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 a[100005], l[100005], r[100005];
const int INF = 1e6 + 1e6 + 1e6;
vector<pair<long long, long long> > v;
int main() {
  long long x, i, tmp;
  cin >> x;
  x *= 6;
  for (i = 2; i <= INF; i++) {
    if (i * (i - 1) > x) break;
    if (x % (i * (i - 1)) != 0) continue;
    tmp = x / (i * (i - 1)) + i + 1;
    if (tmp / 3 < i) break;
    if (tmp % 3 != 0) continue;
    tmp /= 3;
    v.push_back(make_pair(i - 1, tmp - 1));
  }
  int num = (int)v.size();
  if (v[num - 1].first != v[num - 1].second)
    v.push_back(make_pair(v[num - 1].second, v[num - 1].first));
  for (int i = num - 2; i >= 0; i--)
    v.push_back(make_pair(v[i].second, v[i].first));
  cout << (int)v.size() << endl;
  for (int i = 0; i < v.size(); i++)
    printf("%I64d %I64d\n", v[i].first, v[i].second);
}