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 a[1000005][2], k = 0, p, i, f = 0;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long double x;
  cin >> x;
  p = ceil(pow(x, 0.333333333));
  for (i = 1; i <= 2 * p + 2; ++i) {
    if ((long long)(6 * x + i * i * i - i) % (3 * i * (i + 1))) continue;
    if ((6 * x + i * i * i - i) / (3 * i * (i + 1)) < i) break;
    if ((6 * x + i * i * i - i) / (3 * i * (i + 1)) == i) {
      f = i;
      break;
    }
    a[k][0] = i;
    a[k][1] = (6 * x + i * i * i - i) / (3 * i * (i + 1));
    k++;
  }
  cout << 2 * k + !!f << endl;
  for (i = 0; i < k; ++i) cout << a[i][0] << " " << a[i][1] << endl;
  if (f != 0) cout << f << " " << f << endl;
  for (i = k - 1; i >= 0; --i) cout << a[i][1] << " " << a[i][0] << endl;
  return 0;
}