# Worst path P10051

Statement

thehtml

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 × n matrix M, where for every pair (i, j) with ij, mij 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 → 0 → 3, with cost −10 + 90 = 80.

Input

Input consists of several cases, each one with 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 ≤ n ≤ 18, 0 ≤ x < n, that the diagonal has only zeros, and that the rest of numbers are between −106 and 106.

Output

For every case, print the cost of the worst path without repeated vertices that begins at x.

Public test cases
• Input

4
0 -10  30  90
-10   0  50 -12
-60  35   0  15
14 -70 -11   0
1

1
0
0

3
0  6  8
-4  0  3
-7 -2  0
2

Output

80
0
0

• Information
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