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;
vector<long long> ansx, ansy;
long long n;
int main() {
  while (~scanf("%lld", &n)) {
    ansx.clear();
    ansy.clear();
    for (long long x = 1;; x++) {
      long long A = x * (x + 1);
      long long B = 6 * n / A;
      long long y = (B + x - 1) / 3;
      if (y < x) break;
      if ((6 * n) % A != 0) continue;
      if ((B + x - 1) % 3 != 0) continue;
      ansx.push_back(x);
      ansy.push_back(y);
    }
    int u;
    if (ansx[ansx.size() - 1] == ansy[ansx.size() - 1])
      u = 2 * ansx.size() - 1;
    else
      u = 2 * ansx.size();
    printf("%d\n", u);
    for (int i = 0; i < ansx.size(); i++) {
      printf("%lld %lld\n", ansx[i], ansy[i]);
    }
    for (int i = ansx.size() - 1; i >= 0; i--) {
      if (ansy[i] == ansx[i]) continue;
      printf("%lld %lld\n", ansy[i], ansx[i]);
    }
  }
  return 0;
}