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from Numberjack import *
 
 
# Golomb Ruler --- CSPLib prob006
 
# A Golomb ruler may be defined as a set of m marks/integers 0 = a_1 < ... < a_m
# such that the pairwise differences between marks are distinct. The objective
# is to find optimal (minimum length) rulers.
 
 
def get_model(param):
    m = param['marks']
    n = 2 ** (m - 1)
 
    marks = VarArray(m, n, 'm')
    distance = [marks[i] - marks[j] for i in range(1, m) for j in range(i)]
 
    model = Model(
        Minimise(marks[-1]),  # objective function
 
        [marks[i-1] < marks[i] for i in range(1, m)],
        AllDiff(distance),
        marks[0] == 0# symmetry breaking
 
        [distance[i * (i - 1) / 2 + j] >= ruler[i - j] for i in range(1, m) for j in range(0, i - 1) if (i - j < m)]
    )
 
    return marks, model
 
 
def solve(param):
    marks, model = get_model(param)
 
    solver = model.load(param['solver'], marks)
    solver.setHeuristic(param['heuristic'])
    solver.setVerbosity(param['verbose'])
    solver.setTimeLimit(param['tcutoff'])
 
    solver.solve()
 
    out = ''
    if solver.is_sat():
        out = str(marks)
    out += ('\nNodes: ' + str(solver.getNodes()))
    return out
 
 
ruler = (0, 1, 3, 6, 11, 17, 25, 34, 44, 55, 72, 85, 106, 127)
default = {'solver': 'Mistral', 'marks': 6, 'heuristic': 'Impact', 'verbose': 0, 'tcutoff': 60}
 
 
if __name__ == '__main__':
    param = input(default)
    print solve(param)