1023 - The perfect hamilton path

Time Limit: 5s Memory Limit: 128MB

Submissions: 181 Solved: 34
Description
There are N(2 <= N <= 13) cities and M bidirectional roads among the cities. There exist at most one road between any pair of the cities. Along every road, there are G pretty girls and B pretty boys(1 <= G,B <= 1000). You want to visit every city exactly once, and you can start from any city you want to. The degree of satisfaction is the ratio of the number of the pretty girls to the number of the pretty boys. You want to know the highest degree of satisfation.
Input
There are multiply test cases. First line: two integers N, M; The following M lines: every line with four integers i, j, G, B, response that there is a road between i and j with G and B.
Output
The highest degree of the satisfation, rounded to the third place after the decimal point.
Sample Input
3 3
1 2 5 3
2 3 7 4
3 1 13 11
Sample Output
1.714
Hint
Source
dupeng