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;
set<pair<long long, long long> > s;
int main() {
  ios_base::sync_with_stdio(false);
  long long p;
  cin >> p;
  for (long long j = 2; j <= 1442249; j++) {
    long long i = j - 1;
    long long x = (i * i) + (3 * i);
    x = x / 2;
    x = x + 1;
    long long y = (i * i) + (3 * i) + 2;
    y = y / 2;
    y = y * i;
    y = y / 3;
    long long z = p + y;
    if (z % x == 0) {
      if (z / x >= j) {
        s.insert(make_pair(j, z / x));
        s.insert(make_pair(z / x, j));
      }
    }
  }
  s.insert(make_pair(1, p));
  s.insert(make_pair(p, 1));
  cout << s.size() << "\n";
  set<pair<long long, long long> >::iterator it;
  for (it = s.begin(); it != s.end(); it++) {
    cout << it->first << " " << it->second << "\n";
  }
}