1248번 - Guess 스페셜 저지다국어원문과 다름

문제

Given a sequence of integers, a₁, a₂, …, a_n, we define its sign matrix S such that, for 1 ≤ i ≤ j ≤ n, S_ij="+" if a_i + … + a_j > 0; S_ij="−" if a_i + … + a_j < 0; and S_ij="0" otherwise.

For example, if (a₁, a₂, a₃, a₄)=( −1, 5, −4, 2), then its sign matrix S is a 4×4 matrix:

We say that the sequence (−1, 5, −4, 2) generates the sign matrix. A sign matrix is valid if it can be generated by a sequence of integers.

Given a sequence of integers, it is easy to compute its sign matrix. This problem is about the opposite direction: Given a valid sign matrix, find a sequence of integers that generates the sign matrix. Note that two or more different sequences of integers can generate the same sign matrix. For example, the sequence (−2, 5, −3, 1) generates the same sign matrix as the sequence (−1,5, −4,2).

Write a program that, given a valid sign matrix, can find a sequence of integers that generates the sign matrix. You may assume that every integer in a sequence is between −10 and 10, both inclusive.

입력

The first line contains an integer n(1 ≤ n ≤ 10), where n is the length of a sequence of integers. The second line contains a string of n(n+1)/2 characters such that the first n characters correspond to the first row of the sign matrix, the next n−1 characters to the second row, ..., and the last character to the n-th row.

출력

Output exactly one line containing a sequence of n integers which generates the sign matrix. If more than one sequence generates the sign matrix, you may output any one of them. Every integer in the sequence must be between −10 and 10, both inclusive.

제한

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