CF828B.Black Square

Polycarp has a checkered sheet of paper of size n × m. Polycarp painted some of cells with black, the others remained white. Inspired by Malevich's "Black Square", Polycarp wants to paint minimum possible number of white cells with black so that all black cells form a square.

You are to determine the minimum possible number of cells needed to be painted black so that the black cells form a black square with sides parallel to the painting's sides. All the cells that do not belong to the square should be white. The square's side should have positive length.

Polycarp 有一张大小为 $n \times m$ 的方格纸。Polycarp 将其中一些格子涂成了黑色，其余格子保持白色。受马列维奇（Malevich）的《黑方块》启发，Polycarp 希望将尽可能少的白格子涂成黑色，使得所有黑格子构成一个正方形。

你需要确定：最少需要将多少个格子涂成黑色，才能使所有黑格子构成一个边与纸张边平行的黑色正方形；且所有不属于该正方形的格子都必须是白色的。该正方形的边长必须为正整数。

The first line contains two integers n and m (1 ≤ n, m ≤ 100) — the sizes of the sheet.

The next n lines contain m letters 'B' or 'W' each — the description of initial cells' colors. If a letter is 'B', then the corresponding cell is painted black, otherwise it is painted white.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 100$）—— 表示纸张的尺寸。

接下来的 $n$ 行，每行包含 $m$ 个字符，每个字符为 'B' 或 'W' —— 描述初始各格子的颜色。若字符为 'B'，则对应格子被涂成黑色；否则被涂成白色。

Print the minimum number of cells needed to be painted black so that the black cells form a black square with sides parallel to the painting's sides. All the cells that do not belong to the square should be white. If it is impossible, print -1.

输出使黑色格子构成一个边与画布边平行的黑色正方形所需的最少涂黑格子数。所有不属于该正方形的格子都必须为白色。若无法实现，则输出 $-1$。

In the first example it is needed to paint 5 cells — (2, 2), (2, 3), (3, 2), (3, 3) and (4, 2). Then there will be a square with side equal to three, and the upper left corner in (2, 2).

In the second example all the cells are painted black and form a rectangle, so it's impossible to get a square.

In the third example all cells are colored white, so it's sufficient to color any cell black.

在第一个例子中，需要将 5 个格子涂黑——即 $(2,\,2)$、$(2,\,3)$、$(3,\,2)$、$(3,\,3)$ 和 $(4,\,2)$。此时将形成一个边长为 3 的正方形，其左上角位于 $(2,\,2)$。

在第二个例子中，所有格子均被涂黑并构成一个矩形，因此无法得到一个正方形。

在第三个例子中，所有格子均为白色，因此只需将任意一个格子涂黑即可。