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;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
const ll inf = 1;
const ll mod = 1E9;
int main() {
  ios::sync_with_stdio(false);
  ll x;
  while (cin >> x) {
    vector<pll> ans;
    for (ll n = 1; n <= min(2000000LL, x); n++) {
      ll m = 6LL * x;
      m = m + (n * n * n) - n;
      if (m % (3LL * n * (n + 1LL)) == 0) {
        m /= (3LL * n * (n + 1LL));
        if (m >= n) {
          ans.push_back({n, m});
        }
      }
    }
    set<pll> ms;
    for (auto it : ans) {
      ms.insert(it);
      ms.insert({it.second, it.first});
    }
    cout << (int)ms.size() << endl;
    for (auto it : ms) {
      cout << it.first << ' ' << it.second << endl;
    }
  }
  return 0;
}