A15728. One and Two

You are given a sequence $a_1, a_2, \ldots, a_n$ . Each element of $a$ is $1$ or $2$ .

Find out if an integer $k$ exists so that the following conditions are met.

- $1 \leq k \leq n-1$ , and
- $a_1 \cdot a_2 \cdot \ldots \cdot a_k = a_{k+1} \cdot a_{k+2} \cdot \ldots \cdot a_n$ .

If there exist multiple $k$ that satisfy the given condition, print the smallest.

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 one integer $n$ ( $2 \leq n \leq 1000$ ).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 2$ ).

For each test case, if there is no such $k$ , print $-1$ .

Otherwise, print the smallest possible $k$ .

For the first test case, $k=2$ satisfies the condition since $a_1 \cdot a_2 = a_3 \cdot a_4 \cdot a_5 \cdot a_6 = 4$ . $k=3$ also satisfies the given condition, but the smallest should be printed.

For the second test case, there is no $k$ that satisfies $a_1 \cdot a_2 \cdot \ldots \cdot a_k = a_{k+1} \cdot a_{k+2} \cdot \ldots \cdot a_n$

For the third test case, $k=1$ , $2$ , and $3$ satisfy the given condition, so the answer is $1$ .