#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 6;
int prime[maxn], np[maxn], mp[maxn], tot = 0;
void init(int n) {
  np[1] = 1;
  for (int i = 2; i <= n; ++i) {
    if (!np[i]) prime[++tot] = i, mp[i] = i;
    for (int j = 1; j <= tot; ++j) {
      if (i * prime[j] > n) break;
      np[i * prime[j]] = 1;
      mp[i * prime[j]] = prime[j];
      if (i % prime[j] == 0) break;
    }
  }
}
mt19937_64 mrand(chrono::steady_clock::now().time_since_epoch().count());
vector<int> solve(int n) {
  vector<unsigned long long> magic(n + 1);
  for (int i = 2; i <= n; ++i) {
    if (!np[i])
      magic[i] = mrand();
    else
      magic[i] = magic[i / mp[i]] ^ magic[mp[i]];
  }
  vector<unsigned long long> a(n + 1);
  for (int i = 2; i <= n; ++i) {
    a[i] = a[i - 1] ^ magic[i];
  }
  unsigned long long s = 0;
  for (int i = 2; i <= n; ++i) s ^= a[i];
  for (int i = 0; i <= n; ++i) {
    if (s == a[i]) {
      vector<int> ret;
      for (int j = 1; j <= n; ++j) {
        if (i != j) ret.push_back(j);
      }
      return ret;
    }
  }
  vector<pair<unsigned long long, int>> ps;
  for (int i = 2; i <= n; ++i) {
    ps.push_back({a[i], i});
  }
  sort(ps.begin(), ps.end());
  for (int i = 2; i <= n; ++i) {
    unsigned long long target = s ^ a[i];
    auto it = lower_bound(ps.begin(), ps.end(), make_pair(target, -1));
    if (it != ps.end()) {
      if (it->first == target && it->second != i) {
        vector<int> ret;
        for (int j = 1; j <= n; ++j) {
          if (i != j && it->second != j) ret.push_back(j);
        }
        return ret;
      }
      if (next(it) != ps.end() && next(it)->first == target) {
        vector<int> ret;
        for (int j = 1; j <= n; ++j) {
          if (i != j && next(it)->second != j) ret.push_back(j);
        }
        return ret;
      }
    }
  }
  return solve(n - 1);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  init(n);
  auto ans = solve(n);
  cout << ans.size() << '\n';
  for (int i : ans) {
    cout << i << " ";
  }
  cout << '\n';
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 maxn = 1e6 + 6;
int prime[maxn], np[maxn], mp[maxn], tot = 0;
void init(int n) {
  np[1] = 1;
  for (int i = 2; i <= n; ++i) {
    if (!np[i]) prime[++tot] = i, mp[i] = i;
    for (int j = 1; j <= tot; ++j) {
      if (i * prime[j] > n) break;
      np[i * prime[j]] = 1;
      mp[i * prime[j]] = prime[j];
      if (i % prime[j] == 0) break;
    }
  }
}
mt19937_64 mrand(chrono::steady_clock::now().time_since_epoch().count());
vector<int> solve(int n) {
  vector<unsigned long long> magic(n + 1);
  for (int i = 2; i <= n; ++i) {
    if (!np[i])
      magic[i] = mrand();
    else
      magic[i] = magic[i / mp[i]] ^ magic[mp[i]];
  }
  vector<unsigned long long> a(n + 1);
  for (int i = 2; i <= n; ++i) {
    a[i] = a[i - 1] ^ magic[i];
  }
  unsigned long long s = 0;
  for (int i = 2; i <= n; ++i) s ^= a[i];
  for (int i = 0; i <= n; ++i) {
    if (s == a[i]) {
      vector<int> ret;
      for (int j = 1; j <= n; ++j) {
        if (i != j) ret.push_back(j);
      }
      return ret;
    }
  }
  vector<pair<unsigned long long, int>> ps;
  for (int i = 2; i <= n; ++i) {
    ps.push_back({a[i], i});
  }
  sort(ps.begin(), ps.end());
  for (int i = 2; i <= n; ++i) {
    unsigned long long target = s ^ a[i];
    auto it = lower_bound(ps.begin(), ps.end(), make_pair(target, -1));
    if (it != ps.end()) {
      if (it->first == target && it->second != i) {
        vector<int> ret;
        for (int j = 1; j <= n; ++j) {
          if (i != j && it->second != j) ret.push_back(j);
        }
        return ret;
      }
      if (next(it) != ps.end() && next(it)->first == target) {
        vector<int> ret;
        for (int j = 1; j <= n; ++j) {
          if (i != j && next(it)->second != j) ret.push_back(j);
        }
        return ret;
      }
    }
  }
  return solve(n - 1);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  init(n);
  auto ans = solve(n);
  cout << ans.size() << '\n';
  for (int i : ans) {
    cout << i << " ";
  }
  cout << '\n';
}

```