Program in C++ please:

You are given a permutation p1,p2,,pn. Recall that sequence of n integers is called a permutation if it contains all integers from 1 to n exactly once.

Find three indices i, j and k such that:

• 1 I < j < k n;
• p_i < p_j and p_j> p_k .

Or say that there are no such indices.

Input

The first line contains a single integer T (1 T 200) the number of test cases.

Next 2T lines contain test cases two lines per test case. The first line of each test case contains the single integer n (3 n 1000 ) the length of the permutation p.

The second line contains nn integers p1,p2,,pn(1 p_i n; p_i p_j if i j ) the permutation p.

Output

For each test case:

• if there are such indices i, j and k, print YES (case insensitive) and the indices themselves;
• if there are no such indices, print NO (case insensitive).

If there are multiple valid triples of indices, print any of them.

Example

Input

3 4 2 1 4 3 6 4 6 1 2 5 3 5 5 3 1 2 4 

Output

YES 2 3 4 YES 3 5 6 NO