Description

Input

Each test contains multiple test cases. The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \le n \le 50$) — the number of lamps.

The second line of each test case contains a binary string $s$ of size $n$ — the final desired configuration.

Output

For each test case, print on one line "YES" if we can reach the configuration $s$ via applying the given operation any number of times. Otherwise, print "NO".

5
10
1101010110
10
1001001110
6
000000
1
1
12
111111111111
 
 
 
 
 
 

YES
NO
YES
NO
YES

Note

In the first test case, the sequence of operation could have been as follows (note that initially $s$ is all zero): $\mathtt{0000000000} \to \mathtt{\color{red}{1}0000000\color{red}{1}0} \to \mathtt{1\color{red}{1}00000\color{red}{1}10} \to \mathtt{110\color{red}{1}0\color{red}{1}0110}$.

In the third test case, we don't have to do any operation.

In the fourth test case, we cannot do any operation, but we need the first lamp to be on. Therefore, it is impossible to achieve the desired state.