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;
bool chmin(int& a, int b) { return b < a ? a = b, true : false; }
bool chmax(int& a, int b) { return b > a ? a = b, true : false; }
bool chmin(long long& a, long long b) { return b < a ? a = b, true : false; }
bool chmax(long long& a, long long b) { return b > a ? a = b, true : false; }
const int inf = 1e09 + 5e3;
const long long linf = 2e18 + 5e3;
const int mod = 1e9 + 7;
const int mxn = 1e5 + 30;
set<pair<long long, long long> > out;
void gen(unsigned long long x) {
  unsigned long long preva = 0, prevb = 0;
  for (unsigned long long i = 1; i <= 4e6 && i <= x; i++) {
    unsigned long long a = preva + i;
    unsigned long long b = prevb + preva;
    unsigned long long nx = x + b;
    if (nx % a == 0 && i <= nx / a) {
      out.insert({i, nx / a});
      out.insert({nx / a, i});
    }
    preva = a;
    prevb = b;
  }
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long x;
  cin >> x;
  gen(x);
  cout << out.size() << '\n';
  for (auto blah : out) cout << blah.first << ' ' << blah.second << '\n';
}