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[5000010];
int main() {
  long long d = 0;
  long long s = 0, t = 0;
  long long x, m, q;
  bool flag = false;
  cin >> x;
  if (sqrt(x) > 5000000)
    m = 5000000;
  else
    m = sqrt(x);
  for (long long i = 1; i <= m; i++) {
    s += i;
    t += i * i;
    if (t > x) break;
    if ((x - t) % s == 0) {
      d++;
      a[i] = (x - t) / s + i;
      if (a[i] == i) flag = true;
    }
  }
  if (flag == false)
    cout << d * 2 << endl;
  else
    cout << 2 * d - 1 << endl;
  for (int i = 1; i <= 5000001; i++)
    if (a[i] != 0) cout << i << " " << a[i] << endl;
  for (int i = 5000001; i >= 1; i--)
    if (a[i] != 0) {
      if (flag == true)
        flag = false;
      else
        cout << a[i] << " " << i << endl;
    }
}