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 k, n, m, A, B, C, K, oddN = -1, sz, i;
  vector<long long> nn, mm;
  cin >> K;
  for (n = 1;; n++) {
    k = K;
    A = n * n;
    B = (n * n - n) / 2;
    C = B;
    if (C % 3 == 0) {
      C /= 3;
      C *= (2 * n - 1);
    } else {
      C *= (2 * n - 1) / 3;
    }
    C -= B * n;
    A -= B;
    k -= C;
    m = k / A;
    if ((k * 1.0) / (A * 1.0) < n * 1.0) break;
    if (k % A != 0) continue;
    if (n == m) {
      oddN = n;
      break;
    }
    nn.push_back(n);
    mm.push_back(m);
  }
  cout << 2 * nn.size() + (oddN == -1 ? 0 : 1) << endl;
  sz = nn.size();
  for (i = 0; i < sz; i++) cout << nn[i] << " " << mm[i] << endl;
  if (oddN != -1) cout << oddN << " " << oddN << endl;
  for (i = sz - 1; i >= 0; i--) cout << mm[i] << " " << nn[i] << endl;
  return 0;
}