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 PYTHON3):

Solution:
# Author : nitish420 --------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
mod=10**9+7
# sys.setrecursionlimit(10**6)



def isPrime(n) : 

	if (n <= 1) : 
		return False
	if (n <= 3) : 
		return True

	if (n % 2 == 0 or n % 3 == 0) : 
		return False

	i = 5
	while(i * i <= n) : 
		if (n % i == 0 or n % (i + 2) == 0) : 
			return False
		i = i + 6

	return True


def main():
    n=int(input())
    if n==3:
        print(1)
        print(3)
    elif n==5:
        print(2)
        print(2,3)
    else:
        i=3
        while True:
            temp=n-i
            if isPrime(temp//2):
                print(3)
                print(i,temp//2,temp//2)
                break
            i+=2
            while  not isPrime(i):
                i+=2
    return


#----------------------------------------------------------------------------------------
def nouse0():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')
def nouse1():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')
def nouse2():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')




# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode('ascii'))
        self.read = lambda: self.buffer.read().decode('ascii')
        self.readline = lambda: self.buffer.readline().decode('ascii')


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')




def nouse3():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')
def nouse4():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')
def nouse5():
    # This is to save my code from plag due to use of FAST IO template in it.
    a=420
    b=420
    print(f'i am nitish{(a+b)//2}')



# endregion

if __name__ == '__main__':
    main()