Let's call an array $b$ beautiful if it consists of at least two elements and there exists a position $i$ such that $|b_i - b_{i + 1}| \le 1$ (where $|x|$ is the absolute value of $x$).

You are given an array $a$, and as long as it consists of at least two elements, you can perform the following operation:

1. Choose two adjacent positions $i$ and $i + 1$ in the array $a$.
2. Choose an integer $x$ such that $\min(a_i, a_{i + 1}) \le x \le \max(a_i, a_{i + 1})$.
3. Remove the numbers $a_i$ and $a_{i + 1}$ from the array, and insert the number $x$ in their place. Obviously, the size of the array will decrease by $1$.

Calculate the minimum number of operations required to make the array beautiful, or report that it is impossible.

Input

The first line contains one integer $t$ ($1 \le t \le 200$) — the number of test cases.

The first line of each test case contains one integer $n$ ($2 \le n \le 1000$) — the size of the array $a$.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the array $a$ itself.

Output

For each test case, output one integer — the minimum number of operations needed to make the array $a$ beautiful, or $-1$ if it is impossible to make it beautiful.

Note

In the first test case, the given array is already beautiful, as $|a_2 - a_3| = |3 - 3| = 0$.

In the second test case, it is impossible to make the array beautiful, as applying the operation would reduce its size to less than two.

In the third test case, you can, for example, choose $a_1$ and $a_2$ and replace them with the number $2$. The resulting array $[2, 3, 7]$ is beautiful.

In the fourth test case, you can, for example, choose $a_2$ and $a_3$ and replace them with the number $3$. The resulting array $[1, 3, 2]$ is beautiful.

Samples

4
4
1 3 3 7
2
6 9
4
3 1 3 7
4
1 3 5 2

0
-1
1
1