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>
int main() {
  std::ios::sync_with_stdio(false);
  long long n, m;
  unsigned long long x;
  std::cin >> x;
  unsigned long long k;
  std::vector<std::pair<long long, long long> > answ;
  bool has_eq = false;
  for (n = 1; n <= 1500000; n++) {
    long long c = n * (n + 1);
    m = (((x * 6) / c) + n - 1) / 3;
    k = n * (n + 1) * (3 * m - n + 1) / 6;
    if (k == x && n <= m) {
      if (n == m) has_eq = true;
      answ.push_back(std::make_pair(n, m));
    }
    if (n >= m) break;
  }
  std::cout << answ.size() * 2 + (has_eq ? (-1) : 0) << std::endl;
  for (int i = 0; i < answ.size(); i++) {
    std::cout << answ[i].first << " " << answ[i].second << std::endl;
  }
  for (int i = answ.size() - 1; i >= 0; i--) {
    if (answ[i].first != answ[i].second)
      std::cout << answ[i].second << " " << answ[i].first << std::endl;
  }
  return 0;
}