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.

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  unsigned long long n;
  vector<pair<long long, long long> > res;
  cin >> n;
  long long x = 1, y;
  int flag = 0;
  while (1) {
    unsigned long long mo;
    unsigned long long son;
    mo = (6 * n) + (x * x * x) - x;
    son = 3 * (x * x + x);
    y = mo / son;
    if (y < x) break;
    if (mo % son == 0) {
      res.push_back(make_pair(x, y));
      if (x == y) {
        flag = 1;
        break;
      }
    }
    x++;
  }
  int len = res.size();
  if (flag)
    cout << len * 2 - 1 << endl;
  else
    cout << len * 2 << endl;
  int i;
  for (i = 0; i < len; i++) {
    cout << res[i].first << " " << res[i].second << endl;
  }
  i--;
  if (res[len - 1].second == res[len - 1].first) i--;
  for (; i >= 0; i--) {
    cout << res[i].second << " " << res[i].first << endl;
  }
}