CF1080E.Sonya and Matrix Beauty

Sonya had a birthday recently. She was presented with the matrix of size $n\times m$ and consist of lowercase Latin letters. We assume that the rows are numbered by integers from $1$ to $n$ from bottom to top, and the columns are numbered from $1$ to $m$ from left to right.

Let's call a submatrix $(i_1, j_1, i_2, j_2)$ $(1\leq i_1\leq i_2\leq n; 1\leq j_1\leq j_2\leq m)$ elements $a_{ij}$ of this matrix, such that $i_1\leq i\leq i_2$ and $j_1\leq j\leq j_2$. Sonya states that a submatrix is beautiful if we can independently reorder the characters in each row (not in column) so that all rows and columns of this submatrix form palidroms.

Let's recall that a string is called palindrome if it reads the same from left to right and from right to left. For example, strings $abacaba, bcaacb, a$ are palindromes while strings $abca, acbba, ab$ are not.

Help Sonya to find the number of beautiful submatrixes. Submatrixes are different if there is an element that belongs to only one submatrix.

索尼娅最近过生日了。她收到了一个大小为 $n\times m$ 的矩阵，其中每个元素均为小写拉丁字母。我们约定：行编号从下到上依次为 $1$ 到 $n$，列编号从左到右依次为 $1$ 到 $m$。

我们将满足 $1\leq i_1\leq i_2\leq n$ 且 $1\leq j_1\leq j_2\leq m$ 的四元组 $(i_1, j_1, i_2, j_2)$ 称为一个子矩阵，它包含原矩阵中所有满足 $i_1\leq i\leq i_2$ 且 $j_1\leq j\leq j_2$ 的元素 $a_{ij}$。索尼娅定义：若一个子矩阵可以通过独立地对每一行内的字符重新排列（不允许对列重排），使得该子矩阵的每一行和每一列都成为回文串，则称该子矩阵是“优美的”。

我们回顾：若一个字符串从左向右读与从右向左读完全相同，则称其为回文串。例如，字符串 $abacaba$、$bcaacb$、$a$ 是回文串，而 $abca$、$acbba$、$ab$ 不是回文串。

请帮助索尼娅计算优美子矩阵的个数。若两个子矩阵至少有一个元素只属于其中之一，则认为它们是不同的子矩阵。

The first line contains two integers $n$ and $m$ $(1\leq n, m\leq 250)$ — the matrix dimensions.

Each of the next $n$ lines contains $m$ lowercase Latin letters.

第一行包含两个整数 $n$ 和 $m$（$1\leq n, m\leq 250$）——矩阵的维度。

接下来的 $n$ 行，每行包含 $m$ 个小写拉丁字母。

Print one integer — the number of beautiful submatrixes.

输出一个整数——美丽子矩阵的数量。

In the first example, the following submatrixes are beautiful: $((1, 1), (1, 1)); ((1, 2), (1, 2));$ $((1, 3), (1, 3)); ((1, 1), (1, 3))$.

In the second example, all submatrixes that consist of one element and the following are beautiful: $((1, 1), (2, 1));$ $((1, 1), (1, 3)); ((2, 1), (2, 3)); ((1, 1), (2, 3)); ((2, 1), (2, 2))$.

Some of the beautiful submatrixes are: $((1, 1), (1, 5)); ((1, 2), (3, 4));$ $((1, 1), (3, 5))$.

The submatrix $((1, 1), (3, 5))$ is beautiful since it can be reordered as:

accca
aabaa
accca

In such a matrix every row and every column form palindromes.

在第一个例子中，以下子矩阵是优美的：$((1, 1), (1, 1)); ((1, 2), (1, 2));$ $((1, 3), (1, 3)); ((1, 1), (1, 3))$。

在第二个例子中，所有仅含一个元素的子矩阵，以及以下子矩阵是优美的：$((1, 1), (2, 1));$ $((1, 1), (1, 3)); ((2, 1), (2, 3)); ((1, 1), (2, 3)); ((2, 1), (2, 2))$。

一些优美的子矩阵包括：$((1, 1), (1, 5)); ((1, 2), (3, 4));$ $((1, 1), (3, 5))$。

子矩阵 $((1, 1), (3, 5))$ 是优美的，因为它可以重排为：

accca
aabaa
accca

在此矩阵中，每一行和每一列均构成回文。