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.

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
std::vector<std::pair<long long, long long>> answer;
std::set<std::pair<long long, long long>> tmp;
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);
  std::cout.tie(NULL);
  long long x;
  std::cin >> x;
  long long X = (long long)x * (long long)6;
  for (long long n = (long long)1; n <= (long long)3e6 + 7; ++n) {
    if (X % n) continue;
    if (X % (n + (long long)1)) continue;
    long long m = n + (X / (n * (n + (long long)1))) - (long long)1;
    if (m % (long long)3) continue;
    if (m / 3 < n) continue;
    tmp.insert({n, m / 3});
    tmp.insert({m / 3, n});
  }
  for (auto it : tmp) answer.push_back(it);
  std::cout << answer.size() << "\n";
  std::sort(answer.begin(), answer.end());
  for (auto it : answer) std::cout << it.first << " " << it.second << "\n";
  return 0;
}