#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007LL;
int n;
int a[109];
int calc(int x, int y) {
  int cnt = 0;
  for (int i = 1; i <= n; ++i) {
    int res = MOD;
    for (int j = 0; j <= x; ++j) {
      for (int k = 0; k <= y; ++k) {
        if (a[i] - j - k * 2 < 0 || (a[i] - j - k * 2) % 3) continue;
        res = min(res, (a[i] - j - k * 2) / 3);
      }
    }
    cnt = max(cnt, res);
  }
  return cnt + x + y;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int _;
  cin >> _;
  while (_--) {
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    cout << min({calc(0, 0), calc(1, 0), calc(0, 1), calc(1, 1), calc(0, 2)})
         << "\n";
  }
}

### Prompt

Develop a solution in Cpp to the problem described below:

One day, early in the morning, you decided to buy yourself a bag of chips in the nearby store. The store has chips of n different flavors. A bag of the i-th flavor costs a_i burles.

The store may run out of some flavors, so you'll decide which one to buy after arriving there. But there are two major flaws in this plan: 

  1. you have only coins of 1, 2 and 3 burles; 
  2. since it's morning, the store will ask you to pay in exact change, i. e. if you choose the i-th flavor, you'll have to pay exactly a_i burles. 



Coins are heavy, so you'd like to take the least possible number of coins in total. That's why you are wondering: what is the minimum total number of coins you should take with you, so you can buy a bag of chips of any flavor in exact change?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains the single integer n (1 ≤ n ≤ 100) — the number of flavors in the store.

The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the cost of one bag of each flavor.

Output

For each test case, print one integer — the minimum number of coins you need to buy one bag of any flavor you'll choose in exact change.

Example

Input


4
1
1337
3
10 8 10
5
1 2 3 4 5
3
7 77 777


Output


446
4
3
260

Note

In the first test case, you should, for example, take with you 445 coins of value 3 and 1 coin of value 2. So, 1337 = 445 ⋅ 3 + 1 ⋅ 2.

In the second test case, you should, for example, take 2 coins of value 3 and 2 coins of value 2. So you can pay either exactly 8 = 2 ⋅ 3 + 1 ⋅ 2 or 10 = 2 ⋅ 3 + 2 ⋅ 2.

In the third test case, it's enough to take 1 coin of value 3 and 2 coins of value 1.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007LL;
int n;
int a[109];
int calc(int x, int y) {
  int cnt = 0;
  for (int i = 1; i <= n; ++i) {
    int res = MOD;
    for (int j = 0; j <= x; ++j) {
      for (int k = 0; k <= y; ++k) {
        if (a[i] - j - k * 2 < 0 || (a[i] - j - k * 2) % 3) continue;
        res = min(res, (a[i] - j - k * 2) / 3);
      }
    }
    cnt = max(cnt, res);
  }
  return cnt + x + y;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int _;
  cin >> _;
  while (_--) {
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    cout << min({calc(0, 0), calc(1, 0), calc(0, 1), calc(1, 1), calc(0, 2)})
         << "\n";
  }
}

```