Maximum cost of a path (1)

Given a directed and complete graph with $n$ vertices, and an initial vertex $x$ , compute the maximum cost of all the paths without repeated vertices that begin at $x$ . The given graph is represented by an $n \times n$ matrix $M$ , where for every pair $(i, j)$ with $i \ne j$ , $m_{ij}$ is the (perhaps negative) cost of the arc from $i$ to $j$ .

For instance, the maximum cost of the first test is 80, corresponding to the path $1 \to 0 \to 3$ , with cost $-10 + 90 = 80$ .

Input

Input consists of the number of vertices $n$ , followed by the matrix $M$ ( $n$ lines, each one with $n$ integer numbers), followed by the initial vertex $x$ . Vertices are numbered from 0 to $n-1$ . You can assume $1 \le n \le 11$ , $0 \le x < n$ , that the diagonal has only zeros, and that the rest of numbers are between $-10^6$ and $10^6$ .

Output

Print the maximum cost of all the paths without repeated vertices that begin at $x$ .

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T11:22:32.339Z