You are given a positive integer ~N~. Calculate the lower median of the numbers ~N \bmod 1, N \bmod 2, N \bmod 3, \dots, N \bmod N~.

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 ~7 \bmod 1, 7 \bmod 2, 7 \bmod 3, 7 \bmod 4, 7 \bmod 5, 7 \bmod 6, 7 \bmod 7~ 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