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:
Find if it is possible to convert the array A into a permutation of length N.
Input format
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≤T≤1051≤N≤3⋅1051≤Ai≤109Sum of N over all test cases does not exceed 3⋅105.