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 int n, m, x, p, k;
set<pair<long long int, long long int> > v;
map<long long int, long long int> w;
int main() {
  ios::sync_with_stdio(false);
  cin >> x;
  for (long long int k = 1;; k++) {
    if ((6 * x - k * (k - 1) * (2 * k - 1) + 3 * k * k * (k - 1)) %
            (3 * k * (k + 1)) ==
        0) {
      m = (6 * x - k * (k - 1) * (2 * k - 1) + 3 * k * k * (k - 1)) /
          (3 * k * (k + 1));
      if (k <= m) {
        v.insert({k, m});
        v.insert({m, k});
      }
    }
    if (k * k * k >= 8 * x) break;
  }
  cout << v.size() << endl;
  for (auto i : v) cout << i.first << " " << i.second << endl;
  return 0;
}