Problem: Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k. 

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  long n, k = 0;
  scanf("%ld", &n);
  k = n / 2;
  printf("%ld\n", k);
  for (int i = 0; i < k; i++) {
    if (i == k - 1) {
      if (n % 2 == 0)
        printf("2\n");
      else
        printf("3\n");
    } else
      printf("2 ");
  }
  getchar();
  return 0;
}