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 is given from Standard Input in the following format:

```
$N$
$S$
$W_1$ $W_2$ $\ldots$ $W_N$
```

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

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

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.

3

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

4

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