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 i ≠ 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 → 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 −10^{6} and 10^{6}.

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

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++