CF1393D.Rarity and New Dress

Carousel Boutique is busy again! Rarity has decided to visit the pony ball and she surely needs a new dress, because going out in the same dress several times is a sign of bad manners. First of all, she needs a dress pattern, which she is going to cut out from the rectangular piece of the multicolored fabric.

The piece of the multicolored fabric consists of $n \times m$ separate square scraps. Since Rarity likes dresses in style, a dress pattern must only include scraps sharing the same color. A dress pattern must be the square, and since Rarity is fond of rhombuses, the sides of a pattern must form a $45^{\circ}$ angle with sides of a piece of fabric (that way it will be resembling the traditional picture of a rhombus).

Examples of proper dress patterns: Examples of improper dress patterns: The first one consists of multi-colored scraps, the second one goes beyond the bounds of the piece of fabric, the third one is not a square with sides forming a $45^{\circ}$ angle with sides of the piece of fabric.

Rarity wonders how many ways to cut out a dress pattern that satisfies all the conditions that do exist. Please help her and satisfy her curiosity so she can continue working on her new masterpiece!

旋转精品店又忙碌起来了！瑞瑞决定去参加小马舞会，她当然需要一条新裙子，因为多次穿同一条裙子出门是失礼的表现。首先，她需要一个裙装纸样，而这个纸样将从一块矩形的多色布料上裁剪出来。

这块多色布料由 $n \times m$ 个独立的正方形布片组成。由于瑞瑞崇尚时尚，裙装纸样所包含的布片必须颜色完全相同。此外，裙装纸样本身必须是一个正方形；又因瑞瑞钟爱菱形，该正方形的各边必须与布料的边成 $45^{\circ}$ 夹角（这样看起来才像传统意义上的菱形）。

符合要求的裙装纸样示例：

不符合要求的裙装纸样示例：

第一个示例中包含了多种颜色的布片，第二个超出了布料边界，第三个不是与布料边成 $45^{\circ}$ 角的正方形。

瑞瑞很好奇：究竟有多少种满足上述所有条件的裙装纸样裁剪方案？请帮她解答这一疑问，以便她能继续创作她的全新杰作！

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 2000$). Each of the next $n$ lines contains $m$ characters: lowercase English letters, the $j$-th of which corresponds to scrap in the current line and in the $j$-th column. Scraps having the same letter share the same color, scraps having different letters have different colors.

第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 2000$）。接下来的 $n$ 行，每行包含 $m$ 个字符：小写英文字母；其中第 $j$ 个字符表示当前行、第 $j$ 列位置上的碎屑。具有相同字母的碎屑颜色相同，具有不同字母的碎屑颜色不同。

Print a single integer: the number of ways to cut out a dress pattern to satisfy all of Rarity's conditions.

输出一个整数：满足瑞瑞所有条件的连衣裙图案裁剪方案数。

In the first example, all the dress patterns of size $1$ and one of size $2$ are satisfactory.

In the second example, only the dress patterns of size $1$ are satisfactory.

在第一个例子中，所有尺寸为 $1$ 的连衣裙图案以及一个尺寸为 $2$ 的连衣裙图案均满足要求。

在第二个例子中，仅有尺寸为 $1$ 的连衣裙图案满足要求。