Chef considers an array good if it has no subarray of size less than N such that the [GCD] of all the elements of the subarray is equal to 1.

Chef has an array A of size N with him. He wants to convert it into a good array by applying a specific operation.
In one operation, Chef can choose any subarray and reverse it.

Find the minimum number of operations required to convert the array into a good array and the operations themselves. If there are multiple ways to achieve the result, print any.
If it is not possible to convert the array into a good array, print -1 instead.

Note: A subarray of an array is formed by deletion of several (possibly zero) elements from the beginning and several (possibly zero) elements from the end of the array.

------ Input Format ------

• First line will contain T, number of test cases. Then the test cases follow.
• The first line of each test case contains of single integer N denoting the length of the array.
• The second line contains $N space-separated integers A_{1}, A_{2},\ldots, A_{N}$ representing the initial array.

------ Output Format ------

• If there is a way to convert the given array into a good array, then:
• In a single line, output X denoting the minimum number of operations required.
• In the following X lines, output 2 integers - L and R denoting the left and right index of the subarray you want to reverse. Note that, (1≤ L≤ R≤ N).
• If there is no way to convert, print -1 in a single line.

------ Constraints ------

$1 ≤ T ≤ 4000$
$2 ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{18}$
- The sum of $N$ over all test cases won't exceed $10^{5}$.

----- Sample Input 1 ------
3
3
3 2 6
4
3 2 4 8
4
6 15 9 18

----- Sample Output 1 ------
1
2 3
-1
0

----- explanation 1 ------
Test case $1$: We need only one operation to convert the array into a good array. Choose $L = 2, R = 3$ and reverse the subarray $[2, 6]$ to $[6, 2]$. Thus, the final array is $[3, 6, 2]$. Note that in the final array, no subarray of length less than $N$ has gcd equal to $1$.

Test case $2$: It is not possible to convert the given array to a good array using any number of operations.

Test case $3$: The given array is already good. That is, no subarray of length less than $N$ has gcd equal to $1$. Thus, we need $0$ operations.

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