You are give an graph with multiple edges and without loops. Each edge have one of 2 colors -- black or white.

For each i between 0 and $n-1$, inclusive, find number of spanning trees with exactly i white edges and $n - 1 - i$ black edges.

As answers can be large, print them modulo $1,000,000,007$.

Input Format:
First line contain single integer n -- number of vertices in a graph.
Then two tables $n \times n$ follows, separated by an empty line.
First table contains number of white edges between vertices, second black.

n
$w_{11} \dots w_{1n}$
$\vdots$
$w_{n1} \dots w_{nn}$

$b_{11} \dots b_{1n}$
$\vdots$
$b_{n1} \dots b_{nn}$

Output Format:
Output n space-separated numbers, i containing number of trees with i white and $n - 1 - i$ black edges.

Constraints:
$2 \leqslant n \leqslant 100$.
$0 \leqslant w_{ij}, b_{ij} \leqslant 1,000,000,006$.
$w_{ii} = b_{ii} = 0$.
$w_{ij} = w_{ji}, b_{ij} = b_{ji}$.