human
PYTHON3 solution for "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":



What is a Python code to determine what happened with his flower in the end?
assistant
#Here is Python code to determine what happened with his flower in the end.
 def program():
    test_cases = int(input())
    for _ in range(test_cases):
        days_len = int(input())
        sample = input()
        days = [int(day) for day in sample.split(" ")]
        flower_length = 1
        #preconditions
        if days[0] == 1:
            flower_length += 1
        for i in range(1, days_len):
            if days[i-1] == 1 and days[i] == 1:
                flower_length += 5
            elif days[i-1] == 0 and days[i] == 1:
                flower_length += 1
            elif days[i-1] == 0 and days[i] == 0:
                flower_length = -1
                break
        print(flower_length)
    
if __name__ == "__main__":
    program()