Problem Statement

There are N people, each of whom is either a child or an adult. The i-th person has a weight of W_i.
Whether each person is a child or an adult is specified by a string S of length N consisting of 0 and 1.
If the i-th character of S is 0, then the i-th person is a child; if it is 1, then the i-th person is an adult.
When Takahashi the robot is given a real number X,
Takahashi judges a person with a weight less than X to be a child and a person with a weight more than or equal to X to be an adult.
For a real value X, let f(X) be the number of people whom Takahashi correctly judges whether they are children or adults.
Find the maximum value of f(X) for all real values of X.

Input

Input is given from Standard Input in the following format:
N
S
$W_1 W_2 \ldots W_N$

Output

Print the maximum value of f(X) as an integer in a single line.

Constraints

• $1\leq N\leq 2\times 10^5$
• S is a string of length N consisting of 0 and 1.
• $1\leq W_i\leq 10^9$
• N and W_i are integers.

Sample Input 1

5
10101
60 45 30 40 80

Sample Output 1

4

When Takahashi is given X=50, it judges the 2-nd, 3-rd, and 4-th people to be children and the 1-st and 5-th to be adults.
In reality, the 2-nd and 4-th are children, and the 1-st, 3-rd, and 5-th are adults, so the 1-st, 2-nd, 4-th, and 5-th people are correctly judged.
Thus, f(50)=4.
This is the maximum since there is no X that judges correctly for all 5 people. Thus, 4 should be printed.

Sample Input 2

3
000
1 2 3

Sample Output 2

3

For example, X=10 achieves the maximum value f(10)=3.
Note that the people may be all children or all adults.

Sample Input 3

5
10101
60 50 50 50 60

Sample Output 3

4

For example, X=55 achieves the maximum value f(55)=4.
Note that there may be multiple people with the same weight.

见题面 Input 部分

见题面 Output 部分