Problem Statement

$N$ students took a test with $M$ questions with two choices: $0$ and $1$. You are given $N$ strings of length $M$ each: $S_1, S_2, \\ldots, S_N$. The $k$-th character of $S_i$ is 0 or 1, representing the response of the $i$-th student to the $k$-th question. Although we know the response of each student to each question, we do not yet know the correct answer ― $0$ or $1$ ― to each problem. Find the number of pairs $(i, j)$ satisfying $1 \\leq i < j \\leq N$ such that it is impossible for Student $i$ and Student $j$ to have the same number of correct answers.

Constraints

• $2 \\leq N \\leq 10^5$
• $1 \\leq M \\leq 20$
• $S_i$ is a string of length $M$ consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $S_1$ $S_2$ $:$ $S_N$

Output

Print the answer.

Sample Input 1

3 2
00
01
10

Sample Output 1

2

For example, if the correct answers to the $1$-st and $2$-nd questions are both $0$, Student $2$ and Student $3$ have the same number of correct answers ― $1$. On the other hand, Student $1$ and Student $2$ never have the same number of correct answers, nor do Student $1$ and Student $3$.

Sample Input 2

7 5
10101
00001
00110
11110
00100
11111
10000

Sample Output 2

10