Packing Rectangles

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

There are $n$ identical rectangles of width $w$ and height $h$. The rectangles cannot be rotated. Their width-$w$ sides and height-$h$ sides keep their original orientation, their sides are parallel to the sides of the containing square, and rectangles may not overlap. Find the minimum integer side length $x$ of a square that can contain all $n$ rectangles.

Input

The only line contains integers $w$, $h$, and $n$.

Output

Print the minimum side length.

Subtasks

• Subtask 1 — 20%: $1\le w,h,n\le10^4$.
• Subtask 2 — 30%: $1\le w,h,n\le10^7$.
• Subtask 3 — 50%: $1\le w,h,n\le10^9$.

Examples

Input

2 3 10

Output

9

Explanation

A side of $8$ fits only $8$ rectangles, while a side of $9$ fits $12$, so the minimum is $9$.