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>> tables;
  int carry = 0;
  for (long long i = 1; i <= x and x != 1; ++i) {
    long long b = (i * i + i) / 2;
    long long a = (b * (2 * i + 1)) / 3;
    if (a > x) break;
    long long rows = (x - a) / b;
    if ((x - a + b) % b == 0) {
      auto t = make_pair(i, i + rows);
      carry = carry or rows == 0;
      tables.push_back(t);
    }
  }
  if (x == 1) {
    auto t = make_pair(1, 1);
    tables.push_back(t);
    carry = 1;
  }
  cout << 2 * tables.size() - carry << endl;
  for (int i = 0; i < tables.size(); ++i) {
    auto t = tables[i];
    cout << get<0>(t) << " " << get<1>(t) << endl;
  }
  for (int i = tables.size() - 1; i >= 0; --i) {
    auto t = tables[i];
    if (get<1>(t) != get<0>(t)) cout << get<1>(t) << " " << get<0>(t) << endl;
  }
  return 0;
}