Problem 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?
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≤1018).
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.
Sample Input
1
4
Sample Output
2 4
11
01
