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:
#from __builtin__ import xrange


def is_simple(num):
    if num == 2:
        return True
    if num % 2 == 0:
        return False
    i = 3
    threshold = num//2
    while i <= threshold:
        if num % i == 0:
            return False
        else:
            i += 1
            threshold = num//i
    else:
        return True


def get_simple_nums(num):
    if is_simple(num):
        return [num]
    else:
        answer = []
        nearest_simple = -1
        for i in xrange(num, num//2, -1):
            if is_simple(i):
                nearest_simple = i
                break
        if nearest_simple != -1:
            answer.append(nearest_simple)
            left_num = num - nearest_simple
            # now num is even. either 2 or not simple.
            if left_num == 2:
                answer.append(left_num)
                return answer
            else:
                # from the biggest to smallest - check if it's simple
                nearest_simple_2 = -1
                for j in xrange(left_num - 2, left_num//2 - 1, -1):
                    if is_simple(j):
                        nearest_simple_2 = j
                        left_num_2 = left_num - nearest_simple_2
                        if is_simple(left_num_2):
                            answer.append(nearest_simple_2)
                            answer.append(left_num_2)
                            return answer
                if nearest_simple_2 == -1:
                    raise Exception('couldn\'t find combination')
        else:
            raise Exception('couldn\'t find combination, but should have found!')


def main():
    num = input()
    try:
        filtered_num = int(num)
    except:
        raise Exception("incorrect input")
    if filtered_num % 2 == 0:
        raise Exception("number should be odd")
    answer = get_simple_nums(filtered_num)
    print(len(answer))
    print(' '.join(str(x) for x in answer))


if __name__ == '__main__':


# import timeit
# for num in xrange(700000001, 900000001, 2):
#print('time is', timeit.timeit('get_simple_nums(436273289)', number=1, setup="from __main__ import get_simple_nums"))
    # import os
    # import psutil
    # process = psutil.Process(os.getpid())
    # print process.memory_info().rss
    main()
    # print process.memory_info().rss
    # import gc
    # gc.collect()
    # print process.memory_info().rss