There are six persons $A, B, C, D, E$ and $F$ in a school. Each of the teachers teaches two subjects,one compulsory subject and the other optional subject. $D$'s optional subject was History while three others have it as a compulsory subject. $E$ and $F$ have Physics as one of their subjects. $F$'s compulsory subject is Mathematics,which is an optional subject for both $C$ and $E$. History and English are $A$'s subjects,but in terms of compulsory and optional subjects,they are the reverse of $D$'s. Chemistry is an optional subject of only one of them. The only female teacher in the school has English as her compulsory subject. What is $C$'s compulsory subject?