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;
long long gcd(long long i, long long j) {
  if (i == 0) return j;
  if (j == 0) return i;
  if (i % j == 0) return j;
  return gcd(j, i % j);
}
long long a[1005];
int main() {
  long long x;
  cin >> x;
  set<pair<long long, long long> > s;
  for (long long i = 1; i <= 1500000; i++) {
    long long u = x;
    long long o = i * (i - 1LL) * (2LL * i - 1LL) / 6LL;
    long long d = i * (i - 1LL) / 2LL;
    long long e = i * i - d;
    d = d * i;
    u += d - o;
    if (u % e == 0) {
      u = u / (e);
      if (u == i) {
        s.insert(make_pair(i, i));
      }
      if (u > i) {
        s.insert(make_pair(i, u));
        s.insert(make_pair(u, i));
      }
    }
  }
  cout << s.size() << '\n';
  while (!s.empty()) {
    cout << s.begin()->first << " " << s.begin()->second << '\n';
    s.erase(s.begin());
  }
}