Multiplication Table

Source: CSES

Version: Phuoc Hung OJ Extended

Problem Statement

Consider an $n\times n$ multiplication table. For $1\le i,j\le n$, the value in row $i$ and column $j$ is

The integer $n$ is odd. Take all $n^2$ table values with multiplicity, sort them in non-decreasing order, and find the middle element. Its 1-based rank is

Input

One line contains odd $n$.

Output

Print the middle value.

Subtasks

• Subtask 1 — 20%: $n\le101$.
• Subtask 2 — 30%: $n\le10001$.
• Subtask 3 — 50%: $1\le n<10^6$, $n$ odd.

Examples

Input

3

Output

3

Explanation

For $n=3$ the table is

The sorted values are $1,2,2,3,3,4,6,6,9$, so the middle value is $3$.