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 x, a, b;
vector<pair<long long, long long> > res;
int main() {
  cin >> x;
  long long tmp = 1;
  long long iter = 1;
  bool square = false;
  while (tmp <= x) {
    a = iter * (iter + 1) / 2;
    ;
    ;
    ;
    if ((x - tmp) % a) goto nextIter;
    b = iter + (x - tmp) / (a);
    res.push_back({iter, b});
    if (iter == b) square = true;
  nextIter:
    tmp = tmp + iter * (iter + 1) + (iter + 1);
    iter += 1;
  }
  if (square) {
    cout << res.size() * 2 - 1 << endl;
    for (int i = (0); i < ((int)res.size()); i++) {
      cout << res[i].first << " " << res[i].second << endl;
    }
    for (int i = ((int)res.size() - 2); i >= (0); i--) {
      cout << res[i].second << " " << res[i].first << endl;
    }
  } else {
    cout << res.size() * 2 << endl;
    for (int i = (0); i < ((int)res.size()); i++) {
      cout << res[i].first << " " << res[i].second << endl;
    }
    for (int i = ((int)res.size() - 1); i >= (0); i--) {
      cout << res[i].second << " " << res[i].first << endl;
    }
  }
}