Problem:
Score: 500 points

Problem Statement

In the Kingdom of AtCoder, only banknotes are used as currency. There are 10^{100}+1 kinds of banknotes, with the values of 1, 10, 10^2, 10^3, \dots, 10^{(10^{100})}. You have come shopping at a mall and are now buying a takoyaki machine with a value of N. (Takoyaki is the name of a Japanese snack.)

To make the payment, you will choose some amount of money which is at least N and give it to the clerk. Then, the clerk gives you back the change, which is the amount of money you give minus N.

What will be the minimum possible number of total banknotes used by you and the clerk, when both choose the combination of banknotes to minimize this count?

Assume that you have sufficient numbers of banknotes, and so does the clerk.

Constraints

N is an integer between 1 and 10^{1,000,000} (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum possible number of total banknotes used by you and the clerk.

Sample Input 1

36

Sample Output 1

8

If you give four banknotes of value 10 each, and the clerk gives you back four banknotes of value 1 each, a total of eight banknotes are used.

The payment cannot be made with less than eight banknotes in total, so the answer is 8.

Sample Input 2

91

Sample Output 2

3

If you give two banknotes of value 100, 1, and the clerk gives you back one banknote of value 10, a total of three banknotes are used.

Sample Input 3

314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170

Sample Output 3

243

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

//code written by a living bruh moment
import java.io.*;
import java.lang.*;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.*;

public class Main {
    static InputReader in = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        String s = in.next();
        int count = 0;
        int count2 = 2;
        int val = Integer.parseInt(s.substring(0,2));
        while(true){
            ++count2;
            if(val>=90){
                count+=val/90*2;
                if(count2>s.length()){
                    count += val%90;
                    break;
                }
                else{
                    val = val%90 + Integer.parseInt(s.substring(count2-1,count2));
                }
            }
            else{
                count+=val/9*2;
                if(count2>s.length()){
                    count += val%9;
                    break;
                }
                else{
                    val = val%9*10 + Integer.parseInt(s.substring(count2-1,count2));
                }
            }
        }
        out.println(count);
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong()
        {
            return Long.parseLong(next());
        }
        public double nextDouble()
        {
            return Double.parseDouble(next());
        }
        public String nextLine()
        {
            try
            {
                return reader.readLine();
            }
            catch(Exception e)
            {
                e.printStackTrace();
            }
            return null;
        }
        public boolean hasNext()
        {
            String next=null;
            try
            {
                next=reader.readLine();
            }
            catch(Exception e)
            {
            }
            if(next==null)
            {
                return false;
            }
            tokenizer=new StringTokenizer(next);
            return true;
        }
    }
}