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>
using namespace std;
unsigned long long x;
int main() {
  ios::sync_with_stdio(0);
  cin >> x;
  vector<pair<unsigned long long, unsigned long long>> ans;
  for (unsigned long long n = 1;; ++n) {
    unsigned long long le = 6 * x + n * (n * n - 1);
    unsigned long long ri = 3 * (n * n + n);
    unsigned long long m = le / ri;
    if (n > m) break;
    if (le % ri == 0) {
      ans.push_back(make_pair(n, m));
    }
  }
  int a = ans.size();
  for (int i = 0; i < (int)a; ++i)
    if (ans[i].first != ans[i].second) {
      ans.push_back(make_pair(ans[i].second, ans[i].first));
    }
  sort((ans).begin(), (ans).end());
  cout << ans.size() << '\n';
  for (auto p : ans) {
    cout << p.first << ' ' << p.second << '\n';
  }
}