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.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Random;
import java.util.StringTokenizer;

public final class F {

    private static class SegTreeMin {
        int leftMost, rightMost;
        SegTreeMin left, right;
        int min;

        SegTreeMin(int leftMost, int rightMost, int[] arr) {
            this.leftMost = leftMost;
            this.rightMost = rightMost;
            if (leftMost == rightMost) {
                min = arr[leftMost];
            } else {
                final int mid = leftMost + rightMost >>> 1;
                left = new SegTreeMin(leftMost, mid, arr);
                right = new SegTreeMin(mid + 1, rightMost, arr);
                recalc();
            }
        }

        private void recalc() {
            if (leftMost == rightMost) {
                return;
            }
            min = Math.min(left.min, right.min);
        }

        private int query(int l, int r) {
            if (r < leftMost || l > rightMost) {
                return Integer.MAX_VALUE;
            }
            if (l <= leftMost && rightMost <= r) {
                return min;
            }
            return Math.min(left.query(l, r), right.query(l, r));
        }
    }

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int t = fs.nextInt();
        outer:
        for (int test = 0; test < t; test++) {
            final int n = fs.nextInt();
            final int[] arr = fs.nextIntArray(n);
            final SegTreeMin stMin = new SegTreeMin(0, n - 1, arr);
            final int[] preMax = new int[n];
            final int[] suffMax = new int[n];
            final Map<Integer, Integer> first = new HashMap<>();
            final Map<Integer, Integer> last = new HashMap<>();
            int currMax = 0;
            for (int i = 0; i < n; i++) {
                currMax = Math.max(currMax, arr[i]);
                preMax[i] = currMax;
            }
            currMax = 0;
            for (int i = n - 1; i >= 0; i--) {
                currMax = Math.max(currMax, arr[i]);
                suffMax[i] = currMax;
            }
            for (int i = 0; i < n; i++) {
                last.put(suffMax[i], i);
            }
            for (int i = n - 1; i >= 0; i--) {
                first.put(suffMax[i], i);
            }
            for (int l = 0; l < n - 2; l++) {
                final int val = preMax[l];
                int lo = Math.max(l + 2, first.getOrDefault(val, n + 1));
                int hi = last.getOrDefault(val, -1);
                while (lo <= hi) {
                    final int mid = lo + hi >>> 1;
                    final int rmq = stMin.query(l + 1, mid - 1);
                    if (rmq > val) {
                        lo = mid + 1;
                    } else if (rmq < val) {
                        hi = mid - 1;
                    } else {
                        System.out.println("YES");
                        System.out.println((l + 1) + " " + (mid - (l + 1)) + ' ' + (n - mid));
                        continue outer;
                    }
                }
            }
            System.out.println("NO");
        }
    }

    static final class Utils {
        public static void shuffleSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffleSort(long[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffle(int[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void shuffle(long[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void swap(int[] x, int i, int j) {
            final int t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        public static void swap(long[] x, int i, int j) {
            final long t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        private Utils() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        int[] nextIntArray(int n) {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++) { a[i] = nextInt(); }
            return a;
        }

        long[] nextLongArray(int n) {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++) { a[i] = nextLong(); }
            return a;
        }
    }
}