Dividing the graph

Input

The first line contains the number of vertices $n$ (2 \leq n \leq 50) in the graph. Each of the next $n$ lines contains $n$ characters. The $i$-th character in the $j$-th line is $1$ if there is an edge between vertices $i$ and $j$, and $0$ otherwise. The adjacency matrix of the graph is antireflexive (the diagonal elements are $0$) and symmetric (with respect to the main diagonal).

Output

Output two lines. In the first line print the numbers of the vertices in set $A$ separated by spaces, and in the second line print the numbers of the vertices in set $B$ separated by spaces. The vertex numbers may be output in any order.

Examples