Problem: Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two and 3 squares with side three. The total number of distinct squares in a 3 × 5 table is 15 + 8 + 3 = 26.

Input

The first line of the input contains a single integer x (1 ≤ x ≤ 1018) — the number of squares inside the tables Spongebob is interested in.

Output

First print a single integer k — the number of tables with exactly x distinct squares inside.

Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality — in the order of increasing m.

Examples

Input

26


Output

6
1 26
2 9
3 5
5 3
9 2
26 1


Input

2


Output

2
1 2
2 1


Input

8


Output

4
1 8
2 3
3 2
8 1

Note

In a 1 × 2 table there are 2 1 × 1 squares. So, 2 distinct squares in total.

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In a 2 × 3 table there are 6 1 × 1 squares and 2 2 × 2 squares. That is equal to 8 squares in total.

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long k;
vector<pair<long long, long long> > ans;
int main() {
  cin >> k;
  long long sum = 0, tbp = 0;
  for (long long i = 1; i <= sqrt(k); i++) {
    long long n = 1ll * i;
    if (1e18 - tbp + 1ll * i * sum < 0) {
      break;
    }
    long long cl = k + 1ll * n * sum - tbp;
    sum += 1ll * i;
    tbp += 1ll * i * i;
    if (cl % (sum) == 0) {
      long long t = cl / (sum);
      if (t < n)
        break;
      else {
        ans.push_back(make_pair(t, n));
        if (t != n) ans.push_back(make_pair(n, t));
      }
    }
  }
  cout << ans.size() << endl;
  sort(ans.begin(), ans.end());
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i].first << " " << ans[i].second << "\n";
  }
  return 0;
}