#include <bits/stdc++.h>
using namespace std;
struct ins {
  int ans;
  ins() { ans = 1; }
  void read() {}
  void read1(char &s) {
    char c = getchar();
    for (; !isprint(c) || c == ' ' || c == '\n' || c == '\t'; c = getchar())
      ;
    s = c;
    if (c == EOF) ans = 0;
  }
  void read1(string &s) {
    s = "";
    char c = getchar();
    for (; !isprint(c) || c == ' ' || c == '\n' || c == '\t'; c = getchar())
      ;
    for (; isprint(c) && c != ' ' && c != '\n' && c != '\t'; c = getchar())
      s += c;
    if (c == EOF) ans = 0;
  }
  template <typename T>
  void read1(T &n) {
    T x = 0;
    int f = 1;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) {
      if (c == '-') f = -1;
      if (c == EOF) {
        ans = 0;
        return;
      }
    }
    for (; isdigit(c); c = getchar()) x = x * 10 + c - 48;
    n = x * f;
    if (c == EOF) ans = 0;
    if (c != '.') return;
    T l = 0.1;
    while ((c = getchar()) <= '9' && c >= '0') x = x + (c & 15) * l, l *= 0.1;
    n = x * f;
    if (c == EOF) ans = 0;
  }
  void write() {}
  void write1(string s) {
    int n = s.size();
    for (int i = 0; i < n; i++) putchar(s[i]);
  }
  void write1(const char *s) {
    int n = strlen(s);
    for (int i = 0; i < n; i++) putchar(s[i]);
  }
  void write1(char s) { putchar(s); }
  void write1(float s, int x = 6) {
    char y[10001];
    sprintf(y, "%%.%df", x);
    printf(y, s);
  }
  void write1(double s, int x = 6) {
    char y[10001];
    sprintf(y, "%%.%dlf", x);
    printf(y, s);
  }
  void write1(long double s, int x = 6) {
    char y[10001];
    sprintf(y, "%%.%dLf", x);
    printf(y, s);
  }
  template <typename T>
  void write1(T n) {
    if (n < 0) n = -n, putchar('-');
    if (n > 9) write1(n / 10);
    putchar('0' + n % 10);
  }
  template <typename T>
  friend ins operator>>(ins x, T &n);
  template <typename T>
  friend ins operator<<(ins x, T n);
  operator bool() { return ans; }
};
template <typename T>
ins operator>>(ins x, T &n) {
  if (!x.ans) return x;
  x.read1(n);
  return x;
}
template <typename T>
ins operator<<(ins x, T n) {
  x.write1(n);
  return x;
}
ins yin;
ins yout;
const int maxn = 4e4 + 10;
int n;
long long a[maxn], b[maxn], c[maxn], d[maxn];
int cnt;
void pp(long long x, long long y, long long z) {
  ++cnt;
  b[cnt] = x;
  c[cnt] = y;
  d[cnt] = z;
}
void pr() {
  yout << cnt << '\n';
  for (int i = 1; i <= cnt; i++) {
    yout << b[i] << " " << c[i] << ' ' << d[i] << '\n';
  }
}
int main() {
  int TTT;
  yin >> TTT;
  while (TTT--) {
    cnt = 0;
    long long sum = 0;
    yin >> n;
    for (int i = 1; i <= n; i++) yin >> a[i], sum += a[i];
    if (sum % n) {
      yout << -1 << '\n';
      continue;
    }
    sum /= n;
    for (int i = 2; i <= n; i++) {
      if (a[i] % i == 0) {
        pp(i, 1, a[i] / i);
      } else {
        pp(1, i, i - a[i] % i);
        pp(i, 1, a[i] / i + 1);
      }
    }
    for (int i = 2; i <= n; i++) pp(1, i, sum);
    pr();
  }
}

### Prompt

In Cpp, your task is to solve the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct ins {
  int ans;
  ins() { ans = 1; }
  void read() {}
  void read1(char &s) {
    char c = getchar();
    for (; !isprint(c) || c == ' ' || c == '\n' || c == '\t'; c = getchar())
      ;
    s = c;
    if (c == EOF) ans = 0;
  }
  void read1(string &s) {
    s = "";
    char c = getchar();
    for (; !isprint(c) || c == ' ' || c == '\n' || c == '\t'; c = getchar())
      ;
    for (; isprint(c) && c != ' ' && c != '\n' && c != '\t'; c = getchar())
      s += c;
    if (c == EOF) ans = 0;
  }
  template <typename T>
  void read1(T &n) {
    T x = 0;
    int f = 1;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) {
      if (c == '-') f = -1;
      if (c == EOF) {
        ans = 0;
        return;
      }
    }
    for (; isdigit(c); c = getchar()) x = x * 10 + c - 48;
    n = x * f;
    if (c == EOF) ans = 0;
    if (c != '.') return;
    T l = 0.1;
    while ((c = getchar()) <= '9' && c >= '0') x = x + (c & 15) * l, l *= 0.1;
    n = x * f;
    if (c == EOF) ans = 0;
  }
  void write() {}
  void write1(string s) {
    int n = s.size();
    for (int i = 0; i < n; i++) putchar(s[i]);
  }
  void write1(const char *s) {
    int n = strlen(s);
    for (int i = 0; i < n; i++) putchar(s[i]);
  }
  void write1(char s) { putchar(s); }
  void write1(float s, int x = 6) {
    char y[10001];
    sprintf(y, "%%.%df", x);
    printf(y, s);
  }
  void write1(double s, int x = 6) {
    char y[10001];
    sprintf(y, "%%.%dlf", x);
    printf(y, s);
  }
  void write1(long double s, int x = 6) {
    char y[10001];
    sprintf(y, "%%.%dLf", x);
    printf(y, s);
  }
  template <typename T>
  void write1(T n) {
    if (n < 0) n = -n, putchar('-');
    if (n > 9) write1(n / 10);
    putchar('0' + n % 10);
  }
  template <typename T>
  friend ins operator>>(ins x, T &n);
  template <typename T>
  friend ins operator<<(ins x, T n);
  operator bool() { return ans; }
};
template <typename T>
ins operator>>(ins x, T &n) {
  if (!x.ans) return x;
  x.read1(n);
  return x;
}
template <typename T>
ins operator<<(ins x, T n) {
  x.write1(n);
  return x;
}
ins yin;
ins yout;
const int maxn = 4e4 + 10;
int n;
long long a[maxn], b[maxn], c[maxn], d[maxn];
int cnt;
void pp(long long x, long long y, long long z) {
  ++cnt;
  b[cnt] = x;
  c[cnt] = y;
  d[cnt] = z;
}
void pr() {
  yout << cnt << '\n';
  for (int i = 1; i <= cnt; i++) {
    yout << b[i] << " " << c[i] << ' ' << d[i] << '\n';
  }
}
int main() {
  int TTT;
  yin >> TTT;
  while (TTT--) {
    cnt = 0;
    long long sum = 0;
    yin >> n;
    for (int i = 1; i <= n; i++) yin >> a[i], sum += a[i];
    if (sum % n) {
      yout << -1 << '\n';
      continue;
    }
    sum /= n;
    for (int i = 2; i <= n; i++) {
      if (a[i] % i == 0) {
        pp(i, 1, a[i] / i);
      } else {
        pp(1, i, i - a[i] % i);
        pp(i, 1, a[i] / i + 1);
      }
    }
    for (int i = 2; i <= n; i++) pp(1, i, sum);
    pr();
  }
}

```