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;
void omajinai() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}
int main() {
  omajinai();
  long long m, x;
  while (cin >> x) {
    vector<pair<long long, long long>> v;
    v.push_back(make_pair(1, x));
    int count = (x == 1 ? 1 : 2);
    for (long long n = 2; 2 * n * n * n + 3 * n * n + n <= 6 * x; n++) {
      if ((6 * x + n * n * n - n) % (3 * (n * n + n)) == 0) {
        m = (6 * x + n * n * n - n) / (3 * (n * n + n));
        if (m <= 0 || m < n) break;
        v.push_back(make_pair(n, m));
        count += (m == n) ? 1 : 2;
      }
    }
    cout << count << endl;
    for (pair<long long, long long> p : v) {
      cout << p.first << " " << p.second << endl;
    }
    for (int i = v.size() - 1; i >= 0; i--) {
      if (v[i].first != v[i].second)
        cout << v[i].second << " " << v[i].first << endl;
    }
  }
  return 0;
}