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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Scanner;

public class D {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long x = sc.nextLong();
        sc.close();

        ArrayList<Long> A = new ArrayList<Long>();
        ArrayList<Long> B = new ArrayList<Long>();

        for (long a = 1; a * a * a <= 3 * x; a++) {
            long n1 = 6 * x + a * a * a - a;
            long n2 = 3 * a * a + 3 * a;
            long b = n1 / n2;
            if (b < a)
                break;
            if (n1 % n2 == 0) {
                A.add(a);
                B.add(b);
            }
        }

        int n = A.size();
        boolean skip = Long.compare(A.get(n - 1), B.get(n - 1)) == 0;
        System.out.println(n + n - (skip ? 1 : 0));
        for (int i = 0; i < n; i++)
            System.out.println(A.get(i) + " " + B.get(i));
        for (int i = skip ? n - 2 : n - 1; i >= 0; i--)
            System.out.println(B.get(i) + " " + A.get(i));
    }
}