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.math.*;
import java.util.*;

/**
 *
 * @author sarthak
 */
public class rnd332_D {

    public static class Pair implements Comparable {

        long a, z;

        public Pair(long a, long z) {
            this.a = a;
            this.z = z;
        }

        public int compareTo(Object obj) {
            Pair l = (Pair) obj;
            if (this.a == l.a) {
                if (this.z == l.z) {
                    return 0;
                }
                return (this.z < l.z) ? -1 : 1;
            }
            return (this.a < l.a) ? -1 : 1;
        }
    }

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        BigInteger n = s.nextBigInteger();
        HashMap<Long, Long> m = new HashMap<>();
        ArrayList<Long> al = new ArrayList<>();
        n = n.multiply(BigInteger.valueOf(6));
       
        for (int i = 1; i <= 2*1000000; i++) {

            BigInteger a = BigInteger.valueOf(i).multiply(BigInteger.valueOf(i + 1));
            BigInteger b = a.multiply(BigInteger.valueOf(i+2));
            BigInteger Nr = n.add(b);
            BigInteger Dr = a.multiply(BigInteger.valueOf(3));
           
            if (Nr.mod(Dr).compareTo(BigInteger.ZERO) == 0  &&( (Nr.divide(Dr).compareTo(BigInteger.valueOf(i))==1) || (Nr.divide(Dr).compareTo(BigInteger.valueOf(i))==0))) {
                BigInteger temp = Nr.divide(Dr).subtract(BigInteger.ONE);

                long mm = temp.longValue();
                
                if (m.containsKey(mm) || m.containsKey(i)) {
                    break;
                } else {
                    m.put((long) i, mm);
                    al.add((long) i);
                    
                }
            }

        }
        ArrayList<Pair> bl = new ArrayList<>();
        for (long l : al) {
            Pair p = new Pair(l, (long) (m.get(l)));
            bl.add(p);
            if ((long) (m.get(l)) != l) {
                Pair p_r = new Pair((long) (m.get(l)), l);
                bl.add(p_r);

            }
        }

        Collections.sort(bl);
        System.out.println(bl.size());
        for (Pair p : bl) {
            System.out.println(p.a + " " + p.z);

        }

    }

}