You are given an array of variable pairs equations and an array of real numbers values, where equations[i] = [A_i, B_i] and values[i] represent the equation A_i / B_i = values[i]. Each A_i or B_i is a string that represents a single variable.
You are also given some queries, where queries[j] = [C_j, D_j] represents the jth query where you must find the answer for C_j / D_j = ?.
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.
1 <= equations.length <= 20equations[i].length == 21 <= A_i.length, B_i.length <= 5values.length == equations.length0.0 < values[i] <= 20.01 <= queries.length <= 20queries[i].length == 21 <= C_j.length, D_j.length <= 5A_i, B_i, C_j, D_j consist of lower case English letters and digitsequations = [["a","b"],["b","c"]], values = [2.0,3.0], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]][6.00000,0.50000,-1.00000,1.00000,-1.00000]equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5.0], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]][3.75000,0.40000,5.00000,0.20000]equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]][0.50000,2.00000,-1.00000,-1.00000]