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;
inline long long read() {
  long long x;
  cin >> x;
  return x;
}
const int MAX_N = 1e7 + 66666;
vector<pair<long long, long long> > ans;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.precision(9);
  cout.setf(ios::fixed, ios::floatfield);
  long long x, s2 = 0;
  cin >> x;
  for (long long i = (1); i <= (MAX_N - 1); ++i) {
    long long t = i * i;
    s2 += t;
    long long a = i * (i + 1) / 2, b = x - s2 + t * (i + 1) / 2;
    if (b > 0 && (b % a) == 0) {
      long long j = b / a;
      if (j >= i) {
        ans.push_back(make_pair(i, j));
        if (j > i) ans.push_back(make_pair(j, i));
      }
    }
  }
  sort(ans.begin(), ans.end());
  int k = int(ans.size());
  cout << k << '\n';
  for (__typeof(ans.begin()) it = ans.begin(); it != ans.end(); it++)
    cout << it->first << " " << it->second << '\n';
  return 0;
}