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;
const int X = 100000 + 5;
void MAIN() {
  long long x, n, m;
  cin >> x;
  vector<long long> a, b;
  for (long long m = 1; m <= x; m++) {
    long double z = m - 1;
    z += 6 * x / (m * (m + 1));
    z /= 3;
    n = z;
    if (n < m) {
      break;
    }
    for (n = z - 2; n <= z + 2; n++) {
      if ((n * 3LL - m + 1) * m * (m + 1) == 6 * x) {
        a.push_back(m);
        b.push_back(n);
      }
    }
  }
  int k = (int)a.size() - 1;
  if (a[k] == b[k]) k--;
  for (int i = k; i >= 0; i--) {
    a.push_back(b[i]);
    b.push_back(a[i]);
  }
  cout << (int)a.size() << '\n';
  for (int i = 0; i < (int)a.size(); i++) {
    cout << a[i] << " " << b[i] << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(12);
  MAIN();
  return 0;
}