Problem:
Score : 900 points

Problem Statement

Takahashi has an empty string S and a variable x whose initial value is 0.

Also, we have a string T consisting of 0 and 1.

Now, Takahashi will do the operation with the following two steps |T| times.

Insert a 0 or a 1 at any position of S of his choice.

Then, increment x by the sum of the digits in the odd positions (first, third, fifth, ...) of S. For example, if S is 01101, the digits in the odd positions are 0, 1, 1 from left to right, so x is incremented by 2.

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Constraints

1 \leq |T| \leq 2 \times 10^5

T consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

T

Output

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Sample Input 1

1101

Sample Output 1

5

Below is one sequence of operations that maximizes the final value of x to 5.

Insert a 1 at the beginning of S. S becomes 1, and x is incremented by 1.

Insert a 0 to the immediate right of the first character of S. S becomes 10, and x is incremented by 1.

Insert a 1 to the immediate right of the second character of S. S becomes 101, and x is incremented by 2.

Insert a 1 at the beginning of S. S becomes 1101, and x is incremented by 1.

Sample Input 2

0111101101

Sample Output 2

26

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

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

    public static void main(String[] args) {
        String T = in.next();

        int ans = 0;
        int length = T.length();
        for (int i = 0; i < length; i++) {
            ans += score(T);
            T = maxS(T);
        }
        out.println(ans);

        out.flush();
    }

    static String maxS(String s) {
        String ret = s.substring(1);
        int max = score(ret);
        int length = s.length();
        for (int i = 1; i < length; i++) {
            String str = s.substring(0, i) + s.substring(i + 1, length);
            if (max < score(str) || (max == score(str) && s.charAt(i) == '0')) {
                max = score(str);
                ret = str;
            }
        }
        return ret;
    }

    static int score(String s) {
        int ret = 0;
        int length = s.length();
        for (int i = 0; i < length; i += 2) if (s.charAt(i) == '1')
            ret++;
        return ret;
    }

    static class Input {
        private BufferedReader br;
        private String[] buff;
        private int index = 0;

        Input(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }
        String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return null;
        }
        String next() {
            while (buff == null || index >= buff.length) {
                buff = nextLine().split(" ");
                index = 0;
            }
            return buff[index++];
        }
        byte nextByte() {
            return Byte.parseByte(next());
        }
        short nextShort() {
            return Short.parseShort(next());
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        float nextFloat() {
            return Float.parseFloat(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        BigInteger nextBigInteger() {
            return new BigInteger(next());
        }
        BigDecimal nextBigDecimal() {
            return new BigDecimal(next());
        }
    }
}