Competitions

# Math problems 6-8 grade

# Root decomposition problem with large constraints

Positive integer $n$ is given. Find how many different numbers among the numbers $n \bmod 1$, $n \bmod 2$, $\ldots$, $n \bmod n$.
\InputFile
One integer $n$ $(1 \le n \le 10^{12})$.
\OutputFile
Print one number --- the number of different integers among $n \bmod 1$, $n \bmod 2$, $\ldots$, $n \bmod n$.
\Note
In the first example we consider only one number: $1 \ bmod 1 = 0$, so the answer is $1$.
In the second example we have $2 \bmod 1 = 2 \bmod 2 = 0$, so the answer is $1$.
In the third example we have $3 \bmod 1 = 3 \bmod 3 = 0$, and also $3 \bmod 2 = 1$, just two different numbers.

Input example #1

1

Output example #1

1

Input example #2

2

Output example #2

1

Input example #3

3

Output example #3

2