Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in PYTHON):

Solution:
### TEMPLATE BEGIN

from collections import defaultdict

def read_int():
    return int(raw_input())

def read_ints():
    return (int(x) for x in raw_input().split())

def read_int_list():
    return [int(x) for x in raw_input().split()]

def read_float():
    return float(raw_input())

def read_floats():
    return (float(x) for x in raw_input().split())

def read_float_list():
    return [float(x) for x in raw_input().split()]

def read_list():
    return [x for x in raw_input().split()]

### TEMPLATE END

def prime(n):
    i = 3
    while i * i <= n:
        if n%i == 0:
            return False
        i += 2
    return True

def solve():
    n = read_int()
    if n < 9:
        print 1
        print n
        return
    ret = []
    a = 3
    while not ret:
        if not prime(a):
            a += 2
            continue
        b = a
        while not ret and b <= n - a - b:
            c = n - a - b
            if prime(b) and prime(c):
                ret.append(str(a))
                ret.append(str(b))
                ret.append(str(c))
            b += 2
    print len(ret)
    print " ".join(ret)

qq = 1
# qq = 2**30
# qq = read_int()
for _________ in xrange(qq):
    solve()