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 maxn = 2e6;
long long x, n, m;
long long nn[maxn], mm[maxn];
int cnt;
int main() {
  scanf("%lld", &x);
  for (n = 1; n <= 5000000; n++) {
    long long up = 6ll * x + n * n * n - n;
    long long down = 3ll * n * n + 3ll * n;
    if (up % down) continue;
    m = up / down;
    if (n > m) break;
    nn[cnt] = n;
    mm[cnt++] = m;
  }
  if (nn[cnt - 1] == mm[cnt - 1]) {
    printf("%d\n", cnt * 2 - 1);
    for (int i = 0; i < cnt; i++) printf("%lld %lld\n", nn[i], mm[i]);
    for (int i = cnt - 2; i >= 0; i--) printf("%lld %lld\n", mm[i], nn[i]);
  } else {
    printf("%d\n", cnt * 2);
    for (int i = 0; i < cnt; i++) printf("%lld %lld\n", nn[i], mm[i]);
    for (int i = cnt - 1; i >= 0; i--) printf("%lld %lld\n", mm[i], nn[i]);
  }
}