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 ans[105][2];
int cmp(const void *aa, const void *bb) {
  long long *a = (long long *)aa;
  long long *b = (long long *)bb;
  if (*a < *b)
    return -1;
  else
    return 1;
}
int main() {
  long long x, a, b, c, d;
  int k = 0;
  cin >> x;
  a = 1;
  d = (int)pow(3 * x, 1 / 3.0);
  while (a <= d) {
    b = a * (a - 1) * (a + 1) / 6;
    b += x;
    c = (a + 1) * a / 2;
    if (b % c == 0) {
      b /= c;
      ans[k][0] = a;
      ans[k++][1] = b;
      if (a != b) ans[k][0] = b, ans[k++][1] = a;
    }
    a++;
  }
  qsort(ans, k, sizeof(ans[0]), cmp);
  cout << k << endl;
  for (int i = 0; i < k; i++) cout << ans[i][0] << ' ' << ans[i][1] << endl;
  return 0;
}