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.
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jul  7 16:52:06 2021

@author: hienpham
"""
import os
import math
import sys


parse_input = lambda: sys.stdin.readline().rstrip("\r\n")


def func(n_track, arr):
    total_car = sum(arr)
    rem = total_car%n_track
    inconv = rem * (n_track - rem)
    
    return inconv


def main():
    n_cases = int(parse_input())
    for i in range(n_cases):
        n_track = int(parse_input())
        arr = [int(i) for i in parse_input().split()]
        print(func(n_track, arr))
        
if __name__ == "__main__":
    main()