Resolve a Variable Through Literal and Reference Assignments

Resolve a variable whose assignment is either an integer literal or the name of another variable.

Function Signature

resolve_variable(assignments: list[list[str]], target: str) -> int

Input

Each assignment is [variable_name, right_hand_side]. A right-hand side is either a decimal integer literal or another variable name. The order of assignments is arbitrary.

For this exercise, names match [A-Za-z_][A-Za-z0-9_]*. Integer literals use an optional minus sign followed by one or more digits, with no whitespace or plus sign. Literal values are in [-1000000000, 1000000000].

Output

Follow references beginning at target and return the terminal integer value.

Constraints

• 1 <= len(assignments) <= 100000.
• Variable names are unique, and target is defined.
• Every referenced variable is defined.
• The complete reference graph is acyclic, so every chain ends in an integer literal.
• Each string has at most 40 characters.
• These validity rules are explicit baseline assumptions; malformed definitions and cycles are outside this console contract.

Examples

Input: assignments = [["T1","T2"],["T2","-8"],["unused","4"]], target = "T1"

Output: -8

Input: assignments = [["A","007"],["B","A"]], target = "B"

Output: 7

Input: assignments = [["value","0"]], target = "value"

Output: 0