Grime Zoo

题意翻译

给定由字符 `0 1 ?` 所组成的字符串 $s$ 和参数 $x,y$，你需要在所有字符为 `?` 的位置填入字符 `0` 或者 `1`。 我们规定这个字符串的价值为： `01` 子序列的数量 $\times x\ +$ `10` 子序列的数量 $\times y$ 求字符串价值最小值。 $1\leq |s|\leq10^5,0\leq x,y\leq10^6.$

题目描述

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.

输入输出格式

输入格式

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 $ ).

输出格式

Output a single integer — the minimum number of angry comments.

输入输出样例

输入样例 #1

0?1
2 3

输出样例 #1

4

输入样例 #2

?????
13 37

输出样例 #2

0

输入样例 #3

?10?
239 7

输出样例 #3

28

输入样例 #4

01101001
5 7

输出样例 #4

96

说明

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 $ .