Split First N Squares

You are given an integer 'N'. Your task is to split the set of first 'N' squares into two sets such that the difference of their sum is minimized. It is guaranteed that 'N' is always a multiple of eight.

Each square must belong to one and exactly one set. Return a binary string of length 'N', if the ‘i’th character of the string is ‘0’ then ‘i’ * ‘i’ is in Set1 else in Set2.

For example:

N = 8, Set of first 8 squares = [1, 4, 9, 16, 25, 36, 49, 64]

Set1 = [1, 16, 36, 49], Set2 = [64, 25, 9, 4]

Here difference is (64 + 25 + 9 + 4) - (1 + 16 + 36 + 49 ) = 0 and = "01101001"

Input Format:

The first line of input contains an integer 'T' denoting the number of test cases to run. Then the test case follows.

The first line of each test case contains an integer 'N'. 

Output Format:

For each test case return a binary string of length 'N',   if the ‘i’th character of the string is ‘0’ then ‘i’ * ‘i’ is in Set1 else in Set2. 

Output for each test case is printed in a separate line.

Note:

You don’t need to print anything. It has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10
1 <= N <= 5000   

N is always a multiple of 8. 

Time Limit: 1 sec