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 $$$a_i \lt 0$$$, 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.

Input

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 $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^9 \leq a_i \leq 10^9$$$).

Output

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 $$$x$$$.

Note

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.

Least Product

Examples