Hamiltonian cycle in a complete graph

Input

The first line contains an integer $N$ (3 \leq N \leq 4000) — the number of vertices in the graph.

The next $N$ lines contain the adjacency matrix. Since the adjacency matrix is symmetric and the diagonal entries are always zero, the $i$-th line contains i - 1 symbols: zeros and ones. If the $j$-th symbol in the $i$-th line is one, then there is an edge between vertices $i$ and $j$.

It is guaranteed that the graph contains a Hamiltonian cycle and the degree of each vertex is at least $N/2$.

Output

Output a permutation of $N$ numbers — the vertices in the order they appear in the Hamiltonian cycle.

Examples