Implement three coding tasks and design your own unit tests for each. 1) Validate Bracket String with a Stack - Input: a string s containing only '(', ')', '[', ']', '{', '}'. - Output: return true if brackets are correctly matched and nested; otherwise false. - Constraints: O(n) time, O(n) auxiliary space; do not modify the input. - Edge cases to consider: empty string; strings starting with a closing bracket; long runs of the same bracket; deeply nested pairs. 2) Merge Intervals with Open/Closed Endpoints - Input: a list of intervals, each represented as (start: int, end: int, leftClosed: bool, rightClosed: bool) with start <= end. - Task: return the union of the intervals as a minimal, sorted list after merging any that overlap or “touch” under endpoint semantics. Two intervals [a,b] and [c,d] should merge if b > c, or if b == c and (the first is rightClosed OR the second is leftClosed). For example, [1,3] and [3, 5) merge to [1, 5), but [1, 3) and (3,5] remain separate. - Constraints: O(n log n) due to sorting; O(n) extra space. - Edge cases: zero-length intervals like [3,3]; mixed open/closed boundaries; duplicate intervals; very large lists. 3) Evaluate Arithmetic Expression Using Stacks - Input: a string expr containing non-negative integers, '+', '-', '*', '/', parentheses '()', spaces, and unary minus (e.g., "-3+5", "2*(-3+ 4)"). - Output: compute the integer result; division truncates toward zero. - Constraints: O(n) time, O(n) space; handle whitespace and unary operators correctly; assume the expression is valid and the intermediate results fit in 32-bit signed integer range. - Edge cases: multiple nested parentheses, consecutive operators with unary minus (e.g., "1+-2"), spaces in arbitrary places, long inputs. Testing requirement: For each task, write comprehensive unit tests you design yourself (at least 6 per task) covering typical cases, boundary conditions, and tricky edge cases.