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.*;
public class CF599D {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long c = in.nextLong();
		long b = (long)Math.cbrt(c)*2l + 1l;
		ArrayList<Answer> ans = new ArrayList<Answer>();
		for(long n = 1; n < b; n ++)
		{
			long mn = ((n - 1)*n*(2*n-1)-3*n*n*(n-1)-6*c);
			long md = 3*n*(n-1)-6*n*n;
			if(mn%md != 0)
				continue;
			long m = mn/md;
			if(m<n)
				break;
			ans.add(new Answer(n, m));
			if(n!=m)
				ans.add(new Answer(m, n));
		}
			
		Collections.sort(ans);
		System.out.println(ans.size());
		for(int i = 0; i < ans.size(); i ++)
			System.out.println(ans.get(i));
	}
	static class Answer implements Comparable<Answer>
	{
		long n;
		long m;
		
		Answer(long nn, long mm)
		{
			n = nn;
			m = mm;
		}
		public int compareTo(Answer a) 
		{
			return Long.signum(n - a.n);
		}
		
		public String toString()
		{
			return n + " " + m;
		}
	}
}