## AMR10H - Shopping Rush

A shop-keeper is trying to figure out how to arrange gifts in his shop for Christmas. He runs a peculiar shop such that each customer buys exactly two gifts at the shop (he could buy two of the same gifts too). He knows the probability that a customer might want gift i, is P_i.

He needs to arrange the gifts across several floors. Each floor should have exactly one gift. It takes A*(|x - y|)^2 + B*(|x - y|) + C seconds to go from floor x to floor y.

Can you help him arrange the gifts across floors such that, the expected time spent by a shopper is minimized?

For the purpose of this problem assume that the first gift choice and the second gift choice are independent of each other. i.e., Choosing a first gift as i does not change his probability of choosing the second gift as j. It still remains P_j.**INPUT**

The first line contains the number of test cases T. 2*T lines follow, 2 per test case. The first line contains 4 integers : N, A, B, C. The second line contains N integers in the range 1 to 100. The ith integer represents the percentage probability P_i. All P_i's will sum to 100.**OUTPUT**

Output T lines one for each test case. Each line contains the minimum expected travelling time for the corresponding test case. Output the answer as a reduced fraction as below.**CONSTRAINTS**

1 <= T <= 100

1 <= N <= 20

0 <= A,B,C <= 10**SAMPLE INPUT**

4

3 0 1 0

60 10 30

1 1 1 0

100

1 1 1 3

100

4 3 7 2

25 25 25 25**SAMPLE OUTPUT**

3/5

0/1

3/1

73/4

Added by: | Varun Jalan |

Date: | 2010-12-13 |

Time limit: | 0.916s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | own problem, ICPC Asia regionals, Amritapuri 2010 |