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

for _ in range(int(input())):
    n=int(input())
    p=[int(x) for x in input().split()]
    ml=[]
    mr=[]
    m=n
    for x in p:
       m=min(m,x)
       ml.append(m)
    m=n
    for x in p[::-1]:
       m=min(m,x)
       mr.append(m)
    mr=mr[::-1]
    #print(ml)
    #print(mr)            
    a,b,c=[-1,-1,-1]
    for i in range(1,n-1):
        if ml[i-1]<p[i] and p[i]>mr[i+1]:
            a=p.index(ml[i-1])
            b=i
            c=p.index(mr[i+1])  
    if [a,b,c]==[-1,-1,-1]:
       print("NO")
    else:
       print("YES")
       print(str(a+1)+" "+str(b+1)+" "+str(c+1))          
    


