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:
// package NickMikeMurderers;

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.HashMap;

public class ArrayPartition {
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
    public static void main(String[] args)throws IOException {
        Reader s=new Reader();
        StringBuilder print=new StringBuilder();
        int test=s.nextInt();
        while(test--!=0){
            int n=s.nextInt();
            int a[]=new int[n+1];
            for(int i=1;i<=n;i++){
                a[i]=s.nextInt();
            }
            int pre[]=new int[n+2];
            int suf[]=new int[n+2];
            for(int i=1;i<=n;i++){
                pre[i]=Math.max(pre[i-1],a[i]);
            }
            for(int i=n;i>=1;i--){
                suf[i]=Math.max(suf[i+1],a[i]);
            }
            int k=Integer.numberOfTrailingZeros(Integer.highestOneBit(n));
            int table[][]=new int[n+1][k+1];
            for(int i=1;i<=n;i++){
                table[i][0]=a[i];
            }
            for(int j=1;j<=k;j++){
                for(int i=1;i<=n;i++){
                    table[i][j]=Math.min(table[i][j-1],table[Math.min(n,i+(1<<(j-1)))][j-1]);
                }
            }
            HashMap<Integer,Integer> first=new HashMap<>();
            HashMap<Integer,Integer> last=new HashMap<>();
            for(int i=1;i<=n;i++){
                last.put(suf[i],i);
            }
            for(int i=n;i>=1;i--){
                first.put(suf[i],i);
            }
//            System.out.println(first.toString());
//            System.out.println(last.toString());
            boolean flag=false;
            for(int i=1;i+2<=n;i++){
                int val=pre[i];
                int low=Math.max(i+2,first.getOrDefault(val,n+1));
                int high=last.getOrDefault(val,0);
                while(low<=high){
                    int mid=(low+high)>>1;
                    int q=query(table,i+1,mid-1);
                    if(q==val){
                        print.append("YES\n");
                        int midsize=mid-i-1;
                        int end=n-i-midsize;
                        print.append(i+" "+midsize+" "+end+"\n");
                        flag=true;
                        break;
                    }
                    else if(q<val){
                        high=mid-1;
                    }
                    else{
                        low=mid+1;
                    }
                }
                if(flag){
                    break;
                }
            }
            if(!flag){
                print.append("NO\n");
            }
        }
        System.out.print(print.toString());
    }
    public static int query(int table[][],int l,int r){
        int len=r-l+1;
        int temp=Integer.highestOneBit(len);
        int o=Integer.numberOfTrailingZeros(temp);
//        System.out.println(l+" "+r+" "+table.length);
        return Math.min(table[l][o],table[r-temp+1][o]);
    }
}