You are given an array/list ‘BINARYNUMS’ that consists of ‘N’ distinct strings which represent all integers from 0 to N in binary representation except one integer. This integer between 0 to ‘N’ whose binary representation is not present in list ‘BINARYNUMS’ is called ‘Missing Integer’.

Your task is to find the binary representation of that ‘Missing Integer’. You should return a string that represents this ‘Missing Integer’ in binary without leading zeros.

Note

1. There will be no leading zeros in any string in the list ‘BINARYNUMS’.

Example:

Consider N = 5 and the list ‘binaryNums’=  [“0”, “01”, “010”, “100”, “101”].  This list consists of the binary representation of numbers [0, 1, 2, 4, 5]. Clearly, the missing number is 3 and its binary representation will be “11”. So you should return string “11”.

Input format:

The first line of input contains an integer ‘T’ denoting the number of test cases. then ‘T’ test cases follow.

The first line contains single integers ‘N’ represent the size of the list ‘BINARYNUMS’.

The second line contains ‘N’ space-separated string representing the list ‘BINARYNUMS’.

Output format :

For each test case, print a single line containing a single string that represents this ‘Missing Integer’ in binary without leading zeros.

The output of each test case will be printed in a separate line.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 50
1 <= N <= 10 ^ 4

Where ‘T’ is the total number of test cases and ‘N’ is the size of list ‘BINARYNUMS’

Time limit: 1 sec.