#include <bits/stdc++.h>
using namespace std;
const int c = 1000005;
int n, pr[c];
unsigned long long ert[c], xo;
void co(vector<int> sz) {
  int si = sz.size();
  cout << n - si << "\n";
  for (int i = 1; i <= n; i++) {
    bool baj = 0;
    for (auto x : sz)
      if (x == i) baj = 1;
    if (!baj) cout << i << " ";
  }
  cout << "\n";
  exit(0);
}
void solve() {
  if (!xo) co({});
  map<unsigned long long, int> m;
  for (int i = 1; i <= n; i++) {
    if (xo == ert[i]) co({i});
    m[ert[i]] = i;
  }
  for (auto x : m) {
    unsigned long long p = xo ^ x.first;
    if (m.find(p) != m.end()) {
      co({x.second, m[p]});
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  mt19937_64 rng(
      (unsigned int)chrono::steady_clock::now().time_since_epoch().count());
  cin >> n;
  for (int i = 2; i <= n; i++) {
    if (!pr[i]) {
      ert[i] = rng();
      for (int j = i; j <= n; j += i) {
        pr[j] = i;
      }
    } else
      ert[i] = ert[i / pr[i]] ^ ert[pr[i]];
  }
  for (int i = 1; i <= n; i++) {
    ert[i] ^= ert[i - 1];
    xo ^= ert[i];
  }
  solve();
  xo ^= ert[n], n--;
  solve();
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

Let's call a set of positive integers a_1, a_2, ..., a_k quadratic if the product of the factorials of its elements is a square of an integer, i. e. ∏_{i=1}^{k} a_i! = m^2, for some integer m.

You are given a positive integer n.

Your task is to find a quadratic subset of a set 1, 2, ..., n of maximum size. If there are multiple answers, print any of them.

Input

A single line contains a single integer n (1 ≤ n ≤ 10^6).

Output

In the first line, print a single integer — the size of the maximum subset. In the second line, print the subset itself in an arbitrary order.

Examples

Input


1


Output


1
1 


Input


4


Output


3
1 3 4 


Input


7


Output


4
1 4 5 6 


Input


9


Output


7
1 2 4 5 6 7 9 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int c = 1000005;
int n, pr[c];
unsigned long long ert[c], xo;
void co(vector<int> sz) {
  int si = sz.size();
  cout << n - si << "\n";
  for (int i = 1; i <= n; i++) {
    bool baj = 0;
    for (auto x : sz)
      if (x == i) baj = 1;
    if (!baj) cout << i << " ";
  }
  cout << "\n";
  exit(0);
}
void solve() {
  if (!xo) co({});
  map<unsigned long long, int> m;
  for (int i = 1; i <= n; i++) {
    if (xo == ert[i]) co({i});
    m[ert[i]] = i;
  }
  for (auto x : m) {
    unsigned long long p = xo ^ x.first;
    if (m.find(p) != m.end()) {
      co({x.second, m[p]});
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  mt19937_64 rng(
      (unsigned int)chrono::steady_clock::now().time_since_epoch().count());
  cin >> n;
  for (int i = 2; i <= n; i++) {
    if (!pr[i]) {
      ert[i] = rng();
      for (int j = i; j <= n; j += i) {
        pr[j] = i;
      }
    } else
      ert[i] = ert[i / pr[i]] ^ ert[pr[i]];
  }
  for (int i = 1; i <= n; i++) {
    ert[i] ^= ert[i - 1];
    xo ^= ert[i];
  }
  solve();
  xo ^= ert[n], n--;
  solve();
  return 0;
}

```