#include <bits/stdc++.h>
using namespace std;
long long N = 2e5;
pair<long long, string> pa[100000];
vector<long long> v, vv, v2;
map<long long, long long> mp;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t;
  cin >> t;
  while (t--) {
    v.clear();
    long long n, cnt = 1;
    bool q = 0;
    cin >> n;
    for (long long i = 0; i < n; i++) {
      long long x;
      cin >> x;
      v.push_back(x);
    }
    if (n == 1 && v[0] == 1)
      cout << 2 << endl;
    else if (n == 1 && v[0] == 0)
      cout << 1 << endl;
    else {
      if (v[0] == 1) cnt++;
      for (long long i = 1; i < n; i++) {
        if ((v[i] == 1 && v[i - 1] == 0)) {
          cnt++;
        } else if (v[i] == 0 && v[i - 1] == 0) {
          q = 1;
          break;
        } else if (v[i] == 1 && v[i - 1] == 1) {
          cnt += 5;
        }
      }
      if (q)
        cout << -1 << endl;
      else
        cout << cnt << endl;
    }
  }
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

Petya has got an interesting flower. Petya is a busy person, so he sometimes forgets to water it. You are given n days from Petya's live and you have to determine what happened with his flower in the end.

The flower grows as follows: 

  * If the flower isn't watered for two days in a row, it dies. 
  * If the flower is watered in the i-th day, it grows by 1 centimeter. 
  * If the flower is watered in the i-th and in the (i-1)-th day (i > 1), then it grows by 5 centimeters instead of 1. 
  * If the flower is not watered in the i-th day, it does not grow. 



At the beginning of the 1-st day the flower is 1 centimeter tall. What is its height after n days?

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains the only integer n (1 ≤ n ≤ 100).

The second line of each test case contains n integers a_1, a_2, ..., a_n (a_i = 0 or a_i = 1). If a_i = 1, the flower is watered in the i-th day, otherwise it is not watered.

Output

For each test case print a single integer k — the flower's height after n days, or -1, if the flower dies.

Example

Input


4
3
1 0 1
3
0 1 1
4
1 0 0 1
1
0


Output


3
7
-1
1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long N = 2e5;
pair<long long, string> pa[100000];
vector<long long> v, vv, v2;
map<long long, long long> mp;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t;
  cin >> t;
  while (t--) {
    v.clear();
    long long n, cnt = 1;
    bool q = 0;
    cin >> n;
    for (long long i = 0; i < n; i++) {
      long long x;
      cin >> x;
      v.push_back(x);
    }
    if (n == 1 && v[0] == 1)
      cout << 2 << endl;
    else if (n == 1 && v[0] == 0)
      cout << 1 << endl;
    else {
      if (v[0] == 1) cnt++;
      for (long long i = 1; i < n; i++) {
        if ((v[i] == 1 && v[i - 1] == 0)) {
          cnt++;
        } else if (v[i] == 0 && v[i - 1] == 0) {
          q = 1;
          break;
        } else if (v[i] == 1 && v[i - 1] == 1) {
          cnt += 5;
        }
      }
      if (q)
        cout << -1 << endl;
      else
        cout << cnt << endl;
    }
  }
}

```