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.Scanner;
import java.math.BigInteger;
public class CF332D {
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		BigInteger x;
		x=in.nextBigInteger();
		BigInteger limit=BigInteger.ONE;
		while(limit.pow(3).compareTo(x.multiply(BigInteger.valueOf(3)))<1){
			limit=limit.add(BigInteger.ONE);
		}
		int ans=0;
		String[][] arr= new String[1000000][2];
		BigInteger i=BigInteger.ONE;
		
		while(i.compareTo(limit)<1){
			if(x.multiply(BigInteger.valueOf(6)).add(i.pow(3)).subtract(i).mod(i.multiply(BigInteger.valueOf(3)).add(i.pow(2).multiply(BigInteger.valueOf(3)))).equals(BigInteger.ZERO)){
				if(i.compareTo(x.multiply(BigInteger.valueOf(6)).add(i.pow(3)).subtract(i).divide(i.multiply(BigInteger.valueOf(3)).add(i.pow(2).multiply(BigInteger.valueOf(3)))))<1){
					arr[ans][0]=i.toString();
					arr[ans][1]=x.multiply(BigInteger.valueOf(6)).add(i.pow(3)).subtract(i).divide(i.multiply(BigInteger.valueOf(3)).add(i.pow(2).multiply(BigInteger.valueOf(3)))).toString();
					ans++;
				}
			}

			i=i.add(BigInteger.ONE);
		}
		if(ans>0&&arr[ans-1][0].equals(arr[ans-1][1])){
			System.out.println(ans*2-1);
			for(int k=0;k<ans;k++){
				System.out.println(arr[k][0]+" "+arr[k][1]);
			}
			for(int k=ans-2;k>=0;k--){
				System.out.println(arr[k][1]+" "+arr[k][0]);

			}

		}else{
			System.out.println(2*ans);
			for(int k=0;k<ans;k++){
				System.out.println(arr[k][0]+" "+arr[k][1]);
			}
			for(int k=ans-1;k>=0;k--){
				System.out.println(arr[k][1]+" "+arr[k][0]);
			}
		}
		in.close();
		
		
	}
	
}