ANARC09A - Seinfeld


I’m out of stories. For years I’ve been writing stories, some rather silly, just to make simple problems look difficult and complex problems look easy. But, alas, not for this one.

You’re given a non empty string made in its entirety from opening and closing braces. Your task is to find the minimum number of “operations” needed to make the string stable. The definition for being stable is as follows:

  1. An empty string is stable.
  2. If S is stable, then {S} is also stable.
  3. If S and T are both stable, then ST (the concatenation of the two) is also stable.

All of these strings are stable: {}, {}{}, and {{}{}}; But none of these: }{, {{}{, nor {}{.
The only operation allowed on the string is to replace an opening brace with a closing brace, or visa-versa.

Input

Your program will be tested on one or more data sets. Each data set is described on a single line. The line is a non-empty string of opening and closing braces and nothing else. No string has more than 2000 braces. All sequences are of even length.

The last line of the input is made of one or more ’-’ (minus signs.)

Output

For each test case, print the following line:

k. N

Where k is the test case number (starting at one,) and N is the minimum number of operations needed to convert the given string into a balanced one.

Example

Input:
}{
{}{}{}
{{{}
---

Output: 1. 2
2. 0
3. 1

hide comments
KUMAR ABHISHEK: 2015-05-21 11:21:15

The string to be checked should always be even ?

SangKuan: 2015-05-19 14:09:36

notice there is a '\r' at the end of every line,it cost me one time

:.Mohib.:: 2015-05-19 04:38:45

O(n) simple :)

Last edit: 2015-05-19 04:39:08
who cares: 2015-05-04 05:41:05

and the happiest moment when your solution got accepted in first attempt with o(n) ;)

Aadil Ahmad: 2015-04-07 19:06:01

My 50th :) :) :)

Ayman Mostafa: 2015-03-25 13:06:59

{}{{{}}} is this stable?

xxbloodysantaxx: 2015-03-22 11:24:53

That was a total fluke.. I did it by stacks not even thinking what I did (going by intuitions) it went AC .. Now I need to prove the correctness of my algorithm

Daniel Carvalho: 2015-03-03 20:08:33

@Mahesh Kohli, yes, it is.
Watch out for output format.
[edit] By the way, it's easily solvable without stack.

Last edit: 2015-03-03 20:13:08
Mahesh Kohli: 2015-02-18 14:48:29

sir,
is this thing a valid sequence
{{}{}{}{}{}{}}

Last edit: 2015-02-18 14:57:39
Petar Jesic: 2015-02-06 13:27:00

This is one of those problems where the input format gets you into more trouble than the problem itself.


Added by:Mohammad Kotb
Date:2009-11-28
Time limit:3.236s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 BASH JS-RHINO
Resource:http://www.icpc-anarc.org