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>
#pragma comment(linker, "/STACK:16777216")
using namespace std;
const int MAXN = 100000;
int DP[MAXN], MIN[MAXN], MAX[MAXN];
map<int, int> MAP;
int main() {
  long long x;
  cin >> x;
  vector<std::pair<long long, long long> > ans;
  for (long long n = 1; n <= 10000000; n++) {
    long long tmp = x;
    tmp += n * (n - 1) * n / 2;
    n--;
    tmp -= n * (n + 1) * (2 * n + 1) / 6;
    n++;
    long long Left = n * n - (n - 1) * n / 2;
    if (tmp % Left == 0) {
      long long m = tmp / Left;
      if (n < m) {
        ans.push_back(make_pair(n, m));
        ans.push_back(make_pair(m, n));
      } else if (n == m) {
        ans.push_back(make_pair(m, n));
      }
    }
  }
  sort((ans).begin(), (ans).end());
  cout << ans.size() << endl;
  for (long long i = 0; i < (long long)ans.size(); i++)
    cout << ans[i].first << " " << ans[i].second << "\n";
  return 0;
}