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 sys
from collections import deque

input = sys.stdin.readline


def solve():
    n = int(input())
    a = list(map(int, input().split()))
    s = sum(a)
    if s % n != 0:
        print(-1)
    else:
        avg = s // n
        c = 0
        ans = []
        q = []
        qq = []
        for i in range(1, n):
            if a[i] >= i+1:
                x = a[i] // (i+1)
                a[i] -= (i+1) * x
                a[0] += (i+1) * x
                ans.append("{} {} {}".format(i+1, 1, x))
                c += 1
            if a[i] > avg:
                q.append(i)
            elif a[i] > 0:
                qq.append(i)
        f = True
        while len(q) > 0 and f:
            j = 0
            f = False
            while j < len(q):
                i = q[j]
                if a[0] > i - a[i]:
                    ans.append("{} {} {}".format(1, i + 1, i + 1 - a[i]))
                    ans.append("{} {} {}".format(i + 1, 1, 1))
                    a[0] += a[i]
                    a[i] = 0
                    c += 2
                    q.pop(j)
                    f = True
                else:
                    j += 1
            if not f:
                j = 0
                while j < len(qq):
                    i = qq[j]
                    if a[0] > i - a[i]:
                        ans.append("{} {} {}".format(1, i + 1, i + 1 - a[i]))
                        ans.append("{} {} {}".format(i + 1, 1, 1))
                        a[0] += a[i]
                        a[i] = 0
                        c += 2
                        qq.pop(j)
                        f = True
                    else:
                        j += 1

        if q:
            raise Exception("q is not empty")

        for i in range(1, n):
            if a[i] != avg:
                ans.append("{} {} {}".format(1, i + 1, avg - a[i]))
                c += 1
        print(c)
        if ans:
            print("\n".join(ans))


t = int(input())
for _ in range(t):
    solve()
