4680 - Hdu5332 Test for Rikka

As we know, Rikka is poor at math. At the test, Rikka finds that she cannot even do a single problem. There is one of the insane problems: Given an integer K, she needs to come up with an n×n 01 matrix A and an integer m which meet B1,n=K, where B=Am. It is too difficult for Rikka. Can you help her? 输入k,输出一个n*n的有向图,使从1走m条边到n的路径数正好为k

输入

The first line of the input is a single integer T (T=40), indicating the number of testcases. Each of the next T lines contains one integer K (0≤K≤10^18).

输出

For each testcase, the first line contains two space-separated integers n,m (1≤n,m≤30). In each of following n lines print n characters (0 or 1) - the matrix A you find.

样例

输入

1
4

输出

2 4
11
01
时间限制 1 秒
内存限制 128 MB
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