Customising the Track Codeforces Solution

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Customising the Track Solution

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 nn sub-tracks. You are given an array aa where aiai represents the number of traffic cars in the ii-th sub-track. You define the inconvenience of the track as ∑i=1n∑j=i+1n|ai−aj|∑i=1n∑j=i+1n|ai−aj|, where |x||x| is the absolute value of xx.

See Also: Codeforces Round 730 (Div. 2)

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 tt (1≤t≤100001≤t≤10000) — the number of test cases.

The first line of each test case contains a single integer nn (1≤n≤2⋅1051≤n≤2⋅105).

The second line of each test case contains nn integers a1,a2,…,ana1,a2,…,an (0≤ai≤1090≤ai≤109).

It is guaranteed that the sum of nn over all test cases does not exceed 2⋅1052⋅105.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 33-rd sub-track to the 11-st sub-track to obtain 00 inconvenience.

For the second test case, moving any car won’t decrease the inconvenience of the track.

Solution

Program C++:

#include<bits/stdc++.h>
using namespace std;
void process()
{
	long long n;
	cin>>n;
	long long s=0;
	for(long long i=1;i<=n;i++)
	{
		long long u;
		cin>>u;
		s+=u;
	}
	s=s%n;
	cout<<s*(n-s)<<"\n";
}
int main()
{
	long long t;
	cin>>t;
	for(long long i=1;i<=t;i++)
	process();
}

Codeforces Round #730 (Div. 2)

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