Problem: We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.

* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.



It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.

Constraints

* 0 ≤ K ≤ 50 \times 10^{16}

Input

Input is given from Standard Input in the following format:


K


Output

Print a solution in the following format:


N
a_1 a_2 ... a_N


Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.

Examples

Input

0


Output

4
3 3 3 3


Input

1


Output

3
1 0 3


Input

2


Output

2
2 2


Input

3


Output

7
27 0 0 0 0 0 0


Input

1234567894848


Output

10
1000 193 256 777 0 1 1192 1234567891011 48 425

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main implements Runnable {
    static ContestScanner in;
    static Writer out;
    public static void main(String[] args) {
        new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
    }

    public void run() {
        Main main = new Main();
        try {
            in = new ContestScanner();
            out = new Writer();
            main.solve();
            out.close();
            in.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
//        int n = in.nextInt();
//        long[] a = new long[n];
//        for (int i = 0; i < n; i++) {
//            a[i] = in.nextLong();
//        }
//        System.out.println(brute(a));
//        for (int i = 0; i < 100; i++) {
//            long[] a = solve2(i);
//            long k = brute(a);
//            if(k != i) {
//                System.out.println("NG: " + i + " -> " + k);
//                long[] b = solve2(i);
//                brute(b);
//            }
//        }
        long k = in.nextLong();
        long[] a = solve2(k);
        System.out.println(a.length);
        for (int i = 0; i < a.length; i++) {
            if(i > 0) System.out.print(" ");
            System.out.print(a[i]);
        }
        System.out.println();
    }

    long[] solve2(long k) {
        long[] a = new long[50];
        int n = a.length;
        for (int i = 0; i < n; i++) {
            a[i] = n - 1 + k / n;
        }
        for (int i = 0; i < k % n; i++) {
            a[i] += n + 1;
            for (int j = 0; j < n; j++) {
                a[j]--;
            }
        }
        return a;
    }

    long brute(long[] a) {
        int n = a.length;
        int k = 0;
        long max;
        do {
            k++;
            max = 0;
            int mi = 0;
            for(int i = 0; i < n; i++) {
                if(a[i] > max) {
                    max = a[i];
                    mi = i;
                }
                a[i]++;
            }
            a[mi] -= n + 1;
        } while (max >= n);
        return k - 1;
    }

    long solveE(long[] a) {
        Queue<Long> pq = new PriorityQueue<>();
        for(long v: a) pq.add(v);
        long k = 0;
        long add = 0;
        return 0;
    }
}


@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
    @Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
    public void add(T key,int v){put(key,get(key)+v);}
    public void add(T key){put(key,get(key)+1);}
    public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
    public MultiSet<T> merge(MultiSet<T> set)
    {MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
        for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}

class Writer extends PrintWriter{
    public Writer(String filename)throws IOException
    {super(new BufferedWriter(new FileWriter(filename)));}
    public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
    private BufferedReader in;private int c=-2;
    public ContestScanner()throws IOException
    {in=new BufferedReader(new InputStreamReader(System.in));}
    public ContestScanner(String filename)throws IOException
    {in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
    public String nextToken()throws IOException {
        StringBuilder sb=new StringBuilder();
        while((c=in.read())!=-1&&Character.isWhitespace(c));
        while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public String readLine()throws IOException{
        StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
        while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public long nextLong()throws IOException,NumberFormatException
    {return Long.parseLong(nextToken());}
    public int nextInt()throws NumberFormatException,IOException
    {return(int)nextLong();}
    public double nextDouble()throws NumberFormatException,IOException
    {return Double.parseDouble(nextToken());}
    public void close() throws IOException {in.close();}
}