Problem Description

Teacher Mai has $n$ numbers $a_1,a_2,\cdots,a_n$and $n-1$ operators("+", "-" or "*")$op_1,op_2,\cdots,op_{n-1}$, which are arranged in the form $a_1~op_1~a_2~op_2~a_3~\cdots~a_n$.

He wants to erase numbers one by one. In $i$-th round, there are $n+1-i$ numbers remained. He can erase two adjacent numbers and the operator between them, and then put a new number (derived from this one operation) in this position. After $n-1$ rounds, there is the only one number remained. The result of this sequence of operations is the last number remained.


He wants to know the sum of results of all different sequences of operations. Two sequences of operations are considered different if and only if in one round he chooses different numbers.

For example, a possible sequence of operations for "$1+4*6-8*3$" is $1+4*6-8*3\to 1+4*(-2)*3\to 1+(-8)*3\to (-7)*3\to -21$.

Input

There are multiple test cases.

For each test case, the first line contains one number $n(2\leq n\leq 100)$.

The second line contains $n$ integers $a_1,a_2,\cdots,a_n(0\leq a_i\leq 10^9)$.

The third line contains a string with length $n-1$ consisting "+","-" and "*", which represents the operator sequence.

Output

For each test case print the answer modulo $10^9+7$.

3
3 2 1
-+
5
1 4 6 8 3
+*-*

2
999999689

Hint

Two numbers are considered different when they are in different positions.

Author

xudyh