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.*;
import java.io.*;
public class d 
{
	public static void main(String[] arg)
	{
		new d();
	}
	public d()
	{
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		long c = in.nextLong();
		ArrayList<Pair> list = new ArrayList<Pair>();
		for(int i = 1; i < 10_000_000; i++)
		{
			long a = i;
			long num = c + a*a*(a+1)/2 - a*(a+1)*(2*a+1)/6;
			long den = a*(a+1)-a*(a+1)/2;
			if(num % den == 0)
			{
				long b = num/den;
				if(a <= b)
					list.add(new Pair(a, b));
			}
		}
		out.println(2*list.size() - (list.get(list.size()-1).a == list.get(list.size()-1).b ? 1 : 0));
		for(Pair p : list) out.println(p.a + " " + p.b);
		for(int i = list.size()-1-(list.get(list.size()-1).a == list.get(list.size()-1).b ? 1 : 0); i >= 0; i--)
		{
			
			out.println(list.get(i).b + " " + list.get(i).a);
		}
		in.close(); out.close();
	}
	class Pair
	{
		long a, b;
		public Pair(long aa, long bb)
		{
			a = aa;
			b = bb;
		}
	}
}