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Equations are given in the format `A / B = k`

, where `A`

and `B`

are variables represented as strings, and `k`

is a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return `-1.0`

.

**Example:**

Given ` a / b = 2.0, b / c = 3.0.`

queries are: ` a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? .`

return ` [6.0, 0.5, -1.0, 1.0, -1.0 ].`

The input is: ` vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries `

, where `equations.size() == values.size()`

, and the values are positive. This represents the equations. Return ` vector<double>`

.

According to the example above:

equations = [ ["a", "b"], ["b", "c"] ], values = [2.0, 3.0], queries = [ ["a", "c"], ["b", "a"], ["a", "e"], ["a", "a"], ["x", "x"] ].

The input is always valid. You may assume that evaluating the queries will result in no division by zero and there is no contradiction.

b''