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.

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, m, i, j, k, t, cnt = 0;
  vector<pair<long long, long long> > answer;
  cin >> k;
  for (t = 1; t < 10000001; t++) {
    m = t;
    j = 6ll * k + m * (m * m - 1);
    n = j / (3ll * m * (m + 1));
    if (n < m) continue;
    if (k == (m * (m + 1) * (3 * n - m + 1)) / 6) answer.push_back({m, n});
  }
  cnt = 2 * answer.size();
  for (auto x : answer)
    if (x.first == x.second) cnt--;
  cout << cnt << endl;
  for (auto x : answer) cout << x.first << " " << x.second << endl;
  reverse(answer.begin(), answer.end());
  for (auto x : answer) {
    if (x.first != x.second) cout << x.second << " " << x.first << endl;
  }
  return (0);
}