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;
const int mod = 1e9 + 7;
const int inf = 0x3c3c3c3c;
const long long infl = 0x3c3c3c3c3c3c3c3c;
long long x;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL);
  cin >> x;
  vector<pair<long long, long long> > ans;
  for (long long n = 1;; n++) {
    long long up = 6 * x + n * n * n - n;
    long long down = 3 * n * n + 3 * n;
    if (down > up) break;
    if (n > up / down) break;
    if (up % down == 0) {
      ans.push_back({n, up / down});
      if (n != up / down) ans.push_back({up / down, n});
    }
  }
  sort((ans).begin(), (ans).end());
  cout << ((int)(ans).size()) << '\n';
  for (auto p : ans) {
    cout << p.first << ' ' << p.second << '\n';
  }
  return 0;
}