You are given a permutation p_1, p_2, ..., 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 ≤ 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 n integers p_1, p_2, ..., p_n (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
#!/usr/local/bin/python3

"""
Given a permutation perm of [1,..,n], you want to find three indices i, j, k s.t.
    - 1 <= i < j < k <= n
    - pi < pj and pj > pk

Observations:
- Since n <= 1000, can we just brute force this?
    - Ah, i, j, k don't need to necessarily be adjacent.
- Can we just find the maximum?
    - This might not work

- What about sorting? Then, we pick the first index that isn't a distance d from the end.
    - This doesn't work
        - Pick first index where arr[i] != i+1 to be j
        - What to do about i and k?
            - i=0
            - k=j+1?
    - Go from left to right, and just pick a local maximum.
        
1,2,3,4,5,6,7,8,9,10
0 1 2 3 4 5 6 7 8 9

1,2,3,4,5,6,9,10,9,8
0 1 2 3 4 5 6 7  8 9
"""

def fast(arr):
    for i in range(len(arr)-2):
        j = i+1
        k = i+2
        if arr[i] < arr[j] and arr[j] > arr[k]:
            return [i,j,k]
    return None

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        arr = [int(x) for x in input().split()]

        #CHANGE
        result = fast(arr)

        if result:
            print('YES')
            print(' '.join(str(x+1) for x in result))
        else:
            print('NO')
main()
