There are $N$ balls in a row. The $i^{th}$ ball has color $A_i$. Your task is to destroy all the balls by using the following operation any number of times:

Assume that the current number of balls is $k$. All the balls of color $k$ are destroyed at the same moment. In different scenarios, you are required to determine whether you can destroy all the balls or not.

Input format

• First line: $t$ denoting the number of test cases
• Each test case: An integer $N$ denoting the number of balls
• Next line: $N$ space-separated integers corresponding to the color of balls

Output format
For each test case, if all the balls can be destroyed, then print $YES$. Otherwise, $NO$.

Constraints

$1≤ t ≤ 200$
$1≤N≤1000$
$1≤A_i≤1000000000$