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.

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<pair<long long, long long> > res;
int main() {
  long long x;
  int ans = 0;
  scanf("%I64d", &x);
  for (int i = 1; i <= 2000000; i++) {
    long long tmp = 2ll * i * i * i + 3 * i * i + i;
    if (tmp > 6ll * x) continue;
    if ((6ll * x) % (1ll * i * i + i) != 0) continue;
    tmp = (6ll * x) / (1ll * i * i + i) + i - 1;
    if (tmp % 3 != 0) continue;
    tmp = tmp / 3;
    if (tmp >= i) {
      ans++;
      res.push_back(make_pair(i, tmp));
      if (i == tmp) continue;
      ans++;
      res.push_back(make_pair(tmp, i));
    }
  }
  printf("%d\n", ans);
  sort(res.begin(), res.end());
  for (int i = 0; i < ans; i++)
    printf("%I64d %I64d\n", res[i].first, res[i].second);
}