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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.FileNotFoundException;
import java.util.Arrays;
import java.io.InputStream;
import java.util.InputMismatchException;
import java.util.TreeMap;
import java.io.PrintWriter;
import java.io.FileInputStream;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/D4";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        /*
        // String s = in.next();
        for (int i = 1; i <= 1000; i++) {
            int ans1 = solveA(i);
            int ans2 = solveB(i);
            if (ans1 != ans2) {
                System.out.println(i + " " + ans1 + " " + ans2);
            }
        }
        // System.out.println(res);
         */

        String s = in.next();
        int[][] dp = new int[s.length()+1][10];
        for (int i = 0; i <= s.length(); i++) {
            Arrays.fill(dp[i], 1 << 30);
        }
        dp[0][0] = 0;
        for (int i = 0; i < s.length(); i++) {
            int next = s.charAt(i) - '0';
            dp[i + 1][0] = dp[i][0] + next;
            if (next != 0) {
                dp[i + 1][10 - next] = dp[i][0] + 11 - next;
            }
            for (int j = 1; j < 10; j++) {
                dp[i + 1][0] = Math.min(dp[i + 1][0], dp[i][j] + next);
                if (next != 0) {
                    dp[i + 1][10 - next] = Math.min(dp[i + 1][10 - next], dp[i][j] + (9 - next));
                }
            }
        }
        int res = 1 << 30;
        for (int i = 0; i < 10; i++) {
            res = Math.min(res, dp[s.length()][i]);
        }
        System.out.println(res);
    }

    private int solveB(int x) {
        int res = x;
        for (int b = x; b <= 10000; b++) {
            int cnt = count(b) + count(b - x);
            res = Math.min(res, cnt);
        }
        return res;
    }

    int count(int x) {
        int res = 0;
        while (x > 0) {
            res += x % 10;
            x /= 10;
        }
        return res;
    }

    private int solveA(int x) {
        String s = Integer.toString(x);
        int[][] dp = new int[s.length()+1][10];
        for (int i = 0; i <= s.length(); i++) {
            Arrays.fill(dp[i], 1 << 30);
        }
        dp[0][0] = 0;
        for (int i = 0; i < s.length(); i++) {
            int next = s.charAt(i) - '0';
            dp[i + 1][0] = dp[i][0] + next;
            if (next != 0) {
                dp[i + 1][10 - next] = dp[i][0] + 11 - next;
            }
            for (int j = 1; j < 10; j++) {
                dp[i + 1][0] = Math.min(dp[i + 1][0], dp[i][j] + next);
                if (next != 0) {
                    dp[i + 1][10 - next] = Math.min(dp[i + 1][10 - next], dp[i][j] + (9 - next));
                }
            }
        }
        int res = 1 << 30;
        for (int i = 0; i < 10; i++) {
            res = Math.min(res, dp[s.length()][i]);
        }
        return res;
    }


    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                // TODO 自動生成された catch ブロック
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }

}


class FastScanner {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream) {
        this.stream = stream;
        // stream = new FileInputStream(new File("dec.in"));
    }

    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 boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public boolean isEndline(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = nextInt();

        return array;
    }

    public int[][] nextIntMap(int n, int m) {
        int[][] map = new int[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextIntArray(m);
        }
        return map;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int n) {
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nextLong();

        return array;
    }

    public long[][] nextLongMap(int n, int m) {
        long[][] map = new long[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextLongArray(m);
        }
        return map;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) {
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nextDouble();

        return array;
    }

    public double[][] nextDoubleMap(int n, int m) {
        double[][] map = new double[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextDoubleArray(m);
        }
        return map;
    }

    public String next() {
        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 String[] nextStringArray(int n) {
        String[] array = new String[n];
        for (int i = 0; i < n; i++)
            array[i] = next();

        return array;
    }

    public String nextLine() {
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndline(c));
        return res.toString();
    }

    public int[][] nextPackedIntArrays(int packN, int size) {
        int[][] res = new int[packN][size];
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < packN; j++) {
                res[j][i] = nextInt();
            }
        }
        return res;
    }
}