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 java.math.*;
    import java.lang.*;
     
     //@Manan Parmar

    public class Solution2 implements Runnable {


        public void run() {
            
            InputReader sc = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            
            int n=sc.nextInt(),i=1;
            int sum=0;
            ArrayList<Integer> a=new ArrayList<Integer>();
            
            while(n>0)
            {
                if((n-(i))<=i)
                {
                    a.add(n);
                    sum++;
                    break;
                }
                a.add(i);
                sum++;
                n=n-i;
                i++;
            }
            
            out.println(sum);
            for(Integer k:a)
                out.println(k);
            out.close();
        }
     

    //========================================================================
        boolean check(char a,char b)
        {
            if(a==b)
                return true;
            else
                return false;
        }
        long binarySearch(long arr[], long x) 
        { 
            int l = 0, r = arr.length - 1,q=0; 
            while (l<=r) { 
                int m = l + (r - l) / 2; 
                if (arr[l] >=x) 
                {
                    q=1;
                    return l; 
                }
                if (arr[m] < x) 
                    l=m+1; 
                else
                    r=m;
            } 
            return -1;
        }

        static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;
            private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
     
            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 String nextLine() {
                String str = "";
                try {
                    str = br.readLine();
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
                return str;
            }
            public int nextInt() {
                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 long nextLong() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                long 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 double nextDouble() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                double res = 0;
                while (!isSpaceChar(c) && c != '.') {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                if (c == '.') {
                    c = read();
                    double m = 1;
                    while (!isSpaceChar(c)) {
                        if (c == 'e' || c == 'E')
                            return res * Math.pow(10, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        m /= 10;
                        res += (c - '0') * m;
                        c = read();
                    }
                }
                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);
            }
        }

        public static void main(String args[]) throws Exception {
            new Thread(null, new Solution2(),"Main",1<<27).start();
        }
    }
