A16405. Least Product

You are given an array of integers $a_1, a_2, \dots, a_n$ . You can perform the following operation any number of times (possibly zero):

- Choose any element $a_i$ from the array and change its value to any integer between $0$ and $a_i$ (inclusive). More formally, if $a_i < 0$ , replace $a_i$ with any integer in $[a_i, 0]$ , otherwise replace $a_i$ with any integer in $[0, a_i]$ .

Let $r$ be the minimum possible product of all the $a_i$ after performing the operation any number of times.

Find the minimum number of operations required to make the product equal to $r$ . Also, print one such shortest sequence of operations. If there are multiple answers, you can print any of them.

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 500$ ) - the number of test cases. This is followed by their description.

The first line of each test case contains the a single integer $n$ ( $1 \leq n \leq 100$ ) — the length of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $-10^9 \leq a_i \leq 10^9$ ).

For each test case:

- The first line must contain the minimum number of operations $k$ ( $0 \leq k \leq n$ ).
- The $j$ -th of the next $k$ lines must contain two integers $i$ and $x$ , which represent the $j$ -th operation. That operation consists in replacing $a_i$ with $x$ .

In the first test case, we can change the value of the first integer into $0$ and the product will become $0$ , which is the minimum possible.

In the second test case, initially, the product of integers is equal to $2 \cdot 8 \cdot (-1) \cdot 3 = -48$ which is the minimum possible, so we should do nothing in this case.