A. Life of a Flower
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$t$$$ ($$$1 \le t \le 100$$$). Description of the test cases follows.

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

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$a_i = 0$$$ 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