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.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class ArrayPartition implements Closeable {

  private InputReader in = new InputReader(System.in);
  private PrintWriter out = new PrintWriter(System.out);

  private class Node {
    private int lo, hi, value;

    private void merge(Node left, Node right) {
      value = Math.min(left.value, right.value);
    }
  }

  private class SegmentTree {
    private int n;
    private int[] x;
    private Node[] tree;

    private SegmentTree(int[] x) {
      this.x = x;
      this.n = x.length;
      tree = new Node[4 * n + 1];
      for (int i = 0; i < tree.length; i++) {
        tree[i] = new Node();
      }
      init(1, 0, n - 1);
    }

    private void init(int idx, int left, int right) {
      tree[idx].lo = left;
      tree[idx].hi = right;
      if (left == right) {
        tree[idx].value = x[left];
      } else {
        int mid = (left + right) / 2;
        init(idx << 1, left, mid);
        init(idx << 1 | 1, mid + 1, right);
        tree[idx].merge(tree[idx << 1], tree[idx << 1 | 1]);
      }
    }

    public int query(int idx, int left, int right) {
      if (tree[idx].lo > right || tree[idx].hi < left) return Integer.MAX_VALUE;
      if (tree[idx].lo >= left && tree[idx].hi <= right) return tree[idx].value;

      int l = query(idx << 1, left, right);
      int r = query(idx << 1 | 1, left, right);
      return Math.min(l, r);
    }
  }

  public void solve() {
    int t = in.ni();
    while (t-- > 0) {
      int n = in.ni();
      int[] a = new int[n];
      for (int i = 0; i < n; i++) {
        a[i] = in.ni();
      }
      int[] max = new int[n];
      max[n - 1] = a[n - 1];
      for (int i = n - 2; i >= 0; i--) {
        max[i] = Math.max(max[i + 1], a[i]);
      }

      SegmentTree tree = new SegmentTree(a);
      int[] result = null;
      int maxSoFar = -1;
      for (int x = 0; x < n - 2 && result == null; x++) {
        maxSoFar = Math.max(maxSoFar, a[x]);
        int left = x + 2, right = n - 1;
        int z_left = n;
        while (left <= right) {
          int mid = left + (right - left) / 2;
          if (max[mid] == maxSoFar) {
            z_left = Math.min(z_left, mid);
            right = mid - 1;
          } else if (max[mid] > maxSoFar) {
            left = mid + 1;
          } else {
            right = mid - 1;
          }
        }

        int z_right = 0;
        left = x + 2;
        right = n - 1;
        while (left <= right) {
          int mid = left + (right - left) / 2;
          if (max[mid] == maxSoFar) {
            z_right = Math.max(z_right, mid);
            left = mid + 1;
          } else if (max[mid] > maxSoFar) {
            left = mid + 1;
          } else {
            right = mid - 1;
          }
        }

        left = z_left - 1;
        right = z_right - 1;

        while (left <= right) {
          int mid = left + (right - left) / 2;
          int min = tree.query(1, x + 1, mid);
          if (maxSoFar == min) {
            result = new int[3];
            result[0] = x + 1;
            result[1] = mid - x;
            result[2] = n - result[0] - result[1];
            break;
          } else if (maxSoFar < min) {
            left = mid + 1;
          } else {
            right = mid - 1;
          }
        }

      }

      if (result != null) {
        out.println("YES");
        for (int idx : result) {
          out.print(idx);
          out.print(' ');
        }
        out.println();
      } else {
        out.println("NO");
      }
    }
  }

  @Override
  public void close() throws IOException {
    in.close();
    out.close();
  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public int ni() {
      return Integer.parseInt(next());
    }

    public long nl() {
      return Long.parseLong(next());
    }

    public void close() throws IOException {
      reader.close();
    }
  }

  public static void main(String[] args) throws IOException {
    try (ArrayPartition instance = new ArrayPartition()) {
      instance.solve();
    }
  }
}