Parity Shuffle Sorting

2000ms

262144K

Description:

You are given an array $$$a$$$ with $$$n$$$ non-negative integers. You can apply the following operation on it.

Choose two indices $$$l$$$ and $$$r$$$ ($$$1 \le l < r \le n$$$).
If $$$a_l + a_r$$$ is odd, do $$$a_r := a_l$$$. If $$$a_l + a_r$$$ is even, do $$$a_l := a_r$$$.

Find any sequence of at most $$$n$$$ operations that makes $$$a$$$ non-decreasing. It can be proven that it is always possible. Note that you do not have to minimize the number of operations.

An array $$$a_1, a_2, \ldots, a_n$$$ is non-decreasing if and only if $$$a_1 \le a_2 \le \ldots \le a_n$$$.

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases.

Each test case consists of two lines. The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 10^9$$$) — the array itself.

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$10^5$$$.

Output:

For each test case, print one integer $$$m$$$ ($$$0 \le m \le n$$$), the number of operations, in the first line.

Then print $$$m$$$ lines. Each line must contain two integers $$$l_i, r_i$$$, which are the indices you chose in the $$$i$$$-th operation ($$$1 \le l_i < r_i \le n$$$).

If there are multiple solutions, print any of them.

Sample Input:

3
2
7 8
5
1 1000000000 3 0 5
1
0

Sample Output:

Note:

In the second test case, $$$a$$$ changes like this:

Select indices $$$3$$$ and $$$4$$$. $$$a_3 + a_4 = 3$$$ is odd, so do $$$a_4 := a_3$$$. $$$a = [1, 1000000000, 3, 3, 5]$$$ now.
Select indices $$$1$$$ and $$$2$$$. $$$a_1 + a_2 = 1000000001$$$ is odd, so do $$$a_2 := a_1$$$. $$$a = [1, 1, 3, 3, 5]$$$ now, and it is non-decreasing.

In the first and third test cases, $$$a$$$ is already non-decreasing.

Informação

Provedor Codeforces

Código CF1733C