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 count_squares(long long n, long long m) {
  long long squares = 0, holder;
  if (n > m) swap(n, m);
  for (long long i = n; i > 0; i--) {
    holder = m - i + 1;
    squares += holder;
    squares += holder * (n - i);
  }
  return squares;
}
int main() {
  vector<pair<long long, long long> > squares;
  long long n = 1, x, m, holder, sum = 1, num = 1;
  cin >> x;
  m = x;
  while (num <= x) {
    holder = num;
    holder = x - holder;
    if (holder % sum == 0) {
      holder = (holder / sum) + n;
      squares.push_back(make_pair(n, holder));
    }
    n++;
    num += n * n;
    sum += n;
  }
  n = squares.size() - 1;
  if (squares.back().first == squares.back().second) n--;
  for (; n > -1; n--)
    squares.push_back(make_pair(squares[n].second, squares[n].first));
  cout << squares.size() << endl;
  for (long long i = 0; i < squares.size(); i++)
    cout << squares[i].first << " " << squares[i].second << endl;
  return 0;
}