Expression

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

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 $10^9+7$.

Sample Input

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

Sample Output

2 999999689
Hint
Two numbers are considered different when they are in different positions.

Hint

wange2014

Source

2015 Multi-University Training Contest 9

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