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For positive integers $a$ and $b$, we say that a fraction $\frac{a}{b}$ is good if it is equal to $\frac{m}{m+1}$ for some positive integer $m$.

You are given an integer $N$. Find the number of pairs of integers $i, j$ such that $1 ≤ i, j ≤ N$ and the fraction $\frac{i}{i+1} \cdot \frac{j+1}{j}$ is good.

------ Input ------
The first and only line of the input contains a single integer $N$.

------ Output ------
Print a single line containing one integer ― the number of pairs of integers $i, j$ ($1 ≤ i, j ≤ N$) such that $\frac{i}{i + 1} \cdot \frac{j+1}{j}$ is good.

------ Constraints ------
$1 ≤ N ≤ 1,000,000$

------ Subtasks ------
Subtask #1 (5 points): $1 ≤ N ≤ 2,000$

Subtask #2 (10 points): $1 ≤ N ≤ 100,000$

Subtask #3 (85 points): original constraints

----- Sample Input 1 ------
5
----- Sample Output 1 ------
8
----- explanation 1 ------
The following eight pairs $(i, j)$ give good fractions: $(1,2)$, $(1,3)$, $(2,3)$, $(2,4)$, $(2,5)$, $(3,4)$, $(3,5)$ and $(4,5)$.

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