CF1742D.Coprime

Given an array of $n$ positive integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 1000$ ). Find the maximum value of $i + j$ such that $a_i$ and $a_j$ are coprime, $^{\dagger}$ or $-1$ if no such $i$ , $j$ exist.

For example consider the array $[1, 3, 5, 2, 4, 7, 7]$ . The maximum value of $i + j$ that can be obtained is $5 + 7$ , since $a_5 = 4$ and $a_7 = 7$ are coprime.

$^{\dagger}$ Two integers $p$ and $q$ are coprime if the only positive integer that is a divisor of both of them is $1$ (that is, their greatest common divisor is $1$ ).

The input consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 10$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ( $2 \leq n \leq 2\cdot10^5$ ) — the length of the array.

The following line contains $n$ space-separated positive integers $a_1$ , $a_2$ ,..., $a_n$ ( $1 \leq a_i \leq 1000$ ) — the elements of the array.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot10^5$ .

For each test case, output a single integer — the maximum value of $i + j$ such that $i$ and $j$ satisfy the condition that $a_i$ and $a_j$ are coprime, or output $-1$ in case no $i$ , $j$ satisfy the condition.

For the first test case, we can choose $i = j = 3$ , with sum of indices equal to $6$ , since $1$ and $1$ are coprime.

For the second test case, we can choose $i = 7$ and $j = 5$ , with sum of indices equal to $7 + 5 = 12$ , since $7$ and $4$ are coprime.