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.
# cook your dish here
# code
#    ___________________________________
#   |                                   |
#   |                                   |
#   |        _,     _   _     ,_        |
#   |    .-'` /     \'-'/     \ `'-.    |
#   |   /    |      |   |      |    \   |
#   |  ;      \_  _/     \_  _/      ;  |
#   | |         ``         ``         | |
#   | |                               | |
#   |  ;    .-.   .-.   .-.   .-.    ;  |
#   |   \  (   '.'   \ /   '.'   )  /   |
#   |    '-.;         V         ;.-'    |
#   |        `                 `        |
#   |                                   |
#   |___________________________________|
#   |                                   |
#   |  Author      :   Ramzz            |
#   |  Created On  :   21-07-2020       |
#   |___________________________________|
#
#    _ __ __ _ _ __ ___  ________
#   | '__/ _` | '_ ` _ \|_  /_  /
#   | | | (_| | | | | | |/ / / / 
#   |_|  \__,_|_| |_| |_/___/___|
#

import math
import collections
from sys import stdin,stdout,setrecursionlimit
from bisect import bisect_left as bsl
from bisect import bisect_right as bsr
import heapq as hq
setrecursionlimit(2**20)

t = 1
t = int(stdin.readline())

for _ in range(t):
    n = int(stdin.readline())
    #s = stdin.readline().strip('\n')
    a = list(map(int, stdin.readline().rstrip().split()))
    
    su = sum(a)
    if(su%n==0):
        print(0)
    else:
        tmp = su//n
        r = (su - tmp*n)
        
        print((n-r)*r)
    
    
    
    
    
    
    