410251: GYM103993 F Save the Magazines

Monocarp has been collecting rare magazines for quite a while, and now he has decided to cell them. He distributed the magazines between $$$n$$$ boxes, arranged in a row. The $$$i$$$-th box contains $$$a_i$$$ magazines. Some of the boxes are covered with lids, others are not.

Suddenly it started to rain, and now Monocarp has to save as many magazines from the rain as possible. To do this, he can move the lids between boxes as follows: if the $$$i$$$-th box was covered with a lid initially, he can either move the lid from the $$$i$$$-th box to the box $$$(i-1)$$$ (if it exists), or keep the lid on the $$$i$$$-th box. You may assume that Monocarp can move the lids instantly at the same moment, and no lid can be moved more than once. If a box will be covered with a lid after Monocarp moves the lids, the magazines in it will be safe from the rain; otherwise they will soak.

You have to calculate the maximum number of magazines Monocarp can save from the rain.

The first line contains one integer $$$n$$$ ($$$1 \le n \le 200\,000$$$) — the number of boxes.

The second line contains a string of $$$n$$$ characters 0 and/or 1. If the $$$i$$$-th character is 1, the $$$i$$$-th box is initially covered with a lid. If the $$$i$$$-th character is 0, the $$$i$$$-th box is initially not covered.

The third line contains a sequence of integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^4$$$), where $$$a_i$$$ is the number of magazines in the $$$i$$$-th box.

Print one integer — the maximum number of magazines Monocarp can save from the rain.

5
01110
10 5 8 9 6

27

6
011011
20 10 9 30 20 19

80

4
0000
100 100 100 100

0

4
0111
5 4 5 1

14

In the first example, Monocarp can move the lid from the second box to the first box, so the boxes $$$1$$$, $$$3$$$ and $$$4$$$ are covered, and $$$10 + 8 + 9 = 27$$$ magazines are saved.

In the second example, Monocarp can move the lid from the second box to the first box, then from the third box to the second box, then from the fifth box to the fourth box, and then from the sixth box to the fifth box. The boxes $$$1$$$, $$$2$$$, $$$4$$$ and $$$5$$$ will be covered, so $$$20 + 10 + 30 + 20 = 80$$$ magazines can be saved.

There are no lids in the third example, so it's impossible to save even a single magazine.