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 N = 2e6 + 7;
vector<pair<unsigned long long, unsigned long long> > v;
int main() {
  unsigned long long a;
  cin >> a;
  for (int m = 1;; m++) {
    unsigned long long num = 1ull * (m + 1) * m * (m - 1) + 6ull * a;
    unsigned long long den = 3ull * m * (m + 1);
    unsigned long long n = num / den;
    if (n < m) break;
    if (n * den == num) {
      v.push_back(make_pair(n, m));
      if (n != m) v.push_back(make_pair(m, n));
    }
  }
  sort(v.begin(), v.end());
  cout << v.size() << endl;
  for (int i = 0; i < v.size(); i++)
    cout << v[i].first << " " << v[i].second << endl;
  return 0;
}