You are given a string $S$ of length $N$ consisting of `0` and `1`.

A string $T$ of length $N$ consisting of `0` and `1` is a good string if and only if it satisfies the following condition:

-   There is exactly one integer $i$ such that $1 \leq i \leq N - 1$ and the $i$-th and $(i + 1)$-th characters of $T$ are the same.

For each $i = 1,2,\ldots, N$, you can choose whether or not to perform the following operation once:

-   If the $i$-th character of $S$ is `0`, replace it with `1`, and vice versa. The cost of this operation, if performed, is $C_i$.

Find the minimum total cost required to make $S$ a good string.

The input is given from Standard Input in the following format:

```
$N$
$S$
$C_1$ $C_2$ $\ldots$ $C_N$
```

Print the answer.

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

7

Performing the operation for i=1,5 and not performing it for i=2,3,4 makes S= 10010, which is a good string. The cost incurred in this case is 7, and it is impossible to make S a good string for less than 7, so print 7.