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;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long xx;
  cin >> xx;
  if (xx == 1) {
    cout << 1 << '\n';
    cout << 1 << " " << 1 << '\n';
    return 0;
  }
  __int128_t x = xx;
  x *= 6;
  vector<pair<long long, long long>> ans;
  for (__int128_t m = 1; m <= (__int128_t)10000000; m++) {
    __int128_t y = x + m * m * m - m;
    __int128_t z = m * m * 3 + m * 3;
    if (y <= 0) break;
    if (y % z != 0) continue;
    __int128_t n = y / z;
    if (m > n) break;
    ans.emplace_back((long long)m, (long long)n);
  }
  int n = ans.size();
  for (int i = n - 1; i >= 0; i--) {
    if (ans[i].first == ans[i].second) continue;
    ans.emplace_back(ans[i].second, ans[i].first);
  }
  cout << ans.size() << '\n';
  for (auto& p : ans) cout << p.first << " " << p.second << '\n';
  return 0;
}