Parser and evaluator

Write a parser and evaluator for arithmetic expressions using nonnegative decimal integer literals, parentheses, unary signs and binary +, -, *, /, %.

LOCAL grammar and evaluation rules

The archived right-recursive grammar conflicts with its own sample: 789-400+300 evaluates to 689. This platform explicitly uses left-associative binary operators and the precedence already demonstrated by 72/61%7 = 14. The reviewed grammar is:

E = T { ("+" | "-") T }
T = R { ("*" | "/") R }
R = F { "%" F }
F = "(" E ")" | "-" F | "+" F | N
N = D { D }
D = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

Precedence from highest to lowest: unary signs; remainder; multiplication/division; addition/subtraction. Repetition in E, T and R is evaluated left to right. Whitespace may separate tokens, but cannot join separate integer tokens into one number. Implicit multiplication and empty parentheses are not allowed. Division truncates toward zero; remainder is a - trunc(a/b)*b. Division or remainder by zero is reported as syntactically incorrect.

Input

Each input line is an independent expression, with length less than 1024. Read until end of file. All integer calculations are exact.

Output

For each line, print case 1: (using consecutive case numbers), then the result on the next line. If the line is not accepted or contains an undefined division, print syntactically incorrect instead of a number. Print an empty line after each case.

789-(400+300) 
789-400+300 
-9*80+72/61%7 
72+((38-66) 
-101**29 
123/78%23 45

case 1: 
89 
 
case 2: 
689 
 
case 3: 
-706 

case 4: 
syntactically incorrect 

case 5: 
syntactically incorrect 

case 6: 
syntactically incorrect