#include <bits/stdc++.h>
using namespace std;
struct perl {
  int n;
  vector<int> p;
};
int main() {
  int t;
  cin >> t;
  vector<perl> a;
  a.resize(t);
  for (int i = 0; i < t; ++i) {
    cin >> a[i].n;
    for (int j = 0; j < a[i].n; ++j) {
      int x;
      cin >> x;
      a[i].p.push_back(x);
    }
  }
  vector<int> height;
  for (int i = 0; i < t; ++i) {
    bool nn = false;
    int h_now = 1;
    int no = 0;
    vector<int> b;
    b = a[i].p;
    for (int j = 0; j < a[i].n; ++j) {
      if (b[j] == 0) {
        no += 1;
      }
      if (no == 2) {
        height.push_back(-1);
        nn = true;
        break;
      }
      if (j == 0 && b[j] == 1) {
        h_now += 1;
        no = 0;
      } else if (j > 0 && b[j] == 1 && b[j - 1] == 0) {
        h_now += 1;
        no = 0;
      } else if (j > 0 && b[j] == 1 && b[j - 1] == 1) {
        h_now += 5;
        no = 0;
      }
    }
    if (!nn) {
      height.push_back(h_now);
    }
  }
  for (int i = 0; i < t; ++i) {
    cout << height[i] << '\n';
  }
  return 0;
}

### Prompt

Your task is to create 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;
struct perl {
  int n;
  vector<int> p;
};
int main() {
  int t;
  cin >> t;
  vector<perl> a;
  a.resize(t);
  for (int i = 0; i < t; ++i) {
    cin >> a[i].n;
    for (int j = 0; j < a[i].n; ++j) {
      int x;
      cin >> x;
      a[i].p.push_back(x);
    }
  }
  vector<int> height;
  for (int i = 0; i < t; ++i) {
    bool nn = false;
    int h_now = 1;
    int no = 0;
    vector<int> b;
    b = a[i].p;
    for (int j = 0; j < a[i].n; ++j) {
      if (b[j] == 0) {
        no += 1;
      }
      if (no == 2) {
        height.push_back(-1);
        nn = true;
        break;
      }
      if (j == 0 && b[j] == 1) {
        h_now += 1;
        no = 0;
      } else if (j > 0 && b[j] == 1 && b[j - 1] == 0) {
        h_now += 1;
        no = 0;
      } else if (j > 0 && b[j] == 1 && b[j - 1] == 1) {
        h_now += 5;
        no = 0;
      }
    }
    if (!nn) {
      height.push_back(h_now);
    }
  }
  for (int i = 0; i < t; ++i) {
    cout << height[i] << '\n';
  }
  return 0;
}

```