human
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 program to determine what happened with his flower in the end?
assistant
#Here is Python program to determine what happened with his flower in the end.

FAST_IO = 0
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
 
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())
rrmm = lambda n: [rrm() for _ in xrange(n)]
 
####
 
def solve(N, A):
    flower = 1
    for i in xrange(N):
        if i == 0:
            if A[i]:
                flower += 1
        else:
            if A[i]==A[i-1]:
                if A[i]:
                    flower += 5
                else:
                    return -1
            elif A[i]:
                flower += 1
    return flower

T = rri()
for _ in xrange(T):
    N = rri()
    A = rrm()
    ans = solve(N, A)
    print ans