I do not know Graph Theory!

A tournament graph is a directed graph where there is exactly one edge between every two distinct vertices.

A strongly connected graph is a directed graph where there is a path between every two distinct vertices.

You are given a tournament graph. For each edge of the graph, find out whether the graph is strongly connected when that edge is reversed.

The first line contains one integer $T$ ($1 \leq T \leq 40000$), the number of test cases.

For each test case, the first line contains one integer $n$ ($2 \leq n \leq 5000$), the number of vertices.

The next $n-1$ lines give out the compressed lower triangular matrix in the following way:

Each line contains an uppercase hexadecimal string, where the $j$-th hexadecimal of the $i$-th string $S_{i,j}=\sum_{k=0}^{3}{2^k \times E_{i+1,4j+k-3}}$, and $E_{i,j}=1$ iff the direction of the edge between $i,j$ is from $i$ to $j$. All indices start from $1$.

It is guaranteed that there are at most $3$ test cases in which the $n$ is larger than $10$.

For each test case, output $n-1$ lines in the same format of the input: $S_{i,j}=\sum_{k=0}^{3}{2^k \times ans_{i+1,4j+k-3}}$, and $ans_{i,j}=1$ iff the graph is strongly connected when the edge between $i,j$ is reversed.