Maximize Protected City Population

Cities are arranged in a row, and unit[i]=1 means a unit is initially there. A unit may stay or move once to the adjacent city on its left; a unit in the first city can only stay. In the end, a city with at least one unit contributes population[i] once; overlapping units do not contribute again. Find the maximum protected population.

输入格式

The first line contains n, the second line population, and the third line a 01 string unit of length n. The original text only kept the constraint that the two arrays have equal length, with no numeric bounds; this site uses 1≤n≤200000, 0≤population[i]≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

5
10 5 8 9 6
01101

输出：

27

样例 2

输入：

2
7 4
01

输出：

7

样例 3

输入：

3
1 100 1
011

输出：

101

样例说明

The answers are 27, 7 and 101. In the third example two units cannot count the 100 in the middle twice.