There are n block towers in a row, where tower i has a height of a_i. You're part of a building crew, and you want to make the buildings look as nice as possible. In a single day, you can perform the following operation:

  * Choose two indices i and j (1 ≤ i, j ≤ n; i ≠ j), and move a block from tower i to tower j. This essentially decreases a_i by 1 and increases a_j by 1. 



You think the ugliness of the buildings is the height difference between the tallest and shortest buildings. Formally, the ugliness is defined as max(a)-min(a). 

What's the minimum possible ugliness you can achieve, after any number of days?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t cases follow.

The first line of each test case contains one integer n (2 ≤ n ≤ 100) — the number of buildings.

The second line of each test case contains n space separated integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7) — the heights of the buildings.

Output

For each test case, output a single integer — the minimum possible ugliness of the buildings.

Example

Input


3
3
10 10 10
4
3 2 1 2
5
1 2 3 1 5


Output


0
0
1

Note

In the first test case, the ugliness is already 0.

In the second test case, you should do one operation, with i = 1 and j = 3. The new heights will now be [2, 2, 2, 2], with an ugliness of 0.

In the third test case, you may do three operations: 

  1. with i = 3 and j = 1. The new array will now be [2, 2, 2, 1, 5], 
  2. with i = 5 and j = 4. The new array will now be [2, 2, 2, 2, 4], 
  3. with i = 5 and j = 3. The new array will now be [2, 2, 3, 2, 3]. 

The resulting ugliness is 1. It can be proven that this is the minimum possible ugliness for this test.
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define ll long long
//#define int long long
#define nline "\n"
#define _USE_MATH_DEFINES
#define ld long double
#define pb push_back
#define mp make_pair
#define ull unsigned long long
#define pi 3.14159265358979323846
#define vi vector<int>
#define vll vector<ll>
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
ull power(ull x,ull y,int p){ull res=1;x=x%p;if(x==0)return 0;while(y>0){if(y&1)res=(res*x)%p;y=y>>1;x=(x*x)%p;}return res;}
ull powull(ull x,ull y){ull ans=1;while(y--)ans=ans*x;return ans;}



void solve(){
int t=1;       cin>>t;
while(t--)
{
int n;cin>>n;
int a[n];
for(int i=0;i<n;i++)cin>>a[i];
sort(a,a+n);
int i=0,j=n-1;
while(i<j)
{
    int x=(a[i]+a[j]);
    if(x%2==0)
    {
        a[i]=x/2;
        a[j]=x/2;
    }
    else{
        a[i]=x/2;
        a[j]=a[i]+1;
    }
    i++;j--;
}
sort(a,a+n);
cout<<a[n-1]-a[0]<<endl;






}
}



int32_t main()
{

ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    solve();
return 0;
}

