Strain Calibration Destinations

A genetics lab stores strains numbered from 0 to n - 1. Some strains are certified calibration references.

Each entry [a, b, cost] in conversions describes a directed procedure that converts strain a into strain b at the given nonnegative cost. Procedures may be chained, and the total cost is the sum of their costs. A procedure cannot be used backward unless a separate reverse procedure is listed.

For each starting strain, find the certified reference it can reach at minimum total cost. If several references have the same minimum cost, choose the reference with the smallest strain number. A strain can remain unchanged at cost 0, so a certified strain can reach itself without using any procedure.

Return a list of n pairs in starting-strain order. Each pair is [minimum_cost, reference_number]. If no certified reference is reachable, use [-1, -1].

Input: n = 5, conversions = [[0,1,2],[1,2,3],[0,3,5],[1,3,4]], references = [3,2]
Output: [[5,2],[3,2],[0,2],[0,3],[-1,-1]]

Input: n = 3, conversions = [[0,1,0],[1,0,0],[2,1,4]], references = [1,0]
Output: [[0,0],[0,0],[4,0]]

Input: n = 3, conversions = [[0,1,2],[1,2,1]], references = []
Output: [[-1,-1],[-1,-1],[-1,-1]]

The expected running time is O((n + m) log(n + m)), where m is the number of conversions, with O(n + m) auxiliary space. All costs and answers fit exactly in JavaScript's safe integer range.