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
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse4")
using namespace std;
inline long long in() {
  long long x;
  scanf("%lld", &x);
  return x;
}
const long long N = 1e4 + 5;
long long a[N];
struct q {
  long long i;
  long long j;
  long long x;
};
vector<tuple<long long, long long, long long>> mv;
void trans(long long from, long long to, long long amount) {
  long long x = amount / from;
  mv.push_back({from, to, x});
  assert(amount <= a[from]);
  a[from] -= amount;
  a[to] += amount;
}
void solve() {
  long long n = in();
  for (long long i = 1; i <= n; i++) a[i] = in();
  long long sum = accumulate(a + 1, a + n + 1, 0LL);
  if (sum % n != 0) {
    puts("-1");
    return;
  }
  mv = vector<tuple<long long, long long, long long>>();
  long long final = sum / n;
  for (long long i = 2; i <= n; i++) {
    if (a[i] % i) trans(1, i, i - a[i] % i);
    trans(i, 1, a[i]);
  }
  for (long long i = 2; i <= n; i++) {
    trans(1, i, final);
  }
  cout << mv.size() << "\n";
  for (auto v : mv) {
    long long i, j, x;
    tie(i, j, x) = v;
    cout << i << " " << j << " " << x << "\n";
  }
}
int32_t main() {
  long long t = in();
  while (t--) solve();
}
