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.sql.SQLOutput;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
import java.util.Stack;

public class Sample {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int testCase = sc.nextInt();
        while (testCase-->0){
            int n = sc.nextInt();
            int[] arr = new int[n];
            for(int i=0;i<n;i++)
                arr[i] = sc.nextInt();
            Stack<Integer> prevSmall  = new Stack<>();
            Stack<Integer> nextSmall  = new Stack<>();
            int[][]  res = new int[n+2][2];
            for(int i=0;i<n+2;i++){
                res[i] =new int[] {-1,-1};
            }
            for(int i=0;i<n;i++){
                int curr = arr[i];
                while (!prevSmall.isEmpty() && arr[prevSmall.peek()]>curr)
                    prevSmall.pop();
                if(!prevSmall.isEmpty()){
                    res[i][0] = prevSmall.peek();
                }
                prevSmall.push(i);
            }
                for(int i=n-1;i>=0;i--) {
                    int curr = arr[i];
                    while (!nextSmall.isEmpty() && arr[nextSmall.peek()]>curr)
                        nextSmall.pop();
                    if(!nextSmall.isEmpty() ){
                        res[i][1] = nextSmall.peek();
                    }
                    nextSmall.push(i);

                }
                boolean flag = false;
             for(int i=0;i<n+2;i++){
                 if( res[i][0]!=-1 && res[i][1]!=-1 && res[i][0]<i && res[i][1]>i){
                     System.out.println("YES");
                     System.out.println((res[i][0]+1)+" "+(i+1)+" "+(res[i][1]+1));
                     flag  = true;
                     break;
                 }
             }
             if(!flag) System.out.println("NO");
        }
    }


}
