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#3300. [USACO2011 Feb]Best Parenthesis

内存限制：128 MiB 时间限制：10 Sec
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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. 
计算“平衡字符串”的分数，“平衡字符串”是指由相同数量的‘（’和‘）’组成， 
且以‘（’开头，以‘）’结尾的字符串。 
计算规则： 
字符串“（）”的得分是1. 
如果，平衡字符串“A”的得分是是S(A)，那么字符串“（A）”得分是2*S(A) ； 
如果，“A”，“B” 得分分别是S(A)和S(B)，那么平衡字符串“AB”得分为S(A)+S(B) 
例如：s("(())()") =s("(())")+s("()") = 2*s("()")+1 = 2*1+1 = 3.

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 ')'
第1行：N，平衡字符串长度
第2至N+1行：Linei+1 整数0或1,0代表字符‘（’，1代表‘）’

输出格式

* Line 1: The score of the string. Since this number can get quite large, output the score modulo 12345678910.
计算字符串得分，结果对12345678910取模

样例

样例输入


			
6

0

0

1

1

0

1

INPUT DETAILS:

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

样例输出


			
3

数据范围与提示

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