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 fun(long long X, long long M) {
  long long t1, t2, t3;
  t1 = M * (M + 1) / 2;
  t2 = M * (M + 1) * (2 * M + 1) / 6;
  t3 = (M) * (M + 1) / 2;
  long long t4, t5, t6;
  t4 = (t2 - t3) / 2;
  t5 = X + t4;
  if (t5 % t1 == 0) {
    long long a = t5 / t1;
    if (a < M)
      return -1;
    else
      return a;
  }
  return -1;
}
int main() {
  long long X;
  scanf("%lld", &X);
  set<pair<long long, long long> > S;
  S.clear();
  long long i;
  for (i = 1; i <= 2 * cbrt(X); i++) {
    long long n = fun(X, i);
    if (n != -1) {
      S.insert(make_pair(i, n));
      S.insert(make_pair(n, i));
    }
  }
  printf("%d\n", S.size());
  for (set<pair<long long, long long> >::iterator it = S.begin(); it != S.end();
       it++) {
    printf("%lld %lld\n", (it)->first, (it)->second);
  }
}