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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
    public static void main (String[] args) throws java.lang.Exception
    {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        long x = sc.nextLong();
        long i = 0;     
        long curSum = 0;
        long curSumEx = 0;
        ArrayList<Long> res1 = new ArrayList<Long>();
        ArrayList<Long> res2 = new ArrayList<Long>();
        long res = 0;
        while (true){
            long n = i + 1;
            curSum += i;
            curSumEx += (i*i);
            long g = x + curSum * n - curSumEx;
            
            if (g < 0) break;
            long deno = n*n - curSum;
            //System.out.println(i + " " + g + " " + curSum + " " + curSumEx + " " + deno + " " + x);
            if (deno <= 0) break;
            if (g / deno < n ) break;
            if (g % deno == 0){             
                res1.add(n);
                res2.add(g / deno);
                res+=2;
                if (n == (g/deno)) res--;
            
            }
            i++;
        }
        
        out.println(res);
        
        for (int ii = 0; ii < res1.size(); ++ii){
            out.println(res1.get(ii) + " " +res2.get(ii));
        }
        
        for (int ii = res1.size()-1; ii >= 0; --ii){
            if (res2.get(ii).equals(res1.get(ii)) ) continue;
            out.println(res2.get(ii) + " " +res1.get(ii));
        }
        out.close();
    }
    //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
      try {
         str = br.readLine();
      } catch (IOException e) {
         e.printStackTrace();
      }
      return str;
      }

   }
   //--------------------------------------------------------
}