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>
using namespace std;
long double pi = 2.0 * acos(0.0);
mt19937 rng32(chrono::steady_clock::now().time_since_epoch().count());
long long int N;
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int a, b, c, i, j, k, first, r, x, y, z;
  long long int n, m, p, q, t;
  long long int A[1000005];
  long long int B[1000005];
  first = 0;
  r = 0;
  cin >> n;
  k = (n) / 2;
  cout << k << "\n";
  for (i = 0; i < k - 1; i++) cout << "2 ";
  cout << (2 + (n % 2));
  return 0;
}