You and your friends are solving a puzzle called the cross$-$number puzzle. Here the task is to reach the destination by spending a minimum number of coins. You are placed initially at zero, here at th step you can move I steps either to the left or right by spending i coins. Return the minimum number of coins you need to spend to reach the destination.

Function description

Complete the solve$()$ function. This function takes the following argument and returns $1$ if the string word is valid else return $0$:

N$.$ Represents the target

Input format for custom testing

Note: Use this input format if you are testing against custom input or writing code in a language where we don't provide boilerplate code

The first line contains an integer N denoting the target.

Output format

Print the total cost to reach the destination.

Constraints

$-10<$ N $<109$

Sample input

$4$

Sample output

$6$

Explanation

Initial cost$-0$

$1.$ Move from O by $1$ step to the left to $1.$ Cost$-0-1-1$

$2.$ Move from$-1$ by $2$ steps to the right to $1.$ Cost$-1+2-3$

$3.$ Move from $1$ by $3$ steps to the right to $4.$ Cost $=3+3-6$

Therefore, retum $6.$

Note:

Your code must be able to print the sample output from the provided sample input. However, your code is run against multiple hidden test cases. Therefore, your code must pass these hidden test cases to solve the problem statement.