Description:

Teacher Mai has n numbers a1,a2,⋯,anand n−1 operators("+", "-" or "*")op1,op2,⋯,opn−1, which are arranged in the form a1 op1 a2 op2 a3 ⋯ an.

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→1+4∗(−2)∗3→1+(−8)∗3→(−7)∗3→−21.

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→1+4∗(−2)∗3→1+(−8)∗3→(−7)∗3→−21.

Input:

There are multiple test cases.

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

The second line contains n integers a1,a2,⋯,an(0≤ai≤109).

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 109+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

Source:

Submit