Score : $300$ points

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.

3 2
00
01
10

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 $3$.

7 5
10101
00001
00110
11110
00100
11111
10000

10