Hamiltonian cycle of minimum cost

Given several directed graphs with $n$ vertices, each one described with a matrix $m$ of size $n \times n$ such that $m[i][j]$ is the cost of going from vertex $i$ to vertex $j$ , calculate the minimum cost of the Hamiltonian cycles of every graph. A Hamiltonian cycle is a path that visits each vertex exactly once, and that ends at the starting vertex.

Input

Input consists of the description of several graphs. Each one begins with a natural number $n \ge 2$ , followed by the matrix $n \times n$ of costs ( $n$ lines, each with $n$ natural numbers, with zeroes at the diagonal).

Output

Print the minimum cost of the Hamiltonian cycles of every graph.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T11:10:21.515Z