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.

<image>

In a 2 × 3 table there are 6 1 × 1 squares and 2 2 × 2 squares. That is equal to 8 squares in total.

<image>

Solution (in JAVA):

Solution:
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
 
public class Main {
    Scanner sc = new Scanner(System.in);
 
    public static void main(String[] args) {
        new Main(); 
    }
 
    public Main() {
        new D().doIt();
    }
    class D{
        void doIt(){
            ArrayList<Long> array = new ArrayList<Long>();
            ArrayList<Long> array2 = new ArrayList<Long>();
            long squares[] = new long [10000000];
            squares[1] = 1;
            long cnt = 1;
            long num = 1;
            long MAX = 1000000000;
            MAX = MAX*MAX;
            while(true){
                cnt++;
                num = num + cnt * cnt;
                if(num > MAX)break;
                squares[(int) (cnt)] = num;
            }
//          System.out.println(squares[(int)(cnt-1)]);
            int n = (int)(cnt);
            long x = sc.nextLong();
            num = 0;
            for(int i = 1;i < n;i++){
                num = num + (long)(i);
//              System.out.println(num+" "+i+" "+squares[i]);
                if(x - squares[i] < 0)break;
                if((x - squares[i]) % num == 0){
                    array.add((long)i);
                    array2.add(((x - squares[i]) / num)+i);
                }
            }
            int ans = array.size()*2;
            boolean ok = true;
            if(array.get(array.size()-1) - array2.get(array2.size()-1) == 0){
                ans = ans-1;
                ok = false;
            }
            System.out.println(ans);
            for(int i = 0;i < array.size();i++){
                System.out.println(array.get(i)+" "+array2.get(i));
            }
            if(ok){
                for(int i = array.size()-1;i >= 0;i--){
                    System.out.println(array2.get(i)+" "+array.get(i));
                }
            }else{
                for(int i = array.size()-2;i >= 0;i--){
                    System.out.println(array2.get(i)+" "+array.get(i));
                }
            }
        }
    }
}