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;

/**
 *
 * @author User
 */
public class JavaApplication1 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner in=new Scanner(System.in);
        long c=in.nextLong();
        long id=0;
        ArrayList<Pair<Long,Long>> y=new ArrayList<Pair<Long,Long>>();
        for (long i=1;i<=c;i++)
        {
        long f=(2*i*i*i+3*i*i+i)/6;
        if (f==c) 
        {Pair d=new Pair(i,i);y.add(d); id=1;continue;}
        
        long sh=c-f;
        if (sh<0) break;
        long vd= (i*(i+1)) /2;
        if (sh%vd==0)
        {long r=sh/vd; Pair m=new Pair(i,i+r);y.add(m);continue;}
        }
        
            System.out.println(y.size()*2-id);
        for (int i=0;i<y.size();i++)
            System.out.println(y.get(i).getLeft()+" "+y.get(i).getRight());

        for (int i=y.size()-1;i>=0;i--) 
           { if   ((id==1)&&i==y.size()-1) continue;
 System.out.println(y.get(i).getRight()+" "+y.get(i).getLeft());}
    }
    
    
    
    
    
}
 class Pair<L,R> {

  private final L left;
  private final R right;

  public Pair(L left, R right) {
    this.left = left;
    this.right = right;
  }

  public L getLeft() { return left; }
  public R getRight() { return right; }

  @Override
  public int hashCode() { return left.hashCode() ^ right.hashCode(); }

  @Override
  public boolean equals(Object o) {
    if (!(o instanceof Pair)) return false;
    Pair pairo = (Pair) o;
    return this.left.equals(pairo.getLeft()) &&
           this.right.equals(pairo.getRight());
  }

}