Garden 2

The JOI garden is a square grid of $N$ rows and $N$ columns. The cell in row $i$ (counting from the top) and column $j$ (counting from the left) is called cell $(i, j)$.

The soil in the JOI garden is poor, so each cell can hold at most one flower of one color. Cell $(i, j)$ can hold a red flower if $A_{i,j}$ is R, a yellow flower if $A_{i,j}$ is Y, and a blue flower if $A_{i,j}$ is B.

To make the garden look good in aerial photos, the manager K plans to plant flowers with the following steps.

1. Choose an integer $r$ for the size. It must satisfy $0 \leq r \leq \frac{N-1}{2}$.
2. Choose a center cell $(x, y)$. It must satisfy $r+1 \leq x \leq N-r$ and $r+1 \leq y \leq N-r$.
3. Choose colors $c_0, c_1, c_2, \ldots, c_r$, each one of red, yellow, or blue.
4. For each cell $(x', y')$, let $d = |x'-x| + |y'-y|$, where $|t|$ is the absolute value of $t$. Plant flowers as follows.
   • If $d \leq r$, plant a flower of color $c_d$ in cell $(x', y')$.
   • If $d > r$, plant no flower in cell $(x', y')$.

Given $N$ and the color information for each cell, find the maximum number of flowers the manager K can plant.

The first line contains $N$. Each of the next $N$ lines contains the values $A_{i,1}$ through $A_{i,N}$ for row $i$.

Print the maximum number of flowers that K can plant on one line.

$3 \leq N \leq 3500$

Each $A_{i,j}$ is R, Y, or B.

$N$ is an integer.