Problem Description

Consider the following increasing sequence, $S$, of rational numbers:

$$1,\; 2,\; 2\frac{1}{2},\; 3,\; 3\frac{1}{3},\; 3\frac{2}{3} ,\; 4,\; 4\frac{1}{4},\; 4\frac{1}{2},\; 4\frac{3}{4},\; 5,\; 5\frac{1}{5},\; 5\frac{2}{5},\; 5\frac{3}{5},\; 5\frac{4}{5},\; 6,\; \ldots .$$

$S$ is composed of an infinite set of blocks, $N_1, N_2, N_3, \ldots$, where block $N_i$ is $$i,;; i+1/i,;; i+2/i,;; \ldots, ;; i+(i-1)/i .$$ So $S(1) = 1, S(2) = 2, S(3) = 2\frac{1}{2}$, etc. Write a program which takes as input an integer $n$ and outputs $S(n)$.

Input Format

Input is a single line containing an integer, $n$ ($1 \leq n \leq 4\cdot 10^9$).

Output Format

Output $S(n)$ as a single integer if the answer is a whole number. Otherwise, output the integer part, a single space and a proper fraction $a/b$ in lowest terms (i.e. $0 < a < b$ and $GCD(a,b) = 1$). See the sample outputs.

326

26

448

30 2/5

4000000000

89443 19596/89443