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.io.BufferedReader;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Collections;
import java.util.ArrayList;


public class D {

    private static class Solution implements Comparable<Solution> {
        long r;
        long c;
        public Solution(long r, long c) { 
            this.r = r;
            this.c = c;
        }

        @Override
        public int compareTo(Solution other) { 
            if( r < other.r) return -1;
            if(r > other.r ) return 1;
            if(c < other.c) return -1;
            if(c > other.c) return 1;
            return 0;
        
        }


    }

    public static void main(String [] args ) throws IOException  {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        long X = Long.parseLong(br.readLine());
        
        ArrayList<Solution> sol = new ArrayList<Solution>();
        long prod = 8*X;

        for(long c = 1; c*c*c <= prod; c++) { 
            
            long nomin = 6*X + c*c*c - c;
            
            
            long denom = 3 * c *c + 3 *c;
            
            if(nomin%denom == 0) { 
                long r = nomin/denom;
                
                //System.out.println("result: " + result);
                //System.out.println("r: " + r);
                if(r > c) { 
                    sol.add(new Solution(r,c));
                    sol.add(new Solution(c,r));
                } else if( r == c) { 
                    sol.add(new Solution(r,c));
                }
            }
        }
        
        Collections.sort(sol);
        System.out.println(sol.size());
        for(int i=0; i<sol.size(); i++) { 
            System.out.println(sol.get(i).r + " " + sol.get(i).c);
        }       
    }
}