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;
const int N = 10000010;
struct node {
  long long n, m;
  node() {}
  node(long long a, long long b) {
    n = a;
    m = b;
  }
} a[N];
long long num, ans;
bool cmp(node x, node y) {
  if (x.n != y.n) return x.n < y.n;
  return x.m < y.m;
}
int main() {
  scanf("%lld", &num);
  for (long long i = 1; i <= num; i++) {
    long long p = ((i + 1) * i) / 2;
    long long q = ((i - 1) * i * (i + 1)) / 6;
    long long tmp = (num + q) / p;
    if (tmp < i) break;
    if ((num + q) % p == 0) {
      a[++ans] = node(tmp, i);
      if (tmp != i) a[++ans] = node(i, tmp);
    }
  }
  sort(a + 1, a + 1 + ans, cmp);
  printf("%lld\n", ans);
  for (int i = 1; i <= ans; i++) printf("%lld %lld\n", a[i].n, a[i].m);
  return 0;
}