URI Online Judge | 1068

Parenthesis Balance I

By Neilor Tonin, URI Brazil

Timelimit: 1

Considering an expression with parenthesis, print a message informing if the among of parenthesis is correct or incorrect, without considering the rest of the expression. Example:


a+(b*c)-2-a        is correct
(a+b*(2-c)-2+a)*2  is correct

when

(a*b-(2+c)         is incorrect
2*(3-a))           is incorrect
)3+b*(2-c)(        is incorrect

Resuming, all closing parenthesis must have an open parenthesis and it's not possible a closing parenthesis without a previous open parenthesis, and the quantity of closing and open parenthesis must be the same.

Input

The input file contains N expressions (1 <= N <= 10000), each one with up to 1000 characters. 

Output

The output must be correct or incorrect for each test case according with above rules.

Input Sample Output Sample

a+(b*c)-2-a 
(a+b*(2-c)-2+a)*2 
(a*b-(2+c) 
2*(3-a))  
)3+b*(2-c)( 

correct

correct

incorrect

incorrect

incorrect