Solve the programming task below in a Python markdown code block.
Chef is given a number in form of its binary representation S, having length N.

Determine if the number can be represented as a sum of exactly three non-negative powers of 2. Please refer to samples for further explanation.

Note that S will NOT contain leading zeros.

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of multiple lines of input.
- The first line of each test case contains a single integer N, the length of the binary string.
- The next line contains the string S, the binary representation of a number.

------ Output Format ------ 

For each test case, output YES if the number can be represented as sum of exactly three powers of 2.

You can print each character in uppercase or lowercase. For example YES, yes, Yes, and yES are all considered the same.

------ Constraints ------ 

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 2 \cdot 10^{5}$
$S$ consists of $0$ and $1$ only, and has no leading zeros.
- The sum of $N$ over all test cases won't exceed $2 \cdot 10^{5}$.

----- Sample Input 1 ------ 
4
1
1
4
1001
5
11001
7
1101101

----- Sample Output 1 ------ 
NO
YES
YES
NO

----- explanation 1 ------ 
Test case $1$: It is not possible to represent the given number as a sum of exactly three powers of $2$.

Test case $2$: The given string $1001$ corresponds to the number $9$. We can represent $9$ as a sum of exactly three powers of $2$ as $9 = 2^{2} + 2^{2} + 2^{0}$.

Test case $3$: The given string $11001$ corresponds to the number $25$. We can represent $25$ as a sum of exactly three powers of $2$ as $25 = 2^{4} + 2^{3} + 2^{0}$.

Test case $4$: It is not possible to represent the given number as a sum of exactly three powers of $2$.