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;
long long x, y, n, m, i, res, max_n, r[1500000];
int main() {
  cin >> x;
  for (n = 1; n <= x + 1; ++n) {
    if (((2 * n * n * n) + (3 * n * n) + n) / 6 > x) {
      max_n = n;
      break;
    }
  }
  for (n = 1; n < max_n; ++n) {
    m = (6 * x + n * n * n - n) / (3 * (n * n + n));
    if (((3 * n * n * m) + (3 * m * n) - n * n * n + n) == 6 * x) {
      r[n] = m;
      if (n != m)
        res += 2;
      else
        res += 1;
    } else
      r[n] = 0;
  }
  cout << res << "\n";
  for (n = 1; n < max_n; ++n) {
    if (r[n] != 0) cout << n << " " << r[n] << "\n";
  }
  if (res > 1) {
    for (n = max_n - 1; n > 0; --n)
      if (r[n] != 0 && r[n] != n) cout << r[n] << " " << n << "\n";
  }
  return 0;
}