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.
Input
The first line contains one integer T(1≤T≤40000), the number of test cases. For each test case, the first line contains one integer n(2≤n≤5000), the number of vertices. The next n−1lines 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 Si,j=∑3k=02k×Ei+1,4j+k−3, and Ei,j=1iff the direction of the edge between i,jis from ito j. All indices start from 1. It is guaranteed that there are at most 3test cases in which the nis larger than 10.
Output
For each test case, output n−1lines in the same format of the input: Si,j=∑3k=02k×ansi+1,4j+k−3, and ansi,j=1iff the graph is strongly connected when the edge between i,jis reversed.