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 long long INF = 1000000000 + 7;
const double esp = 1e-13;
long long N, ans, ans2;
vector<pair<long long, long long> > res;
vector<pair<long long, long long> >::iterator it;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie();
  cin >> N;
  for (long long n = 1; n <= 2000000; n++)
    if (6 * N % n == 0) {
      ans = 6 * N / n - 1 + n * n;
      ans2 = 3 * n + 3;
      if (ans % ans2 == 0 && ans / ans2 > 0 && ans / ans2 >= n) {
        res.push_back(pair<long long, long long>(n, ans / ans2));
        if (n != ans / ans2)
          res.push_back(pair<long long, long long>(ans / ans2, n));
      }
    }
  sort(res.begin(), res.end());
  cout << res.size() << "\n";
  for (it = res.begin(); it != res.end(); it++)
    cout << it->first << " " << it->second << "\n";
}