$4.$ Design a context$-$free grammar $($CFG$)$ that generates arithmetic expressions involving addition and multiplication with integers. $(10$ points$)$

Your grammar should handle:

$$ Integers $($positive numbers only$).$

$$ Addition $(+)$ and multiplication $(*)$ operations.

$$ The correct precedence, where multiplication has higher precedence than addition.

Example:

The grammar should generate expressions like:

$3+4*5$

$7*(2+3)$

Expected Output:

For $3+4*5,$ the grammar should respect the precedence, evaluating $4*5$ first and then adding $3.$