#include <bits/stdc++.h>
using namespace std;
const int N = 1000005;
mt19937_64 rng(chrono::steady_clock().now().time_since_epoch().count());
int n, lp[N];
long long hsh[N];
map<long long, int> mp;
void out(vector<int> v) {
  for (auto x : v) lp[x] = -1;
  cout << n - v.size() << '\n';
  for (int i = 1; i <= n; ++i)
    if (lp[i] >= 0) cout << i << ' ';
  cout << '\n';
  exit(0);
}
int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin >> n;
  for (int i = 2; i <= n; ++i) {
    if (lp[i]) continue;
    lp[i] = i;
    for (int j = i; j <= n; j += i)
      if (!lp[j]) lp[j] = i;
  }
  for (int i = 2; i <= n; ++i)
    if (lp[i] == i) hsh[i] = rng();
  for (int i = 2; i <= n; ++i) hsh[i] = hsh[i / lp[i]] ^ hsh[lp[i]];
  for (int i = 2; i <= n; ++i) hsh[i] ^= hsh[i - 1];
  long long tot = 0;
  for (int i = 1; i <= n; ++i) tot ^= hsh[i];
  if (tot == 0) out({});
  for (int i = 1; i <= n; ++i)
    if (tot == hsh[i]) out({i});
  for (int i = 1; i <= n; ++i) mp[hsh[i]] = i;
  for (int i = 1; i <= n; ++i)
    if (mp.count(tot ^ hsh[i])) out({i, mp[tot ^ hsh[i]]});
  tot ^= hsh[n];
  for (int i = 1; i <= n; ++i)
    if (mp.count(tot ^ hsh[i])) out({i, mp[tot ^ hsh[i]], n});
}

### Prompt

Please formulate a CPP solution to 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 N = 1000005;
mt19937_64 rng(chrono::steady_clock().now().time_since_epoch().count());
int n, lp[N];
long long hsh[N];
map<long long, int> mp;
void out(vector<int> v) {
  for (auto x : v) lp[x] = -1;
  cout << n - v.size() << '\n';
  for (int i = 1; i <= n; ++i)
    if (lp[i] >= 0) cout << i << ' ';
  cout << '\n';
  exit(0);
}
int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin >> n;
  for (int i = 2; i <= n; ++i) {
    if (lp[i]) continue;
    lp[i] = i;
    for (int j = i; j <= n; j += i)
      if (!lp[j]) lp[j] = i;
  }
  for (int i = 2; i <= n; ++i)
    if (lp[i] == i) hsh[i] = rng();
  for (int i = 2; i <= n; ++i) hsh[i] = hsh[i / lp[i]] ^ hsh[lp[i]];
  for (int i = 2; i <= n; ++i) hsh[i] ^= hsh[i - 1];
  long long tot = 0;
  for (int i = 1; i <= n; ++i) tot ^= hsh[i];
  if (tot == 0) out({});
  for (int i = 1; i <= n; ++i)
    if (tot == hsh[i]) out({i});
  for (int i = 1; i <= n; ++i) mp[hsh[i]] = i;
  for (int i = 1; i <= n; ++i)
    if (mp.count(tot ^ hsh[i])) out({i, mp[tot ^ hsh[i]]});
  tot ^= hsh[n];
  for (int i = 1; i <= n; ++i)
    if (mp.count(tot ^ hsh[i])) out({i, mp[tot ^ hsh[i]], n});
}

```