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":


 Give me 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 height(n, ls):
    high = 1
    for k in range(n-1):
        if ls[k] == 0 and ls[k+1] == 0:
            return -1
    for i in range(n):
        if ls[i] == 1:
            high += 1
    for k in range(n - 1):
        if ls[k] == 1 and ls[k + 1] == 1:
            high = high + 5 - 1
    return high

def main():
    t = int(input())
    for i in range(t):
        n = int(input())
        ls = list(map(int, input().split()))
        print(height(n, ls))

main()