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;
const int mod = 1000000007;
const double eps = 1e-7;
vector<pair<long long, long long> > ans;
vector<pair<long long, long long> > ans2;
int a[111111];
int main() {
  long long lol;
  cin >> lol;
  for (int x = 1; x < 2000000; x++) {
    long long cur = lol;
    cur *= 3ll;
    long long let = 1ll * x * (x + 1) / 2ll;
    if (cur % let == 0) {
      cur /= let;
      cur -= 1 + 2ll * x;
      if (cur % 3 == 0 && cur >= 0) {
        cur /= 3;
        long long y = cur;
        y += x;
        ans.push_back(make_pair(y, x));
        if (x != y) ans2.push_back(make_pair(x, y));
      }
    }
  }
  cout << ans.size() + ans2.size() << endl;
  for (int i = 0; i < ans2.size(); i++) {
    cout << ans2[i].first << " " << ans2[i].second << endl;
  }
  for (int i = ans.size() - 1; i >= 0; i--) {
    cout << ans[i].first << " " << ans[i].second << endl;
  }
  return 0;
}