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.util.*;
import java.io.*;
public class EdE {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner sc;
    public static PrintWriter out;
	public static void main(String[] omkar) throws Exception{
		// TODO Auto-generated method stub
 		sc = new MyScanner();
 		out = new PrintWriter(System.out);
 		int t = sc.nextInt();
 		for(int i = 0;i<t;i++){
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
//			COMPARING INTEGER OBJECTS U DO DOT EQUALS NOT ==
 			int n = sc.nextInt();
	 		int []array = readArrayInt(n);
	 		
	 		int[] prefixmax = new int[n];
	 		int[] suffixmax = new int[n];
	 		prefixmax[0] = array[0];
	 		suffixmax[n-1] = array[n-1];
	 		for(int j = 1;j<n;j++){
	 			prefixmax[j] = Math.max(array[j],  prefixmax[j-1]);
	 		}
	 		for(int j = n-2;j>=0;j--){
	 			suffixmax[j] = Math.max(suffixmax[j+1], array[j]);
	 		}
	 		boolean found = false;
	 		int l1 = -1;
	 		int r1 = -1;
	 		SegTreeMin st = new SegTreeMin(0, n-1, array);
	 		for(int left = 0;left<n-2;left++){
	 			int l = left;
	 			int r = n;
	 			while(l < r){
	 				int mid = (l+r)/2;
	 				if (suffixmax[mid] > prefixmax[left])
	 					l = mid+1;
	 				else if (suffixmax[mid] < prefixmax[left])
	 					r = mid;
	 				else{  
	 					int val = st.rangeMin(left+1, mid-1);
	 					if (val > prefixmax[left]){
	 						l = mid+1;
	 					}
	 					else if (val < prefixmax[left]){
	 						r = mid;
	 					}
	 					else{
		 					found = true;
		 					l1 = left;
		 					r1 = mid;
		 					break;
	 					}
	 				}
	 			}
	 			if (found)
	 				break;
	 			
	 		}
	 		verdict(found);
	 		if (found)
	 			out.println((l1+1) + " " + (n-(l1+1)-(n-r1)) + " " + (n-r1));
	 		
	 		
 		}
 		out.println();
	 		
 		out.close();	
 	}
	static class SegTreeMin{
		int leftmost, rightmost;
		SegTreeMin left, right;
		int min;
		public SegTreeMin(int leftmost, int rightmost, int[] a){
			this.leftmost = leftmost;
			this.rightmost = rightmost;
			if (leftmost == rightmost){
				// it is a leaf
				min = a[leftmost];
			}
			else{
				// it is not a leaf
				int mid = (leftmost+rightmost)/2;
				left = new SegTreeMin(leftmost, mid, a);
				right = new SegTreeMin(mid+1, rightmost, a);
				recalc();
			}
		}
		public void recalc(){
			if (leftmost == rightmost){
				return;
			}
			min = Math.min(left.min, right.min);
			
		}
		public void pointUpdate(int index, int newVal){
			if (leftmost == rightmost){
				min = newVal;
				return;
			}
			if (index <= left.rightmost){
				left.pointUpdate(index, newVal);
			}
			else{
				right.pointUpdate(index,  newVal);
			}
			recalc();
		}
		public int rangeMin(int l, int r){
			// entirely disjoint
			if (l > rightmost || r < leftmost) 
				return Integer.MAX_VALUE;
			//covers us
			if (l <= leftmost && r >= rightmost){
				return min;
			}
			//others
			return Math.min(left.rangeMin(l,  r),  right.rangeMin(l, r));
		}
	}
	public static void sort(int[] array){
		ArrayList<Integer> copy = new ArrayList<Integer>();
		for (int i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.next();
		return array;
	}
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = sc.nextInt();
    	return array;
    }
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = sc.nextInt();
		}
		return array;
	}
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextLong();
		return array;
	}
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextDouble();
		return array;
	}
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        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());
        }
        String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            } 
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
    }	
}

//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is