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
import java.util.*;
// scanner.nextInt();
public class Solution {
    public static void main(String[] args) {       

        Scanner scanner = new Scanner(System.in);
        int test_case = scanner.nextInt();
            
            for(int z = 0; z < test_case; ++z)
            {
                int n = scanner.nextInt();
		int[] array = new int[n];
                

                for(int i = 0; i < n; ++i)
                    {
                        array[i] = scanner.nextInt();
                    }
                 
                boolean posible = false;
                
                int ii = -1;
                int jj = -1;
                int kk = -1;
                
                if(n <= 4)
                {
                            for(int j = 1; j < n-1; ++j)
                        {
                            for(int k = j+1; k < n; ++k)
                            {
                                    if(array[j] > array[k])
                                {
                                    for(int i = 0; i < j; ++i)
                                    {
                                        if(array[i] < array[j]) 
                                        {
                                            posible = true;
                                            ii = i+1;
                                            jj = j+1;
                                            kk = k+1;
                                            break;
                                        }

                                    }
                                    if(posible) break;
                                }
                            }                  
                        } 
                }
                
                else
                {
                    int index = 0;
                    if(array[0] > array[1])
                    {
                        ++index;
                    }
                    for(int i = index; i < n-1; ++i)
                    {
                        if(array[i] < array[i+1])
                        {
                            for(int j = i+2; j < n; ++j)
                            {
                                if(array[i+1] > array[j])
                                {
                                    ii = i+1;
                                    jj = i+2;
                                    kk = j+1;
                                    posible = true;
                                    break;
                                }
                            }
                            if(posible) break;
                         }
                    }
                }
              
                
                if(posible)
                {
                    System.out.println("YES");
                    System.out.println(ii + " " + jj + " " + kk);
                }
                else System.out.println("No");
                //String[] arr = {"a","b","c", "d","e", "f" , "g" , "h", "i" , "j" , "k" , "l", "m", "n", "o", "p", "q" , "r", "s", "t", "u" , "v", "w" ,"x", "y", "z"};
 
            }
                    
    }
}

