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
// CodeForces Round #1330 B training done.

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class ThreeIndexes {

	int t;
	int n;
	boolean can;
	int []p;
	int ir,jr,kr;
	
	int []readIArray(int n, BufferedReader bin) throws IOException {
		String s = bin.readLine();
		String[] ss = s.trim().split(" ");
		if (ss.length != n) {
			return null;
		}
		int []a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(ss[i]);
		}
		return a;
	}

	private void readData(BufferedReader bin) throws IOException {
		String s = bin.readLine();
		String[] ss = s.trim().split(" ");
		t = Integer.parseInt(ss[0]);
		for (int i = 0; i < t; i++) {
			// read m,k,a
			s = bin.readLine().trim();
			n = Integer.parseInt(s);
			p = readIArray(n, bin);
			calculate();
			printRes();
		}
	}

	void printRes() {
		if (!can) {
			System.out.println("NO");
		} else {
			System.out.println("YES");
			System.out.printf("%d %d %d\n", ir, jr, kr);
		}
	}

	private void calculate() {
		// skip initial decrease
		int iinc = -1;
		for (int i=0; i<n-1; i++) {
			if (p[i] < p[i+1]) {
				iinc = i;
				break;
			}
		}
		if (iinc < 0) {
			can = false;
			return;
		}

		// look for decrease
		for (int i=iinc+1; i<n-1; i++) {
			if (p[i] > p[i+1]) {
				ir = i-1+1;
				jr = i+1;
				kr = i+1+1;
				can = true;
				return;
			}
		}
		can = false;
	}

	public static void main(String[] args) throws IOException {
		// BufferedReader bin = new BufferedReader(new FileReader("cactus.in"));
		BufferedReader bin = new BufferedReader(new InputStreamReader(System.in));
		ThreeIndexes l = new ThreeIndexes();
		l.readData(bin);
		// l.calculate();
		// l.printRes();
	}
}
