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.

<image>

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 solveform(long long i) {
  long long l = 0, u = 3e9;
  long long pl, pu;
  while (u != l) {
    long long mid = (l + u) / 2;
    pl = l;
    pu = u;
    if (mid * (mid + 1) > i)
      l = mid;
    else
      u = mid;
    if (pl == l && pu == u) return -1;
  }
  if (l * (l + 1) == i) return l;
  return -1;
}
int main() {
  long long x, y, a, b, c, d;
  cin >> x;
  y = 6 * x;
  set<pair<long long, long long> > ans;
  long long n, k;
  for (long long m = 1; m < 5000000; m++) {
    if (y % (m * (m + 1)) == 0) {
      k = y / (m * (m + 1));
      if ((m + k - 1) % 3) continue;
      n = (m + k - 1) / 3;
      if (n > 0 && m <= n) {
        ans.insert(pair<long long, long long>(n, m));
        ans.insert(pair<long long, long long>(m, n));
      }
    }
  }
  for (long long g = 1; g < 5000000; g++) {
    if (y % g) continue;
    long long m;
    m = solveform(y / g);
    if (m == -1) continue;
    k = y / (m * (m + 1));
    if ((m + k - 1) % 3) continue;
    n = (m + k - 1) / 3;
    if (n > 0 && m <= n) {
      ans.insert(pair<long long, long long>(n, m));
      ans.insert(pair<long long, long long>(m, n));
    }
  }
  cout << ans.size() << endl;
  for (auto it = ans.begin(); it != ans.end(); it++) {
    cout << it->first << ' ' << it->second << endl;
  }
  return 0;
}