Interpersonal dislikes

Given $n$ people and the grade of dislike between them, choose how to make them sit at a long table, in such a way that the sum of the interpersonal dislikes of the neighbor persons is minimum, with one restriction: the leftmost person must be the first person given.

Input

Input consists of several cases, each with $n$ , followed by $n$ different names, followed by an $n \times n$ matrix of natural numbers between 0 and $10^6$ , where the position $(i, j)$ has the dislike between people $i$ and $j$ . The matrix is symmetric, with zeroes at the diagonal. You can assume $1 \le n \le 12$ .

Output

For every case, print the minimum sum of dislikes, followed by the optimum placement of people at the table. The test cases are such that there is always a unique solution.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T12:16:13.113Z