C. Challenge to the Reader
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

A mathematician from ancient times left behind a riddle for future generations. Carved into stone lies a challenge about numbers and operations : Any number can be represented using a sequence of $$$+$$$ and $$$-$$$ signs applied to the numbers 1, 2, 3, ...

You, a bright and curious mind from the future, decide to take up this challenge and makes it even more challenging.

Given an integer $$$X$$$, your task is to express it in the form $$$1 \pm 2 \pm 3 \pm 4 \pm \ldots \pm N$$$ so that the result equals $$$X$$$ and $$$N$$$ is the smallest number.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

Each testcase contains a single line of one integer $$$X$$$ ( $$$|X| \le 2 \cdot 10^5$$$ )

It is guaranteed that the sum $$$|X|$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each testcase:

First, print a line with an integer $$$N$$$.

Then print one valid expression in the format $$$1+2-3+4-5 \ldots N$$$. No spaces are allowed, and the sequence must include all numbers from $$$1$$$ to $$$N$$$.

If there are many expressions, output any of them.

Example
Input
5
0
-2
1
4
-6
Output
3
1+2-3
4
1-2+3-4
1
1
4
1+2-3+4
7
1+2+3-4+5-6-7