Problem: You are given an array a consisting of n integers.

Let min(l, r) be the minimum value among a_l, a_{l + 1}, …, a_r and max(l, r) be the maximum value among a_l, a_{l + 1}, …, a_r.

Your task is to choose three positive (greater than 0) integers x, y and z such that:

  * x + y + z = n; 
  * max(1, x) = min(x + 1, x + y) = max(x + y + 1, n). 



In other words, you have to split the array a into three consecutive non-empty parts that cover the whole array and the maximum in the first part equals the minimum in the second part and equals the maximum in the third part (or determine it is impossible to find such a partition).

Among all such triples (partitions), you can choose any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the length of a.

The second line of the test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer: NO in the only line if there is no such partition of a that satisfies the conditions from the problem statement. Otherwise, print YES in the first line and three integers x, y and z (x + y + z = n) in the second line.

If there are several answers, you can print any.

Example

Input


6
11
1 2 3 3 3 4 4 3 4 2 1
8
2 9 1 7 3 9 4 1
9
2 1 4 2 4 3 3 1 2
7
4 2 1 1 4 1 4
5
1 1 1 1 1
7
4 3 4 3 3 3 4


Output


YES
6 1 4
NO
YES
2 5 2
YES
4 1 2
YES
1 1 3
YES
2 1 4

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.stream.Stream;
import java.util.Iterator;
import java.util.List;


public class Main {
	

static class MaxTree {
    public int get(int[] t, int i) {
        return t[i + t.length / 2];
    }

    public void add(int[] t, int i, int value) {
        i += t.length / 2;
        t[i] += value;
        for (; i > 1; i >>= 1) t[i >> 1] = Math.max(t[i], t[i ^ 1]);
    }

    public int max(int[] t, int a, int b) {
        int res = 0;
        for (a += t.length / 2, b += t.length / 2; a <= b; a = (a + 1) >> 1, b = (b - 1) >> 1) {
            if ((a & 1) != 0)
                res = Math.max(res, t[a]);
            if ((b & 1) == 0)
                res = Math.max(res, t[b]);
        }
        return res;
    }
    
}


static class MinTree {
    public int get(int[] t, int i) {
        return t[i + t.length / 2];
    }

    public void add(int[] t, int i, int value) {
        i += t.length / 2;
        t[i] += value;
        for (; i > 1; i >>= 1) t[i >> 1] = Math.min(t[i], t[i ^ 1]);
    }

    public int min(int[] t, int a, int b) {
        int res = INF;
        for (a += t.length / 2, b += t.length / 2; a <= b; a = (a + 1) >> 1, b = (b - 1) >> 1) {
            if ((a & 1) != 0)
                res = Math.min(res, t[a]);
            if ((b & 1) == 0)
                res = Math.min(res, t[b]);
        }
        return res;
    }
    
}
	


public static void main(String[] args){
 
   new Thread(null, null, "Anshum Gupta", 99999999) {
        public void run() {
            try {
                solve();
            } catch(Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }.start();
}
 
static final long INF_LONG = (long)(1e18 + 5), MOD = 998244353; //(long)1e9 + 7
static final int MXN = (int)(1001), MXV = (int)(1e6), log = 18, INF = (int)1e9 + 500;
static boolean[]vis;
static ArrayList<ArrayList<Integer>> adj;
static int n, m, q, k, h, w;
static char[] str;
static int[] a, minT, maxT;
static MaxTree maxTree;
static MinTree minTree;



public static void solve() throws Exception {
	   // solve the problem here
		s = new MyScanner();
   		out = new MyWriter(new BufferedOutputStream(System.out));
        int tc = s.nextInt();   
    	for(int i=1; i<=tc; i++) {
    		testcase();
    	}
          
        out.flush();
        out.close();
}


static void testcase() {
	
	n = s.nextInt();
	a = s.nextIntArray(n);
	maxTree = new MaxTree();
	minTree = new MinTree();
	minT = new int[2 * n];
	maxT = new int[2 * n];
	for(int i = 0; i < n; i++) {
		minTree.add(minT, i, a[i]);
		maxTree.add(maxT, i, a[i]);
	}
	
	
	int mx = 0;
	for(int i = 0; i < n - 2; i++) {
		
		mx = Math.max(mx, a[i]);
		
		int pos = find(mx, i + 1, n - 1);
		if(pos != -1) {
			
			// found valid partition
			
			out.println("YES");
			
			out.println((i + 1) + " " + (pos - i) + " " + (n - 1 - pos));
			
			return;
			
		}
		
	}
	
	
	out.println("NO");
	
	
	
	
}





private static int find(int firstMax, int lo, int hi) {
	
	int left = lo, right = hi;
	
	while(lo <= hi) {
		
		int mid = (lo + hi) >> 1;
		
		int leftMin = minTree.min(minT, left, mid);
		
		int rightMax = maxTree.max(maxT, mid + 1, right);
		
//		out.println("lo = " + lo + " hi = " + hi + " mid = " + mid);
//		out.println("leftmin = " + leftMin + " rightMax = " + rightMax);
		
		if(leftMin == firstMax && rightMax == firstMax) return mid;
		
		if(leftMin > firstMax) {
			
			// have to go forward
			
			lo = mid + 1;
		}
		
		else if(leftMin < firstMax){
			
			// have to go back
			
			hi = mid - 1;
		}
		
		else {
			
			// it is equal to firstMax
			// depends on rightMax now
			
			if(rightMax < firstMax) {
				hi = mid - 1;
			}
			
			else lo = mid + 1;
			
		}
		
		
		
		
	}
	
	return -1;
	
	
}

public static MyWriter out;
public static MyScanner s;
static void shuffleArray(int[] a) {
	Random random = new Random();
	for (int i = a.length-1; i > 0; i--) {
		int index = random.nextInt(i + 1);
		int tmp = a[index];
		a[index] = a[i];
		a[i] = tmp;
	}
}
static void shuffleSort(int[] a) {
	shuffleArray(a);
	Arrays.parallelSort(a);
}
static class MyScanner {
 
    BufferedReader br;
    StringTokenizer st;
 
    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    public MyScanner(String fileName) {
    	try {
			br = new BufferedReader(new FileReader(fileName));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
    }
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() { return Integer.parseInt(next()); }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
    int[] nextIntArray(int n){
    	int[]a = new int[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    long[] nextlongArray(int n) {
    	long[]a = new long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    Integer[] nextIntegerArray(int n){
    	Integer[]a = new Integer[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    Long[] nextLongArray(int n) {
    	Long[]a = new Long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    char[][] next2DCharArray(int n, int m){
    	char[][]arr = new char[n][m];
    	for(int i=0; i<n; i++) {
    		arr[i] = this.next().toCharArray();
    	}
    	return arr;
    }
    ArrayList<ArrayList<Integer>> readUndirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    		adj.get(v).add(u);
    	}
    	return adj;
    }
    ArrayList<ArrayList<Integer>> readDirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    	}
    	return adj;
    }
    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
 
static class MyWriter extends PrintWriter {
    MyWriter(OutputStream out) {
        super(out);
    }
    void println(int[] x) {
        println(x, " ");
    }
    void println(int[] x, String delimiter) {
        if (x.length > 0) {
            print(x[0]);
            for (int i = 1; i < x.length; i++) {
                print(delimiter);
                print(x[i]);
            }
        }
        println();
    }
    void println(long[] x) {
        println(x, " ");
    }
    void println(long[] x, String delimiter) {
        if (x.length > 0) {
            print(x[0]);
            for (int i = 1; i < x.length; i++) {
                print(delimiter);
                print(x[i]);
            }
        }
        println();
    }
    void println(Iterable<?> iterable) {
        println(iterable, " ");
    }
    void println(Iterable<?> iterable, String delimiter) {
        Iterator<?> i = iterable.iterator();
        if (i.hasNext()) {
            print(i.next());
            while (i.hasNext()) {
                print(delimiter);
                print(i.next());
            }
        }
        println();
    }
    void printLines(int[] x) {
        println(x, System.lineSeparator());
    }
    void printLines(long[] x) {
        println(x, System.lineSeparator());
    }
    void printLines(Iterable<?> iterable) {
        println(iterable, System.lineSeparator());
    }
}
 
}