Jzzhu 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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'apples=int(input())\n\nif apples<=3:\n\n    print(0)\n\nelse:\n\n    halfpr=int(apples/2)\n\n    def primes(n):\n\n        isPrime = [True for i in range(n + 1)]\n\n        isPrime[0] = isPrime[1] = False\n\n        \n\n        idx = 2\n\n        while idx * idx <= n:\n\n            if isPrime[idx]:\n\n                for i in range(idx * 2, n, idx):\n\n                    isPrime[i] = False\n\n            idx += 1\n\n        \n\n        return isPrime\n\n\n\n    primeslist=primes(halfpr)\n\n    totallist=[False]*(apples+1)\n\n    applepairs=[]\n\n    for prime in range(len(primeslist)-1, 1, -1):\n\n        if primeslist[prime]:\n\n            numprimes=int(apples/prime)\n\n            primesx=[int(i*prime) for i in range(1, numprimes+1) if not totallist[i*prime]]\n\n            if len(primesx)%2==1:\n\n                primesx.remove(2*prime)\n\n            for pr in primesx:\n\n                 applepairs.append(pr)\n\n                 totallist[pr]=True\n\n    print(int(len(applepairs)/2))\n\n    for t in range(int(len(applepairs)/2)):\n\n        print(applepairs[2*t], applepairs[2*t+1])\n\n        \n\n\n\n\n\n# Made By Mostafa_Khaled\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13381