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.
#from itertools import product
#from itertools import combinations
from collections import Counter
#from collections import defaultdict
#from collections import deque # deque([iterable[, maxlen]]) #appendleft popleft rotate
#from heapq import heapify, heappop, heappush # func(heapifiedlist, item)
# sadness lies below
#from bisect import bisect_left, bisect_right, insort # func(sortedlist, item)
#from sys import setrecursionlimit

from sys import stdin, stderr
input = stdin.readline

def dbp(*args, **kwargs): # calling with dbp(locals()) is perfectly cromulent
	print(*args, file=stderr, **kwargs)

def get_int_list():
	return [int(x) for x in input().strip().split()]

def slow_match(n, extras):
	count = 0
	for i in range(n):
		for j in range(i+1, n):
			if i < extras and j >= extras:
				count += 1
	return count


def do_thing():
	n = int(input())
	alist = get_int_list()

	total = sum(alist)
	flravg, extras = divmod(sum(alist), len(alist))
	#sr = slow_match(n, extras)
	r = (n-extras) * extras
	#dbp(sr, r)
	#assert(sr==r)
	return r

def multicase():
	maxcc = int(input().strip())
	for cc in range(maxcc):
		print(do_thing())

if __name__ == "__main__":
	multicase()
	#print(do_thing())