .4`%) / .4`%)
    454      4      (4! / .(4!) / .(sqrt(4))') + 4
             3      4 + (sqrt(4) / .4`%)
    455      4      (sqrt(4) / .4' %) + (sqrt(4) / .4)
    456      4      4! * (4! - sqrt(4) / .4)
    457      4      ((sqrt(4) + 4 % ) / .4' % ) - sqrt(4)
    458      4      (4*4!) / .sqrt(4)' + 4!
             4      4 + 4 + (sqrt(4) / .4`%)
    459      4      ((4! / .(4!)) + sqrt(4)) / .(sqrt(4))'
             3      (sqrt(4) + 4%) / .4`%
    460      4      (4! - sqrt(4))^sqrt(4) - 4!
             3      (4!% + sqrt(.4`%)) / sqrt(.4`%)%
    461      4      ((sqrt(4) + 4 % ) / .4' % ) + sqrt(4)
    462      4      (4! - sqrt(4))! / (4! - 4)!
    463      4      ((sqrt(4) + 4 % ) / .4' % ) + 4
    464      4      (4^4 - 4!) * sqrt(4)
    465      4      (sqrt(4) / .4' %) + (sqrt(.4') / 4' %)
             3      (sqrt(4) + sqrt(.4`%)) / .4`%
    466      4      (sqrt(4) / .4' %) + (4 * 4)
    467      4      ((sqrt(4) + sqrt(.4' % )) / .4' % ) + sqrt(4)
    468      4      444 + 4!
    469      4      ((sqrt(4) + sqrt(.4' % )) / .4' % ) + 4
    470      4      (sqrt(4) / .4' %) + (4! - 4)
    471      4      (((sqrt(sqrt(sqrt(.4))))^(-4!)) + (4)) * (4!)
    472      4      (4! - 4) * (4! - .4)
    473      4      ((sqrt(4) - .4' % ) / .4' % ) + 4!
    474      4      (4! / .(4!) / .(sqrt(4))') + 4!
             3      (sqrt(4) / .4`%) + 4!
    475      4      ((4! / .(4!)') - 4) / .(sqrt(4))
             4      (sqrt(4) - (.4 / 4)) / .4%
    476      4      4! * (4! - 4) - 4
             3      (sqrt(4) / .4%) - 4!
    477      4      4! * 4! - 4! / .(4!)'
             4      (4 + 4!%) / (sqrt(4) * .4`)%
    478      4      4! * (4! - 4) - sqrt(4)
    479      4      (4 * 4!) - .(sqrt(4)) / .(sqrt(4))
             4      ((4 * 4!) - sqrt(4%)) / sqrt(4%)
    480      3      4! * (4! - 4)
    481      4      (4 * 4!) + .(sqrt(4)) / .(sqrt(4))
             4      ((4 * 4!) + sqrt(4%)) / sqrt(4%)
    482      4      sqrt(4) + 4! * (4! - 4)
    483      4      (4! / .(sqrt(4))' - sqrt(.4')) / .(sqrt(4))'
             4      ((sqrt(4) + 4%) / .4`%) + 4!
    484      3      (4! - sqrt(4))^sqrt(4)
    485      4      ((4! / .(sqrt(4))') - .(sqrt(4))') / .(sqrt(4))'
             4      (sqrt(4) - (4 + sqrt(4))%) / .4%
    486      4      4 * 4! / (.4` * .4`)
    487      4      (((4! / .(sqrt(4))') + .(sqrt(4))') / .(sqrt(4))'
    488      4      sqrt(4) * 4 ^ 4 - 4!
    489      4      ((4! / .(sqrt(4))') + sqrt(.4') / .(sqrt(4))'
             4      (sqrt(4) - 4.4%) / .4%
    490      4      (4! / .(sqrt(4))' / .(sqrt(4))') + 4
             3      (sqrt(4) - 4%) / .4%
    491      4      ((sqrt(4) / .4)! / .(4!)' - 4
             4      (sqrt(4) / .4%) - (4 / .4`)
    492      4      root(.(sqrt(4))' ,4)  -  (4 / .(sqrt(4)))
             4      (sqrt(4) / .4%) - (4 + 4)
    493      4      ((sqrt(4) / .4)! / .(4!)' - sqrt(4)
             4      ((sqrt(4) - sqrt(4)%) / .4%) - sqrt(4)
    494      4      (((sqrt(4) / .4)! - .(4!)') / .(4!)'
             4      (sqrt(4) / .4`%) + 44
    495      4      (4! - sqrt(4)) / (.4` - .4)
             3      ((sqrt(4) / .4)! / .(4!)'
             3      (sqrt(4) - sqrt(4)%) / .4%
    496      4      4 * (4 + (sqrt(4) / .4)!)
             3      (sqrt(4) / .4%) - 4
    497      4      ((sqrt(4) / .4)! / .(4!)' + sqrt(4)
             4      ((sqrt(4) + .4%) / .4%) - 4
    498      4      ((4! / .(4!) - .4) / .(sqrt(4))
             3      (sqrt(4) / .4%) - sqrt(4)
    499      4      ((sqrt(4) / .4)! / .(4!)' + 4
             3      (sqrt(4) - .4%) / .4%
    500      4      4 * sqrt(sqrt(sqrt((sqrt(4) / .4)^4!)))
             2      sqrt(4) / .4%
    501      4      ((sqrt(4) / .4)! + .(4!)) / .(4!)
             3      (sqrt(4) + .4%) / .4%
    502      4      root(.(sqrt(4))' ,4)  -  (4 /.4)
             3      sqrt(4) + (sqrt(4) / .4%)
    503      4      root(.(sqrt(4))' ,4)  -  (4 / .4')
             4      4 + ((sqrt(4) - .4%) / .4%)
    504      4      (4^4 - 4) * sqrt(4)
             3      4 + (sqrt(4) / .4%)
    505      4      .(sqrt(4))^(-4)  -  (sqrt(4) / .4)!
             3      (sqrt(4) + sqrt(4)%) / .4%
    506      4      root(.(sqrt(4))' ,4)  -  (4 / sqrt(.4'))
             4      4 + sqrt(4) + (sqrt(4) / .4%)
    507      4      root(.(sqrt(4))' ,4)  -  (sqrt(4) / .4)
             4      sqrt(4) + ((sqrt(4) + sqrt(4)%) / .4%)
    508      4      4^4 * sqrt(4) - 4
    509      4      root(.(sqrt(4))' ,4)  -  (sqrt(4 / .4'))
             4      (4 / .4`) + (sqrt(4) / .4%)
    510      4      sqrt(4) * 4^4 - sqrt(4)
             3      (sqrt(4) + 4%) / .4%
    511      4      root(.(sqrt(4))' ,4)  -  (4 / 4)
             4      (4.4% + sqrt(4)) / .4%
    512      3      sqrt(4) * 4^4
             2      root(.(sqrt(4))',4)
    513      4      root(.(sqrt(4))' ,4)  +  (4 / 4)
             4      (sqrt(4) + root(sqrt(4%), 4)) / sqrt(4)
    514      4      sqrt(4) * 4 ^ 4 + sqrt(4)
    515      4      root(.(sqrt(4))' ,4)  +  (sqrt(4 / .4'))
             4      ((4 + sqrt(4))% + sqrt(4)) / .4%
    516      4      sqrt(4) * 4 ^ 4 + 4
    517      4      root(.(sqrt(4))' ,4)  +  (sqrt(4) / .4))
    518      4      root(.(sqrt(4))' ,4)  +  (4 / sqrt(.4'))   
             4      ((4 + sqrt(4))!%% + sqrt(4)) / .4%
    519      4      ((sqrt(4) / .4)! / .(4!)' + 4!
             4      ((sqrt(4) - sqrt(4)%) / .4%) + 4!
    520      4      sqrt(4) * (4 + 4^4)
    521      4      root(.(sqrt(4))' ,4)  +  (4 / .4')
    522      4      (4^4 - 4!) / .4`
    523      4      ((sqrt(4) - .4 % ) / .4 % )  +  4!
    524      4      4! * (4! - sqrt(4)) - 4
             3      (sqrt(4) / .4%) + 4!
    525      4      (4! - sqrt(.4`)) / (.4` - .4)
    526      4      4! * (4! - sqrt(4)) - sqrt(4)
    527      4      ((4! - sqrt(.4')) / 4' % )  +  sqrt(4)
    528      3      (4! - sqrt(4)) * 4!
    529      4      (4! - 4 / 4) ^ sqrt(4)
    530      4      sqrt(4) + 4! * (4! - sqrt(4))
    531      4      (4! - .4) / (.4` - .4)
    532      4      4!^sqrt(4) - 44
    533      4      (4! * .4' - sqrt(.4)%) / sqrt(4)%
    534      4      root(.(sqrt(4))' ,4)  +  (4! - sqrt(4))
             4      (4 - 44%) / sqrt(.4`)%
    535      4      (4! - .(sqrt(4))') / (.4' - .4)
             4      4% ^ -sqrt(4) - (.4 / .4`%)
    536      4      sqrt(4) * 4 ^ 4 + 4!
    537      4      ((sqrt(4) / .4')! - .4') / .(sqrt(4))'
             4      (4 - (sqrt(4)% + .4)) / sqrt(.4`)%
    538      4      4! / (.4` - .4) - sqrt(4)
    539      4      (((sqrt(4) / .4)! - .(sqrt(4)')) / .(sqrt(4)')
             4      (sqrt(4) + .4 - .4`%) / .4`%
    540      3      4! / (.4` - .4)
             2      4! / 4' % 
    541      4      (((sqrt(4) / .4)! + .(sqrt(4)')) / .(sqrt(4)')
             4      (sqrt(4) - 4% + .4`) / .4`%
    542      4      4! / (.4` - .4) + sqrt(4)
    543      4      ((sqrt(4) / .4)! + .4') / .(sqrt(4))'
             4      (4 + sqrt(4)% - .4) / sqrt(.4`)%
    544      4      4! / (.4` - .4) + 4
    545      4      (4! + .(sqrt(4))') / (.4' - .4)
             4      (4! - sqrt(4)%) / 4.4%
    546      4      ((4! - sqrt(4)) / 4%) - 4
    547      4      (4! + .(sqrt(4))') / 4' % )  +  sqrt(4)
    548      4      4!^sqrt(4) - 4! - 4
    549      4      (4! + .4) / (.4` - .4)
    550      4      4!^sqrt(4) - 4! - sqrt(4)
             3      (4! - sqrt(4)) / 4%
    551      4      4! * 4! - .(sqrt(4))^(-sqrt(4))
             4      (4! - sqrt(4) + 4%) / 4%
    552      3      4!^sqrt(4) - 4!
    553      4      ((4! + sqrt(.4')) / 4' % )  - sqrt(4)
    554      4      4!^sqrt(4) - 4! + sqrt(4)
    555      4      (4! + sqrt(.4`)) / (.4` - .4)
    556      4      4!^sqrt(4) - 4! + 4
    557      4      ((4! + sqrt(.4')) / 4' % )  +  sqrt(4)
    558      4      (4! - sqrt(.4`)) * 4! - sqrt(4)
    559      4      (sqrt(4) + .(4!) - .4 % ) / .4 %
             4      (sqrt(4) + (4! - .4)%) / .4%
    560      3      (4! - sqrt(.4`)) * 4!
    561      4      .(sqrt(4))^(-4)  -  (sqrt(sqrt(sqrt(4^4!)
             4      (sqrt(4) + (4! + .4)%) / .4%
    562      4      (4! - sqrt(.4`)) * 4! + sqrt(4)
    563      4      ((4! - 4' % ) / 4' % )  +  4!
    564      4      4!^sqrt(4) - 4! / sqrt(4)
             3      (4 - 4!%) / sqrt(.4`)%
    565      4      .(sqrt(4))^(-4)  -  (4! / .4)
             4      4% ^ -sqrt(4) - (4! / .4)
    566      4      4!^sqrt(4) - 4 / .4
    567      4      (4^4 - 4) / .4'
    568      4      4!^sqrt(4) - 4 - 4
    569      4      ((4! + .(sqrt(4))') / 4' % )  + 4!
             4      (4 - (sqrt(4%) + sqrt(.4`)%)) / sqrt(.4`)%
    570      4      4!^sqrt(4) - 4 - sqrt(4)
             3      (4 - sqrt(4%)) / sqrt(.4`)%
    571      4      4!^sqrt(4) - sqrt(4) / .4
    572      3      4!^sqrt(4) - 4
    573      4      4!^sqrt(4) - sqrt(4 / .4`)
    574      3      4!^sqrt(4) - sqrt(4)
    575      4      4!^sqrt(4) - 4/4
    576      2      4!^sqrt(4)
    577      4      4!^sqrt(4) + 4/4
    578      3      4!^sqrt(4) + sqrt(4)
    579      4      4!^sqrt(4) + sqrt(4) / sqrt(.4`)
    580      3      4!^sqrt(4) + 4
    581      4      4!^sqrt(4) + sqrt(4) / .4
    582      4      4!^sqrt(4) + 4 + sqrt(4)
    583      4      ((sqrt(4) + 4!) / 4' % )  -  sqrt(4)
    584      4      4!^sqrt(4) + 4 + 4
    585      4      (4^4 + 4) / .4`
    586      4      4!^sqrt(4) + 4 / .4
    587      4      ((sqrt(4) + 4!) / 4' % )  +  sqrt(4)
    588      4      4!^sqrt(4) + 4! / sqrt(4)
    589      4      .(sqrt(4))^(-4)  -  (4! / sqrt(.4'))
             4      (4! - 44%) / 4%
    590      4      (4! + sqrt(.4`)) * 4! - sqrt(4)   
             3      (4! - .4) / 4%
    591      4      (4! / 4%) - (4 / .4')
    592      3      4! (sqrt(.4') + 4!) 
    593      4      .(sqrt(4))^(-4)  -  root(.4,4)
             4      4% ^ -sqrt(4) - root(.4, 4)
    594      4      (4! + sqrt(.4`)) * 4! + sqrt(4)
             3      4! - .(4!)) / 4 %
             3      (4! - 4!%) / 4%
    595      4      (4!/4)! - sqrt(sqrt(sqrt(.(sqrt(4)))))^(-4!)
             3      (4! - sqrt(4%)) / 4%
    596      4      4!^sqrt(4) + 4! - 4
             3      (4! / 4%) - 4
    597      4      .(sqrt(4))^(-4)  -  (4! + 4)
             3      (4 - sqrt(4)%) / sqrt(.4`)%
    598      4      4!^sqrt(4) + 4! - sqrt(4)
             3      (4! / 4%) - sqrt(4)
    599      4      .(sqrt(4))^(-4)  -  (4! + sqrt(4))
             3      (4! - 4%) / 4%
    600      3      4!^sqrt(4) + 4!
             2      4! / 4%
    601      4      (sqrt(4) / .4)^4 - 4!
             3      (4! + 4%) / 4%
    602      4      4!^sqrt(4) + 4! + sqrt(4)
             3      sqrt(4) + (4! / 4%)
    603      4      .(sqrt(4))^(-4)  -  (4! - sqrt(4))
             3      (4 + sqrt(4)%) / sqrt(.4`)%
    604      4      4!^sqrt(4) + 4! + 4
             3      4 + (4! / 4%)
    605      4      .(sqrt(4))^(-4)  -  (4! - 4)
             3      (4! + sqrt(4%)) / 4%
    606      4      (4! + .(4!)' + .(4!)') / .4'%
             3      (4! + 4!%) / 4%
    607      4      (4 % + .(4!) + 4!) / 4 %
             4      ((4 + 4!)% + 4!) / 4%
    608      4      (4! + sqrt(.4`) + sqrt(.4`)) * 4!
    609      4      .(sqrt(4))^(-4)  -  (4 * 4)
             4      (4 / .4`) + (4! / 4%)
    610      4      ((sqrt(4) / .4)! + sqrt(4)) / .(sqrt(4))   
             3      (4! + .4) / 4%
    611      4      root(.(sqrt(4))' ,4)  +  (4! / .(4!)')
             4      (4! + 44%) / 4%
    612      4      4! * (4! + sqrt(.4`) / .4`)
    613      4      .(sqrt(4))^-(4)  -  (4! / sqrt(4))  
             4      4% ^ -sqrt(4) - (4! / sqrt(4))
    614      4      ((4! - .4) / 4 % )  +  4!
    615      4      .(sqrt(4))^(-4)  -  (4 / .4)
             4      (4 + (.4 / 4)) / sqrt(.4`)%
    616      4      4^4 / .4 - 4!
    617      4      .(sqrt(4))^(-4)  -  (4 + 4)
             4      4% ^ -sqrt(4) - (4 + 4)
    618      4      (4! / 4 % )  +  (4 / .(sqrt(4))')
             4      4! + ((4! - 4!%) / 4%)
    619      4      .(sqrt(4))^(-4)  -  (4 / sqrt(.4'))
             4      4% ^ -sqrt(4) - (4 + sqrt(4))
    620      4      4!^sqrt(4) + 44
    621      4      (sqrt(4) / .4)^4 - 4
             3      4% ^ -sqrt(4) - 4
    622      4      4! * (4! + sqrt(4)) - sqrt(4)
    623      4      (sqrt(4) / .4)^4 - sqrt(4)
             3      4% ^ -sqrt(4) - sqrt(4)
    624      3      4! * (4! + sqrt(4))
    625      3      (sqrt(4) / .4) ^ 4
             2      .(sqrt(4))^-(4)
             2      4% ^ -sqrt(4)
    626      4      sqrt(4) + 4! * (4! + sqrt(4))
    627      4      sqrt(4) + (sqrt(4) / .4)^4
             3      sqrt(4) + 4% ^ -sqrt(4)
    628      4      4 + 4! * (4! + sqrt(4))
    629      4      4 + (sqrt(4) / .4)^4
             3      4 + 4% ^ -sqrt(4)
    630      4      (4 / .4')! / (4! * 4!)
             3      (4 + sqrt(4%)) / sqrt(.4`)%
    631      4      .(sqrt(4))^(-4)  +  (4 / sqrt(.4'))
             4      4 + sqrt(4) + 4% ^ -sqrt(4)
    632      4      root(.(sqrt(4))' ,4)  +  (sqrt(4) / .4)!
             4      (4! / 4%) + root(.4, 4)
    633      4      .(sqrt(4))^(-4)  +  4  +  4
             4      4 + 4 + 4% ^ -sqrt(4)
    634      4      .(sqrt(4))^(-4)  +  (4 / .4')
             4      4! + ((4! + .4) / 4%)
    635      4      (4^4 - sqrt(4)) / .4
    636      4      4^4 / .4 - 4
             3      (4 + 4!%) / sqrt(.4`)%
    637      4      .(sqrt(4))^-(4) + (4! / sqrt(4))
             4      (4! / sqrt(4)) + 4% ^ -sqrt(4)
    638      4      4^4 / .4 - sqrt(4)
    639      4      (4^4 - .4) / .4
    640      3      4^4 / .4
    641      4      (.4 + 4^4) / .4
    642      4      sqrt(4) + 4^4 / .4
    643      4      .(sqrt(4)) ^ (- 4) + (4 / .(sqrt(4))')  
             4      ((sqrt(4%) - 4!)% + sqrt(.4`)) / sqrt(.4`%)%
    644      4      4 + 4^4 / .4
    645      4      (sqrt(4) + 4^4) / .4
    646      4      (4! + sqrt(4))! / (4!)! - 4
    647      4      .(sqrt(4))^(-4)  +  (4! - sqrt(4))
             4      4! - sqrt(4) + 4% ^ -sqrt(4)
    648      4      (sqrt(4) + 4)^4 / sqrt(4)
    649      4      4! + (sqrt(4) / .4)^4
             3      4! + 4% ^ -sqrt(4)
    650      3      (4! + sqrt(4))! / (4!)!
    651      4      (4! + sqrt(4))! + (4!)!) / (4!)!
    652      4      (4! + sqrt(4))^sqrt(4) - 4!
    653      4      .(sqrt(4))^(-4)  +  4! + 4
             4      4 + 4! + 4% ^ -sqrt(4)
    654      4      4 + (4! + sqrt(4))! / (4!)!
    655      4      (.(sqrt(4)) + sqrt(4) + 4!) / 4 %
             4      (sqrt(4) + 4! + sqrt(4%)) / 4%
    656      4      4! * (4! + 4 - sqrt(.4`))
    657      4      (4!) * (4!) + root( - (sqrt(.4')), .4')))
    658      4      (44 / sqrt(.4' % )) - sqrt(4)
    659      4      (44 - sqrt(.4' %)) / sqrt(.4' %)
    660      4      (4! / 4)! - 4! / .4
             3      44 / sqrt(.4`%)
    661      4      .(sqrt(4))^(-4)  +  (4! / sqrt(.4'))
             4      (44 + sqrt(.4`%)) / sqrt(.4`%)
    662      4      (44 / sqrt(.4' %)) + sqrt(4)
    663      4      (44 + .(sqrt(4))) / sqrt(.4' %)
             4      (sqrt(4%) + 44) / sqrt(.4`%)
    664      4      4! + 4^4 / .4
    665      4      (4! / 4' %) + (.(sqrt(4)) ^ - (sqrt(sqrt(sqrt(4!)))))
             4      ((4 * sqrt(.4`)) - sqrt(.4`)%) / .4%
    666      4      444 / sqrt(.4`)
             3      (.4` / sqrt(.4`%)%) - sqrt(.4`)
    667      4      (sqrt(4) - sqrt(.4') +(sqrt(.4' % ) % ) / .(sqrt(4)) %
             4      (4 + sqrt(4%)%) / (4! / .4)%%
    668      4      4! * (4! + 4) - 4
    669      4      .(sqrt(4))^(-4)  +  44 
             4      4% ^ -sqrt(4) + 44
    670      4      4! * (4! + 4) - sqrt(4)
    671      4      (sqrt(4) / .4' % / sqrt(.4')) - 4
    672      3      4! * (4! + 4)
    673      4      .(sqrt(4))^(-4)  +  (4! * sqrt(4))
             4      (4! / (4 - .4`)%) - sqrt(4)
    674      4      (4! + sqrt(4))^sqrt(4) - sqrt(4)
    675      4      (sqrt(4) / .4)! / (.4 * .4`)
             3      4! / (4 - .4`)%
    676      3      (4! + sqrt(4))^sqrt(4)
    677      4      (sqrt(4) / .4' % / sqrt(.4')) + sqrt(4)
    678      4      (4! + sqrt(4))^sqrt(4) + sqrt(4)
    679      4      .(sqrt(4))^(-4)  +  (4! / .4')
             4      4 + (4! / (4 - .4`)%)
    680      4      (4! + sqrt(4))^sqrt(4) + 4
    681      4      ((sqrt(4) / 4' %) + .4) / sqrt(.4' %)
    682      4      (sqrt(4)  -  .4'  -  4 % )  / .(sqrt(4))' %
             4      (root(sqrt(4%), 4) * sqrt(.4`)) - sqrt(.4`)
    683      4      ((.(4!)' + (4 % )') / (4 % % )') - 4!
    684      4      4! * (4! + sqrt(4) / .4`)
    685      4      .(sqrt(4))^(-4)  +  (4! / .4)
             4      (4! / .4) + 4% ^ -sqrt(4)
    686      4      ((.(4!)  + sqrt(.4' % ) / (4 % )' % ) - 4
             4      root(sqrt(.4`), sqrt(4) - 4%) / .4%
    687      4      (((sqrt(.4') / .(4!)% )% ) - .(sqrt(4)% ) / .4 %
    688      4      (4! + 4 + sqrt(.4`)) * 4!
    689      4      .(sqrt(4))^(-4)  +  sqrt(sqrt(sqrt(4)^4!)))
    690      4      (4! / 4)!  -  ((sqrt(4) / sqrt(.4' %))
    691      4      (sqrt(4) - .4' - sqrt(4) % ) /  .(sqrt(4))' %
    692      4      (4 + sqrt(4))! - 4! - 4
    693      4      ((sqrt(.4') / .4' % ) + 4) / .(sqrt(4))'
    694      4      (4 + sqrt(4))! - 4! - sqrt(4)
    695      4      (4! / 4)! - .(sqrt(4))^(-sqrt(4))
             4      (4 + 4! - sqrt(4%)) / 4%
    696      3      (4 + sqrt(4))! - 4!
    697      4      (sqrt(4) - .4' - sqrt(.4') % ) / .(sqrt(4))' %
             4      (4 - sqrt(4)% + sqrt(.4`)) / sqrt(.4`)%
    698      4      (4 + sqrt(4))! - 4! + sqrt(4)
    699      4      (sqrt(.4') / .4' % / .(sqrt(4))') + 4!
             4      (4 + 4! - 4%) / 4%
    700      4      (4^4 + 4!) / .4
             3      (4 + 4!) / 4%
    701      4      (sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!))) + 4! * 4!
             4      (4 + 4! + 4%) / 4%
    702      4      (4!/4)!  -  (4/.(sqrt(4))')
             4      ((4 + 4!) / 4%) + sqrt(4)
    703      4      (sqrt(4) - .4' + sqrt(.4') % )  /  .(sqrt(4))' %
             4      (4 + sqrt(4)% + sqrt(.4`)) / sqrt(.4`)%
    704      4      4 * 4 * 44
    705      4      (sqrt(sqrt(sqrt(4/.4')))^(4!)) - 4!
    706      4      (.(4!) + 4 + 4!) / 4 %
             4      4 ^ 4 + (sqrt(4) / .4`%)
    707      4      (sqrt(4) - .4')  /  ((4! - sqrt(4)) % % )'
    708      4      (4 + sqrt(4))! - 4! / sqrt(4)
    709      4      (sqrt(4) - .4' + sqrt(4) % )  /  .(sqrt(4))' %
    710      4      (4 + sqrt(4))! - 4 / .4
    711      4      (4 + sqrt(4))! - 4 / .4`
    712      4      (4 + sqrt(4))! - 4 - 4
    713      4      ((.(4!) - sqrt(.4' % )) / .(4!)' %o ) - sqrt(4)
             5      (sqrt(sqrt(sqrt(4/.4')))^(4!)) - (4 * 4)
    714      4      (4 + sqrt(4))! - 4 - sqrt(4)
    715      4      (4 + sqrt(4))! - sqrt(4) / .4
    716      3      (4 + sqrt(4))! - 4
    717      4      (4 + sqrt(4))! - sqrt(4) / sqrt(.4`)
    718      3      (4 + sqrt(4))! - sqrt(4)
    719      4      (4 + sqrt(4))! - 4/4
    720      2      (4 + sqrt(4))!
    721      4      (4 + sqrt(4))! + 4/4
    722      3      (4 + sqrt(4))! + sqrt(4)
    723      4      (4 + sqrt(4))! + sqrt(4) / sqrt(.4`)
    724      3      (4 + sqrt(4))! + 4
    725      4      (4 + sqrt(4))! + sqrt(4) / .4
    726      4      (4 + sqrt(4))! + 4 + sqrt(4)
    727      4      (sqrt(sqrt(sqrt(4/.4')))^(4!)) - sqrt(4)
    728      4      (4 + sqrt(4))! + 4 + 4
    729      4      (4 + sqrt(4))! + 4 / .4`
             3      sqrt(sqrt(sqrt((4/.4')^4!)))
    730      4      (4 + sqrt(4))! + 4 / .4
    731      4      (sqrt(sqrt(sqrt(4/.4')))^(4!)) + sqrt(4)
    732      4      (4 + sqrt(4))! + 4! / sqrt(4)
    733      4      (sqrt(sqrt(sqrt(4/.4')))^(4!)) + 4
    734      4      ((.4' + (4%)')  /  sqrt(.4' % ) % )  + sqrt(.4')
    735      4      (sqrt(.4') / 4' % ) + (4! / 4)!
    736      4      (4 + sqrt(4))! + 4 * 4
    737      4      (.4' + .(sqrt(4))' % )  /  (.(4!)' %o ) / .4)
    738      4      (4 / .(sqrt(4))') + (4! / 4)! 
             4      (root(-sqrt(4), .4`%) - 4!%) / sqrt(4)%
    739      4      ((.(4!)  -  sqrt(.4' % ))  /  .(4!)  %o )  +  4!
    740      4      (4 + sqrt(4))! + 4! - 4
    741      4      (4 - sqrt(.4') - 4 % ) / .4' %
    742      4      (4 + sqrt(4))! + 4! - sqrt(4)
    743      4      (.(sqrt(4))'  +  (4!) %o / .(sqrt(4))')  /  (.4') %o
    744      3      (4 + sqrt(4))! + 4!
    745      4      .(sqrt(4))^(-4)  +  (sqrt(4) / .4)!
             4      (sqrt(4 / .4`) - sqrt(4)%) / .4%
    746      4      (4 + sqrt(4))! + 4! + sqrt(4)
    747      4      ((sqrt(4) / .4 %) - sqrt(4)) / sqrt(.4')
    748      4      (4 + sqrt(4))! + 4! + 4
    749      4      ((sqrt(4) / .4 %) - sqrt(.4')) / sqrt(.4')
    750      4      (sqrt(4) / .4)! / .4 / .4
             3      sqrt(4 / .4`) / .4%
    751      4      ((sqrt(4) / .4 %) + sqrt(.4')) / sqrt(.4')
    752      4      (sqrt(4) + 4)! + root.4(4)
    753      4      (sqrt(sqrt(sqrt(4/.4')))^(4!)) + 4!
    754      4      (sqrt(4) / .4 %) / sqrt(.4')) + 4
    755      4      (4 - .(sqrt(4)) - .4')  /  .4' %
             4      (4 - (sqrt(4%) + .4`)) / .4`%
    756      4      (4! + 4)! / (4! + sqrt(4))!
    757      4      (.(sqrt(4))'  -  ((4!) %o / .4'))  /  .(sqrt(4))' %o
    758      4      (root(.(sqrt(4))',4) %  -  sqrt(.4' % ))  /  sqrt(.4') %
    759      4      (4- sqrt(.4') + 4 % ) / .4' %
    760      4      (4! + 4)^sqrt(4) - 4!
    761      4      (sqrt(4) / .(4!)' % )  - sqrt(sqrt(sqrt(4 ^ (4!))))
    762      4      (root(.(sqrt(4))' ,4)  - 4)  /  sqrt(.4')
             4      (root(-sqrt(4), .4`%) + 4!%) / sqrt(4)%
    763      
    764      4      (4 + sqrt(4))! + 44
    765      4      (root(.(sqrt(4))' ,4)  -  sqrt(4))  /  sqrt(.4')
             4      (4 - (4! / .4)%) / .4`%
    766      4      root.4(4)*4! - sqrt(4)
    767      4      (root(.(sqrt(4))' ,4)  -  sqrt(.4'))  /  sqrt(.4') 
    768      4      (4 + 4) * 4! * 4   
             3      root.4(4)  *  4!
    769      4      (root(.(sqrt(4))' ,4)  +  sqrt(.4'))  /  sqrt(.4')
    770      4      root.4(4)*4! + sqrt(4)
    771      3      (root(.(sqrt(4))' ,4)  +  2)  /  sqrt(.4')
    772      4      root.4(4)*4! + 4
    773      4      ((sqrt(4) - .4') / (.(sqrt(4)) % )') - 4
    774      4      (4 + sqrt(4))! + 4! / .4`
    775      4      (sqrt(.4') / .4' % )  +  .(sqrt(4)) ^ (- 4)
             4      (4 - (.4 / .4`)) / .4%
    776      4      ((4 - .4') / .4' % ) - 4!  
    777      4      (sqrt(4) / .(4!)' % )  -  (4! + 4!)
             3      (sqrt(4) - .4') / (sqrt(4%)%)'
    778      4      ((sqrt(4) - .4') / .(sqrt(4)) % )  +  .(sqrt(4))'
    779      4      (.(4!) - sqrt(.4'%) - .(sqrt(4))'%o) / .(sqrt(4))'%o
    780      4      (4! + 4)^sqrt(4) - 4
    781      4      (sqrt(4) / .(4!)' % )  -  44
    782      4      (4! + 4)^sqrt(4) - sqrt(4)
    783      4      ((sqrt(.4') / .4' % ) + 4!) / .(sqrt(4))'
             4      (4 + sqrt(4%)%) / (.4` + sqrt(.4`%))%
    784      3      (4! + 4)^sqrt(4)
    785      4      (4 - .4' - sqrt(.4' %))  /  .4' %
    786      4      (4! + 4)^sqrt(4) + sqrt(4)
    787      4      (sqrt(.4') / .(4!)' % ) + root(.(sqrt(4))',4)
    788      4      (4! + 4)^sqrt(4) + 4
    789      4      (sqrt(4) - .(4!) - sqrt(.4') % )  /  .(sqrt(4))' %
    790      4      (4 - .4' - 4' % ) / .4' %
    791      4      (4 - .4' - 4 % ) / .4' %
    792      4      (4! - sqrt(4)) * 4! / sqrt(.4`)
             3      (sqrt(4) - (4!)%) / (.(sqrt(4))')%
    793      4      (sqrt(4) - .(4!) + .(sqrt(4))' % ) / .(sqrt(4))' %
    794      4      (sqrt(4) - .(4!)) / .(sqrt(4))' % )  +  sqrt(4)
             4      (root(.4, 4) - 4!%) / 4%
    795      4      (4 - sqrt(.4') - .4) / .4' %
    796      4      ((4 - .4') / .4' % ) - 4
    797      4      (sqrt(4) - .(sqrt(4))' - sqrt(.4') %  /  .(sqrt(4))' %
    798      4      ((4 - .4') / .4' % ) - sqrt(4)
    799      4      (4 - .4' - .4' % ) / .4' %
    800      4      sqrt(4) * (4! - 4)^sqrt(4)
             3      root(.4, 4) / 4%
    801      4      (4 - .4' + .4' % ) / .4' %
    802      4      ((4 - .4') / .4' % ) + sqrt(4)
    803      4      (sqrt(4) - .(sqrt(4))' + sqrt(.4') %  /  .(sqrt(4))' %
    804      4      ((4 - .4') / .4' % ) + 4
    805      4      (root .4,(4)  +  .(sqrt(4))  /  4 %
             4      (sqrt(4%) + root(.4, 4)) / 4%
    806      4      ((4 - .4) / .4' % ) - 4
    807      4      ((4! / 4' %) - sqrt(4)) / sqrt(.4')
    808      4      (4! + 4)^sqrt(4) + 4!
    809      4      ((4! / 4' %) - sqrt(.4')) / sqrt(.4')
    810      4      4! / sqrt(.4`) / (.4` - .4)
             3      (4 - .4) / .4`%
    811      4      ((4! / 4' %) + sqrt(.4')) / sqrt(.4')
    812      4      ((4! / 4' %) / sqrt(.4')) + sqrt(4)
    813      4      ((4! / 4'%) + sqrt(4)) / sqrt(.4')
    814      4      ((4! / 4' %) / sqrt(.4')) + 4
    815      4      (4! / sqrt(.4') + .(sqrt(4))')  /  4' %
             4      (4 - .4` + sqrt(.4`%)) / .4`%
    816      4      4! * (4! + 4 / .4)
    817      4      (sqrt(4) / .(4!)' % )  -  (4 + 4)
    818      4      (sqrt(4) - .(sqrt(4))' + 4 % )  /  .(sqrt(4))' %
    819      4      (4! / .(4!)' + (4!/4)!
             4      (4 / sqrt(.4'))! + 4! / .(4!)'
             4      (4 + 4% - .4) / .4`%
    820      4      (4! / .(4!)) + (4!/4)!
             4      ((4 * 4) + .4) / sqrt(4)%
    821      4      (.4'  /  .(sqrt(4))' %   /  .(4!)')  -  4
             3      sqrt(4)/.(4!)'% - 4
    822      4      ((4 - .(4!)) / .4' % ) - 4!
             4      ((4 - 4!%) / .4`%) - 4!
    823      4      (.4'  /  .(sqrt(4))' %   /  .(4!)')  -  sqrt(4)
             3      sqrt(4)/.(4!)'% - sqrt(4)
    824      4      ((4 - .4') / .4' % ) + 4!
             3      (sqrt(4) - .(4!)'%) / .(4!)'%
    825      4      ((4!/.(4!)' / .(4!)) * sqrt(4)
             3      sqrt(4) / (.(4!)'  -  .(4!))
             2      sqrt(4) / .(4!)'%
             2      sqrt(4) / .(4!)' %
             4      ((4 / .4`) + 4!) / 4%
    826      4      ((4 - .(sqrt(4))' / .4' % ) - 4!
             4      (4! * 4!) + sqrt(.4% ^ -sqrt(4))
             3      (sqrt(4) + .(4!)'%) / .(4!)'%
    827      4      (.4'  /  .(sqrt(4))' %   /  .(4!)')  +  sqrt(4)
             3      sqrt(4)/.(4!)'% + sqrt(4)
    828      4      (4! * 4! - 4!) / sqrt(.4`)
    829      4      (.4'  /  .(sqrt(4))' %   /  .(4!)')  +  4    
             3      sqrt(4)/.(4!)'% + 4
    830      4      (sqrt(4) + sqrt(.4' % ) - .(sqrt(4))')  /  .(sqrt(4))' %
             4      ((4 / 4!%) - sqrt(.4`%)) / sqrt(4)%
    831      4      ((4 - .(sqrt(4)) / .4' % ) - 4!
             4      ((4 - sqrt(4%)) / .4`%) - 4!
    832      4      4! * 4! + 4^4
    833      4      ((4 / 4!%) - sqrt(.4`)%) / sqrt(4)%
    834      4      (4! / 4' % / sqrt(.4')) + 4!
             3      sqrt(4)/.(4!)% + sqrt(.4')
    835      4      ((.4'  /  .(sqrt(4))' % )  + .4)  /  .(4!)
             4      ((4 / sqrt(4)%) + .4) / 4!%
             3      (sqrt(4) + .4%) / .(4!)%
    836      4      ((.4'  +  (sqrt(4))' % )  /  .(sqrt(4))' % )  *  4
    837      4      (4 - .(4!) - 4 %) / .4' %
             4      (4 - (4 + 4!)%) / .4`%
    838      4      sqrt(.4')  +  4  +  (sqrt(4)  /  .(4!) % )
    839      4      ((sqrt(4)  +  .4 % )  /  .(4!) % )  +  4
    840      4      (4 + 4)! / (4! + 4!)
    841      4      (4! + sqrt(4) / .4)^sqrt(4)
    842      4      ((4 - .(4!)) / .4' % ) - 4
             4      ((4 - 4!%) / .4`%) - 4
    843      4      (sqrt(4) / .(4!)' % )  +  (4 / .(sqrt(4))')
    844      4      ((4 - .(4!)) / .4' % ) - sqrt(4)
             4      ((4 - 4!%) / .4`%) - sqrt(4)
    845      4      sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!)) + (4 / sqrt(.4'))!
             4      (4 - (4! + .4`)%) / .4`%
    846      4      (4! + (4! / 4' %)) / sqrt(.4')
             3      (4 - 4!%) / .4`%
    847      4      (4 - .(4!) + .4' % ) / .4' %
             4      (4 - (4! - .4`)%) / .4`%
    848      4      4! * (4! - .4`) / sqrt(.4`)
    849      4      (4 - .(sqrt(4))' - .4' % ) / .4' %
             3      sqrt(4)/.(4!)'% + 4!
    850      4      ((4 - .(4!)) / .4' % ) + 4
             4      ((4 / .4) + 4!) / 4%
             3      (4 - .(sqrt(4))') / .4'%
    851      4      (4 - .(sqrt(4))' + .4' % ) / .4' %
             4      ((4 - sqrt(4%)) / .4`%) - 4
    852      4      ((4 - .(sqrt(4))') / .4' % ) + sqrt(4)
             4      (4 / .4`%) - (sqrt(4) * 4!)
    853      4      ((4 - .(sqrt(4))) / .4' % ) - sqrt(4)
             4      ((4 - sqrt(4%)) / .4`%) - sqrt(4)
    854      4      ((4 - .(sqrt(4)) - .4' % ) / .4' %
             4      (4 + 4!% - .4`) / .4`%
    855      3      (4 - .(sqrt(4)) / .4' %
             3      (4 - sqrt(4%)) / .4`%
    856      4      4! * (4! - .(sqrt(4))') / sqrt(.4')
             4      (4 / .4`%) - 44
    857      4      (4 - .(sqrt(4)) / .4' % ) + sqrt(4)
             4      ((4 - sqrt(4%)) / .4`%) + sqrt(4)
    858      4      (4! * 4! - 4) / sqrt(.4`)
    859      4      (4 - .(sqrt(4))' + 4 % ) / .4' %
             4      4 + ((4 - sqrt(4%)) / .4`%)
    860      4      4! * 4! / sqrt(.4`) - 4
    861      4      (4! * 4! - sqrt(4)) / sqrt(.4`)
    862      4      4! * 4! / sqrt(.4`) - sqrt(4)
    863      4      (4! * 4! - sqrt(.4`)) / sqrt(.4`)
    864      3      4! * 4! / sqrt(.4`)
    865      4      (4! * 4! + sqrt(.4`)) / sqrt(.4`)
    866      4      4! * 4! / sqrt(.4`) + sqrt(4)
    867      4      (4! * 4! + sqrt(4)) / sqrt(.4`)
    868      4      4! * 4! / sqrt(.4`) + 4
    869      4      (sqrt(4) - sqrt(.4' % ) - .(sqrt(4))' % )  /  .(sqrt(4))' %
    870      4      (4! * 4! + 4) / sqrt(.4`)
             3      (sqrt(4) - sqrt(.4'%)) / .sqrt(4)'%
    871      4      (sqrt(4) - sqrt(.4' % ) + .(sqrt(4))' % )  /  .(sqrt(4))' %
    872      4      (4 / .4' % )  -  (4 + 4!)
    873      4      (sqrt(4) - sqrt(.4' % ) + sqrt(.4') % )  /  .(sqrt(4))' %
             4      (4 - (4! / sqrt(4))%) / .4`%
    874      4      ((4 - .(sqrt(4))') / .4' % ) + 4!
             4      (4 / .4`%) - (sqrt(4) + 4!)
    875      4      (4 - sqrt(.4' % ) - 4' % ) / .4' %
    876      4      (4 - sqrt(.4' % ) - 4 % ) / .4' % 
             3      (4 / .4`%) - 4!
    877      4      ((4 + .4' % ) / .4' %)  -  4!
    878      4      (4 / .4' % )  -  (4! - sqrt(4))
    879      4      ((4 - .(sqrt(4))) / .4' % ) + 4!
             4      ((4 - sqrt(4%)) / .4`%) + 4!
    880      4      44 * (4! - 4)
             3      (sqrt(4) - 4!%) / sqrt(4%)%
    881      4      .(sqrt(4))^(-4)  +  (4 ^ 4)
             4      4 ^ 4 + 4% ^ -sqrt(4)
    882      4      (4 / .4' %) - (4 / .(sqrt(4))')
             4      (4 - (4 + 4)%) / .4`%
             3      (sqrt(4) - 4%) / .sqrt(4)'%
    883      4      ((4 - sqrt(.4' %)) / .4' % ) - sqrt(4)
    884      4      (4 - sqrt(.4' % ) - .4' % ) / .4' % 
    885      3      (4 - sqrt(.4' % )) / .4' %
    886      4      ((4 + 4'%) / .4'%) - 4!
    887      4      ((4 - sqrt(.4' % ) / .4' % ) + sqrt(4)
    888      4      444 * sqrt(4)
    889      4      ((4 - sqrt(.4' % )) / .4' % ) + 4
    890      4      (4 - .4' % - 4 % ) / .4' %
             3      (4 - 4'%) / .4'%
             4      (4 - (4 + .4')%) / .sqrt(4)'%
    891      4      ((4! / .(4!)') / .4') * 4
             3      (4 - 4%) / .4`%
    892      4      (4 - 4 % + .4' % ) / .4' %
    893      4      ((4 - 4 % ) / .4' ) + sqrt(4)
    894      4      ((4 - 4' % ) / .4' % ) + 4
    895      4      ((4 - 4 % ) / .4' % ) + 4
    896      4      4! * 4! * (sqrt(4) - .4`)
             3      (4 / .4`%) - 4
    897      4      ((4 - .4' % ) / .4' % ) - sqrt(4)
    898      4      (4 - .4' % - .4' % ) / .4' %
             3      (4 / .4`%) - sqrt(4)
    899      4      root(.(sqrt(4)),4) - sqrt(sqrt(sqrt(.(sqrt(4)))))^(-4!)
             3      (4 - .4`%) / .4`%
    900      4      (4! + 4! / 4)^sqrt(4)
             2      4 / .4' %
    901      3      (4 + .4' % ) / .4' %
    902      4      (4 + .4' % + .4' % ) / .4' %
             3      (4 / .4`%) + sqrt(4)
    903      4      ((4 + .4' % ) / .4' % ) + sqrt(4)  
    904      4      root(.(sqrt(4)),4) - (sqrt(4) / .4)!
             3      4 + (4 / .4`%)
    905      4      (4 / .4' %) + (sqrt(4) / .4)
    906      4      (4 / .4' %) + (4! / 4)
    907      4      ((4 + 4 %) / .4' % ) - sqrt(4)
    908      4      (4 / .4' %) + 4 + 4
    909      4      (4 / .4' %) + (4 / .4')
             3      (4 + 4%) / .4`%
    910      4      sqrt(4)^(4!) * .(sqrt(4)' - .(sqrt(4)'
             4      (4 / .4) + (4 / .4`%)
             3      (4 + 4'%) / .4'%
             4      (4 + (4 + .4')%) / .4'%
    911      4      ((4 + 4' %) + .4' %) / .4' %
    912      4      4! * (4! / sqrt(.4`) + sqrt(4))
    913      4      ((4 + 4 % ) / .4' % ) + 4
    914      4      ((4 + 4' %) / .4' %) + 4
    915      3      (4 + sqrt(.4' %)) / .4' %
    916      4      root(.(sqrt(4)),4) - (4! / .(sqrt(4))'
             4      (4 * 4) + (4 / .4`%)
    917      4      ((4 + sqrt(.4' % )) / .4' % ) + sqrt(4)
    918      4      (4 / .4' % ) + (4 / .(sqrt(4))')
             4      (4 + (4 + 4)%) / .4`%
             3      (sqrt(4) + 4%) / (.sqrt(4)')%
    919      4      ((4 + sqrt(.4' % )) / .4' % ) + 4
    920      4      (4 / .4' %) + 4! - 4
    921      4      (4 + .(sqrt(4)) / .4' %) - 4!
             4      ((4 + sqrt(4%)) / .4`%) - 4!
    922      4      (4 / .4' %) + 4! - sqrt(4)
    923      4      ((4 - .4' % ) / .4' % ) + 4!
    924      4      root(.(sqrt(4)),4) - (4! / .(4!))
             3      (4 / .4`%) + 4!
    925      4      root(.(sqrt(4)),4) - (4! / .(4!)')
             4      (4 + (.4` / 4)) / .4`%
    926      4      (4 / .4' %) + 4! + sqrt(4)
    927      4      (sqrt(4) + sqrt(.4' % ) - (sqrt(.4')) %  /  .(sqrt(4))' %
             4      (4 + (4! / sqrt(4))%) / .4`%
    928      4      4 * (4^4 - 4!)
    929      4      (sqrt(4) + sqrt(.4' % ) - .(sqrt(4))' % )  /  .(sqrt(4))' %
    930      4      ((4 + .(4!)) / .4' %) - 4!
             4      (4 - (4 + 4!)%) / .4%
             3      (sqrt(4) + sqrt(.4'%)) / (.sqrt(4)')%
    931      4      (sqrt(4) + sqrt(.4' % ) + .(sqrt(4))' % )  /  .(sqrt(4))' %
    932      4      (4 / .4' %) + root(.4,4) 
    933      4      ((4 + 4 % ) / .4' % ) + 4!
    934      4      ((4 + 4' %) / .4' % ) + 4!
    935      4      (4 + .(sqrt(4)) - 4' % ) / .4' %
             4      (4 - (sqrt(4) + 4!)%) / .4%
    936      4      (4! + sqrt(4)) * 4! / sqrt(.4`)
    937      4      (sqrt(.4') - 4 % - .(sqrt(4)) %  /  sqrt(.4' % ) %
             4      (sqrt(.4`) - (4 + sqrt(4%))%) / sqrt(.4`%)%
    938      4      ((4 - .(4!)) / .4 % ) - sqrt(4)
             4      ((4 - 4!%) / .4%) - sqrt(4)
    939      4      (4 - .(4!) - .4 % ) / .4 %
             4      (4 - (4! + .4)%) / .4%
    940      4      (4 / .4%) - (4! / .4)
             3      (4 - 4!%) / .4%
    941      4      ((4 + 4'%) / .4'%) - 4!  
    942      4      (4 - .(4!)) / .4 % ) + sqrt(4)
             4      ((4 - 4!%) / .4%) + sqrt(4)
    943      4      ((4 + .(sqrt(4))) / .4' %) - sqrt(4)
             4      ((4 + sqrt(4%)) / .4`%) - sqrt(4)
    944      4      (4 / .4' %) + 44
    945      4      (4 / .4' %) + (sqrt(4) / 4' %)
             3      (4 + sqrt(4%)) / .4`%
    946      4      (4 / .4 %) - (4! / .4')
    947      4      (4 + .(sqrt(4)) / .4' %) + sqrt(4)
             4      ((4 + sqrt(4%)) / .4`%) + sqrt(4)
    948      4      (4 / .4' %) + 4! + 4!
    949      4      (4 + .(sqrt(4)) / .4' %) + 4
             4      4 + ((4 + sqrt(4%)) / .4`%)
    950      3      (4 + .(sqrt(4))') / .4' %
             3      (4 - sqrt(4%)) / .4%
    951      4      ((4!) + (sqrt(sqrt(sqrt(.4))))^(-4!)) * (4!)
    952      4      (4 / .4 %) - (4! + 4!)
    953      4      (4 + .(4!) - .4' % ) / .4' %
             4      (4 + (4! - .4`)%) / .4`%
    954      3      (4 + .(4!)) / .4' %
             3      (4 + 4!%) / .4`%
    955      4      (4 / .4 %) - (sqrt(4)/ 4' %)
    956      4      (4 / .4 %) - 44
    957      4      ((4^4) - 4!) / .(4!)'
             4      ((4! - sqrt(4%))% + .4) / sqrt(.4`%)%
    958      4      ((4 + .(4!)) / .4' %) + 4
             4      4 + ((4 + 4!%) / .4`%)
    959      4      (sqrt(sqrt(sqrt(4 ^ 4!)))) - sqrt(.4' %)) / sqrt(.4' %)
    960      4      (4 * 4!) * 4 / .4
             3      4! / sqrt(.4 ^ -sqrt(4))%
    961      4      (sqrt(sqrt(sqrt(4 ^ 4!)))) + sqrt(.4' %)) / sqrt(.4' %)
    962      4      (sqrt(4) / .4' %) + root(.(sqrt(4))' ,4)
             4      sqrt(4) + (4! / sqrt(.4 ^ -sqrt(4))%)
    963      4      (sqrt(sqrt(sqrt(4 ^ 4!)))) + .(sqrt(4)) / sqrt(.4' %)
             4      (4 + (4 + 4!)%) / .4`%
    964      4      root(.(sqrt(4)),4) - 4! / .4
             4      root(sqrt(4%), 4) - (4! / .4)
    965      4      (4 + sqrt(.4' % ) + .(sqrt(4))')  / .4' %
    966      4      (4.4 / .4' %) - 4!
    967      4      (sqrt(4) - sqrt(.4'%) + (sqrt(.4'%))%) / .(sqrt(4)%) 
             4      (sqrt(.4`) - (sqrt(4) + sqrt(4%))%) / sqrt(.4`%)%
    968      4      44 * (4! - sqrt(4))
    969      4      ((4 + 4'%) / .4'%) - 4!  
    970      4      root(.(sqrt(4)),4) - 4! / .4'
             3      (sqrt(.4`) - sqrt(4)%) / sqrt(.4`%)%
    971      4      sqrt(4^4!) - (root(-(.(sqrt(4)),.(sqrt(4))
             4      ((4 - sqrt(4)%) / .4%) - 4!
    972      4      4 * (root.4(4/.4'))
             4      (4 / .4 %) - (4 + 4!)
    973      4      ((sqrt(.4') - .(sqrt(4)) % )  /  sqrt(.4' % ) % )  -  4!
             4      ((sqrt(4%) - sqrt(4))% + sqrt(.4`)) / sqrt(.4`%)%
    974      4      ((4 + .(sqrt(4))') / .4' % ) + 4!   
             4      (4 / .4%) - (sqrt(4) + 4!)
    975      4      (4! + sqrt(4))! / sqrt(.4') * (4!)!
    976      4      (4! / 4)! + 4 ^ 4
             3      (4 / .4%) - 4!
    977      4      ((4 + .4 % ) / .4 %) - 4!
    978      4      (4 / .4 %) - (4! - sqrt(4))
    979      4      root(.(sqrt(4))' ,4) - (sqrt(4) / 4' %
             4      root(sqrt(4%), 4) - (sqrt(4%) / .4`%)
    980      4      root(.(sqrt(4)),4) - 44
             3      (sqrt(4) - 4%) / sqrt(4%)%
    981      4      (4.4 - 4 % ) / .4' %
    982      4      (4 / .4 % ) - (4 / .(sqrt(4))')
             4      (4 - (4 + sqrt(4))!%%) / .4%
    983      4      (sqrt(4 ^ 4!) * .(4!)) - 4 %
    984      4      sqrt(((4 + 4)! + 4!) * 4!)
    985      4      (4 / .4 %) - (sqrt(.4') / 4' %)
    986      4      (4.4 / .4' %) - 4
    987      4      (4! - sqrt(4) - sqrt(.4' % ))  /  (sqrt(4) % )'   
             4      (sqrt(.4`) - (sqrt(4%) + sqrt(.4`))%) / sqrt(.4`%)%
    988      4      root(.(sqrt(4)),4) - (4! / sqrt(.4'))
             4      ((4 - 4%) / .4%) - sqrt(4)
    989      4      (4.4 - .4' % ) / .4' %
    990      4      44 / (.4` - .4)
             2      4! / (4!)' %o
             3      (4 - 4%) / .4%
    991      4      (4 / .4 %) - (4 / .4')
    992      4      root(.(sqrt(4)),4) - root(.4,4)
             4      (4 / .4%) - (4 + 4)
    993      4      (4! - sqrt(4) + sqrt(.4' % ))  /  sqrt(4) % )' 
             4      ((4 - sqrt(4)%) / .4%) - sqrt(4)
    994      4      (4 / .4 %) - (4! / 4)
             3      (sqrt(.4`) - .4%) / sqrt(.4`%)%
    995      4      (4 / .4 %) - (sqrt(4) / .4)
             3      (4 - sqrt(4)%) / .4%
    996      4      sqrt(sqrt(sqrt((4 / .4)^4!))) - 4
             3      (4 / .4%) - 4
    997      4      (4 / .4 %) - sqrt(4 / .4')
             3      (sqrt(.4`) - sqrt(4%)%) / sqrt(.4`%)%
    998      4      sqrt(sqrt(sqrt((4 / .4)^4!))) - sqrt(4)
             3      (4 / .4%) - sqrt(4)
    999      4      444 / .4`
             3      (4 - .4%) / .4%
             2      4/(.4%)'

   1000      4      4 * 4^4 - 4!
             3      sqrt(sqrt(sqrt((4 / .4)^4!)))
             2      4 / .4 %
   1001      4      4/.4 %  +  4/4
             3      (4 + .4%) / .4%
   1002      3      4/.4 %  +  sqrt(4)
   1003      4      4/.4 %  +  sqrt(4/.4')
             3      (sqrt(4%)% + sqrt(.4`)) / sqrt(.4`%)%
   1004      3      4/.4 %  +  4
   1005      4      4/.4 %  +  sqrt(4)/.4
             3      (4 + sqrt(4)%) / .4%
   1006      4      4/.4 %  +  sqrt(4) + 4
             3      (.4% + sqrt(.4`)) / sqrt(.4`%)%
   1007      4      (4 + 4! %o + .4 %) / .4 %
             4      ((4 + 4)!% - .4) / .4
   1008      4      4/.4 %  +  4 + 4
             3      ((4 + 4)! / .4)%
   1009      4      4/.4 %  +  4/.4'
   1010      4      4/.4 %  +  4/.4
             3      (4 + 4%) / .4%
   1011      4      ((sqrt(4)/.4' %) - sqrt(.4'))  /  .4'
   1012      4      4/.4 %  +  4!/sqrt(4)
   1013      4      ((sqrt(4)/.4' %) + .(sqrt(4))'  /  .4'
             4      ((4 + 4)!% + sqrt(4)) / .4
   1014      3      (4!/(4!)' %o  +  4! 
             4      4 + ((4 + 4%) / .4%)
   1015      4      4/.4 %  +  sqrt(.4')/(4)' %
             4      root(sqrt(4%), 4) - (4 / .4`)
   1016      4      4/.4 %  +  (4 * 4)
   1017      4      ((sqrt(4)/,4' %) + sqrt(4))  /  .4'
   1018      4      4/.4 %  +  4/.(sqrt(4))'
             4      (4 + (4 + 4)!%) / .4
   1019      4      root(.(sqrt(4)),4)  -  (sqrt(4)/.4)
             4      root(sqrt(4%), 4) - (sqrt(4) / .4)
   1020      4      4/.4 %  +  (4! - 4)
             3      root(sqrt(4%), 4) - 4
   1021      4      root(.(sqrt(4)),4)  -  sqrt(4/.4')
             4      root(sqrt(4%), 4) - sqrt(4 / .4`)
   1022      4      4/.4 %  +  (4! - sqrt(4))
             3      root(sqrt(4%), 4) - sqrt(4)
   1023      4      root(.(sqrt(4)),4)  -  4/4
             4      root(sqrt(4%), 4) - (4 / 4)
             3      4/(.4%)' + 4!
   1024      2      root(.(sqrt(4)),4)
             2      root(sqrt(4%), 4)
   1025      4      root(.(sqrt(4)),4)  +  4/4
             4      (4 + (.4 / 4)) / .4%
   1026      3      root(.(sqrt(4)),4)  +  sqrt(4)
             3      sqrt(4) + root(sqrt(4%), 4)
   1027      4      root(.(sqrt(4)),4)  +  sqrt(4/.4')
             4      sqrt(4 / .4`) + root(sqrt(4%), 4)
   1028      3      root(.(sqrt(4)),4)  +  4
             3      4 + root(sqrt(4%), 4)
   1029      4      root(.(sqrt(4)),4)  +  sqrt(4)/.4
             4      (sqrt(4) / .4) + root(sqrt(4%), 4)
   1030      4      root(.(sqrt(4)),4)  +  sqrt(4) + 4
             3      (sqrt(4)% + sqrt(.4`)) / sqrt(.4`%)%
   1031      4      (sqrt(.4') + sqrt(4) % + sqrt(.4' %)%)  /  sqrt(.4' %)%  
   1032      4      root(.(sqrt(4)),4)  +  4 + 4
             4      (4! * 44) - 4!
   1033      4      root(.(sqrt(4)),4)  +  4/.4'
             4      (4 / .4`) + root(sqrt(4%), 4)
   1034      4      root(.(sqrt(4)),4)  +  4/.4
             4      (4 / .4) + root(sqrt(4%), 4)
   1035      4      (4!/sqrt(4) %)  -  (.4/.(4!)' %)
             4      ((sqrt(4) / .4) - .4) / .4`%
   1036      4      (4!/sqrt(4)' %)  -  44  
             4      (4! / sqrt(4)) + root(sqrt(4%), 4)
   1037      4      (sqrt(.4') + 4! %o + sqrt(.4' %) %)  /  (sqrt.4' %) %)
   1038      4      (4!/(4!)' %o)  + 4! + 4!
   1039      4      root(.(sqrt(4)),4)  +  sqrt(.4')/4' %
             4      root(-sqrt(4), .4`%) + root(sqrt(4%), 4)
   1040      4      root(.(sqrt(4)),4)  +  (4 * 4)
             4      4 * (4 + 4 ^ 4)
   1041      4      ((.(sqrt(4) ^ -(sqrt(4)) / 4! %o)  -  sqrt(.4')
             4      (4 - 4% + sqrt(.4`)) / .4`%
   1042      4      root(.(sqrt(4)),4)  +  (4/.(sqrt(4))')
   1043      5      ((4!/4)! - 4! - sqrt(.4')) / sqrt(.4')
             4      44 + (sqrt(4) / (.(sqrt(4)) % )')
   1044      4      (4/.4 %)  +  44
   1045      4      (4/.4 %)  +  (sqrt(4)/4' %)
   1046      4      (4! - sqrt(4))  +  root(.(sqrt(4)),4)
             4      ((4 + sqrt(4%)) / .4%) - 4
   1047      4      (4! - sqrt(.4') - sqrt(.4' %))  /  sqrt(4)' %
   1048      3      4!  +  root(.(sqrt(4)),4)
             3      4! + root(sqrt(4%), 4)
   1049      4      .(sqrt(4)) ^ -(sqrt(4))  + root(.(sqrt(4)),4)
             4      (4 + sqrt(4%) - .4%) / .4%
   1050      4      (4/.4 %)  +  sqrt(4) / 4 %
             3      (4 + sqrt(4%)) / .4%
   1051      4      (.4' - 4! %o - .4' % %)  /  4 % %
             4      (4 + sqrt(4%) + .4%) / .4%
   1052      4      (4! * 44) - 4
   1053      4      (.4' + 4! %o - 4 % %)  /  4' % %
   1054      4      (4/.4 %)  +  (4!/.4')
   1055      4      (4!/sqrt(4)' %)  -  (.(sqrt(4)) ^ -(sqrt(4))
             4      (4 - (sqrt(4) - 4!)%) / .4%
   1056      3      (4!/sqrt(4)' %)  -  4!
             3      4! * 44
   1057      4      ((4 ^ 4)  +  .(4!)')  /  .(4!)'
             4      ((4 - sqrt(4%))% + sqrt(.4`)) / sqrt(.4`%)%
   1058      4      (4!/sqrt(4)' %)  -  (4! - sqrt(4))
             4      sqrt(4) + (4! * 44)
   1059      4      (4! - .4 - (sqrt(.4' % )) / sqrt(4)' %
             4      (4 + (4! - .4)%) / .4%
   1060      4      (4! / sqrt(4)' %) - (4! - 4)
             3      (4 + 4!%) / .4%
   1061      4      (4! - (.4 + sqrt(4)' % )) / sqrt(4)' %
             4      (4 + (4! + .4)%) / .4%
   1062      4      (4! / sqrt(4)' %) - 4 / .(sqrt(4))'
             4      ((4 + 4!%) / .4%) + sqrt(4)
             3      (4! - .4) / (sqrt(4))'%
             4      (4! - .4) / (sqrt(4) + sqrt(4%)')%
   1063      4      (4! - .4 + sqrt(4)' % ) / sqrt(4)' %
             4      ((4 + sqrt(4%))% + sqrt(.4`)) / sqrt(.4`%)%
   1064      4      (4! / sqrt(4)' %) - (4 * 4) 
             4      4 + ((4 + 4!%) / .4%)
   1065      4      (4! / sqrt(4)' %) - sqrt(.4') / 4' %
             4      (4 ^ 4 - .4) / 4!%
   1066      4      ((4 ^ 4) / .(4!)) -  sqrt(.4')
             4      (4 ^ 4 / 4!%) - sqrt(.4`)
   1067      4      ((4! - .(sqrt(4)) / sqrt(4)' % ) -  4
   1068      4      (4! / sqrt(4)' %) - 4!/sqrt(4) 
             4      root(sqrt(4%), 4) + 44
   1069      4      ((4! - .(sqrt(4)) / sqrt(4)' % ) - sqrt(4)
             4      root(sqrt(4%), 4) + (sqrt(4%) / .4`%)
   1070      4      (4! / sqrt(4)' %) - 4/.4
             4      (4 + (4 + 4!)%) / .4%
             3      (4! - .sqrt(4)') / (sqrt(4))'%
             4      (4! - .sqrt(4)') / (sqrt(4) + sqrt(4%)')%
   1071      4      (4! / sqrt(4)' %) - 4/.4'
             4      ((sqrt(4) / .4%) - 4!) / .4`
   1072      4      (4! / sqrt(4)' %) - (4 + 4)
             4      4! * (44 + sqrt(.4`))
   1073      4      (4! - .(sqrt(4)) + 4' % ) / sqrt(4)' %
   1074      4      (4! / sqrt(4)' %) - (4 + sqrt(4))
             4      ((4 + sqrt(4))! - 4) / sqrt(.4`)
   1075      4      (4! / sqrt(4)' %) - sqrt(4)/.4
             4      (4 ^ 4 + sqrt(4)) / 4!%
   1076      3      (4! / sqrt(4)' %) - 4
             4      (44 / 4%) - 4!
   1077      4      (4! / sqrt(4)' %) - sqrt(4/.4')
             4      ((4 + sqrt(4))! - sqrt(4)) / sqrt(.4`)
             3      (4! - sqrt(.4'%)) / (sqrt(4))'%
             4      (4! - sqrt(.4'%)) / (sqrt(4) + sqrt(4%)')%
   1078      3      (4! / sqrt(4)' %) - sqrt(4)
             4      (4! / .4`) + root(sqrt(4%), 4)
   1079      4      (4! / sqrt(4)' %) - 4/4
             4      ((4 + sqrt(4))! - sqrt(.4`)) / sqrt(.4`)
   1080      2      4! / sqrt(4)' %
             3      (4 + sqrt(4))! / sqrt(.4`)
   1081      3      (4! + sqrt(4)' % ) / sqrt(4)' %
             4      ((4 + sqrt(4))! + sqrt(.4`)) / sqrt(.4`)
   1082      3      (4! / sqrt(4)' % ) + sqrt(4)
             4      ((4 + sqrt(4))! / sqrt(.4`)) + sqrt(4)
   1083      4      (4! / sqrt(4)' % ) + sqrt(4/.4')
             4      ((4 + sqrt(4))! + sqrt(4)) / sqrt(.4`)
   1084      3      (4! / sqrt(4)' % ) + 4
             4      (4! / .4) + root(sqrt(4%), 4)
   1085      4      (4! / sqrt(4)' % ) + sqrt(4)/.4
   1086      4      (4! / sqrt(4)' % ) + sqrt(4) + 4 
             4      (4 + (4 + sqrt(4))!) / sqrt(.4`)
   1087      4      ((.(4!) + 4! %o) / 4! % %o) - sqrt(4) 
   1088      4      (4! / sqrt(4)' % ) + 4 + 4
             4      (4! - (sqrt(4) + 4!%)) / sqrt(4)%
   1089      4      (4! / sqrt(4)' % ) + 4/.4'
             4      ((4 / .4`) + 4!) ^ sqrt(4)
             3      (4! + sqrt(4%)) / (sqrt(4))'%
             4      (4! + sqrt(4%)) / (sqrt(4) + sqrt(4%)')%
   1090      4      (4! / sqrt(4)' % ) + 4/.4
             4      (44 - .4) / 4%
   1091      3      ((.(4!) + 4! % %o) + sqrt(4)
             4      (4! + sqrt(4%)%) / (sqrt(4) + sqrt(4%))%
   1092      4      (4! / sqrt(4)' % ) + 4! / sqrt(4)
   1093      4      ((.(4!) + 4! %o) / (4!)' % %o) + 4
   1094      4      (44 - .(4!)) / 4 %
             4      (44 - 4!%) / 4%
   1095      4      (4! / sqrt(4)' % ) + (sqrt(.4') / 4' % )
             4      (44 - sqrt(4%)) / 4%
   1096      4      (4! / sqrt(4)' % ) + (4 * 4)
             4      (44 / 4%) - 4
   1097      4      (4! + .4 - sqrt(4)' % ) / sqrt(4)' %
             4      (sqrt(.4`) - sqrt(4%)% + sqrt(.4`%)) / sqrt(.4`%)%
   1098      3      (4! + .4) / sqrt(4)' %
             4      (44 / 4%) - sqrt(4)
   1099      4      (4! + .4 + sqrt(4)' % ) / sqrt(4)' % 
             4      (44 - 4%) / 4%
   1100      4      (4! / sqrt(4)' % ) + (4! - 4)
             3      44 / 4%
   1101      4      (4.4 + .4 % ) / .4 %
   1102      4      (4! / sqrt(4)' % ) + (4! - sqrt(4))
             4      sqrt(4) + (44 / 4%)
   1103      4      ((4! - sqrt(4)' %)  /  sqrt(4)' % )  +  4!
             4      (sqrt(4%)% + sqrt(.4`) + sqrt(.4`%)) / sqrt(.4`%)%
   1104      4      (4! / sqrt(4)' % ) + 4!
             4      4 + (44 / 4%)
             3      4!/(sqrt(4))'% + 4!
             4      4! / (sqrt(4) + sqrt(4%)')% + 4!
   1105      4      (4! / sqrt(4)' % ) + .(sqrt(4)) ^ - (sqrt(4))
             4      (sqrt(4%) + 44) / 4%
   1106      4      (4! / sqrt(4)' % ) + 4! + sqrt(4)
             4      (4!% + 44) / 4%
   1107      4      (4! + .4 + .(sqrt(4))) / (sqrt(4))' %
   1108      4      (4! / sqrt(4)' % ) +  4!  +  4
             4      ((4 + 4)!%% + .4) / .4%
   1109      4      (4! + .4' + .(sqrt(4)) / (sqrt(4))' %
   1110      4      (4! / sqrt(4)' % )  +  (sqrt(4) / sqrt(.4' % )
             4      444 / .4
             3      (4! + sqrt(.4')) / (sqrt(4))'%
             4      (4! + sqrt(.4')) / (sqrt(4) + sqrt(4%)')%
   1111      4      (4!  +  sqrt(.4')  +  sqrt(4)' % ) / (sqrt(4))' %
             2      .4' / (4%%)'
   1112      4      (4! / sqrt(4)' % )  +  root.4,(4)
             4      (4! - sqrt(4) + 4!%) / sqrt(4)%
   1113      4      (4!  +  sqrt(.4')  +  sqrt(.4' % ))  /  sqrt(4)' %
             4      (sqrt((.4`% ^ -sqrt(4))%) - 4!%) / sqrt(4)%
             3      .4'/(4%%)' + sqrt(4)
   1114      4      ((4!  +  sqrt(.4')) / sqrt(4)' % )  +  4
             4      root(sqrt(4%), 4) + (.4 / .4`%)
   1115      4      ((.(sqrt(4)) ^ -(sqrt(4)) - (.(sqrt(4)))  /  (sqrt(4))' %
             4      ((sqrt(4) / .4`%) - 4) / .4
             3      .4'/(4%%)' + 4
   1116      4      (4! / sqrt(4)' % )  +  (4! / sqrt(.4'))
             4      ((sqrt(4) / .4%) - 4) / .4`
   1117      4      ((.4' + .(4!) %  - .4' % % )  /  4 % %
   1118      4      (sqrt(4) + (4! - .4)%) / sqrt(4%)%
   1119      4      ((sqrt(4%) / .4`%) - 4!%) / 4%
   1120      3      (sqrt(4) + 4!%) / sqrt(4%)%
   1121      4      (sqrt(4) / (.4 * .4`)%) - 4
   1122      4      (sqrt(4) + (4! + .4)%) / sqrt(4%)%
   1123      4      (sqrt(4) / (.4 * .4`)%) - sqrt(4)
   1124      4      4! + (44 / 4%)
   1125      3      sqrt(4) / (.4 * .4`)%
   1126      4      ((sqrt(4) / .4`%) + .4) / .4
   1127      4      sqrt(4) + (sqrt(4) / (.4 * .4`)%)
   1128      4      (sqrt(4) * 4! * 4!) - 4!
   1129      4      4 + (sqrt(4) / (.4 * .4`)%)
   1130      4      (sqrt(4) + (sqrt(4) / .4`%)) / .4
   1131      4      (4!% + (sqrt(4%) / .4`%)) / 4%
   1132      4      (4! / .(sqrt(4))')  +  root(.(sqrt(4)), 4)
   1133      4      (.(sqrt(4))'  +  .4' %  -  sqrt(.4') % % )  /  sqrt(4) % %
   1134      4      (4 + (sqrt(4) / .4%)) / .4`
   1135      4      (4 + (sqrt(4) / .4`%)) / .4
             3      .4'/(4%%)' + 4!
   1136      4      ((sqrt(4) * 4!) - sqrt(.4`)) * 4!
   1137      4      (4!% + sqrt((.4`% ^ -sqrt(4))%)) / sqrt(4)%
   1138      4      (4 / .(4!)' % )  -  root(.(sqrt(4))', 4)
   1139      4      (4 + 4!)  +  (.(sqrt(4))'  /  sqrt(4) % % )'
   1140      4      (4 + 4 - .4) / sqrt(.4`)%
   1141      4      sqrt(4 / .4' % )  +  (.(sqrt(4))'  /  sqrt(4) % % )'
   1142      4      ((.4 ^ 4)  -  sqrt4)' % % )  /  .(sqrt(4)) % %
   1143      4      (root(.(sqrt(4))', 4)) - 4)  /  .4'
   1144      4      (sqrt(4) + 4!) * 44
   1145      4      (4 + sqrt(.4`% ^ -sqrt(4))) / sqrt(4%)
   1146      4      (4! / sqrt(4)%) - (4! / .4`)
   1147      4      (4!  /  sqrt(.4'))  +  (.(sqrt(4))'  /  sqrt(4) % % )'
   1148      4      (sqrt(4) * 4! * 4!) - 4
   1149      4      (sqrt(4) / (.4 * .4`)%) + 4!
   1150      4      (sqrt(4) + 44) / 4%
   1151      4      (root(.(sqrt(4))', 4)  -  .4')  /  .4'
   1152      3      sqrt(4) * 4! * 4!
   1153      4      root(.(sqrt(4))' 4)  +  .4')  /  .4'
   1154      4      sqrt(4) + (sqrt(4) * 4! * 4!)
   1155      4      (4! - (.4 / .4`)) / sqrt(4)%
             3      (4! - sqrt(.4')) / (sqrt(4)%)'
   1156      4      (4! / sqrt(4)%) - 44
   1157      4      ((4 + 4!)  /  (4!)' %o )  +  sqrt(4)
   1158      4      (4!  /  (sqrt(4) % )')  -  sqrt(4  /  .4' % )
   1159      4      ((4 + 4!)  /  (4!)' %o )  +  4  
   1160      4      (4 + (4! * 4!)) * sqrt(4)
   1161      4      ((4 ^ 4)  +  sqrt(4))  /  .(sqrt(4))'
   1162      4      (.(sqrt(4))'  +  ((4! / sqrt(.4')) %o )  /  .(sqrt(4))' %o
   1163      4      (4! / (sqrt(4) % )')  -  .(sqrt(4)) ^ -(sqrt(4))
   1164      4      (4 + 4 - 4!%) / sqrt(.4`)%
   1165      4      (4 + sqrt(.4`) - sqrt(.4`)%) / .4%
   1166      4      ((4 + sqrt(.4`)) / .4%) - sqrt(.4`)
             3      (4! - .4') / (sqrt(4)%)'
   1167      4      (4! - sqrt(.4`) + sqrt(.4`)%) / sqrt(4)%
   1168      4      (4! / sqrt(4)%) - root(.4, 4)
   1169      4      (sqrt(4) + 4! - sqrt(4)' % )  /  sqrt(4)' %
   1170      4      (4 + 4 - sqrt(4%)) / sqrt(.4`)%
             3      (4! + sqrt(4)) / (sqrt(4))'%
             4      (4! + sqrt(4)) / (sqrt(4) + sqrt(4%)')%
   1171      4      (sqrt(4) + 4! + sqrt(4)' % )  /  sqrt(4)' %   
   1172      4      (4! / sqrt(4)%) - (4 + 4!)
   1173      4      (4! - (4! / .4`)%) / sqrt(4)%
   1174      4      (4! / sqrt(4)%) - (sqrt(4) + 4!)
   1175      4      (4! - (sqrt(4) / 4)) / sqrt(4)%
   1176      3      (4! / sqrt(4)%) - 4!
   1177      4      ((sqrt(4)% + 4!) / sqrt(4)%) - 4!
             3      (4! - .(sqrt(4))') / (sqrt(4)%)'
   1178      4      (4! - 44%) / sqrt(4)%
   1179      4      ((sqrt(4) / .4%) + 4!) / .4`
   1180      3      (4! - .4) / sqrt(4)%
   1181      4      (sqrt(4)% + 4! - .4) / sqrt(4)%
   1182      4      sqrt(4) + ((4! - .4) / sqrt(4)%)
   1183      4      (4! / (sqrt(4) % )')  -  (sqrt(4) / .4)
   1184      4      (4! / sqrt(4)%) - (4 * 4)
             3      4!/(sqrt(4)%)' - 4
   1185      4      ((sqrt(4) / .4`%) + 4!) / .4
   1186      4      (4! - (4 + 4!)%) / sqrt(4)%
             3      (4! - (4%)') / (sqrt(4)%)'
             3      4!/(sqrt(4)%)' - sqrt(4)
   1187      4      (4! - (sqrt(4) + 4!)%) / sqrt(4)%
             3      (4! - (sqrt(4)%)') / (sqrt(4)%)'
   1188      3      (4! - 4!%) / sqrt(4)%
   1189      4      ((sqrt(4) - 4!)% + 4!) / sqrt(4)%
             3      (4! + (sqrt(4)%)') / (sqrt(4)%)'
   1190      3      (4! - sqrt(4%)) / sqrt(4)%
   1191      4      (4! / sqrt(4)%) - (4 / .4`)
   1192      4      sqrt(4) * ((4! / 4%) - 4)
             3      4!/(sqrt(4)%)' + 4
   1193      4      (4! / (sqrt(4) % )')  +  (sqrt(4) / .4)
   1194      4      (4! / sqrt(4)%) - (4 + sqrt(4))
   1195      4      (4! - (.4 / 4)) / sqrt(4)%
   1196      3      (4! / sqrt(4)%) - 4
   1197      4      ((sqrt(4)% + 4!) / sqrt(4)%) - 4
   1198      3      (4! / sqrt(4)%) - sqrt(4)
   1199      3      (4! - sqrt(4)%) / sqrt(4)%
   1200      2      4! / sqrt(4) %
   1201      3      (sqrt(4)% + 4!) / sqrt(4)%
   1202      3      sqrt(4) + (4! / sqrt(4)%)
   1203      4      4!/(sqrt(4))% + sqrt(4/.4')
   1204      3      4 + (4! / sqrt(4)%)
   1205      4      4!/(sqrt(4))% + sqrt(4)/.4
   1206      4      4+sqrt(4)+(4!/sqrt(4)%)
   1207      4      .4'/(4%%)' + (4! x 4)
   1208      4      4!/(sqrt(4))% + (4 x sqrt(4))
   1209      4      4!/(sqrt(4))% + 4/.4'
   1210      3      (4! + sqrt(4%)) / sqrt(4)%
   1211      4      .4'/(4%%)' + 4/4%
   1212      3      (4! + 4!%) / sqrt(4)%
   1220      3      (4! + .4) / sqrt(4)%
   1224      3      (4! / sqrt(4)%) + 4!
   1250      3      sqrt(4) / 4 % / 4 %
   1280      3      4 ^ 4 / sqrt(4%)
   1296      3      (4!/4)^4
   1300      3      (sqrt(4)  +  4!) / sqrt(4) %
   1350      3      (4 + sqrt(4)) / .4`%
   1360      3      (4!% + sqrt(.4`)) / sqrt(.4`%)%
   1400      3      (4 + 4!) / sqrt(4) %    
   1440      3      (4!/4)!  *  sqrt(4)
   1500      4      sqrt(.4') / 4'% * 4 / 4%       
             3      (4 + sqrt(4)) / .4%
             2      sqrt(.4') / .4' %o 
   1536      3      root(sqrt(4%), 4) / sqrt(.4`)
   1577      4      (((4%)' - .(sqrt(4))') / .(4!)' % % ) + sqrt(4)
   1600      4      (4*4+4!)^sqrt(4)
             3      ((4! - 4) ^ 4)%
   1620      3      (4 + sqrt(4))! / .4`
   1650      2      4 / .(4!)' %
   1680      3      (4 + 4)! / 4!
   1700      4      (root.4(4)  +  sqrt(4))  /  sqrt(4) %
   1736      4      .4' + .4' + (4!%o ^ -sqrt(4))
   1776      4      4 (444)
   1800      4      4 / .(sqrt(4))' * 4 / 4%
             2      4 / .(sqrt(4))' %
             3      (4 + 4) / .4`%
   1880      3      (4 - 4!%) / sqrt(4%)%
   1900      4      (4! / sqrt(.4')  +  sqrt(4))  /  sqrt(4) %          
             3      (4 - sqrt(4%)) / sqrt(4%)%
   1936      4      (44) * (44)
             3      44^sqrt(4)
   1976      3      (4 / sqrt(4%)%) - 4!
   1980      3      (4 - 4%) / sqrt(4%)%
   1990      3      (4 - sqrt(4)%) / sqrt(4%)%
   1996      3      (4 / sqrt(4%)%) - 4
   1998      3      (4 / sqrt(4%)%) - sqrt(4)
   1999      3      (4 - sqrt(4%)%) / sqrt(4%)%
   2000      4      (4! - 4) * 4 / 4%
             2      .4' / .(sqrt(4))' %o
             2      4 / sqrt(4%)%
   2001      3      (4 + sqrt(4%)%) / sqrt(4%)%
   2002      3      (4 / sqrt(4%)%) + sqrt(4)
   2004      3      4 + (4 / sqrt(4%)%)
   2010      3      (4 + sqrt(4)%) / sqrt(4%)%
   2016      3      ((4 + 4)! / sqrt(4%))%
   2020      3      (4 + 4%) / sqrt(4%)%
   2024      3      (4 / sqrt(4%)%) + 4!
   2025      3      (4 * .4`% ^ -sqrt(4))%
   2048      3      sqrt(4) * root(sqrt(4%), 4)
   2100      4      (44 - sqrt(4))  /  sqrt(4) %
             3      (4 + sqrt(4%)) / sqrt(4%)%
   2120      3      (4 + 4!%) / sqrt(4%)%
   2160      3      4! * .4 / .4`%
   2200      4      (4! - sqrt(4)) * 4 / 4% 
             3      44 / sqrt(4)%
   2208      4      4 * (4!)! / (4! - sqrt(4))
   2250      3      4 / (.4 * .4`)%
   2300      4      (44 + sqrt(4))  /  sqrt(4) %
   2304      3      4*4!^sqrt(4)
   2400      3      4! * 4 / 4%
   2476      3      sqrt(4)% ^ -sqrt(4) - 4!
   2496      3      sqrt(4)% ^ -sqrt(4) - 4
   2498      3      sqrt(4)% ^ -sqrt(4) - sqrt(4)
   2500      4      sqrt(4)  /  .4  /  .(sqrt(4)) %    
             2      sqrt(4)% ^ -sqrt(4)
   2502      3      sqrt(4) + sqrt(4)% ^ -sqrt(4)
   2504      3      4 + sqrt(4)% ^ -sqrt(4)
   2517      4      ((4)' % + (((4! / (4 % )') %o)' % ) / (.(sqrt(4)) % )' %
   2524      3      sqrt(4)% ^ -sqrt(4) + 4!
   2560      4      4^4 * 4 / .4
             3      root(sqrt(4%), 4) / .4
   2592      4      sqrt(4) * (4! / 4)^4
   2600      4      (4! + sqrt(4)) * 4 / 4% 
   2640      3      (sqrt(4) - 4!%) / sqrt(.4`%)%
   2688      3      (4 + 4)! * sqrt(.4`%)
   2700      4      4!  /  (4)' %  /  .(sqrt(4))    
             3      4! / (sqrt(4) * .4`)%
   2750      2      sqrt(.4') / (4!) %o
   2800      4      (4! + 4) * 4 / 4% 
   2880      3      (4!^sqrt(4)) * sqrt(4)
   2900      4      ((4! / .4')  +  4)  /  sqrt(4) % 
             3      (sqrt(4) - sqrt(.4`%)) / sqrt(.4`%)%
   2916      3      (4! / .4')^sqrt(4)
   2940      3      (sqrt(4) - 4%) / sqrt(.4`%)%
   2970      3      (sqrt(4) - sqrt(4)%) / sqrt(.4`%)%
   2976      3      (sqrt(4) / sqrt(.4`%)%) - 4!
   2990      3      (sqrt(4) - sqrt(.4`)%) / sqrt(.4`%)%
   2994      3      (sqrt(4) - .4%) / sqrt(.4`%)%
   2996      3      (sqrt(4) / sqrt(.4`%)%) - 4
   2997      3      (sqrt(4) - sqrt(4%)%) / sqrt(.4`%)%
   2998      3      (sqrt(4) / sqrt(.4`%)%) - sqrt(4)
   2999      3      (sqrt(4) - sqrt(.4`%)%) / sqrt(.4`%)%
   3000      4      sqrt(4 / .4`) * 4 / .4% 
             2      sqrt(.4') / .(sqrt(4))' %o
             2      sqrt(4) / sqrt(.4`%)%
   3001      3      (sqrt(4) + sqrt(.4`%)%) / sqrt(.4`%)%
   3002      3      sqrt(4) + (sqrt(4) / sqrt(.4`%)%)
   3003      3      (sqrt(4) + sqrt(4%)%) / sqrt(.4`%)%
   3004      3      4 + (sqrt(4) / sqrt(.4`%)%)
   3006      3      (sqrt(4) + .4%) / sqrt(.4`%)%
   3010      3      (sqrt(4) + sqrt(.4`)%) / sqrt(.4`%)%
   3024      3      (sqrt(4) / sqrt(.4`%)%) + 4!
   3030      3      (sqrt(4) + sqrt(4)%) / sqrt(.4`%)%
   3060      3      (sqrt(4) + 4%) / sqrt(.4`%)%
   3100      4      ((4! / .4)  +  sqrt(4))  /  sqrt(4) % 
             3      (sqrt(4) + sqrt(.4`%)) / sqrt(.4`%)%
   3125      2      root(-.(sqrt(4), .(sqrt(4))
             3      4% ^ -sqrt(4) / sqrt(4%)
   3200      3      sqrt(sqrt(sqrt(4 ^ (4!)))  /  sqrt(4) % 
   3240      4      (4! / 4)^4 / .4
   3300      4      (sqrt(sqrt(sqrt(4 ^ (4!))) + sqrt(4))  /  sqrt(4) % 
             3      (4! - sqrt(4)) / sqrt(.4`)%
   3360      3      (sqrt(4) + 4!%) / sqrt(.4`%)%
   3375      3      root(-sqrt(4), .4`%) / .4`%
   3400      4      (sqrt(sqrt(sqrt(4 ^ (4!)))  +  4)  /  sqrt(4) % 
   3472      4      ((sqrt(sqrt(.(sqrt(4) ^ -4!) * .(sqrt(4))') - .(sqrt(4))'
   3500      4      (4! / sqrt(.4') % )  -  (4! / .(4!)) 
             3      (4! - sqrt(.4`)) / sqrt(.4`)%
   3540      3      (4! - .4) / sqrt(.4`)%
   3564      3      (4! - 4!%) / sqrt(.4`)%
   3570      3      (4! - sqrt(4%)) / sqrt(.4`)%
   3576      3      (4! / sqrt(.4`)%) - 4!
   3590      3      (4! - sqrt(.4`%)) / sqrt(.4`)%
   3594      3      (4! - 4%) / sqrt(.4`)%
   3596      3      (4! / sqrt(.4`)%) - 4
   3597      3      (4! - sqrt(4)%) / sqrt(.4`)%
   3598      3      (4! / sqrt(.4`)%) - sqrt(4)
   3599      3      (4! - sqrt(.4`)%) / sqrt(.4`)%
   3600      3      (4! / .4)^sqrt(4)
             2      4! / sqrt(.4') %
   3601      3      (4! + sqrt(.4`)%) / sqrt(.4`)%
   3602      3      sqrt(4) + (4! / sqrt(.4`)%)
   3603      3      (sqrt(4)% + 4!) / sqrt(.4`)%
   3604      3      4 + (4! / sqrt(.4`)%)
   3606      3      (4! + 4%) / sqrt(.4`)%
   3610      3      (4! + sqrt(.4`%)) / sqrt(.4`)%
   3624      3      4! + (4! / sqrt(.4`)%)
   3630      3      (4! + sqrt(4%)) / sqrt(.4`)%
   3636      3      (4! + 4!%) / sqrt(.4`)%
   3660      3      (4! + .4) / sqrt(.4`)%
   3700      4      (4! / .(4!))  +  (4! / sqrt(.4') % ) 
             3      (4! + sqrt(.4`)) / sqrt(.4`)%
   3750      3      root(-sqrt(4), .4`%) / .4%
   3800      4      (sqrt(.4')  /  (.4') %  +  sqrt(4))  /  4 % 
   3840      3      4 ^ 4 / sqrt(.4`%)
   3900      4      ((4 * 4)  -  .4)  /  .4 %
             3      (sqrt(4) + 4!) / sqrt(.4`)%
   4000      3      4 * 4 / .4% 
   4096      3      (4 + 4)^4
             2      sqrt(sqrt(4 ^ 4!))
   4100      3      sqrt(sqrt(4 ^ (4!))  +  4
   4200      4      (sqrt(4)  /  .4' %o )  -  (sqrt(.4')   /  .(sqrt(4))' % )
             3      (4 + 4!) / sqrt(.4`)%
   4300      4      ((4 / (4)' % )  -  4)  /  sqrt(4)
   4336      4      ((4! / sqrt(4)'%) + 4) * 4
   4392      4      (4! + .4) / sqrt(4)'% * 4
   4400      4      44 * 4 / 4%
   4444      4      4444
   4500      2      sqrt(4) / .4' %o
             3      (4! - 4) / .4`%
   4600      4      (sqrt(4) / .4' %o )  +  (4! / .(4!))
   4700      4      (sqrt(4) / .4' %o )  +  (.4' / .(sqrt(4))' % )
   4800      4      (4! + 4!) * 4 / 4%
             3      (4 / sqrt(4)%) * 4!
   4900      4      (4!  /  4' %o )  -  (sqrt(4) / .4 %)
   4950      3      (4! - sqrt(4)) / .4`%
   5000      4      sqrt(4) / .4% * 4 / .4
             3      (4! - 4) / .4%
   5040      3      ((4 + 4!) / 4)!
   5100      4      (4!  /  4' %o )  -  (sqrt(.4')  /  .(sqrt(4))' % )
   5120      3      root(sqrt(4%), 4) / sqrt(4%)
   5184      4      4 * (4! / 4)^4
   5200      4      (4! / 4' %o )  -  (.4' / (sqrt(4))' % )
   5250      3      (4! - sqrt(.4`)) / .4`%
   5300      4      (4! / 4' %o )  -  (4! / .(4!)) 
             3      (4! - .4`) / .4`%
   5310      3      (4! - .4) / .4`%
   5346      3      (4! - 4!%) / .4`%
   5355      3      (4! - sqrt(4%)) / .4`%
   5376      3      (4! / .4`%) - 4!
   5385      3      (4! - sqrt(.4`%)) / .4`%
   5391      3      (4! - 4%) / .4`%
   5396      3      (4! / .4`%) - 4
   5398      3      (4! / .4`%) - sqrt(4)
   5399      3      (4! - .4`%) / .4`%
   5400      4      4! / 4'% * 4 / .4
             2      4! / (4)' %o
             2      4! / .4`%
   5401      3      (4! + .4`%) / .4`%
   5402      3      sqrt(4) + (4! / .4`%)
   5404      3      4 + (4! / .4`%)
   5409      3      (4! + 4%) / .4`%
   5415      3      (4! + sqrt(.4`%)) / .4`%
   5424      3      4! + (4! / .4`%)
   5445      3      (4! + sqrt(4%)) / .4`%
   5454      3      (4! + 4!%) / .4`%
   5490      3      (4! + .4) / .4`%
   5500      4      (4! / 4' %o )  +  (4! / .(4!))
             3      (4! - sqrt(4)) / .4%
   5550      3      (4! + sqrt(.4`)) / .4`%
   5600      4      (4! / 4' %o )  +  (.4' / .(sqrt(4))' % )
   5625      3      sqrt(4)% ^ -sqrt(4) / .4`
   5640      3      (4 - 4!%) / sqrt(.4`%)%
   5700      4      (4! / 4' %o )  +  (sqrt(.4') / .(sqrt(4))' % ) 
             3      (4 - sqrt(4%)) / sqrt(.4`%)%
   5760      3      (4!^sqrt(4)) * 4
   5800      4      (4! / 4 %o )  -  (.4' / .(sqrt(4))' % ) 
   5850      3      (sqrt(4) + 4!) / .4`%
   5900      4      (4! / 4 %o )  -  (4! / .(4!))
             3      (4! - .4) / .4%
   5940      3      (4! - 4!%) / .4%
   5950      3      (4! - sqrt(4%)) / .4%
   5970      3      (4 - sqrt(4)%) / sqrt(.4`%)%
   5976      3      (4! / .4%) - 4!
   5990      3      (4! - 4%) / .4%
   5994      3      (4 - .4%) / sqrt(.4`%)%
   5995      3      (4! - sqrt(4)%) / .4%
   5996      3      (4! / .4%) - 4
   5997      3      (4 - sqrt(4%)%) / sqrt(.4`%)%
   5998      3      (4! / .4%) - sqrt(4)
   5999      3      (4! - .4%) / .4%
   6000      4      4! / 4% * 4 / .4
             2      4! / 4 %o
   6001      3      (4! + .4%) / .4%
   6002      3      sqrt(4) + (4! / .4%)
   6003      3      (4 + sqrt(4%)%) / sqrt(.4`%)%
   6004      3      4 + (4! / .4%)
   6005      3      (sqrt(4)% + 4!) / .4%
   6006      3      (4 + .4%) / sqrt(.4`%)%
   6010      3      (4! + 4%) / .4%
   6024      3      4! + (4! / .4%)
   6030      3      (4 + sqrt(4)%) / sqrt(.4`%)%
   6050      3      (4! + sqrt(4%)) / .4%
   6060      3      (4! + 4!%) / .4%
   6100      4      (4! / 4 %o )  +  (4! / .(4!)) 
             3      (4! + .4) / .4%
   6120      4      4^4*4!-4!
   6144      3      4!*4^4
   6200      4      (4! / 4 %o )  +  (.4' / .(sqrt(4))' % ) 
   6250      3      sqrt(4)% ^ -sqrt(4) / .4
   6300      4      (4! / 4 %o )  +  (sqrt(.4') / .(sqrt(4))' % )
             3      (4 + 4!) / .4`%
   6360      3      (4 + 4!%) / sqrt(.4`%)%
   6400      4      sqrt(sqrt(sqrt(4^(4!)))) * 4 / 4% 
             3      4 ^ 4 / 4%
   6500      4      (4! / 4 %o )  +  (sqrt(4) / .4 % ) 
             3      (sqrt(4) + 4!) / .4%
   6561      3      (4 / .4')^4
   6600      4      ((4 * 4)  +  .(4!)')  /  .(4!)' %
             3      44 / sqrt(.4`)%
   6700      4      ((4 * 4)  +  .(4!)')  /  .(4!)' %
   6750      3      sqrt(4 / .4`%) / .4`%
   6800      4      (4 / .(sqrt(4))' % )  +  (sqrt(4) / 4 % % )
   6900      4      (4! / 4 %o )  +  (4 / .4' % )
   7000      4      (4! / 4 %o )  +  (4 / .4 % )
             3      (4 + 4!) / .4%
   7100      4      ((4 * 4)  -  .(sqrt(4))')  /  .(sqrt(4))' %
   7200      4      (4! / 4 %o )  +  (4! / sqrt(4) % )
             3      root(.4, 4) / .4`%
   7300      4      ((4 * 4)  +  .(sqrt(4))')  / .(sqrt(4))' %
   7400      4      (.4' / .(sqrt(4))' %o )  +  (4! / 4' %o )
   7500      4      (4! / 4 %o )  +  (sqrt(.4') / .4' %o )
             3      sqrt(4 / .4`%) / .4%
   7600      4      ((sqrt(4) / 4 % ) + sqrt(.4'))  /  sqrt(.4') %
   7700      4      ((sqrt(.4') / 4' % ) + .4)  /  .(sqrt(4)) %
   7776      3      root(-sqrt(4%), 4 / 4!)
   7800      4      (4! / 4 %o )  +  (4 / .(sqrt(4))' % )
   7744      4      44^sqrt(4) * 4
   7800      4      (4! / 4 %o )  +  (4 / .(sqrt(4))' % )
   7900      4      ((4 * 4) - .(sqrt(4)))  /  .(sqrt4)) %
   8000      4      (4 + 4) * 4 / .4% 
             3      root(.4, 4) / .4%
   8064      3      (4 + 4)! * sqrt(4%)
   8100      3      (.4 / .4`%) ^ sqrt(4)
   8192      4      sqrt(4) * (4 + 4)^4
             3      root(sqrt(.4`%), sqrt(4)) / 4
   8250      2      sqrt(4) / .(4!)' %o
   8640      3      4! * 4! / sqrt(.4`%)
   9000      4      4 / .4'% * 4 / .4
             2      4 / .4' %o
             3      4 / (.4` - .4)%
   9216      3      (4*4!)^sqrt(4)
   9375      3      4% ^ -sqrt(4) / sqrt(.4`%)
   9600      4      4 * 4! * 4 / 4%
   9900      2      4! / .(4!)' 

  10000      3      (4/.4)^4
             2      4 / 4 %%
  10626      4      (4!)! / (4! - 4) / 4!
  10800      2      4! / sqrt(4)' %o
  11100      4      444 / 4%
  12000      4      (sqrt(4) / .4)! * 4 / 4%
             2      4! / sqrt(4) %o
  12144      4      (4!)! / (4! - sqrt(4) / sqrt(.4`))
  12288      4      sqrt(4) * 4! * 4^4 
  13122      4      sqrt(4) * (4/.4')^4
  13248      4      4! * (4!)! / (4! - sqrt(4))
  13824      3      4! * 4! * 4!
             2      4! ^ sqrt(sqrt(sqrt(4!)))
  14400      4      (4!^sqrt(4)) * 4 / .4%
  14641      4      (44 / 4)^4
  15000      4      sqrt(.4') / 4'% * 4 / .4%
             2      sqrt(.4') / .4' %%
  16000      4      4 * 4 * 4 / .4% 
  16384      4      ((4^4)^sqrt(4))/4
  16500      2      4 / .(4!)' %o
  18000      4      4 / .(sqrt(4))' * 4 / .4%
             2      4 / .(sqrt(4))' %%
  18432      4      (4*4!)^sqrt(4) * sqrt(4)
  20000      4      (4! - 4) * 4 / .4%
             2      .4' / .(sqrt(4))' %%
  20736      3      (4! / sqrt(4))^4
  21984      4      (4! / .4')^sqrt(4) * 4!
  22000      4      (4! - sqrt(4)) * 4 / .4%
  24000      3      4! * 4 / .4% 
  24576      4      4 * 4! * 4^4 
  25600      4      4^4 * 4 / 4%
  26000      4      (4! + sqrt(4)) * 4 / .4%
  26016      4      ((4! / sqrt(4)' % ) + 4) * 4!
  26244      4      4 * (4/.4')^4
  26352      4      (4! + .4) / sqrt(4)'% * 4!
  27500      2      sqrt(.4') / (4!) %%
  28000      4      (4! + 4) * 4 / .4%
  30000      4      sqrt(4) / sqrt(.4'%) * 4 / .4%
             2      sqrt(.4') / .(sqrt(4))' %%
  31104      4      4! * (4! / 4)^4
  32400      4      (4!/4)^4 / 4%
  34560      3      (4!^sqrt(4)) * 4!
  36000      4      4! / sqrt(.4`) * 4 / .4% 
             2      4! / sqrt(.4') %o
  36864      4      (4*4!)^sqrt(4) * 4
  40000      4      (4/.4)^4 * 4
  40320      2      (4 + 4)!
  41472      4      (4!)^4 / (4 * sqrt(4))
  44000      4      44 * 4 / .4%
  45000      2      sqrt(4) / .4' %%
  48000      4      (4! + 4!) * 4 / .4%
  50000      4      sqrt(4) / .4% * 4 / 4%
  54000      4      4! / 4'% * 4 / 4%
             2      4! / (4)' %%
  55296      4      4*4!^sqrt(4) * 4!
  57600      4      4!^sqrt(4) * 4 / 4%
  60000      4      4! / 4% * 4 / 4%
             2      4! / 4 %%
  64000      4      sqrt(sqrt(sqrt(4^(4!)))) * 4 / .4%
  65536      3      (4 * 4)^4
             4      4 * 4 * 4 * 4
  63756      4      (4!)! / (4! - 4) / 4
  69120      4      (4!^sqrt(4)) * 4! * sqrt(4)
  72000      4      (4 + sqrt(4))! * 4 / 4%
  82944      3      (4!)^4 / 4
  85184      3      sqrt(sqrt(sqrt(44^4!)))
  86400      4      (4! / .4)^sqrt(4) * 4!
  90000      4      4 / .4'% * 4 / 4%
  95040      4      (4! / sqrt(4))! / (4 * sqrt(4))
  96000      4      4 * 4! * 4 / .4%
  98304      4      (4 + 4)^4 * 4!

 100000      4      4! / .(4!) * 4 / .4% 
 111000      4      444 / .4%
 120000      4      (sqrt(4) / .4)! * 4 / .4% 
 127512      4      (4!)! / (4! - 4) / sqrt(4)
 131072      4      sqrt(4) 4^(4 * sqrt(4))
 138240      4      (4!^sqrt(4)) * 4! * 4
 144000      4      (4!^sqrt(4)) * 4 / 4%
 147456      4      4^(4 * sqrt(4)) / .4'
 157464      4      (4 / .4')^4 * 4!
 163840      4      4^(4 * sqrt(4)) / .4
 165888      3      4!^4 / sqrt(4) 
 197136      4      444^sqrt(4)
 221184      4      (4*4!)^sqrt(4) * 4!
 234256      3      (4! - sqrt(4))^4
 255024      3      (4!)! / (4! - 4)
 256000      4      4^4 * 4 / .4$
 262144      4      4 * 4^(4 * sqrt(4))
 324000      4      (4! / 4)^4 / .4%
 331776      2      4!^4
 362880      2      (4 / .4')!
 390625      4      (4! + 4/4)^4
 409600      4      (4^4 / .4) ^ sqrt(4)
 422500      4      ((4! + sqrt(4))! / (4!)!) ^ sqrt(4)
 451584      4      (4! * (4! + 4)) ^ sqrt(4)
 456976      3      (4! + sqrt(4))^4
 483025      4      ((4 + sqrt(4))! - 4!) ^ sqrt(4)
 500000      4      sqrt(4) / .4% * 4 / .4%
 512656      4      ((4 + sqrt(4))! - 4) ^ sqrt(4)
 515524      4      ((4 + sqrt(4))! - sqrt(4)) ^ sqrt(4)
 518400      3      ((4 + sqrt(4))!) ^ sqrt(4)
 521284      4      ((4 + sqrt(4))! + sqrt(4)) ^ sqrt(4)
 524176      4      ((4 + sqrt(4))! + 4) ^ sqrt(4)
 540000      4      4! / 4'% * 4 / .4%
 553536      4      ((4 + sqrt(4))! + 4!) ^ sqrt(4)
 576000      4      4!^sqrt(4) * 4 / .4%
 600000      4      4! / 4% * 4 / .4%
 614652      4      (((4!)+4)^4)-4
 614656      3      (4! + 4)^4
 614660      4      (4! + 4)^4 + 4
 663552      3      sqrt(4) * 4!^4 
 720000      4      (4 + sqrt(4))! * 4 / .4%
 731025      4      ((4 - .(sqrt(4)) / .4'%) ^ sqrt(4)
 746496      4      (4! * 4! / sqrt(.4`)) ^ sqrt(4)
 810000      3      (sqrt(4) / sqrt(.4'%))^4
 811801      4      ((4 + .4' % ) / .4'%) ^ sqrt(4)
 883225      4      ((4 - sqrt(.4' % )) / .4' %) ^ sqrt(4)
 900000      4      4 / .4'% * 4 / .4%
 937024      4      44^4 / 4
 990000      2      4! / .(4!)'%%

1000000      4      (4 / .4) ^ (4 + sqrt(4))
1048576      4      sqrt(sqrt(4^44)) / 4
             4      (4! + 4 + 4)^4
1098304      4      (4!  +  root(.(sqrt(4)),4)) ^ sqrt(4)
1106704      4      (sqrt(4)*4!^sqrt(4)) ^ sqrt(4)
1327104      3      4 * 4!^4
1440000      4      (4!^sqrt(4)) * 4 / .4%
1572864      4      4! 4^(4 * sqrt(4))
1600000      3      (4! - 4)^4
1679616      3      (4! / sqrt(.4`))^4
1874048      4      44^4 / sqrt(4)
2097152      4      sqrt(sqrt(4^44)) / sqrt(4)
2654208      4      4 * 4!^4 * sqrt(4)
2916000      4      (4! / 4)^4 / .4'%
3628800      2      (4 / .4)!
3748096      3      44^4
4194304      3      sqrt(sqrt(4^44))
5308416      4      4 * 4!^4 * 4
7496192      4      sqrt(4) * 44^4
7962624      3      4!^(sqrt(4)/.4)
9370240      4      44^4 / .4

Infinity     3      4 / (4-4)


Contributors

The first contributors to the solutions I didn't find are listed below, note that in many cases the solution may have subsequently been replaced by simpler solutions.

Ewart Shaw 219, 267, 351, 371, 373, 377, 379, 705, 727, 731, 733, 753, 972, 975

Richard Schorn First to uncover a solution for 113 but it uses rather "non-standard" combination of decimal place (.) and repeated digit (`), see 2/9.

Ewald R. de Wit 103, 121, 125, 142, 146

Martin Olivella 181, 186, 188, 190, 194, 286, 290, 292, 362, 380, 384, 386, 388, 408, 488, 514, 536, 832, 900, 976, 1000

Heiner Marxen 154, 164, 169, 179, 182, 184, 204, 238, 242, 251, 275, 287, 289, 295, 296, 298, 299, 301, 302, 305, 310, 316,325,338, 348, 356, 358, 359, 361, 364, 372, 375, 426, 450, 472, 476, 478, 482, 496, 510, 520, 524, 526, 530, 601, 621, 622, 623, 626, 627, 628, 629, 635, 636, 638, 639, 641, 642, 644, 645, 646, 649, 654, 660, 664, 660, 670, 750, 841

Scott Forschler The solutions for 90, 100, 113, 165 using "%"

Wayne Goode 202, 214, 218, and a simpler solution to 66

Jörg Wiegels 165, 177, 183, 195, 269, 270, 271, 274, 279, 294, 318, 322, 344, 378, 381, 383, 385, 387, 390, 405, 441, 495, 522, 525, 531, 538, 542, 544, 549, 555, 608, 612, 656, 666, 675, 684, 688, 768, 774, 810, 828, 848, 856, 860, 861, 862, 863, 865, 867, 868, 870, 896, 990, 1008, 1014, 1016
Simpler solutions for 13, 39, 41, 47, 57, 58, 78, 90, 116, 118, 120, 122, 124, 180, 288, 300, 320, 360, 484, 640, 540, 560, 567, 585, 592, 864

Charles Dillingham Pointed out that there are simpler solutions for some numbers than those listed above. For example "4 * 4 * 4" for 64 instead of "sqrt(sqrt(sqrt(4^(4!))))". The definition of the simplest was determined by the number of 4's needed, consideration of the operator complexity was only used when there was the same number of 4's. This has been partially resolved by giving double solutions for some numbers where the solution with the minimum number of 4's is particularly clumsy.

Peter Karsanow Donated some solutions which have five 4's, (See the comment above regarding the use of 2 instead of sqrt(4)) for example, 157, 167, 193, 197, 203, 223, 231, 281, 337, 406, 551, 657 836, 856, and 881. Also some three 4 solutions for numbers over 1000, namely 1440, 1936, 2304, 2916, 3600, 4096, 6144, 6561, 9216, 10000, >3824, and 16384. Some simpler solutions for 81, 567, and 650.

Brad McInnes Provided solution for 984, 996, 998, and a three 4's solution for 1000.

Frank Mrazik 73, 167, 171, 173, 185, 187, 191, 193, 197, 198, 199, 201, 203, 205, 206, 209, 211, 213, 217, 221, 223, 226, 227, 229, 231, 233, 237, 249, 263, 273, 277, 283, 285, 291, 293, 297, 303, 306 - 309, 311, 313, 314, 315, 317, 319, 321, 323, 326 - 335, 337, 339 - 342, 345, 346, 347, 349, 353, 354, 355, 357, 363, 365 - 370, 374, 391, 393 - 397, 399, 401, 403, 406, 407, 409, 411, 412, 413, 415, 417, 419, 421, 423, 425, 429, 435, 437, 439, 414, 418, 428, 422, 430, 431, 432, 433, 434, 436, 438, 443, 445, 447, 449, 451 - 455, 457 - 461, 463, 465, 466, 467, 469, 470, 471, 473, 474, 475, 477, 479, 481, 483, 485, 487, 489 - 495, 497, 498, 499, 501, 502, 503, 505, 506, 507, 509, 511, 513, 515, 517, 518, 519, 521, 523, 527, 533, 534, 535, 537, 539, 541, 543, 545, 547, 553, 557, 559, 561, 563, 565, 583, 587, 589, 593 - 597, 599, 603, 606, 607, 609 - 611, 613 - 615, 617, 619, 630 - 634, 637, 643, 647, 651, 653, 655, 657 - 659, 661 - 663, 665, 667, 669, 671, 673, 677, 679, 681, 682, 683, 685 - 687, 689 - 691, 693, 695, 697, 699, 701, 702, 703, 706, 709, 713, 734, 735, 737, 738, 739, 741, 743, 745, 747, 749, 751, 752, 754, 755, 757 - 759, 761, 762, 765, 767, 771, 773, 775 - 779, 781, 783, 785, 787, 789 - 791, 793 - 799, 801 - 807, 809, 811 - 815, 817 - 827, 829 - 831, 834 - 839, 842 - 847, 849 - 857, 859, 869, 871 - 879, 881 - 887, 889 - 895, 897, 898, 899, 901 - 911, 913 - 927, 929 - 935, 937 - 952, 954 - 959, 961 - 967, 969, 970, 971, 973, 974, 977 - 983, 985 - 989, 991 - 995, 997, 1001 - 1117, 1132, 1133, 1138, 1139, 1141, 1142, 1143, 1147, 1151, 1153, 1157 - 1163, 1169, 1171, 1183, 1193, 1250, 1577, 2517.

Rick Hevener Provided solution for 18, 157 and 163 using the very imaginative 24/99. Contributed more elegant solutions for 31, 49, 76, 89, 125, 146, 159 and interesting alternatives for 17, 21, 36, 100, 102, 107, 109, 126, 140, 141, 162, 279.

David Bevan Provided lots of solutions based upon a computer search, this includes lots of more elegant solutions. In particular he pointed out a third solution for 17 and noted the following cleaner notations, .(4!) is the same as 4!% and .(sqrt(4)) is the same as sqrt(4%).

Vijay Kailas Came up with 1206.

Guido Roach An alternative 4 four solution for 113, namely ( sqrt(4) / .4' + sqrt(4)% ) / 4%

Joe Martin An improved solution for 533 = (4! * .4' - sqrt(.4)%) / sqrt(4)%

Toufic Batouli Toufic proposed the use of degrees, minutes, and seconds as standard notation. Using these symbols provides some additional solutions to numbers using only two 4s. Since each degree is 60 minutes, or 3600 seconds, we have
[(4!) Deg / 4 Sec] = 21,600
[(4!) Deg / 4 Sec]% = 216
[(4!) Deg / 2 Sec] = 43,200
[(4!) Deg / 2 Sec]% = 432
We also have additional results for both 0 and 1 using only one 4 because 24! is an integer (N) multiple of 360:
Sin((4!)! Deg) = Sin(N * 360 Deg) = 0
Cos((4!)! Deg) = Cos(N * 360 Deg) = 1
Also, since one degree is equal to pi/180 radians we can get many additional numbers using only two 4s. The additional solutions come from the relationship arccos(x) = 90 Deg - x. So only two 4's are needed for:
Arccos(Sin(4 Deg))/(Sqrt(4) Deg) = 86 Deg / 2 Deg = 43
Further examples are given below.
23 = Arccos(Sin(-4 Deg)/(4 Deg)
27 = [Acrcos(Sin(0))/2"]%
33 = Arccos(Sin(24 Deg))/(2 Deg)
43 = Arccos(Sin(4 Deg))/(2 Deg)
45 = Acrcos(0)/(2 Deg)
46 = Arccos(Sin(-2 Deg)/(2 Deg)
47 = Arccos(Sin(-4 Deg))/(2 Deg)
57 = Arccos(Sin(-24 Deg))/(2 Deg)
66 = Arccos(Sin(24 Deg))/(1 Deg)
88 = Arccos(Sin(2 Deg)/(1 Deg)
89 = Arccos(Sin(1 Deg)/(1 Deg)
90 = Acrcos(0)/(1 Deg)
129 = [Arccos(Sin(4 Deg))/24"]%
132 = [Arccos(Sin(2 Deg))/24"]%
135 = [Acrcos(0))/24"]%
138 = [Arccos(Sin(-2 Deg)/24"]%
141 = [Arccos(Sin(-4 Deg))/24"]%
171 = [Arccos(Sin(-24 Deg))/24"]%
198 = Arccos(Sin(2 Deg))/(.444444444444444444444 Deg)
207 = [Arccos(Sin(-4 Deg)/4"]%
215 = Arccos(Sin(4 Deg))/24'
220 = Arccos(Sin(2 Deg))/24'
224 = Arccos(Sin(24'))/24'
235 = Arccos(Sin(-4 Deg))/24'
240 = Arccos(Sin(-2 Deg)/24'
285 = Arccos(Sin(-24 Deg))/24'
375 = Arccos(0)/(24% Deg)
414 = [Arccos(Sin(-4 Deg)/2"]%
594 = [Arccos(Sin(24 Deg))/4"]%
774 = [Arccos(Sin(4 Deg))/4"]%
792 = [Arccos(Sin(2 Deg))/4"]%
810 = [Acrcos(0))/4"]%
828 = [Arccos(Sin(-2 Deg)/4"]%
846 = [Arccos(Sin(-4 Deg))/4"]%
990 = Arccos(Sin(24 Deg))/(4')
1026 = [Arccos(Sin(-24 Deg))/4"]%
1188 = [Arccos(Sin(24 Deg))/(2")]%
1290 = Arccos(Sin(4 Deg))/(4')
1320 = Arccos(Sin(2 Deg))/4'
1344 = Arccos(Sin(24'))/4'
1349 = Arccos(Sin(4'))/2'
1350 = Acrcos(0)/4'
1380 = Arccos(Sin(-2 Deg)/4'
1410 = Arccos(Sin(-4 Deg))/4'
1548 = [Arccos(Sin(2 Deg))/2"]%
1584 = [Arccos(Sin(2 Deg))/2"]%
1620 = [Acrcos(0))/2"]%
1650 = Arccos(Sin(24 Deg))/(4% Deg)
1656 = [Arccos(Sin(-2 Deg)/2"]%
1692 = [Arccos(Sin(-4 Deg))/4"]%
1710 = Arccos(Sin(-24 Deg))/4'
1980 = Arccos(Sin(24 Deg))/2'
2052 = [Arccos(Sin(-24 Deg))/2"]%
2225 = Arccos(Sin(1 Deg)/(4% Deg)
2250 = Acrcos(0)/(2% Deg)
2580 = Arccos(Sin(4 Deg))/2'
2640 = Arccos(Sin(2 Deg))/2'
2688 = Arccos(Sin(24'))/2'
2698 = Arccos(Sin(4'))/2'
2699 = Arccos(Sin(2'))/2'
2700 = Acrcos(0)/2'
2760 = Arccos(Sin(-2 Deg)/2"
2820 = Arccos(Sin(-4 Deg))/2'
3300 = Arccos(Sin(24 Deg)/(2% Deg)
3420 = Arccos(Sin(-24 Deg))/4'
6600 = Arccos(Sin(24 Deg)/(1% Deg)
4450 = Arccos(Sin(1 Deg)/(2% Deg)
4500 = Arccos(0)/(2% Deg)
9900 = Arccos(Sin(24 Deg))/24"
11250 = [Acrcos(Sin(0))/2"]% Deg)
12900 = Arccos(Sin(4 Deg))/24"
13200 = Arccos(Sin(2 Deg))/24"
13440 = Arccos(Sin(24'))/24"
13490 = Arccos(Sin(4'))/24"
13495 = Arccos(Sin(2'))/24"
13500 = Acrcos(0)/24"
13800 = Arccos(Sin(-2 Deg)/24"
14100 = Arccos(Sin(-4 Deg))/24"
17100 = Arccos(Sin(-24 Deg))/24"
20025 = Arccos(1 Deg)/(.4444444444444444% Deg)
20250 = Arccos(0)/(.44444444444444444444% Deg)
20700 = Arccos(Sin(-4 Deg)/4"
34500 = Arccos(Sin(-4 Deg)/(4%)'
41400 = Arccos(Sin(-4 Deg)/2"
59400 = Arccos(Sin(24 Deg))/4"
77400 = Arccos(Sin(4 Deg))/4"
79200 = Arccos(Sin(2 Deg))/4"
80640 = Arccos(Sin(24'))/4"
80940 = Arccos(Sin(4'))/4"
80970 = Arccos(Sin(2'))/4"
81000 = Acrcos(0)/4"
82800 = Arccos(Sin(-2 Deg)/4"
84600 = Arccos(Sin(-4 Deg))/4"
102600 = Arccos(Sin(-24 Deg))/4"
118800 = Arccos(Sin(24 Deg))/2"
154800 = Arccos(Sin(4 Deg))/2"
158400 = Arccos(Sin(2 Deg))/2"
161280 = Arccos(Sin(24'))/2"
161880 = Arccos(Sin(4'))/2"
161940 = Arccos(Sin(2'))/2"
162000 = Acrcos(0)/2"
165600 = Arccos(Sin(-2 Deg)/2"
169200 = Arccos(Sin(-4 Deg))/2"
205200 = Arccos(Sin(-24 Deg))/2"
222750 = Arccos(0)/(.040404040404040404% Deg)
And of course the well known problem of 113 without using the double factorial:
129 - 16 = [Arccos(Sin(4 Deg))/(4! Sec)]% - 4*4 = 113


Nikkol Bauer New or alternative answers for the following: 729, 777, 792, 821, 823, 824, 825, 826, 827, 829, 834, 835, 849, 850, 870, 882, 890, 910, 918, 930, 999, 1023, 1062, 1062, 1070, 1070, 1077, 1089, 1089, 1104, 1104, 1110, 1111, 1113, 1115, 1135, 1155, 1166, 1170, 1177, 1184, 1186, 1187, 1189, 1192, 1203, 1205, 1207, 1208, 1209, 1211 largely based upon the following relationships and observations.
.(4!)'%                = .002424242424...
.sqrt(4)'%             = .002222222...
.4'%                   = .0044444....
4'%                    = .04444444.... (this is really stretching it because
                                        four repeating divided by 100 is infinity)
(4 + .4')%             = same as above with two fours
(sqrt(4))'%            = .022222222 ... (also pushing it)
(4%%)'                 = 0.000400040004 ...
(sqrt(4) + sqrt(4%)')% = same as above with two fours