Chef loves bitwise operations. So, he creates the following problem but needs your help to solve it.

Chef calls a sequence of integers $A_{1}, A_{2}, \ldots, A_{N}$ tasty if it satisfies the following condition:
parity(A_{i} \& $A_{i+1}) \neq parity(A_{i} | A_{i+1})$ for 1 ≤ i < N.

Chef gives you $a sequence A_{1}, A_{2}, \ldots, A_{N}.$ You may perform the following operation on the sequence any number of times (possibly 0):
Choose 2 indices i and j (1 ≤ i, j ≤ $n ; i \neq j)$ and change A_{i} to $A_{i} \oplus A_{j}$.

Chef is asking you to make the sequence tasty using the minimum number of operations, or report that it is impossible.

As a friendly reminder,
parity(x) denotes the remainder of dividing x by 2
\& denotes the [bitwise AND operation]
| denotes the [bitwise OR operation]
$\oplus$ denotes the [bitwise XOR operation].

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

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first line of each test case contains a single integer N.
• The second line contains $N space-separated integers A_{1}, A_{2}, \ldots, A_{N}$.

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

For each test case:
- If it is impossible to convert the given sequence into a tasty sequence using the given operations, print a single line containing the integer -1.
- Otherwise, first, print a line containing a single integer M ― the minimum number of operations you have to perform.
- Then, print M lines describing these operations in the order in which you want to perform them. For each k (1 ≤ k ≤ M), the k-th of these lines should contain two space-separated integers i and j (1 ≤ i, j ≤ $n ; i \neq j)$ ― the indices on which the k-th operation is performed.

If there are multiple solutions, you may find any one of them.

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

$1 ≤ T ≤ 3 \cdot 10^{3}$
$2 ≤ N ≤ 10^{5}$
$0 ≤ A_{i} < 2^{30}$ for each valid $i$
- The sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$

------ subtasks ------

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------
2
2
0 0
3
6 16 69
----- Sample Output 1 ------
-1
1
1 3
----- explanation 1 ------
Test case $1$: It is impossible to make $A$ tasty using the given operations.

Test case $2$: We can choose $i=1$ and $j=3$ and apply the operation which converts $A$ into $[\textcolor{blue}{67},16,\textcolor{blue}{69}]$ which is tasty.

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