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;
import java.util.Stack;

public class Main {
	public static class Pair{
		long x;
		long y;
		public Pair(long x,long y){
			this.x = x;
			this.y = y;
		}
		@Override
		public boolean equals(Object p){
			return ((this.x == ((Pair)p).x) && (this.y == ((Pair)p).y));
		}
	}
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		long sum1 = 0;
		long sum2 = 0;
		Stack<Pair> stack = new Stack<Pair>();
		ArrayList<Pair> queue = new ArrayList<Pair>();
		for(long i=1;i<=10000000;i++){
			long min = i;
			sum1 = sum1 + i;
			sum2 = sum2 + (i*i);
			long max = ((x - sum2)/sum1) + min;
			
			if((x-sum2)%sum1 == 0 && max>=min){
				queue.add(new Pair(min,max));
				stack.add(new Pair(max,min));
			}
		}
		if(queue.get(queue.size()-1).equals(stack.peek())){
			System.out.println(queue.size()*2 - 1);
			for(Pair curr : queue){
				System.out.println(curr.x + " " + curr.y);
			}
			stack.pop();
			while(!stack.isEmpty()){
				Pair curr = stack.pop();
				System.out.println(curr.x + " " + curr.y);
			}
		}
		else{
			System.out.println((queue.size()*2));
			for(Pair curr : queue){
				System.out.println(curr.x + " " + curr.y);
			}
			
			while(!stack.isEmpty()){
				Pair curr = stack.pop();
				System.out.println(curr.x + " " + curr.y);
			}
		}
		
	}
}