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.*;
import java.util.*;

public class Main {
	static int[]log,min[],max[],arr;
	static int inf=(int)1e9;
	static void preSparseTable(int[]in,int n) {
		arr=in;
		log = new int[n+1];
		for (int i = 2; i <= n; i++)
			log[i] = log[i / 2] + 1;
		
		min=new int[n][22];
		for(int i=0;i<n;i++) {
			min[i][0]=i;
		}
		max=new int[n][22];
		for(int i=0;i<n;i++) {
			max[i][0]=i;
		}
		for(int i=1,len=2;len<=n;i++,len<<=1) {
			for(int j=0;j<n;j++) {
				int u=min[j][i-1],v=j+(len>>1)>=n?inf:min[j+(len>>1)][i-1];
				if(v==inf) {
					min[j][i]=u;
				}
				else
					min[j][i]=(arr[u]<arr[v]?u:v);
			}
		}
		for(int i=1,len=2;len<=n;i++,len<<=1) {
			for(int j=0;j<n;j++) {
				int u=max[j][i-1],v=j+(len>>1)>=n?inf:max[j+(len>>1)][i-1];
				if(v==inf) {
					max[j][i]=u;
				}
				else
					max[j][i]=(arr[u]>arr[v]?u:v);
			}
		}
	}
	static int queryMin(int l,int r) {
		int len = r - l + 1;
		int lg = log[len];
		int u = min[l][lg];
		int v = min[r - (1 << lg) + 1][lg];
		int bestIdx = arr[u] < arr[v] ? u : v;
		return arr[bestIdx];//or return bestIdx if we want the best index
	}
	static int queryMax(int l,int r) {
		int len = r - l + 1;
		int lg = log[len];
		int u = max[l][lg];
		int v = max[r - (1 << lg) + 1][lg];
		int bestIdx = arr[u] > arr[v] ? u : v;
		return arr[bestIdx];//or return bestIdx if we want the best index
	}
	static void main() throws Exception {
		int n=sc.nextInt();
		int[]in=sc.intArr(n);
		preSparseTable(in, n);
		for(int i=0;i<n-2;i++) {
			int max=queryMax(0, i);
			
			int firsty=-1;
			int lo=i+1,hi=n-1;
			while(lo<=hi) {
				int mid=(lo+hi)>>1;
				int curMin=queryMin(i+1, mid);
				if(curMin==max) {
					firsty=mid;
					hi=mid-1;
				}
				else {
					if(curMin>max) {
						lo=mid+1;
					}
					else {
						hi=mid-1;
					}
				}
			}
			
			if(firsty==-1)continue;
			
			int lasty=-1;
			lo=i+1;hi=n-1;
			while(lo<=hi) {
				int mid=(lo+hi)>>1;
				int curMin=queryMin(i+1, mid);
				if(curMin==max) {
					lasty=mid;
					lo=mid+1;
				}
				else {
					if(curMin>max) {
						lo=mid+1;
					}
					else {
						hi=mid-1;
					}
				}
			}
			
			
			
			int lastz=-1;
			lo=i+1;hi=n-1;
			while(lo<=hi) {
				int mid=(lo+hi)>>1;
				int curMax=queryMax(mid, n-1);
				if(curMax==max) {
					lastz=mid;
					lo=mid+1;
				}
				else {
					if(curMax>max) {
						lo=mid+1;
					}
					else {
						hi=mid-1;
					}
				}
			}
			
			if(lastz==-1)continue;
			
			int firstz=-1;
			lo=i+1;hi=n-1;
			while(lo<=hi) {
				int mid=(lo+hi)>>1;
				int curMax=queryMax(mid, n-1);
				if(curMax==max) {
					firstz=mid;
					hi=mid-1;
				}
				else {
					if(curMax>max) {
						lo=mid+1;
					}
					else {
						hi=mid-1;
					}
				}
			}
			
			firsty++;lasty++;
			if(Math.max(firsty, firstz)>Math.min(lasty, lastz))continue;
			
			int intersection=Math.max(firsty, firstz)-1;
			
			pw.println("YES");
			pw.println((i+1)+" "+(intersection-i)+" "+(n-i-(intersection-i+1)));
			return;
		}
		pw.println("NO");
	}
	public static void main(String[] args) throws Exception {
		sc = new MScanner(System.in);
		pw = new PrintWriter(System.out);
		int tc = 1;
		tc=sc.nextInt();
		for (int test = 1; test <= tc; test++) {
			main();
		}
		pw.flush();
	}

	static PrintWriter pw;
	static MScanner sc;

	static class MScanner {
		StringTokenizer st;
		BufferedReader br;

		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int[] intArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public long[] longArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public int[] intSortedArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public long[] longSortedArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public Integer[] IntegerArr(int n) throws IOException {
			Integer[] in = new Integer[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public Long[] LongArr(int n) throws IOException {
			Long[] in = new Long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}

	}

	static void shuffle(int[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * in.length);
			int tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}

	static void shuffle(long[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * in.length);
			long tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}
}