BORDER

Interview

Time limit1sMemory limit1024 MB

Summary

Given rectangle sides a and b and strips of length k, find the minimum number of strips to cover the border when each side gets at most one piece from any cut strip.

Level: Medium4 of 10
Topics: Greedy, Math, Implementation
Solved: No attempts yet

Problem

Each of the four sides of a rectangular sheet of paper with length $a$ centimeters and width $b$ centimeters must be covered with strips of glossy paper to form a border. You have enough strips, and each strip has length $k$ centimeters. A strip may be used whole or cut into several pieces, as long as the length of every piece is an integer.

At most one piece of a cut strip may be glued onto each side of the sheet.

Write a program border that finds the minimum number of strips needed to cover the sheet.

Input

The first line of standard input contains three integers $a$ , $b$ , and $k$ , separated by a single space. $a$ is the length of the rectangular sheet, $b$ is its width, and $k$ is the length of one strip.

Output

On a single line of standard output, print one integer: the minimum number of strips needed to form the border.

Constraints

$1 \le a, b, k \le 100\,000$

Examples3

Example 1
Input
```
56 14 7
```
Expected output
```
20
```
Example 2
Input
```
33 41 8
```
Expected output
```
19
```
Example 3
Input
```
68 49 10
```
Expected output
```
24
```