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 long int n, m, cnt, ans, sum, ram, a, b, c, d, e, r, k, x;
float fl, tl, sl, hl;
double gd, fd, sd;
long double l;
string s, t;
vector<string> vs;
vector<int> vi;
vector<char> vc;
vector<pair<long long int, long long int>> vp;
map<string, long long int> mp;
int main() {
  cin >> n;
  k = 0;
  if (n % 2 == 0)
    a = n / 2;
  else {
    a = (n - 3) / 2;
    k = 1;
  }
  if (k == 1)
    cout << a + 1 << endl;
  else
    cout << a << endl;
  for (int i = 0; i < a; i++) cout << 2 << " ";
  if (k == 1) cout << 3;
  return 0;
}