You are given an array of variable pairs equations and an array of real numbers values, where equations[i] = [Ai, Bi] and values[i] represent the equation Ai / Bi = values[i]. Each Ai or Bi is a string that represents a single variable.
You are also given some queries, where queries[j] = [Cj, Dj] represents the jth query where you must find the answer for Cj / Dj = ?.
Return the answers to all queries. If a single answer cannot be determined, return -1.0.
Note: The input is always valid. You may assume that evaluating the queries will not result in division by zero and that there is no contradiction.
Note: The variables that do not occur in the list of equations are undefined, so the answer cannot be determined for them.
Example 1:
Input: equations = [["a","b"],["b","c"],["ab","bc"]], values = [4.0,1.0,3.25], queries = [["a","c"],["b","a"],["c","c"],["ab","a"],["d","d"]]
Output: [4.00000,0.25000,1.00000,-1.00000,-1.00000]Example 2:
Input: equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"]]
Output: [0.50000,2.00000]Constraints:
1 <= equations.length, queries.length <= 20equations[i].length == queries[i].length == 21 <= Ai.length, Bi.length, Cj.length, Dj.length <= 5values.length == equations.length0.0 < values[i] <= 20.0Ai, Bi, Cj, Dj consist of lower case English letters and digits.