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/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using  namespace std;

#define int           long long
#define vi            vector<int>
#define vpii          vector<pair<int,int>>
#define pii           pair<int,int>
#define all(x)        x.begin(), x.end()
#define ms            multiset
#define pb            push_back
#define pob           pop_back
#define ff            first
#define ss            second
#define setbits(x)    __builtin_popcountll(x)
#define stp(x)        fixed << setprecision(x)
#define fast          ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define inf           1e18
#define mod           1000000007

typedef tree<vpii, null_type, less<vpii>, rb_tree_tag, tree_order_statistics_node_update> pbds;

void io(){
  fast

  #ifndef ONLINE_JUDGE
    freopen("INPUT.txt", "r", stdin);
    freopen("OUTPUT.txt", "w", stdout);
  #endif
}

int32_t main() {

  io();

  int t = 1;
  cin>>t;
  while(t--){
    int n; cin >> n;
    vi a(n);
    int sum = 0;

    for(int i = 0; i < n; i++) cin >>  a[i], sum += a[i];

    cout << sum << " ";
    if(sum % n >= 1)
    {
      cout << 1 << '\n';
    }
    else
    {
      cout << 0 << '\n';  
    }
  }
  return 0;
}