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;
int main() {
  std::ios::sync_with_stdio(false);
  {
    int a, b, c;
    long long m, n;
    cin >> (n);
    set<pair<long long, long long> > ans;
    ans.insert(make_pair(1, n));
    ans.insert(make_pair(n, 1));
    double k = ceil(pow(n, 1.0 / 3));
    long long k2 = 2 * k;
    for (long long i = 2; i <= k2; i++) {
      double intm = ((n * 6.0) / (i * (i + 1.0))) + i - 1.0;
      m = intm / 3;
      if (i <= m && (n == ((i * (i + 1) * (3 * m - i + 1)) / 6))) {
        ans.insert(make_pair(i, m));
        ans.insert(make_pair(m, i));
      }
    }
    cout << ans.size() << "\n";
    set<pair<long long, long long> >::iterator it = ans.begin();
    for (; it != ans.end(); it++)
      cout << it->first << " " << it->second << "\n";
  }
}