Problem: Max wants to buy a new skateboard. He has calculated the amount of money that is needed to buy a new skateboard. He left a calculator on the floor and went to ask some money from his parents. Meanwhile his little brother Yusuf came and started to press the keys randomly. Unfortunately Max has forgotten the number which he had calculated. The only thing he knows is that the number is divisible by 4.

You are given a string s consisting of digits (the number on the display of the calculator after Yusuf randomly pressed the keys). Your task is to find the number of substrings which are divisible by 4. A substring can start with a zero.

A substring of a string is a nonempty sequence of consecutive characters.

For example if string s is 124 then we have four substrings that are divisible by 4: 12, 4, 24 and 124. For the string 04 the answer is three: 0, 4, 04.

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use gets/scanf/printf instead of getline/cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input

The only line contains string s (1 ≤ |s| ≤ 3·105). The string s contains only digits from 0 to 9.

Output

Print integer a — the number of substrings of the string s that are divisible by 4.

Note that the answer can be huge, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Examples

Input

124


Output

4


Input

04


Output

3


Input

5810438174


Output

9

Solution (in JAVA):

Solution:
// Author @ BlackRise :) //
// Birla Institute of Technology, Mesra//
import java.io.*;
import java.util.*;

public class newSkateBoard {


    static void Blackrise() {                                                //The name Blackrise is my pen name... you can change the name according to your wish

        char ch[]=ns().toCharArray();

        tsc();

        long ans=0;
        if((ch[0]-48)%4==0)ans++;
        for(int i=1;i<ch.length;i++)
        {
            if((ch[i]-48)%4==0)ans++;
            int x=(ch[i-1]-48)*10 + (ch[i]-48);
            if(x%4==0)ans+=i;
        }
        pl(ans);


        tec();                  //calculates the ending time of execution
        //pwt();                //prints the time taken to execute the program

        flush();
    }


    /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////


    static Calendar ts, te;                                                  //For time calculation
    static int mod9 = 1000000007;
    static int n,t,MOD=998244353;
    static Lelo input = new Lelo(System.in);
    static PrintWriter pw = new PrintWriter(System.out, true);


    public static void main(String[] args) {                                 //threading has been used to increase the stack size.

        new Thread(null, null, "BlackRise", 1<<25)  //the last parameter is stack size which is desired,
        {
            public void run() {

                try {
                    Blackrise();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

    static class Lelo {                                              //Lelo class for fast input
        private InputStream ayega;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public Lelo(InputStream ayega) {
            this.ayega = ayega;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = ayega.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            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);
        }
    }

    // functions to take input//
    static int ni() {
        return input.nextInt();
    }

    static long nl() {
        return input.nextLong();
    }

    static double nd() {
        return input.nextDouble();
    }

    static String ns() {
        return input.readString();
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o){
        pw.print(o+"");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    static void tsc()                                          //calculates the starting time of execution
    {
        ts = Calendar.getInstance();
        ts.setTime(new Date());
    }

    static void tec()                                          //calculates the ending time of execution
    {
        te = Calendar.getInstance();
        te.setTime(new Date());
    }

    static void pwt()                                          //prints the time taken for execution
    {
        pw.printf("\nExecution time was :- %f s\n", (te.getTimeInMillis() - ts.getTimeInMillis()) / 1000.00);
    }
    static void flush()
    {
        pw.flush();pw.close();
    }

    static void sort(int ar[])
    {
        for(int i=0;i<n;i++)
        {
            int ran=(int)(Math.random()*n);
            int temp=ar[i];
            ar[i]=ar[ran];
            ar[ran]=temp;
        }
        Arrays.sort(ar);
    }
    static void sort(long ar[])
    {
        for(int i=0;i<n;i++)
        {
            int ran=(int)(Math.random()*n);
            long temp=ar[i];
            ar[i]=ar[ran];
            ar[ran]=temp;
        }
        Arrays.sort(ar);
    }
    static void sort(char ar[])
    {
        for(int i=0;i<n;i++)
        {
            int ran=(int)(Math.random()*n);
            char temp=ar[i];
            ar[i]=ar[ran];
            ar[ran]=temp;
        }
        Arrays.sort(ar);
    }
}