Restore the permutation

A permutation of length $N$ is a sequence in which each integer from $1$ to $N$ appears exactly once. For example, $[1]$ and $[3,1,4,2,5]$ are permutations, but $[-1,0,1,3,2]$ and $[1,3,5,4]$ are not.

For a permutation $P$ of length $N$, the comparison matrix $A$ is an $N \times N$ matrix. Each element $A_{ij}$ is set as follows, based on how $P_i$ compares with $P_j$.

• If $P_i > P_j$, then $A_{ij} = -1$.
• If $P_i = P_j$, then $A_{ij} = 0$.
• If $P_i < P_j$, then $A_{ij} = 1$.

Given the comparison matrix $A$, write a program that restores the permutation $P$. If no permutation satisfies $A$, print -1.

The first line contains an integer $N$. ($1 \leq N \leq 1000$)

Each of the next $N$ lines contains a row of the comparison matrix $A$. The $i$-th line holds $A_{i1}, A_{i2}, \cdots, A_{iN}$, separated by spaces. Every element of the matrix is $-1$, $0$, or $1$.

If a permutation $P$ satisfies the comparison matrix $A$, print $P_1, P_2, \cdots, P_N$ separated by spaces, in order. If several permutations work, print any of them.

If no such permutation exists, print -1.