Training Camp

Description:

Input:

The first line contains $$$n$$$ ($$$1 \leq n \leq 128$$$) — the size of the grid.

The following $$$n$$$ lines describe the ages of the kids. Specifically, the $$$i$$$-th line contains $$$n$$$ integers $$$a_{i,1}, \, a_{i,2}, \, \dots, \, a_{i, n}$$$ ($$$1 \le a_{i,j} \le n$$$) — where $$$a_{i,j}$$$ is the age of the kid in the $$$i$$$-th row and $$$j$$$-th column. It is guaranteed that two kids on the same row or column have different ages, i.e., $$$a_{i,j} \ne a_{i,j'}$$$ for any $$$1\le i\le n$$$, $$$1\le j < j'\le n$$$, and $$$a_{i,j} \ne a_{i',j}$$$ for any $$$1\le i < i'\le n$$$, $$$1\le j\le n$$$.

The following $$$n$$$ lines describe the programming skills of the kids. Specifically, the $$$i$$$-th line contains $$$n$$$ integers $$$c_{i,1}, \, c_{i,2}, \, \dots, \, c_{i, n}$$$ ($$$c_{i,j} \in \{0, \, 1\}$$$) — where $$$c_{i,j}=1$$$ if the kid in the $$$i$$$-th row and $$$j$$$-th column is good at programming and $$$c_{i,j}=0$$$ otherwise.

Output:

Print the maximum number of kids good at programming that you can select while satisfying all the requirements.

Sample Input:

3
1 2 3
3 1 2
2 3 1
1 0 0
0 0 1
0 0 0

Sample Output:

1

Sample Input:

4
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
1 1 1 0
0 0 1 0
1 1 0 1
0 0 0 1

Sample Output:

2

Note:

In the first sample, it is not possible to select the two kids good at programming (in row $$$1$$$ and column $$$1$$$, and in row $$$2$$$ and column $$$3$$$), because then you would have to select the kid in row $$$3$$$ and column $$$2$$$, and in that case two kids would complain (the one in row $$$1$$$ and column $$$2$$$, and the one in row $$$3$$$ and column $$$1$$$).

A valid selection which contains $$$1$$$ kid good at programming is achieved by choosing the $$$3$$$ kids who are $$$1$$$ year old.

In the second sample, there are $$$10$$$ valid choices of the $$$n$$$ kids that satisfy the requirements, and each of them selects exactly $$$2$$$ kids good at programming.