While passwords generally have few restrictions, they are normally not totally free. Suppose that in a certain system passwords can be of arbitrary length, but must contain at least one letter, a...z and one number 0...9. Construct a grammar that generates the set of such legal passwords. Suppose that in some programming language numbers are restricted as follows:(a) a number may be signed or unsigned, (b) the value field consists of two nonempty parts, separated by a decimal point, (c) there is an optional exponent field. If present this field must contain the letter e, followed by a signed two-digit integer. Design a grammar for the such numbers. Suppose that a certain programming language permits only identifiers that begin with a letter, contain at least one but no more than three digits, and can have any number of letters. Give a grammar and an accepted for such a set of identifiers