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

\(1≤ t ≤ 200\)
\(1≤N≤1000\)
\(1≤A_i≤1000000000\)