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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

import static java.lang.Integer.MIN_VALUE;
import static java.lang.Math.max;

public class SolutionF extends Thread {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }

    private static final FastReader scanner = new FastReader();
    private static final PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Thread(null, new SolutionF(), "Main", 1 << 26).start();
    }

    public void run() {
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            solve();
        }
        out.close();
    }


    static class SimpleSegmentTree {
        int size;
        int[] segments;

        //TODO: Change following Code to customize the Segment Tree
        //Currently its calculating the max of a segment
        /*==========*/
        int NEUTRAL_ELEMENT = Integer.MAX_VALUE;
        public int merge(int left, int right) {
            return Math.min(left, right);
        }
        /*==========*/;

        public SimpleSegmentTree(int n) {
            size = 1;
            while (size < n) {
                size *= 2;
            }
            segments = new int[size * 2 - 1];
        }

        private void build(int[] arr, int x, int lx, int rx) {
            if (rx - lx == 1) {
                if (lx < arr.length) {
                    segments[x] = arr[lx];
                } else {
                    segments[x] = NEUTRAL_ELEMENT;
                }
            } else {
                int mid = (lx + rx) / 2;
                build(arr, x * 2 + 1, lx, mid);
                build(arr, x * 2 + 2, mid, rx);
                segments[x] = merge(segments[x * 2 + 1], segments[x * 2 + 2]);
            }
        }

        public void build(int[] arr) {
            build(arr, 0, 0, size);
        }

        private void set(int i, int v, int x, int lx, int rx) {
            if (rx - lx == 1) {
                segments[x] = v;
            } else {
                int mid = (lx + rx) / 2;
                if (i < mid) {
                    set(i, v, x * 2 + 1, lx, mid);
                } else {
                    set(i, v, x * 2 + 2, mid, rx);
                }
                segments[x] = merge(segments[x * 2 + 1], segments[x * 2 + 2]);
            }
        }

        public void set(int i, int v) {
            set(i, v, 0, 0, size);
        }

        private int calcSegment(int l, int r, int x, int lx, int rx) {
            if (l <= lx && r >= rx) {
                return segments[x];
            } else if (l >= rx || r <= lx) {
                return NEUTRAL_ELEMENT;
            } else {
                int mid = (lx + rx) / 2;
                return merge(calcSegment(l, r, x * 2 + 1, lx, mid), calcSegment(l, r, x * 2 + 2, mid, rx));
            }
        }

        public int calcSegment(int l, int r) {
            return calcSegment(l, r, 0, 0, size);
        }
    }

    private static void solve() {
        int n = scanner.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        SimpleSegmentTree segmentTree = new SimpleSegmentTree(n);
        segmentTree.build(a);

        int[] prefixA = new int[n];
        prefixA[0] = a[0];
        for (int i = 1; i < n; i++) {
            prefixA[i] = Math.max(prefixA[i-1], a[i]);
        }

        int[] suffixA = new int[n];
        suffixA[n-1] = a[n-1];
        for (int i = n-2; i >= 0; i--) {
            suffixA[i] = Math.max(suffixA[i+1],  a[i]);
        }


        for (int i = 0; i < n; i++) {
            int low = i+1;
            int high = n;

            while (high - low > 1) {
                int mid = (low + high) / 2;

                if (suffixA[mid] <= prefixA[i]) {
                    high = mid;
                } else {
                    low = mid;
                }
            }

            if (high < n && suffixA[high] == prefixA[i] && i + 1 < high && segmentTree.calcSegment(i+1, high) == prefixA[i]) {
                int x = i + 1;
                int y = high - x;
                System.out.println("YES");
                System.out.println(x + " " + y + " " + (n - x - y));
                return;
            } else if (high + 1 < n && suffixA[high+1] == prefixA[i] && segmentTree.calcSegment(i+1, high + 1) == prefixA[i]) {
                int x = i + 1;
                int y = high + 1 - x;
                System.out.println("YES");
                System.out.println(x + " " + y + " " + (n - x - y));
                return;
            }
        }
        System.out.println("NO");
    }



    //REMINDERS:
    //- CHECK FOR INTEGER-OVERFLOW BEFORE SUBMITTING

    //- CAN U BRUTEFORCE OVER SOMETHING, TO MAKE IT EASIER TO CALCULATE THE SOLUTION
}