Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Jzzhu and Apples

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputJzzhu has picked *n* apples from his big apple tree. All the apples are numbered from 1 to *n*. Now he wants to sell them to an apple store.

Jzzhu will pack his apples into groups and then sell them. Each group must contain two apples, and the greatest common divisor of numbers of the apples in each group must be greater than 1. Of course, each apple can be part of at most one group.

Jzzhu wonders how to get the maximum possible number of groups. Can you help him?

Input

A single integer *n* (1 ≤ *n* ≤ 10^{5}), the number of the apples.

Output

The first line must contain a single integer *m*, representing the maximum number of groups he can get. Each of the next *m* lines must contain two integers — the numbers of apples in the current group.

If there are several optimal answers you can print any of them.

Examples

Input

6

Output

2

6 3

2 4

Input

9

Output

3

9 3

2 4

6 8

Input

2

Output

0

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/20/2020 16:04:21 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|