Highway 201 is the most busy street in Rockport. Traffic cars cause a lot of hindrances to races, especially when there are a lot of them. The track which passes through this highway can be divided into n sub-tracks. You are given an array a where a_i represents the number of traffic cars in the i-th sub-track. You define the inconvenience of the track as ∑_{i=1}^{n} ∑_{j=i+1}^{n} \lvert a_i-a_j\rvert, where |x| is the absolute value of x. 

You can perform the following operation any (possibly zero) number of times: choose a traffic car and move it from its current sub-track to any other sub-track.

Find the minimum inconvenience you can achieve.

Input

The first line of input contains a single integer t (1≤ t≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 2⋅ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (0≤ a_i≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2⋅ 10^5.

Output

For each test case, print a single line containing a single integer: the minimum inconvenience you can achieve by applying the given operation any (possibly zero) number of times.

Example

Input


3
3
1 2 3
4
0 1 1 0
10
8 3 6 11 5 2 1 7 10 4


Output


0
4
21

Note

For the first test case, you can move a car from the 3-rd sub-track to the 1-st sub-track to obtain 0 inconvenience.

For the second test case, moving any car won't decrease the inconvenience of the track.
def main():
    alpha = 'abcdefghijklmnopqrstuvwxyz'
    ALPHA = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
    inf = 1e17
    mod = 10 ** 9 + 7

    # Max = 10 ** 1
    # primes = []
    # prime = [True for i in range(Max + 1)]
    # p = 2
    # while (p * p <= Max + 1):
    #
    #     # If prime[p] is not
    #     # changed, then it is a prime
    #     if (prime[p] == True):
    #
    #         # Update all multiples of p
    #         for i in range(p * p, Max + 1, p):
    #             prime[i] = False
    #     p += 1
    #
    # for p in range(2, Max + 1):
    #     if prime[p]:
    #         primes.append(p)
    #
    # print(primes)

    def factorial(n):
        f = 1

        for i in range(1, n + 1):
            f = (f * i) % mod  # Now f never can
        # exceed 10^9+7

        return f

    def ncr(n, r):
        # initialize numerator
        # and denominator
        num = den = 1
        for i in range(r):
            num = (num * (n - i)) % mod
            den = (den * (i + 1)) % mod
        return (num * pow(den,
                          mod - 2, mod)) % mod


    def solve(n,arr):

        rem = sum(arr)%n

        print((n-rem)*rem)















































        pass

    t = int(input())
    ans = []
    for _ in range(t):
        n = int(input())
        #a,b = map(int, input().split())
        # s = input()
        arr = [int(x) for x in input().split()]
        # a2 = [int(x) for x in input().split()]
        # grid = []
        # for i in range(n):
        #     grid.append([int(x) for x in input().split()][::-1])

        ans.append(solve(n,arr))

    # for answer in ans:
    #     print(answer)


if __name__ == "__main__":
    import sys, threading
    import bisect
    import math
    import itertools
    from sys import stdout

    # Sorted Containers
    import heapq
    from queue import PriorityQueue

    # Tree Problems
    #sys.setrecursionlimit(2 ** 32 // 2 - 1)
    #threading.stack_size(1 << 27)

    # fast io
    input = sys.stdin.readline

    thread = threading.Thread(target=main)
    thread.start()
    thread.join()
