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 = '"""\nCodeforces Round 257 Div 1 Problem C\n\nAuthor  : chaotic_iak\nLanguage: Python 3.3.4\n"""\n\ndef read(mode=2):\n    # 0: String\n    # 1: List of strings\n    # 2: List of integers\n    inputs = input().strip()\n    if mode == 0:\n        return inputs\n    if mode == 1:\n        return inputs.split()\n    if mode == 2:\n        return [int(x) for x in inputs.split()]\n\ndef write(s="\\n"):\n    if isinstance(s, list): s = " ".join(map(str,s))\n    s = str(s)\n    print(s, end="")\n\n################################################### SOLUTION\n\n# croft algorithm to generate primes\n# from pyprimes library, not built-in, just google it\nfrom itertools import compress\nimport itertools\ndef croft():\n    """Yield prime integers using the Croft Spiral sieve.\n\n    This is a variant of wheel factorisation modulo 30.\n    """\n    # Implementation is based on erat3 from here:\n    #   http://stackoverflow.com/q/2211990\n    # and this website:\n    #   http://www.primesdemystified.com/\n    # Memory usage increases roughly linearly with the number of primes seen.\n    # dict ``roots`` stores an entry x:p for every prime p.\n    for p in (2, 3, 5):\n        yield p\n    roots = {9: 3, 25: 5}  # Map d**2 -> d.\n    primeroots = frozenset((1, 7, 11, 13, 17, 19, 23, 29))\n    selectors = (1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0)\n    for q in compress(\n            # Iterate over prime candidates 7, 9, 11, 13, ...\n            itertools.islice(itertools.count(7), 0, None, 2),\n            # Mask out those that can\'t possibly be prime.\n            itertools.cycle(selectors)\n            ):\n        # Using dict membership testing instead of pop gives a\n        # 5-10% speedup over the first three million primes.\n        if q in roots:\n            p = roots[q]\n            del roots[q]\n            x = q + 2*p\n            while x in roots or (x % 30) not in primeroots:\n                x += 2*p\n            roots[x] = p\n        else:\n            roots[q*q] = q\n            yield q\n\nn, = read()\ncr = croft()\nprimes = []\nfor i in cr:\n    if i < n:\n        primes.append(i)\n    else:\n        break\nprimes.reverse()\n\nused = [0] * (n+1)\nres = []\nfor p in primes:\n    k = n//p\n    tmp = []\n    while k:\n        if not used[k*p]:\n            tmp.append(k*p)\n            used[k*p] = 1\n        if len(tmp) == 2:\n            res.append(tmp)\n            tmp = []\n        k -= 1\n    if tmp == [p] and p > 2 and p*2 <= n and len(res) and res[-1][1] == p*2:\n        res[-1][1] = p\n        used[p*2] = 0\n        used[p] = 1\n\nprint(len(res))\nfor i in res:\n    print(" ".join(map(str, i)))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14301