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;
int main() {
  long long x;
  cin >> x;
  vector<pair<long long, long long> > v;
  int i;
  long long m = 1;
  v.push_back(make_pair(m, x));
  long long xsq = (long long)(2. * powl((long double)x, 1 / 3.));
  while (++m <= xsq) {
    long long a = m * (m + 1);
    if ((6LL * x) % a != 0) continue;
    a = (6LL * x) / a;
    a += m - 1LL;
    if (a % 3LL != 0) continue;
    a /= 3LL;
    if (a < m) break;
    v.push_back(make_pair(m, a));
  }
  long long ans = v.size() * 2;
  bool odd = false;
  if (v[v.size() - 1].first == v[v.size() - 1].second) {
    odd = true;
    ans--;
  }
  cout << ans << endl;
  for (i = 0; i < v.size(); i++) {
    cout << v[i].first << " " << v[i].second << endl;
  }
  ans = v.size() - 1;
  if (odd) ans--;
  for (i = ans; i >= 0; i--) {
    cout << v[i].second << " " << v[i].first << endl;
  }
  int xx;
  cin >> xx;
  return 0;
}