Python 3 Befunge number thing

import time

NUMBERS = '0123456789'
NUMBERS_WITH_DUP = NUMBERS + ":"
OPERATIONS = '+-/*'


def solve(length):
    depth = (length - 1)/2
    solutions = {}
    for a in NUMBERS:
        solutions[int(a)] = [1, a]
        solutions = solve_depth(depth - 1, a, a, solutions)
    out_file = open('output_file.txt', 'w')
    for result, solution in sorted(solutions.items()):
        out_file.write(str(result)+'\t'+solution[1] + '\n')
    out_file.close()


def solve_depth(depth, string, top_stack, solutions):
    for num in NUMBERS_WITH_DUP:
        for operation in OPERATIONS:
            eval_num = top_stack if num == ':' else num
            try:
                result = int(eval(top_stack + operation + eval_num))
            except:
                continue
            new_string = string + num + operation
            length = len(new_string)
            # If result is on the top of the stack and we already have a shorter or equivalent way to get there
            # Then there is no point in going further down the recursion.
            if (result not in solutions or solutions[result][0] > length) and result >= 0:
                solutions[result] = [length, new_string]
                if depth != 0:
                    solutions = solve_depth(depth - 1, new_string, str(result), solutions)
    return solutions

start_time = time.time()
solve(11)
print("Finished in " + str(time.time() - start_time))