You are given a permutation $p_1, p_2, \dots, p_n$. 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:

• $1 \le i \lt j \lt k \le n$;
• $p_i \lt p_j$ and $p_j \gt p_k$.

Or say that there are no such indices.

Input

The first line contains a single integer $T$ ($1 \le T \le 200$) — 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 $n$ ($3 \le n \le 1000$) — the length of the permutation $p$.

The second line contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$; $p_i \neq p_j$ if $i \neq j$) — 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.

Samples

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

YES
2 3 4
YES
3 5 6
NO