# [USACO2011 Feb]Best Parenthesis

### 题目描述

Recently, the cows have been competing with strings of balanced
parentheses and comparing them with each other to see who has the
best one.

Such strings are scored as follows (all strings are balanced): the
string "()" has score 1; if "A" has score s(A) then "(A)" has score
2*s(A); and if "A" and "B" have scores s(A) and s(B), respectively,
then "AB" has score s(A)+s(B). For example, s("(())()") =
s("(())")+s("()") = 2*s("()")+1 = 2*1+1 = 3.

Bessie wants to beat all of her fellow cows, so she needs to calculate
the score of some strings. Given a string of balanced parentheses
of length N (2 <= N <= 100,000), help Bessie compute its score.

### 输入格式

* Line 1: A single integer: N

* Lines 2..N + 1: Line i+1 will contain 1 integer: 0 if the ith
character of the string is '(', and 1 if the ith character of
the string is ')'

### 输出格式

* Line 1: The score of the string. Since this number can get quite
large, output the score modulo 12345678910.

### 样例输入

```6
0
0
1
1
0
1
INPUT DETAILS:

This corresponds to the string "(())()".

```

```3
```

Silver