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;
const long long M = 3e5 + 7, mod = 1e9 + 7;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  {
    long long x;
    cin >> x;
    vector<pair<long long, long long>> v;
    for (long long i = 1;; i++) {
      long long y = (i * (i + 1) * (2 * i + 1)) / 6;
      if (x < y) break;
      long long temp = x - y;
      long long t1 = i, t2 = (i + 1);
      if (t1 % 2 == 0)
        t1 /= 2;
      else
        t2 /= 2;
      if (temp % t1 != 0 || temp % t2 != 0) continue;
      temp /= t1;
      temp /= t2;
      long long j = i + temp;
      v.push_back({i, j});
      if (i != j) v.push_back({j, i});
    }
    cout << v.size() << '\n';
    sort(v.begin(), v.end());
    for (auto u : v) cout << u.first << " " << u.second << "\n";
  }
  return 0;
}