Longest Shortest Path

Example

Input

3 2 3 1 3 1 2 2 1 2 3 1 2

Output

6.0000000

inputFormat

Input

3 2 3 1 3 1 2 2 1 2 3 1 2

outputFormat

Output

6.0000000

样例

3 2 3 1 3
1 2 2 1
2 3 1 2

6.0000000