You are given an array a consisting of n positive integers, numbered from 1 to n. You can perform the following operation no more than 3n times:

  1. choose three integers i, j and x (1 ≤ i, j ≤ n; 0 ≤ x ≤ 10^9); 
  2. assign a_i := a_i - x ⋅ i, a_j := a_j + x ⋅ i. 



After each operation, all elements of the array should be non-negative.

Can you find a sequence of no more than 3n operations after which all elements of the array are equal?

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 10^4) — the number of elements in the array. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^5) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 10^4.

Output

For each test case print the answer to it as follows:

  * if there is no suitable sequence of operations, print -1; 
  * otherwise, print one integer k (0 ≤ k ≤ 3n) — the number of operations in the sequence. Then print k lines, the m-th of which should contain three integers i, j and x (1 ≤ i, j ≤ n; 0 ≤ x ≤ 10^9) for the m-th operation. 



If there are multiple suitable sequences of operations, print any of them. Note that you don't have to minimize k.

Example

Input


3
4
2 16 4 18
6
1 2 3 4 5 6
5
11 19 1 1 3


Output


2
4 1 2
2 3 3
-1
4
1 2 4
2 4 5
2 3 3
4 5 1
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author htvu
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    DMakeThemEqual solver = new DMakeThemEqual();
    solver.solve(1, in, out);
    out.close();
  }

  static class DMakeThemEqual {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      for (int test = in.nextInt(); test > 0; --test) {
        int n = in.nextInt();
        int[] a = new int[n + 1];
        int sum = 0;
        for (int i = 1; i <= n; ++i) {
          a[i] = in.nextInt();
          sum += a[i];
        }
        if (sum % n != 0) {
          out.println(-1);
          continue;
        }

        List<int[]> ans = new ArrayList<>();
        int target = sum / n;
        for (int i = 2; i <= n; ++i) {
          if (a[i] % i > 0) {
            move(1, i, i - (a[i] % i), ans, a);
          }
          move(i, 1, a[i] / i, ans, a);
        }
        for (int i = 2; i <= n; ++i) {
          move(1, i, target, ans, a);
        }
        out.println(ans.size());
        for (int[] step : ans) {
          out.println(step[0] + " " + step[1] + " " + step[2]);
        }
      }
    }

    private void move(int i, int j, int x, List<int[]> ans, int[] a) {
      ans.add(new int[]{i, j, x});
      a[i] -= i * x;
      a[j] += i * x;
    }

  }

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

  }
}

