402226: GYM100703 I Endeavor for perfection

As a matter of fact, Dragon knows what Prince is interested in now. Prince uses to spend his rare off days learning different courses and trainings. But Dragon doubts whether he should tell Princess about it.

Prince decided that he needs some extra knowledge and skills. He chose n fields in which he wanted to gain knowledge and skills most of all. After this, he learned that m₁, m₂, ..., m_n courses and trainings of each of fields exist.

Prince took a close look at descriptions of courses and trainings and drew a table, in which s_ij is a value by which ith skill is increased after studying jth course (j = 1, 2, ..., m_i).

Prince believes that his basic knowledge and skills in all these fields are negligible, so they can be considered zero. He wants to evolve his knowledge and skills harmonically. In his opinion, he will reach the greatest harmony if he chooses one course for each field in such a way that difference between the highest and the lowest their increases would be as minimum as possible.

Your task is to find the courses which Prince should choose.

The first line contains integer n (1 ≤ n ≤ 200) — the number of fields which Prince is interested in.

The second line contains n integers m₁, m₂, ..., m_n (1 ≤ m_j ≤ 1000,  j = 1, 2, ..., n) — the number of courses for each of fields.

The next n lines contain values s_ij (1 ≤ s_ij ≤ 10⁹) — knowledges and skills, which Prince would gain at the courses. The first of these n lines contains values s₁₁, s₁₂, ..., s_1m1, the second — values s₂₁, s₂₂, ..., s_2m2, etc.

The values s_ij are listed in the numerical order of courses for each of the fields.

In the first line print one integer — minimum difference between the highest and the lowest numbers of increase.

In the second line print n integers — numbers of courses which Prince should choose. List the numbers in the same order in which the fields are listed.

If there is more than one answer — choose any of them.

2
2 3
4 3
3 1 2

0
2 1 

4
3 5 4 5
8 7 15
3 10 4 8 5
4 4 4 5
1 2 12 8 9

3
2 5 4 4