Description

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

Format

Input

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).

Output

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.

Samples

1
4

2 4
11
01