Every year, Farmer John loves to attend the county fair. The fair has N booths (1 <= N <= 400), and each booth i is planning to give away a fabulous prize at a particular time P(i) (0 <= P(i) <= 1,000,000,000) during the day. Farmer John has heard about this and would like to collect as many fabulous prizes as possible to share with the cows. He would like to show up at a maximum possible number of booths at the exact times the prizes are going to be awarded. Farmer John investigated and has determined the time T(i,j) (always in range 1..1,000,000) that it takes him to walk from booth i to booth j. The county fair's unusual layout means that perhaps FJ could travel from booth i to booth j by a faster route if he were to visit intermediate booths along the way. Being a poor map reader, Farmer John never considers taking such routes -- he will only walk from booth i to booth j in the event that he can actually collect a fabulous prize at booth j, and he never visits intermediate booths along the way. Furthermore, T(i,j) might not have the same value as T(j,i) owing to FJ's slow walking up hills. Farmer John starts at booth #1 at time 0. Help him collect as many fabulous prizes as possible.
* Line 1: A single integer, N.
* Lines 2..1+N: Line i+1 contains a single integer, P(i). * Lines 2+N..1+N+N^2: These N^2 lines each contain a single integer T(i,j) for each pair (i,j) of booths. The first N of these lines respectively contain T(1,1), T(1,2), ..., T(1,N). The next N lines contain T(2,1), T(2,2), ..., T(2,N), and so on. Each T(i,j) value is in the range 1...1,000,000 except for the diagonals T(1,1), T(2,2), ..., T(N,N), which have the value zero.
* Line 1: A single integer, containing the maximum number of prizes Farmer John can acquire.
Sample Input4 //有四个收藏品可以去收集,下面四行给出这四个东西下落的时间
Farmer John first walks to booth #4 and arrives at time 3, just in
time to receive the fabulous prize there. He them walks to booth
#2 (always walking directly, never using intermediate booths!) and
arrives at time 8, so after waiting 1 unit of time he receives the
fabulous prize there. Finally, he walks back to booth #1, arrives
at time 13, and collects his third fabulous prize.