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P4365染色
 限制 : 时间限制 : 2000 MS   空间限制 : 65536 KB
###### 问题描述

ou are given an undirected graph with n vertices numbered 0 through n-1.

Obviously, the vertices have 2^n - 1 non-empty subsets. For a non-empty subset S, we define a proper coloring of S is a way to assign each vertex in S a color, so that no two vertices in S with the same color are directly connected by an edge. Assume we've used k different kinds of colors in a proper coloring. We define the chromatic number of subset S is the minimum possible k among all the proper colorings of S.

Now your task is to compute the chromatic number of every non-empty subset of the n vertices.

###### 输入格式

First line contains an integer t. Then t testcases follow.

In each testcase: First line contains an integer n. Next n lines each contains a string consisting of '0' and '1'. For 0<=i<=n-1 and 0<=j<=n-1, if the j-th character of the i-th line is '1', then vertices i and j are directly connected by an edge, otherwise they are not directly connected.

The i-th character of the i-th line is always '0'. The i-th character of the j-th line is always the same as the j-th character of the i-th line.

For all testcases, 1<=n<=18. There are no more than 100 testcases with 1<=n<=10, no more than 3 testcases with 11<=n<=15, and no more than 2 testcases with 16<=n<=18.

2
4
0110
1010
1101
0010
4
0111
1010
1101
1010

1022423354
2538351020

###### 提示
第一组数据, ans[1..15]= {1, 1, 2, 1, 2, 2, 3, 1, 1, 1, 2, 2, 2, 2, 3}