Problem Description

Given a tournament, you need to determine the direction of the remaining sides to maximize the answer. The answer is calculated in the following way. The vertices are labeled from $0$ to $n-1$, and the matrix $s$ is used to represent the edges.

Input

The first line of input is a single line of integer $T (2 \le T \le 10)$, the number of test cases. In each test case, there are $1$ integers $n(5 \le n \le 200)$, denoting the number of vertices. Then in the following $n$ lines, the $i$-th line has a string of length $n$. If $s[i][j]=1$, there is an edge from $i$ to $j$. If $s[i][j]=2$ means you need to determine the direction for that edge. The input is guaranteed to be legal, and the number of $(i, j) (i < j)$ satisfying $s[i][j]=s[j][i]=2$ is less than $200$. The data is randomly generated.

Output

For each set of test samples, output one line to represent the maximized answer.

2
5
02112
20221
02001
02102
20020
5
01112
00022
01012
02002
22220

40
24

Hint

One solution to the first case is:
00110
10001
01001
01100
10010