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.*;
import static java.lang.Math.*;

public class santaandcandies2
{
	static int[] arr;
	static int inser_p;
	static int n;
	public static void main(String[] args)throws IOException {
		InputReader ir=new InputReader(System.in);
		OutputWriter ow=new OutputWriter(System.out);
		precompute();
		inser_p=((inser_p=Arrays.binarySearch(arr,n=ir.readInt()))<0?(abs(inser_p)-2):inser_p);
		ow.printLine(inser_p);
		int i=1;
		for(;i<inser_p;++i)
			ow.print(i+" ");
		ow.printLine(i+(n-arr[inser_p]));        
		ow.flush();
		ow.close();
	}
	static void precompute()
	{
		int mul=0,n=1;
		arr=new int[45];
       while((mul=(n*(n+1)/2))<=1000)
       	 arr[n++]=mul;
	}
	  static  class InputReader {     
    	private InputStream stream;
    	private byte[] buf = new byte[1024];
    	private int curChar;
    	private int numChars;
    	private SpaceCharFilter filter;
     
    	public InputReader(InputStream stream) {
    		this.stream = stream;
    		}     
    	public int read() {
    		if (numChars == -1)
    		    throw new InputMismatchException();
    		if (curChar >= numChars) {
    			curChar = 0;
    		try {
    				numChars = stream.read(buf);
    			} catch (IOException e) {
    				throw new InputMismatchException();
    			}
    		if (numChars <= 0)
    			return -1;
    			}
    			return buf[curChar++];
    		}     
    	public int readInt() {
    	    int c = read();
    		while (isSpaceChar(c))
    				c = read();
    		int sgn = 1;
    		if (c == '-') {
    			sgn = -1;
    			c = read();
    	}
    			int res = 0;
    			do {
    				if (c < '0' || c > '9')
    					throw new InputMismatchException();
    				res *= 10;
    				res += c - '0';
    				c = read();
    			} while (!isSpaceChar(c));
    			return res * sgn;
    		}     
    		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 boolean isSpaceChar(int c) {
    			if (filter != null)
    				return filter.isSpaceChar(c);
    			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    		}     
    		public String next() {
    			return readString();
    		}     
    		public interface SpaceCharFilter {
    			public boolean isSpaceChar(int ch);
    		}
    	}     
   static class OutputWriter {
    		private final PrintWriter writer;     
    		public OutputWriter(OutputStream outputStream) {
    			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    		}    
    		public OutputWriter(Writer writer) {
    			this.writer = new PrintWriter(writer);
    		}     
    		public void print(Object...objects) {
    			for (int i = 0; i < objects.length; i++) {
    				if (i != 0)
    					writer.print(' ');
    				writer.print(objects[i]);
    			}
    		}     
    		public void printLine(Object...objects) {
    			print(objects);
    			writer.println();
    		}     
    		public void close() {
    			writer.close();
    		}     
    		public void flush() {
    			writer.flush();
    		}     
    		}     
}