Root decomposition problem with large constraints

Positive integer $n$ is given. Find how many different numbers among the numbers $n\mathrm{mod}1$, $n\mathrm{mod}2$, $\dots$, $n\mathrm{mod}n$.

Input

One integer $n$ $(1\le n\le 10^{12})$.

Output

Print one number — the number of different integers among $n\mathrm{mod}1$, $n\mathrm{mod}2$, $\dots$, $n\mathrm{mod}n$.

Examples

Note

In the first example we consider only one number: $1bmod1=0$, so the answer is $1$.

In the second example we have $2\mathrm{mod}1=2\mathrm{mod}2=0$, so the answer is $1$.

In the third example we have $3\mathrm{mod}1=3\mathrm{mod}3=0$, and also $3\mathrm{mod}2=1$, just two different numbers.