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;
int main() {
  ios_base::sync_with_stdio(0);
  long long x;
  cin >> x;
  vector<pair<long long, long long> > v;
  long long s = 0, t = 0;
  for (long long i = 1; i <= x; ++i) {
    s += i;
    if (x + t < s) break;
    if ((x + t) % s == 0) {
      if ((x + t) / s < i) break;
      v.push_back(make_pair(i, (x + t) / s));
    }
    t = s * i + s;
    t -= (2ll * i * i * i + 3ll * i * i + i) / 6;
  }
  int n = 2 * v.size();
  n -= (v.back().first == v.back().second);
  cout << n << "\n";
  for (int i = 0; i < (n + 1) / 2; ++i)
    cout << v[i].first << " " << v[i].second << "\n";
  if (n & 1) v.pop_back();
  reverse(v.begin(), v.end());
  n /= 2;
  for (int i = 0; i < n; ++i) cout << v[i].second << " " << v[i].first << "\n";
  return 0;
}