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;
const int maxn = 1e5 + 20;
vector<pair<long long, long long> > ans;
int main() {
  long long x;
  cin >> x;
  for (long long i = 1;; i++) {
    long long a = i * i - (i) * (i - 1) / 2,
              b = i * i * (i - 1) / 2 - (i) * (i - 1) * (2 * i - 1) / 6;
    if (x + b <= 0) break;
    if ((x + b) % a) continue;
    long long y = (x + b) / a;
    if (y < i) break;
    ans.push_back({i, y});
    if (i != y) ans.push_back({y, i});
  }
  sort(ans.begin(), ans.end());
  cout << ans.size() << endl;
  for (auto a : ans) cout << a.first << " " << a.second << endl;
}