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.

<image>

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;
void solve() {
  long long x;
  cin >> x;
  set<pair<long long, long long>> s;
  for (long long n = 1, y, z; (y = n * (n + 1) * (2 * n + 1) / 6) <= x; ++n) {
    if ((x - y) % (z = n * (n + 1) / 2) == 0) {
      long long k = (x - y) / z;
      s.insert({n, n + k});
      s.insert({n + k, n});
    }
  }
  cout << s.size() << '\n';
  for (auto i = s.begin(); i != s.end(); ++i) {
    cout << i->first << ' ' << i->second << '\n';
  }
}
void init() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
}
int main() {
  init();
  solve();
  return 0;
}