import tables
import docopt
import strutils

const base = {
  4: 4.55,
  5: 5.70,
  6: 6.80,
  7: 7.95,
  8: 9.10,
  9: 10.20,
  10: 11.35,
  11: 12.50,
  12: 13.60,
  13: 14.75,
  14: 15.90,
  15: 17.00,
  16: 18.15,
  17: 19.30,
  18: 20.40,
  19: 21.55,
  20: 22.70,
  21: 23.80,
  22: 24.95,
  23: 26.10,
  24: 27.25,
  25: 27.80,
  26: 28.95,
  27: 30.10,
  28: 31.20,
  29: 32.35,
  30: 33.50,
  35: 39.15,
  40: 44.80,
  45: 50.50,
  50: 55.60,
  60: 67.00,
  70: 78.30,
  75: 83.45,
  80: 89.10,
  90: 100.45,
  100: 111.25,
  125: 139.00,
  150: 166.85,
  200: 222.50}.toTable

proc solve(n: int): (float64, string) =
  var
    arr = newSeq[float](n+1)
    tre = newSeq[string](n+1)
  for i in 1 .. n:
    arr[i] = base.getOrDefault(i, Inf)
    tre[i] = $i
    var j = 0
    while 2*j < i:
      if arr[j] + arr[i-j] < arr[i]:
        arr[i] = arr[j] + arr[i-j]
        tre[i] = "(" & tre[j] & "," & tre[i-j] & ")"
      j.inc
  (arr[n], tre[n])

let args = docopt("""
Usage: wing <num>
""")

echo solve(parseInt($args["<num>"]))