Hamiltonian path

A directed graph $G$ has $N$ vertices and $N(N-1)/2$ edges. The vertices are numbered from $0$ to $N-1$. For any two different vertices $i$ and $j$, exactly one of the edge from $i$ to $j$ and the edge from $j$ to $i$ is present. Ignoring the directions, $G$ is a complete graph.

$X$ is the adjacency matrix of $G$. When $X_{i,j}$ is +, the edge from $i$ to $j$ exists, and when it is -, that edge does not exist. $X_{i,i}$ is always ..

A Hamiltonian path of $G$ is a path of length $N$ that visits every vertex exactly once. $G$ can have many Hamiltonian paths, so find the one whose sequence of visited vertex numbers comes first in lexicographic order. Sequence $a$ comes before sequence $b$ when $a$ holds the smaller value at the first position where the two sequences differ.

The first line contains the number of vertices $N$. Each of the next $N$ lines contains one row of the adjacency matrix $X$. The $j$-th character of the $i$-th of those lines is $X_{i,j}$, and both lines and characters are numbered from $0$.

If $G$ has a Hamiltonian path, print the vertices of the lexicographically first Hamiltonian path in order on one line, separated by single spaces. Otherwise print $-1$.

• $2 \le N \le 100$