Eye of Sauron

Little Elrond is obsessed with the Lord of the Rings series. Between lectures he likes to doodle the central tower of the great fortress Barad-dûr in the margins of his notebook. Afterward, he always double checks his drawings to ensure they are accurate: with the Eye of Sauron located in the very center of the tower. If any are incorrect, he makes sure to fix them.

You are to write a program that reads a representation of his tower, and ensures that the drawing is correct, with a properly centered eye.

Input

Input consists of a single string of length ${n}$, where $4\leq n \leq 100$. Input strings will consist only of three types of characters: vertical bars, open parentheses, and closing parentheses. Input strings contain one or more vertical bars followed by a set of matching parentheses (the “eye”), followed by one or more vertical bars. For a drawing to be “correct”, the number of vertical bars on either side of the “eye” must match. Input will always contain a pair of correctly matched parentheses, with no characters between them. No other characters will appear in the string.

Output

On a single line print the word “correct” if the drawing is accurate or the word “fix” if there is an error that needs addressing.

Sample Input 1 Sample Output 1
|()||
fix
Sample Input 2 Sample Output 2
||||()||||
correct
Sample Input 3 Sample Output 3
|()|
correct
Sample Input 4 Sample Output 4
|||()|
fix