HoloBinary Generation

You are given an even integer N. Your task is to generate all valid HoloBinary numbers of length N. A HoloBinary number is defined as a binary string of length N which contains exactly \(\frac{N}{2}\) zeros and \(\frac{N}{2}\) ones. The generated binary strings should be listed in lexicographical order.

Note: It is guaranteed that N will always be an even integer.

inputFormat

The input is read from the standard input and consists of multiple test cases. The first line contains a single integer T denoting the number of test cases. Then, T lines follow; each line contains one even integer N, representing the length of the binary string to be generated.

Example:

2
2
4

outputFormat

For each test case, output all valid HoloBinary numbers, each on a separate line. The binary strings for different test cases should be separated by an empty line.

Example corresponding to the input above:

01
10
0011
0101
0110
1001
1010
1100

## sample</p>

2
2
4

01
10
0011
0101
0110
1001
1010
1100

</p>