A. Lover's Gift
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Cookie Sigma is quite the romantic and wishes to give an amazing gift to his lover on Valentine's Day — a permutation of size $$$n$$$ $$$(2 \leq n \leq 10^5)$$$.

Let the beauty of a permutation of size $$$n$$$ be

$$$$$$ \min \limits_{1 \leq i \lt n} |a_i - a_{i+1}| $$$$$$

Cookie only wants to give a gift of the highest beauty possible to his lover. Help Cookie Sigma determine the maximum beauty of a permutation of size $$$n$$$ he could give to his lover.

$$$^\dagger$$$ A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from 1 to $$$n$$$ in any order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation (the number $$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$, but the array contains a $$$4$$$)

Input

The first line contains one integer, $$$n$$$ $$$(2 \leq n \leq 10^5)$$$, the size of the permutation Cookie will give.

Output

Output one number, the maximum beauty of a permutation of size $$$n$$$ Cookie Sigma can give.

Examples
Input
2
Output
1
Input
4
Output
2
Note

In the first test case, there are only two possible permutations Cookie Sigma can make of size $$$2$$$: $$$[1,2]$$$ and $$$[2,1]$$$. In both of these, $$$|1-2| = |2-1| = 1$$$, thus $$$1$$$ is the maximum beauty of a permutation we can construct.

In the second test case, one permutation of size 4 and beauty 2 is $$$[3,1,4,2]$$$. $$$|3-1| = 2$$$, $$$|1-4| = 3$$$, $$$|4-2| = 2$$$. The minimum of these is $$$2$$$, thus this is the beauty of our permutation. It can be proven that for $$$n=4$$$ there is no permutation of beauty $$$ \gt 2$$$.