Text Document Analysis
Contest: Codeforces Round 375 (Div. 2)
Difficulty rating: 1100
Tags: expression parsing, implementation, strings

Modern text editors usually show some information regarding the document being edited. For example, the number of words, the number of pages, or the number of characters.

In this problem you should implement the similar functionality.

You are given a string which only consists of:

- uppercase and lowercase English letters,
- underscore symbols (they are used as separators),
- parentheses (both opening and closing).

It is guaranteed that each opening parenthesis has a succeeding closing parenthesis. Similarly, each closing parentheses has a preceding opening parentheses matching it. For each pair of matching parentheses there are no other parenthesis between them. In other words, each parenthesis in the string belongs to a matching "opening-closing" pair, and such pairs can't be nested.

For example, the following string is valid: "_Hello_Vasya(and_Petya)__bye_(and_OK)".

Word is a maximal sequence of consecutive letters, i.e. such sequence that the first character to the left and the first character to the right of it is an underscore, a parenthesis, or it just does not exist. For example, the string above consists of seven words: "Hello", "Vasya", "and", "Petya", "bye", "and" and "OK". Write a program that finds:

- the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses),
- the number of words inside the parentheses (print 0, if there is no word inside the parentheses).

Input format:
The first line of the input contains a single integer n (1 ≤ n ≤ 255) — the length of the given string. The second line contains the string consisting of only lowercase and uppercase English letters, parentheses and underscore symbols.

Output format:
Print two space-separated integers:

- the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses),
- the number of words inside the parentheses (print 0, if there is no word inside the parentheses).

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
In the first sample, the words "Hello", "Vasya" and "bye" are outside any of the parentheses, and the words "and", "Petya", "and" and "OK" are inside. Note, that the word "and" is given twice and you should count it twice in the answer.

Example input:
37
_Hello_Vasya(and_Petya)__bye_(and_OK)

Example output:
5 4

Example input:
37
_a_(_b___c)__de_f(g_)__h__i(j_k_l)m__

Example output:
2 6

Editorial:
It is an implementation problem. Let's store in the variable cnt the number of words inside brackets and in the variable maxL — the maximum length of the word outside brackets. You can add the symbol «_» to the end of the given string, to correctly process the last word.
Let's iterate through the given string from the left to the right and store in the variable cur the current word. Also in the variable bal we need to store balance of the open and close brackets.
If the current symbol is letter — add it to the end of the string cur and go to the next symbol of the given string.
If the current symbol is open bracket, make bal = bal + 1. If the current symbol is close bracket, make bal = bal - 1. After that if cur is non-empty string add 1 to cnt if bal equals to 1. Else if bal equals to 0 update maxL with length of the string cur. After that we need to assign cur to the empty string and go to the next symbol of the given string.