# N Fractions - non-generalized version
#
# You must assign the digits 1 to 9 to the variables
# A, B, C, D, E, F, G, H, I, such that each digit may
# occur only once, and the following equation is satisfied:
#
#  A      D      G
# ---- + ---- + ---- = 1
#  BC     EF     HI
#
# CSPlib Problem 041 - http://www.csplib.org/Problems/prob041/

from Numberjack import *

def modelNFractions():
a, b, c, d, e, f, g, h, i = VarArray(9, 1, 9)

model = Model(
# Rearrange the equation to avoid the usage of floats.
a * (10 * e + f) * (10 * h + i) +
d * (10 * b + c) * (10 * h + i) +
g * (10 * b + c) * (10 * e + f) ==
(10 * b + c) * (10 * e + f) * (10 * h + i),

# Each digit must occurr once
AllDiff([a, b, c, d, e, f, g, h, i]))

return (a, b, c, d, e, f, g, h, i, model)

def solve(param):
(a, b, c, d, e, f, g, h, i, model) = modelNFractions()
solver.solve()

if solver.is_sat():
print "(" + str(a) + " / " + str(b) + str(c) + ") + " + \
"(" + str(d) + " / " + str(e) + str(f) + ") + " + \
"(" + str(g) + " / " + str(h) + str(i) + ") = 1"
elif solver.is_unsat():
print "Unsatisfiable"
else:
print "Timed out"

if __name__ == '__main__':
default = {'solver': 'Mistral', 'verbose': 1}
param = input(default)
solve(param)