#include <bits/stdc++.h>
using namespace std;
int multiply(int x, int res[], int res_size);
long long nCr(long long n, long long r) {
  if (r > n) return 0;
  double res = 1;
  for (long long i = 1; i <= r; i++) res = (res * (n - r + i)) / i;
  return (long long)(res + 0.01);
}
void mergea(int arr[], int l, int m, int r) {
  int n1 = m - l + 1;
  int n2 = r - m;
  int L[n1], R[n2];
  for (long long int i = 0; i < n1; i++) L[i] = arr[l + i];
  for (long long int i = 0; i < n2; i++) R[i] = arr[m + 1 + i];
  int i = 0, j = 0, k = l;
  while (i < n1 && j < n2) {
    if (L[i] <= R[j]) {
      arr[k] = L[i];
      i++;
    } else {
      arr[k] = R[j];
      j++;
    }
    k++;
  }
  while (i < n1) {
    arr[k] = L[i];
    i++;
    k++;
  }
  while (j < n2) {
    arr[k] = R[j];
    j++;
    k++;
  }
}
void MergeSort(int arr[], int l, int r) {
  if (l >= r) return;
  int m = l + (r - l) / 2;
  MergeSort(arr, l, m);
  MergeSort(arr, m + 1, r);
  mergea(arr, l, m, r);
}
void bin(unsigned n) {
  unsigned i;
  for (i = 1 << 31; i > 0; i = i / 2) (n & i) ? printf("1") : printf("0");
}
int maxSubArraySum(int a[], int size) {
  int max_so_far = INT_MIN, max_ending_here = 0;
  for (int i = 0; i < size; i++) {
    max_ending_here = max_ending_here + a[i];
    if (max_so_far < max_ending_here) max_so_far = max_ending_here;
    if (max_ending_here < 0) max_ending_here = 0;
  }
  return max_so_far;
}
bool checkprime(unsigned long long N) {
  int count = 0;
  for (int i = 1; i * i <= N; ++i) {
    if (N % i == 0) {
      if (i * i == N)
        count++;
      else
        count += 2;
    }
  }
  if (count == 2)
    return true;
  else
    return false;
}
int gcd(int a, int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
int gcd_extended(int a, int b, int& x, int& y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  int x1, y1;
  int d = gcd_extended(b, a % b, x1, y1);
  x1 = y1;
  y1 = x1 - y1 * (a / b);
  return d;
}
void prime_sieve(int* p, int n) {
  int MAX = n;
  for (int i = 3; i <= MAX; i += 2) p[i] = 1;
  for (long long i = 3; i <= MAX; i += 2) {
    if (p[i] == 1) {
      for (long long j = i * i; j <= MAX; j += i) p[j] = 0;
    }
  }
  p[2] = 1;
  p[1] = p[0] = 0;
}
void decToBinary(int n) {
  vector<long long int> binary;
  int i = 0;
  while (n > 0) {
    binary.push_back(n % 2);
    n = n / 2;
  }
  for (int j = binary.size() - 1; j >= 0; j--) cout << binary[j];
}
void factorial(int n) {
  int MAX = 500;
  int res[MAX];
  res[0] = 1;
  int res_size = 1;
  for (int x = 2; x <= n; x++) res_size = multiply(x, res, res_size);
  cout << "Factorial of given number " << n << " is \n";
  for (int i = res_size - 1; i >= 0; i--) cout << res[i];
}
int multiply(int x, int res[], int res_size) {
  int carry = 0;
  for (int i = 0; i < res_size; i++) {
    int prod = res[i] * x + carry;
    res[i] = prod % 10;
    carry = prod / 10;
  }
  while (carry) {
    res[res_size] = carry % 10;
    carry = carry / 10;
    res_size++;
  }
  return res_size;
}
unsigned long int catalan_DP(unsigned int n) {
  unsigned long int catalan[n + 1];
  catalan[0] = catalan[1] = 1;
  for (int i = 2; i <= n; i++) {
    catalan[i] = 0;
    for (int j = 0; j < i; j++) catalan[i] += catalan[j] * catalan[i - j - 1];
  }
  return catalan[n];
}
long long binomial_coeff(int n, int r) {
  if (r > n - r) r = n - r;
  long long res = 1;
  for (int i = 0; i < r; i++) {
    res *= (n - i);
    res /= (i + 1);
  }
  return res;
}
unsigned long int catalan_bino(unsigned int n) {
  unsigned long int c = binomial_coeff(2 * n, n);
  return c / (n + 1);
}
bool is_mot_prime(int n) {
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) return 1;
  }
  return 0;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  if (n % 2 == 0) {
    cout << n / 2 << '\n';
    for (int i = 0; i < n / 2; i++) cout << 2 << " ";
  } else {
    cout << 1 + (n - 3) / 2 << '\n';
    for (int i = 0; i < (n - 3) / 2; i++) cout << 2 << " ";
    cout << 3;
  }
  return 0;
}

### Prompt

Create a solution in Cpp for the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int multiply(int x, int res[], int res_size);
long long nCr(long long n, long long r) {
  if (r > n) return 0;
  double res = 1;
  for (long long i = 1; i <= r; i++) res = (res * (n - r + i)) / i;
  return (long long)(res + 0.01);
}
void mergea(int arr[], int l, int m, int r) {
  int n1 = m - l + 1;
  int n2 = r - m;
  int L[n1], R[n2];
  for (long long int i = 0; i < n1; i++) L[i] = arr[l + i];
  for (long long int i = 0; i < n2; i++) R[i] = arr[m + 1 + i];
  int i = 0, j = 0, k = l;
  while (i < n1 && j < n2) {
    if (L[i] <= R[j]) {
      arr[k] = L[i];
      i++;
    } else {
      arr[k] = R[j];
      j++;
    }
    k++;
  }
  while (i < n1) {
    arr[k] = L[i];
    i++;
    k++;
  }
  while (j < n2) {
    arr[k] = R[j];
    j++;
    k++;
  }
}
void MergeSort(int arr[], int l, int r) {
  if (l >= r) return;
  int m = l + (r - l) / 2;
  MergeSort(arr, l, m);
  MergeSort(arr, m + 1, r);
  mergea(arr, l, m, r);
}
void bin(unsigned n) {
  unsigned i;
  for (i = 1 << 31; i > 0; i = i / 2) (n & i) ? printf("1") : printf("0");
}
int maxSubArraySum(int a[], int size) {
  int max_so_far = INT_MIN, max_ending_here = 0;
  for (int i = 0; i < size; i++) {
    max_ending_here = max_ending_here + a[i];
    if (max_so_far < max_ending_here) max_so_far = max_ending_here;
    if (max_ending_here < 0) max_ending_here = 0;
  }
  return max_so_far;
}
bool checkprime(unsigned long long N) {
  int count = 0;
  for (int i = 1; i * i <= N; ++i) {
    if (N % i == 0) {
      if (i * i == N)
        count++;
      else
        count += 2;
    }
  }
  if (count == 2)
    return true;
  else
    return false;
}
int gcd(int a, int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
int gcd_extended(int a, int b, int& x, int& y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  int x1, y1;
  int d = gcd_extended(b, a % b, x1, y1);
  x1 = y1;
  y1 = x1 - y1 * (a / b);
  return d;
}
void prime_sieve(int* p, int n) {
  int MAX = n;
  for (int i = 3; i <= MAX; i += 2) p[i] = 1;
  for (long long i = 3; i <= MAX; i += 2) {
    if (p[i] == 1) {
      for (long long j = i * i; j <= MAX; j += i) p[j] = 0;
    }
  }
  p[2] = 1;
  p[1] = p[0] = 0;
}
void decToBinary(int n) {
  vector<long long int> binary;
  int i = 0;
  while (n > 0) {
    binary.push_back(n % 2);
    n = n / 2;
  }
  for (int j = binary.size() - 1; j >= 0; j--) cout << binary[j];
}
void factorial(int n) {
  int MAX = 500;
  int res[MAX];
  res[0] = 1;
  int res_size = 1;
  for (int x = 2; x <= n; x++) res_size = multiply(x, res, res_size);
  cout << "Factorial of given number " << n << " is \n";
  for (int i = res_size - 1; i >= 0; i--) cout << res[i];
}
int multiply(int x, int res[], int res_size) {
  int carry = 0;
  for (int i = 0; i < res_size; i++) {
    int prod = res[i] * x + carry;
    res[i] = prod % 10;
    carry = prod / 10;
  }
  while (carry) {
    res[res_size] = carry % 10;
    carry = carry / 10;
    res_size++;
  }
  return res_size;
}
unsigned long int catalan_DP(unsigned int n) {
  unsigned long int catalan[n + 1];
  catalan[0] = catalan[1] = 1;
  for (int i = 2; i <= n; i++) {
    catalan[i] = 0;
    for (int j = 0; j < i; j++) catalan[i] += catalan[j] * catalan[i - j - 1];
  }
  return catalan[n];
}
long long binomial_coeff(int n, int r) {
  if (r > n - r) r = n - r;
  long long res = 1;
  for (int i = 0; i < r; i++) {
    res *= (n - i);
    res /= (i + 1);
  }
  return res;
}
unsigned long int catalan_bino(unsigned int n) {
  unsigned long int c = binomial_coeff(2 * n, n);
  return c / (n + 1);
}
bool is_mot_prime(int n) {
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) return 1;
  }
  return 0;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  if (n % 2 == 0) {
    cout << n / 2 << '\n';
    for (int i = 0; i < n / 2; i++) cout << 2 << " ";
  } else {
    cout << 1 + (n - 3) / 2 << '\n';
    for (int i = 0; i < (n - 3) / 2; i++) cout << 2 << " ";
    cout << 3;
  }
  return 0;
}

```