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;
unsigned long long k;
unsigned long long ans[100010][2];
int main(int argc, char const *argv[]) {
  int cnt = 0;
  scanf("%lld", &k);
  for (unsigned long long i = 1; i * (i + 1) * (2 * i + 1) / 6 <= k; i++)
    if (k * 6 % (i * (i + 1)) == 0) {
      unsigned long long j = k * 6 / i / (i + 1) - 1 + i;
      if (j % 3 == 0)
        j = j / 3;
      else
        continue;
      if (i <= j) {
        cnt++;
        ans[cnt][0] = i;
        ans[cnt][1] = j;
      } else
        break;
    }
  int aa = cnt * 2;
  if (ans[cnt][0] == ans[cnt][1]) aa--;
  printf("%d\n", aa);
  for (int i = 1; i <= cnt; i++) printf("%lld %lld\n", ans[i][0], ans[i][1]);
  if (ans[cnt][0] == ans[cnt][1]) cnt--;
  for (int i = cnt; i > 0; i--) printf("%lld %lld\n", ans[i][1], ans[i][0]);
  return 0;
}