Consider the grammar below, which generates arithmetic expressions involving operator $+$ and integer or floating$-$point operands. Floating$-$point numbers are distinguished by having a decimal point.

E $->$ E$+$T$|$T

T$->$ num. num $|$ num

Focus on the data type of the arithmetic expression, generated by B$.$ The data type of an arithmetic expression, involving addition $(+$ operator$)$ of two integer operands becomes an integer expression, whereas data type of an arithmetic expression involving one integer and one floating point operand becomes a floating point expression. For instance, the data type of expression $7+4$ is integer, whereas $8+3\mathrm{.}4,5\mathrm{.}6+3,7\mathrm{.}5+2\mathrm{.}9$ are floating point expressions.

Consider a SDD$,$ which determines the data type of the expression E$.$ In this SDD$,$ type is the only $($synthesized$)$ attribute, defined for the non$-$terminals E and T$,$ where E$.$type stores the data type of the expression E$.$ Write the complete SDD which computes E$.$type to determine the data type of the expression E$.$