Root decomposition problem with large constraints

Input

One integer $n$ $(1 \leq n \leq 1 0^{12})$ (1 \le n \le 10^{12}).

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

Example 1

Loading

Example 2

Loading

Example 3

Loading

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

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

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