A. Three Indices

A. Three Indices

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a permutation 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$. Recall that sequence of 𝑛$n$ integers is called a permutation if it contains all integers from 1$1$ to 𝑛$n$exactly once.

Find three indices 𝑖$i$, 𝑗$j$ and 𝑘$k$ such that: 

• 1≤𝑖<𝑗<𝑘≤𝑛$1\le i<j<k\le n$; 
• 𝑝𝑖<𝑝𝑗$p_i<p_j$ and 𝑝𝑗>𝑝𝑘$p_j>p_k$. 

Or say that there are no such indices.

Input

The first line contains a single integer 𝑇$T$ (1≤𝑇≤200$1\le T\le 200$) — the number of test cases.

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

The second line contains 𝑛$n$ integers 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$ (1≤𝑝𝑖≤𝑛$1\le p_i\le n$; 𝑝𝑖≠𝑝𝑗$p_i\ne p_j$ if 𝑖≠𝑗$i\ne j$) — the permutation 𝑝$p$.

Output

For each test case: 

• if there are such indices 𝑖$i$, 𝑗$j$ and 𝑘$k$, 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

Copy

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

output

Copy

YES
2 3 4
YES
3 5 6
NO