You are given an array equations in the form [Ai, Bi] and an array values (Ai / Bi = values[i]). Given some queries [Ci, Di], return the answers. If the answer does not exist, return -1.0.

Example 1:

Input:
2
a b
b c
2.0 3.0
3
a c
b a
a e
Output: 6.0 0.5 -1.0

Constraints:

• 1 ≤ equations.length ≤ 20
• equations[i].length == 2
• 1 ≤ Ai.length, Bi.length ≤ 5
• values[i] > 0
• 1 ≤ queries.length ≤ 20

Input format: First line: number of equations. Second line: pairs "Ai Bi" per line. Third line: values. Then queries count, then one "Ci Di" per line.

Output format: Space-separated answers (6 decimal places).