You are given a positive integer $N$. Calculate the lower median of the numbers $Nmod1,Nmod2,Nmod3,\dots ,NmodN$.

The lower median of a sequence of $k$ numbers is the number at position $\lfloor \frac{k+1}{2}\rfloor$ when the sequence is sorted. For example, the lower median of the sequence $1,3,5,7$ is $3$ and the lower median of the sequence $1,1,2,3,5$ is $2$.

Input Specification

The first and only line of input contains the integer $N$.

Constraints

Subtask 1 [10%]

$1\le N\le {10}^6$

Subtask 2 [20%]

$1\le N\le {10}^9$

Subtask 3 [20%]

$1\le N\le {10}^{12}$

Subtask 4 [25%]

$1\le N\le {10}^{15}$

Subtask 5 [25%]

$1\le N\le {10}^{18}$

Output Specification

Output one number: the lower median in the problem statement.

Sample Input 1

7

Sample Output 1

1

Explanation for Sample Output 1

The sequence $7mod1,7mod2,7mod3,7mod4,7mod5,7mod6,7mod7$ is equal to $0,1,1,3,2,1,0$. When sorted, this becomes $0,0,1,1,1,2,3$. The lower median is the $4^{\text{th}}$ element of this sorted sequence, which is $1$.

Sample Input 2

50

Sample Output 2

6