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.*;
/*
 1000000000000000000
 999999999999999999
 999999999999999989
 973067066176384512
 999999853754584125
 
 */
public class D {
	
	public static void main(String[] args) {		
		
		Scanner qwe = new Scanner(System.in);
		
		long x = qwe.nextLong();
		
		TreeSet<sol> ans = new TreeSet<sol>();
		for(long a = 1; a <= 1442249; a++){
			
			//System.out.println("at: " + a);
			
			long add = (a-1)*(a)*(a+1)/6;
			long div = (a)*(a+1)/2;
			
			
			if((x+add) % div == 0){
				long other = (x+add)/div;
				
				if(other < a) continue;
				
				ans.add(new sol(a,other));
				if(other != a)
					ans.add(new sol(other,a));
			}
			
		}
		
		System.out.println(ans.size());
		for(sol s : ans){
			System.out.println(s.n + " " + s.m);
		}
		
		
		qwe.close();
	}
	
	static class sol implements Comparable<sol>{
		long n,m;
		
		public sol(long nn, long mm){
			n =nn;
			m =mm;
		}
		
		@Override
		public int compareTo(sol o) {
			if(n != o.n)
				return Long.compare(n, o.n);
			else return Long.compare(m, o.m);
		}
		
	}

}