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

public class _753_A_SantaClausAndCandies {

	public static void main(String[] args) throws IOException {
		int N = readInt(); Stack<Integer> stk = new Stack<Integer>(); 
		for(int i = 1; i<=N; i++) {stk.add(i); N -= i;} stk.add(stk.pop() + N);
		println(stk.size()); while(!stk.isEmpty()) print(stk.pop() + " ");
		exit();
	}

	final private static int BUFFER_SIZE = 1 << 16;
	private static DataInputStream din = new DataInputStream(System.in);
	private static byte[] buffer = new byte[BUFFER_SIZE];
	private static int bufferPointer = 0, bytesRead = 0;
	static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

	public static String readLine() throws IOException {
		byte[] buf = new byte[64]; // line length
		int cnt = 0, c;
		while ((c = Read()) != -1) {
			if (c == '\n')
				break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}

	public static String read() throws IOException {
		byte[] ret = new byte[1024];
		int idx = 0;
		byte c = Read();
		while (c <= ' ') {
			c = Read();
		}
		do {
			ret[idx++] = c;
			c = Read();
		} while (c != -1 && c != ' ' && c != '\n' && c != '\r');
		return new String(ret, 0, idx);
	}

	public static int readInt() throws IOException {
		int ret = 0;
		byte c = Read();
		while (c <= ' ')
			c = Read();
		boolean neg = (c == '-');
		if (neg)
			c = Read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = Read()) >= '0' && c <= '9');

		if (neg)
			return -ret;
		return ret;
	}

	public static long readLong() throws IOException {
		long ret = 0;
		byte c = Read();
		while (c <= ' ')
			c = Read();
		boolean neg = (c == '-');
		if (neg)
			c = Read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = Read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}

	public static double readDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = Read();
		while (c <= ' ')
			c = Read();
		boolean neg = (c == '-');
		if (neg)
			c = Read();

		do {
			ret = ret * 10 + c - '0';
		} while ((c = Read()) >= '0' && c <= '9');

		if (c == '.') {
			while ((c = Read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}

		if (neg)
			return -ret;
		return ret;
	}

	private static void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1)
			buffer[0] = -1;
	}

	private static byte Read() throws IOException {
		if (bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}

	public void close() throws IOException {
		if (din == null)
			return;
		din.close();
	}

	static void print(Object o) {
		pr.print(o);
	}

	static void println(Object o) {
		pr.println(o);
	}

	static void flush() {
		pr.flush();
	}

	static void println() {
		pr.println();
	}

	static void exit() throws IOException {
		din.close();
		pr.close();
		System.exit(0);
	}
}
