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 _1454F {
    static int[] MODS = {1000000007, 998244353, 1000000009};
    static int MOD = MODS[0];

    public static void main(String[] args) {
        sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int[] arr = new int[n];
            scan(arr);
            SegmentTreeRMQ tree = new SegmentTreeRMQ(n, arr);
            int left = 0;
            int leftMax = Integer.MIN_VALUE;
            int right = -1;
            int[] maxFromRight = new int[n];
            maxFromRight[n - 1] = arr[n - 1];
            for (int i = n - 2; i >= 0; i--) {
                maxFromRight[i] = Math.max(maxFromRight[i + 1], arr[i]);
            }
            while (left < n - 2) {
                leftMax = Math.max(arr[left], leftMax);
                int low = left + 2;
                int high = n - 1;
                while (low <= high) {
                    int middle = (low + high) / 2;
                    int min = tree.RMQ(left + 1, middle - 1);
                    int max = maxFromRight[middle];
                    if (leftMax == max && leftMax == min) {
                        right = middle;
                        break;
                    } else if (max > leftMax) {
                        low = middle + 1;
                    } else if (max < leftMax) {
                        high = middle - 1;
                    } else if (min > leftMax) {
                        low = middle + 1;
                    } else {
                        high = middle - 1;
                    }
                }
                if (right != -1) {
                    break;
                }
                left++;
            }
            if (right != -1) {
                out.println("YES");
                out.println((left + 1) + " " + (right - left - 1) + " " + (n - right));
            } else {
                out.println("NO");
            }
        }
        out.close();
    }

    static class SegmentTreeRMQ {
        int st[];
        int n;
        SegmentTreeRMQ(int n, int[] arr) {
            this.n = n;
            constructST(arr, n);
        }
        int minVal(int x, int y) {
            return Math.min(x, y);
        }
        int getMid(int s, int e) {
            return s + (e - s) / 2;
        }
        int RMQUtil(int ss, int se, int qs, int qe, int index) {
            if (qs <= ss && qe >= se)
                return st[index];
            if (se < qs || ss > qe)
                return Integer.MAX_VALUE;
            int mid = getMid(ss, se);
            return minVal(RMQUtil(ss, mid, qs, qe, 2 * index + 1),
                    RMQUtil(mid + 1, se, qs, qe, 2 * index + 2));
        }
        int RMQ(int qs, int qe) {
            if (qs < 0 || qe > n - 1 || qs > qe) {
                System.out.println("Invalid Input");
                return -1;
            }
            return RMQUtil(0, n - 1, qs, qe, 0);
        }
        int constructSTUtil(int arr[], int ss, int se, int si) {
            if (ss == se) {
                st[si] = arr[ss];
                return arr[ss];
            }
            int mid = getMid(ss, se);
            st[si] = minVal(constructSTUtil(arr, ss, mid, si * 2 + 1),
                    constructSTUtil(arr, mid + 1, se, si * 2 + 2));
            return st[si];
        }
        void constructST(int arr[], int n) {
            int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
            int max_size = 2 * (int) Math.pow(2, x) - 1;
            st = new int[max_size];
            constructSTUtil(arr, 0, n - 1, 0);
        }
    }

    public static int[] sort(int[] arr) {
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < arr.length; i++) {
            list.add(arr[i]);
        }
        Collections.sort(list);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = list.get(i);
        }
        return arr;
    }

    public static void scan(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextInt();
        }
    }

    public static MyScanner sc;
    public static PrintWriter out;

    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;
        }
    }
}