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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(){
  int i,n,d=0,c[2]={},f;
  char t[200005];
  long x=0;
  scanf("%s",&t);
  for(n=0;t[n]!=0;n++){
    if(t[n]=='1'){
      d++;
      x+=(d+1)>>1;
    }
  }
  f=d&1;
  for(i=n-1;i>=0;i--){
    f^=1;
    if(t[i]=='1'){
      d--;
      c[f]++;
    }else{
      x+=(d+1)>>1;
      x+=c[f];
    }
  }
  printf("%ld",x);
  return(0);
}