Problem Description

Several friends are planning to take tourism during the next holiday. They have selected some places to visit. They have decided which place to start their tourism and in which order to visit these places. However, anyone can leave  halfway during the tourism and will never back to the tourism again if he or she is not interested in the following places. And anyone can choose not to attend the tourism if he or she is not interested in any of the places.

Each place they visited will cost every person certain amount of money. And each person has a positive value for each place, representing his or her interest in this place. To make things more complicated, if two friends visited a place together, they will  get a non negative bonus because they enjoyed each other’s companion. If more than two friends visited a place together, the total bonus will be the sum of each pair of friends’ bonuses. Your task is to decide which people should take the tourism and when each of them should leave so that the sum of the interest plus the sum of the bonuses minus the total costs is the largest. If you can’t find a plan that have a result larger than 0, just  tell them to STAY HOME.

Input 

There are several cases. Each case starts with a line containing two numbers N and M ( 1<=N<=10, 1<=M<=10). N is the number of friends and M is the number of places. The next line will contain M integers Pi (1<=i<=M) , 1<=Pi<=1000,  representing how much it costs for one person to visit the ith place. Then N line follows, and each line contains M integers Vij (1<=i<=N, 1<=j<=M), 1<=Vij<=1000, representing how much the ith person is interested in the jth place. Then N line follows, and  each line contains N integers Bij (1<=i<=N, 1<=j<=N), 0<=Bij<=1000, Bij=0 if i=j, Bij=Bji. A case starting with 0 0 indicates the end of input and you needn’t give an output.

Output

For each case, if you can arrange a plan lead to a positive result, output the result in one line, otherwise, output STAY HOME in one line.

Sample Input

2 1 10 15 5 0 5 5 0 3 2 30 50 24 48 40 70 35 20 0 4 1 4 0 5 1 5 0 2 2 100 100 50 50 50 50 0 20 20 0 0 0

Sample Output

5 41 STAY HOME

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題意：從起點 0 開始，去其他 n 個點，再回到起點 0，每個點可經過多次，求最少花費時間

思路：類似 TSP 問題，但每個點可以走多次，先用Floyd演算法的預處理一下兩點之間的距離，然後使用狀壓 DP 解即可

用一個二進位制數表示點是否走過，用 dp[state][i] 表示到達 i 點狀態為 state 的最短距離

Source Program