353_C. Find Maximum
Valera has array a, consisting of n integers a0, a1, ..., an - 1, and function f(x), taking an integer from 0 to 2n - 1 as its single argument. Value f(x) is calculated by formula <image>, where value bit(i) equals one if the binary representation of number x contains a 1 on the i-th position, and zero otherwise.

For example, if n = 4 and x = 11 (11 = 20 + 21 + 23), then f(x) = a0 + a1 + a3.

Help Valera find the maximum of function f(x) among all x, for which an inequality holds: 0 ≤ x ≤ m.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of array elements. The next line contains n space-separated integers a0, a1, ..., an - 1 (0 ≤ ai ≤ 104) — elements of array a.

The third line contains a sequence of digits zero and one without spaces s0s1... sn - 1 — the binary representation of number m. Number m equals <image>.

Output

Print a single integer — the maximum value of function f(x) for all <image>.

Examples

Input

2
3 8
10


Output

3


Input

5
17 0 10 2 1
11010


Output

27

Note

In the first test case m = 20 = 1, f(0) = 0, f(1) = a0 = 3.

In the second sample m = 20 + 21 + 23 = 11, the maximum value of function equals f(5) = a0 + a2 = 17 + 10 = 27.
```python
n = int(input())
a = list(map(int, input().split()))
s = input()
 
ans = 0
sm = 0
 
for i in range(n):
    if s[i] == '1':
        ans = max(ans + a[i], sm)
    sm += a[i]
 
print(ans)
```