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;
struct Size {
  uint64_t n;
  uint64_t m;
};
bool operator==(const Size& d1, const Size& d2) {
  return (d1.n == d2.n) && (d1.m == d2.m);
}
bool operator<(const Size& d1, const Size& d2) {
  if (d1.n < d2.n) {
    return true;
  } else {
    if (d1.n == d2.n) {
      if (d1.m < d2.m) {
        return true;
      }
    }
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  vector<uint64_t> numberSums(1442250);
  uint64_t currentSum{};
  uint64_t currentNumber{};
  for (auto& numberSum : numberSums) {
    numberSum = currentSum += ++currentNumber;
  }
  uint64_t x;
  cin >> x;
  const uint64_t x3 = x * 3;
  const uint64_t maxN =
      numberSums.rend() - lower_bound(numberSums.rbegin(), numberSums.rend(), x,
                                      greater<uint64_t>());
  vector<Size> sizes;
  for (uint64_t n = 1; n <= maxN; ++n) {
    const uint64_t numberSum = numberSums[n - 1];
    if (x3 % numberSum != 0) {
      continue;
    }
    uint64_t m = x3 / numberSum + n - 1;
    if (m % 3 == 0) {
      m /= 3;
    } else {
      continue;
    }
    if (m < n) {
      continue;
    }
    if (numberSum * (3 * m - n + 1) / 3 != x) {
      continue;
    }
    sizes.push_back({n, m});
    if (n != m) {
      sizes.push_back({m, n});
    }
  }
  sort(sizes.begin(), sizes.end());
  sizes.erase(unique(sizes.begin(), sizes.end()), sizes.end());
  cout << sizes.size() << endl;
  for (const auto& size : sizes) {
    cout << size.n << ' ' << size.m << endl;
  }
}