Grime Zoo
Description
Currently, XXOC's rap is a string consisting of zeroes, ones, and question marks. Unfortunately, haters gonna hate. They will write $x$ angry comments for every occurrence of subsequence 01 and $y$ angry comments for every occurrence of subsequence 10. You should replace all the question marks with 0 or 1 in such a way that the number of angry comments would be as small as possible.
String $b$ is a subsequence of string $a$, if it can be obtained by removing some characters from $a$. Two occurrences of a subsequence are considered distinct if sets of positions of remaining characters are distinct.
The first line contains string $s$ — XXOC's rap ($1 \le |s| \leq 10^5$). The second line contains two integers $x$ and $y$ — the number of angry comments XXOC will recieve for every occurrence of 01 and 10 accordingly ($0 \leq x, y \leq 10^6$).
Output a single integer — the minimum number of angry comments.
Input
The first line contains string $s$ — XXOC's rap ($1 \le |s| \leq 10^5$). The second line contains two integers $x$ and $y$ — the number of angry comments XXOC will recieve for every occurrence of 01 and 10 accordingly ($0 \leq x, y \leq 10^6$).
Output
Output a single integer — the minimum number of angry comments.
Samples
0?1
2 3
4
?????
13 37
0
?10?
239 7
28
01101001
5 7
96
Note
In the first example one of the optimum ways to replace is 001. Then there will be $2$ subsequences 01 and $0$ subsequences 10. Total number of angry comments will be equal to $2 \cdot 2 + 0 \cdot 3 = 4$.
In the second example one of the optimum ways to replace is 11111. Then there will be $0$ subsequences 01 and $0$ subsequences 10. Total number of angry comments will be equal to $0 \cdot 13 + 0 \cdot 37 = 0$.
In the third example one of the optimum ways to replace is 1100. Then there will be $0$ subsequences 01 and $4$ subsequences 10. Total number of angry comments will be equal to $0 \cdot 239 + 4 \cdot 7 = 28$.
In the fourth example one of the optimum ways to replace is 01101001. Then there will be $8$ subsequences 01 and $8$ subsequences 10. Total number of angry comments will be equal to $8 \cdot 5 + 8 \cdot 7 = 96$.