Parser and evaluator

Write a parser and an evaluator for the arithmetic expressions generated by the following grammar:

E →

T + E | T - E | T

(Addition/subtraction)

T →

F * T | F / T | F % T | F

F →

( E ) | - F| + F | N

(Plus/minus sign)

N →

D | DN

D →

0 | 1 | 2 | ... | 9

Observe that an expression may contain only integers (generated by N). Hence, the value of an expression is defined to be an integer. In particular, as in C and C++, / and % are integer division for quotient and remainder, respectively. The meanings of other operators are standard.

The priority of operator:

1. – (Negative)

2. %

3. *, /

4. +, – (Minus)

Input

Each line contains an expression string, with length < 1024.

Output

• For each case, the first line is a prompt as following: “case 1:”. The next line is the answer.

• Print “syntactically incorrect”, if the input is not accepted.

• The last line of each case is an empty line.

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