A permutation of length \(N\) is an array of \(N\) integers such that every integer from \(1\) to \(N\) appears exactly once. For example, \([2, 3, 5, 4, 1] \) is a permutation of length \(5\), while \([1,2, 2], [4, 5, 1, 3] \) are not permutations.

You are given an array \(A\) having \(N\) integers. You can apply the following operation on the array \(A\) any number of times:

Choose two indices \(i, j\) such that \(1 \le i \lt j \le N\), then decrease \(1\) from \(A_i\) and add \(1\) to \(A_j\).

Find if it is possible to convert the array \(A\) into a permutation of length \(N\).

Input format

The first line of input contains an integer \(T\) denoting the number of test cases. The description of each test case is as follows:
The first line of each test case contains an integer \(N\) denoting the length of the array \(A\).
The second line of each test case contains \(N\) integers \(A_1, A_2,\dots, A_N\), denoting the elements of the array \(A\).

Output format

For each test case, print YES if it is possible to obtain a permutation from the array \(A\) using the given operation, otherwise print NO.

Constraints

\(1\le T \le 10^5 \\ 1 \leq N \le 3\cdot 10^5\\ 1\le A_i \le 10^9\\ \text{Sum of $N$ over all test cases does not exceed }3\cdot 10^5.\)