Enchanted Forest

Mirko lives in a big enchanted forest where the trees are very tall and grow quickly. The forest is an $N \times N$ matrix and every cell holds exactly one tree.

Mirko likes the trees of the enchanted forest. He watched them for years and measured, for every tree, how many meters it grows in a year. The trees grow continuously. A tree that grows 5 meters in a year grows 2.5 meters in half a year.

Mirko also likes the mushrooms of the enchanted forest. Now and then he eats a suspicious colorful mushroom and starts asking odd questions. Yesterday it happened again, and he wondered how large the biggest connected group of trees of equal height would be if the trees kept growing at their current speed.

He measured the current height of every tree and asked you for the answer.

• Two trees are adjacent if their cells share a common edge.
• Two trees are connected if a sequence of adjacent trees leads from the first one to the second one.
• A group of trees is connected if every pair of trees in the group is connected by such a sequence that uses only trees of the group.

The first line contains the integer $N$ ($1 \le N \le 700$).

The next $N$ lines contain $N$ integers each. The $j$th integer of the $i$th line is $h_{ij}$ ($1 \le h_{ij} \le 10^6$), the current height in meters of the tree in row $i$ and column $j$.

The next $N$ lines again contain $N$ integers each. The $j$th integer of the $i$th line is $v_{ij}$ ($1 \le v_{ij} \le 10^6$), the number of meters the tree in row $i$ and column $j$ grows in a year.

The input is large, so use a fast reading method.

Print one line with the number of trees in the largest connected group of trees of equal height.

The moment of the comparison is any real moment from now on, so the best moment can fall inside a year. Trees can reach the same height after 8 months, which is two thirds of a year.