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: Wrong Answer)

import java.util.Scanner;


public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		long sum =0;
		int a= 0;
		int b= 0;
		for (int i=0;i<s.length();i++) {
			if (s.charAt(i)=='1') {
				if (i%2==0) {
					a++;
				} else {
					b++;
				}
			}
			if (a>b) {
				sum +=a;
			} else {
				sum +=b;
			}
		}
		System.out.println(sum);
	}
}