Evaluate Division

Statement

You are given an array of variable pairs equations and an array of real numbers, values, where the equations[i] = [A[i], B[i]] and values[i] represent the equation values[i] = A[i] / B[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 $j^{th}$ query where you must find the answer for C[j] / D[j].

Return the answers to all queries. If any 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.

Constraints:

• $1 \leq$ equations.length $\leq 20$

• equations[i].length $== 2$

• $1 \leq$ A[i].length, B[i].length $\leq 5$

• values.length $==$ equations.length

• $0.0 <$ values[i] $\leq 20.0$

• $1 \leq$ queries.length $\leq 20$

• queries[i].length $== 2$

• $1 \leq$ C[j].length, D[j].length $\leq 5$

• A[i], B[i], C[j], D[j] consist of lower case English letters and digits.

Examples