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 n, m, x;
vector<pair<long long, long long> > ans;
set<pair<long long, long long> > s;
long long getm(long long t) {}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> x;
  x = x;
  for (long long i = 1; i <= 2000003; i++) {
    long long temp = 6 * x;
    if (temp % i == 0 && temp % (i + 1) == 0) {
      temp /= i;
      temp /= (i + 1);
      if (temp <= 0) continue;
      if (temp < 2 * i + 1) continue;
      temp += i;
      temp--;
      if (temp <= 0) continue;
      if (temp % 3 == 0) {
        ans.push_back({i, temp / 3});
      }
    }
  }
  for (auto t : ans) {
    s.insert({t.first, t.second});
    s.insert({t.second, t.first});
  }
  cout << s.size() << endl;
  for (auto t : s) {
    cout << t.first << " " << t.second << endl;
  }
  return 0;
}