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 cbrt(long long x) {
  long long y = 1;
  while ((y * y * y) < x) y++;
  return y;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << setprecision(30);
  long long x;
  cin >> x;
  x *= 6;
  long long lim = cbrt(x / 2);
  set<pair<long long, long long> > arr;
  for (long long n = 1; n <= lim; n++) {
    if (x % (n * (n + 1)) != 0) continue;
    long long y = x / (n * (n + 1));
    y += n - 1;
    if (y % 3 != 0) continue;
    long long m = y / 3;
    arr.insert({n, m});
    arr.insert({m, n});
  }
  cout << arr.size() << endl;
  for (auto x : arr) {
    cout << x.first << " " << x.second << endl;
  }
}