Santa Claus has n candies, he dreams to give them as gifts to children.

What is the maximal number of children for whose he can give candies if Santa Claus want each kid should get distinct positive integer number of candies. Santa Class wants to give all n candies he has.

Input

The only line contains positive integer number n (1 ≤ n ≤ 1000) — number of candies Santa Claus has.

Output

Print to the first line integer number k — maximal number of kids which can get candies.

Print to the second line k distinct integer numbers: number of candies for each of k kid. The sum of k printed numbers should be exactly n.

If there are many solutions, print any of them.

Examples

Input

5


Output

2
2 3


Input

9


Output

3
3 5 1


Input

2


Output

1
2 
import java.io.*;
import java.util.*;

public class Main {
     
  public static void main(String[] args) {
    InputReader sc = new InputReader(System.in);
    PrintWriter pw = new PrintWriter(System.out);
   // Random gen = new Random();
    int test = 1;//sc.nextInt();
    while(test-- > 0)
    {
        
     	int n = sc.nextInt();
     	StringBuffer sb = new StringBuffer();
     	int p = 1;
     	
     	while(p*(p+1)<=2*n)
     	{
     	    p++;
     	}
     	
     	pw.println(p-1);
     	
     	for(int i=1;i<p-1;i++)
     	    {
     	        sb.append(i).append(" ");
     	        n-=i;
     	    }
     	    sb.append(n);
     	    pw.println(sb);
        
     	 	
    }
     pw.close();
}



























































































































































































  static class InputReader {

    private final InputStream stream;
    private final byte[] buf = new byte[8192];
    private int curChar, snumChars;

    public InputReader(InputStream st) {
      this.stream = st;
    }

    public int read() {
      if (snumChars == -1)
        throw new InputMismatchException();
      if (curChar >= snumChars) {
        curChar = 0;
        try {
          snumChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (snumChars <= 0)
          return -1;
      }
      return buf[curChar++];
    }

    public int nextInt() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public long nextLong() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      long res = 0;
      do {
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public int[] nextIntArray(int n) {
      int a[] = new int[n];
      for (int i = 0; i < n; i++) {
        a[i] = nextInt();
      }
      return a;
    }
    
    public static int[] shuffle(int[] a, Random gen)
    { for(int i = 0, n = a.length;i < n;i++)
        { int ind = gen.nextInt(n-i)+i;
        int d = a[i];
        a[i] = a[ind];
        a[ind] = d;
            
        }
        return a;
    }
    

    public String readString() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        res.appendCodePoint(c);
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public String nextLine() {
      int c = read();
      while (isSpaceChar(c))
        c = read();
      StringBuilder res = new StringBuilder();
      do {
        res.appendCodePoint(c);
        c = read();
      } while (!isEndOfLine(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private boolean isEndOfLine(int c) {
      return c == '\n' || c == '\r' || c == -1;
    }

  }

}