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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long x;
  cin >> x;
  x *= 6;
  long long ans = 0;
  vector<pair<long long, long long> > answers;
  for (long long m = 1; m * (m + 1) * (2 * m + 1) <= x; ++m) {
    long long d = m * (m + 1);
    if (x % d != 0) {
      continue;
    }
    long long xx = x / d;
    xx += (m - 1);
    if ((xx < 3 * m) || (xx % 3 != 0)) {
      continue;
    }
    long long n = xx / 3;
    answers.push_back(make_pair(m, n));
    if (n != m) answers.push_back(make_pair(n, m));
  }
  sort(answers.begin(), answers.end());
  cout << answers.size() << "\n";
  for (int i = 0; i < answers.size(); ++i) {
    cout << answers[i].first << " " << answers[i].second << "\n";
  }
  return 14 / 88;
}