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 long long mod = 1e9 + 7;
const long long modx = 998244353;
const long long Nx = 1e5 + 2;
const long long inf = (long long)(1e19 + 10LL);
void solve() {
  long long x;
  cin >> x;
  x = x * 6;
  vector<pair<long long, long long> > ans;
  for (long long n = 1; n * (n + 1) * (2 * n + 1) <= x; n++) {
    long long kya = (n * (n + 1));
    if (x % kya == 0) {
      long long div = x / kya + n - 1;
      if (div / 3 < n) break;
      if (div % 3 == 0) {
        ans.push_back({n, div / 3});
        if (3 * n != div) ans.push_back({div / 3, n});
      }
    }
  }
  sort(ans.begin(), ans.end());
  cout << (long long)(ans.size()) << endl;
  for (auto it : ans) cout << it.first << " " << it.second << endl;
}
signed main() {
  long long test = 1;
  while (test--) {
    solve();
  }
  return 0;
}