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.

Input

Input is given from Standard Input in the following format:
N M
S_1
S_2
:
S_N

Output

Print the answer.

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.

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

见题面 Input 部分

见题面 Output 部分