Valera has array $*a*$, consisting of $*n*$ integers $*a*_{0}, *a*_{1}, ..., *a*_{*n* - 1}$, and function $*f*(*x*)$, taking an integer from $0$ to $2^{*n*} - 1$ as its single argument. Value $*f*(*x*)$ is calculated by formula , 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 $*x* = 11$ $(11 = 2^{0} + 2^{1} + 2^{3})$, then $*f*(*x*) = *a*_{0} + *a*_{1} + *a*_{3}$.

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 $*n*$ $(1 ≤ *n* ≤ 10^{5})$ — the number of array elements. The next line contains $*n*$ space-separated integers $*a*_{0}, *a*_{1}, ..., *a*_{*n* - 1}$ $(0 ≤ *a*_{*i*} ≤ 10^{4})$ — elements of array $*a*$.

The third line contains a sequence of digits zero and one without spaces $*s*_{0}*s*_{1}... *s*_{*n* - 1}$ — the binary representation of number $*m*$. Number $*m*$ equals .

Output

Print a single integer — the maximum value of function $*f*(*x*)$ for all .

Note

In the first test case $*m* = 2^{0} = 1, *f*(0) = 0, *f*(1) = *a*_{0} = 3$.

In the second sample $*m* = 2^{0} + 2^{1} + 2^{3} = 11$, the maximum value of function equals $*f*(5) = *a*_{0} + *a*_{2} = 17 + 10 = 27$.