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 D {

    public static void main ( String [] args ) {
        Scanner s = new Scanner ( System.in );
        long x = s.nextLong();

        //System.out.println( Long.MAX_VALUE  );

        List<Point> sol = new ArrayList();

        for ( long n=1; n*n*n<= 3 * x; n++ ){
            long a = 6 * x + n * n * n - n;
            long b = 3*n*n + 3 * n;
            if ( a % b == 0 ){
                long m = a/b;
                if ( n> m  ){
                    break;
                }
                //System.out.println( n + " " + m );
                sol.add( new Point( n, m ) );
                if ( n != m ){
                    sol.add( new Point( m, n ) );
                }
            }
        }

        Collections.sort( sol );
        System.out.println ( sol.size() );
        for ( Point p : sol ){
            System.out.println( p.a + " " + p.b );
        }

    }


    public static class Point implements Comparable<Point> {
        long a;
        long b;

        public Point( long a, long b ){
            this.a = a;
            this.b = b;
        }


        @Override
        public int compareTo(Point o) {
            int ret = Long.compare( a, o.a );
            if ( ret == 0 ){
                ret = Long.compare( b, o.b );
            }
            return ret;
        }
    }
}