Problem Statement

There are N sequences of length M, denoted as $A_1, A_2, \ldots, A_N$. The i-th sequence is represented by $M integers A_{i,1}, A_{i,2}, \ldots, A_{i,M}$.
Two sequences X and Y of length M are said to be similar if and only if the number of indices $i (1 \leq i \leq M)$ such that X_i = Y_i is odd.
Find the number of pairs of integers $(i,j) satisfying 1 \leq i < j \leq N$ such that A_i and A_j are similar.

Input

The input is given from Standard Input in the following format:
N M
$A_{1,1} A_{1,2} \ldots A_{1,M}$
$A_{2,1} A_{2,2} \ldots A_{2,M}$
$\vdots$
$A_{N,1} A_{N,2} \ldots A_{N,M}$

Output

Print the answer as an integer.

Constraints

• $1 \leq N \leq 2000$
• $1 \leq M \leq 2000$
• $1 \leq A_{i,j} \leq 999$
• All input values are integers.

Sample Input 1

3 3
1 2 3
1 3 4
2 3 4

Sample Output 1

1

The pair (i,j) = (1,2) satisfies the condition because there is only one index k such that A_{1,k} = A_{2,k}, which is k=1.
The pairs (i,j) = (1,3), (2,3) do not satisfy the condition, making (1,2) the only pair that does.

Sample Input 2

6 5
8 27 27 10 24
27 8 2 4 5
15 27 26 17 24
27 27 27 27 27
27 7 22 11 27
19 27 27 27 27

Sample Output 2

5

见题面 Input 部分

见题面 Output 部分