Problem Statement

The wizard Koa has made $N$ magic items numbered $1,2,\dots,N$.

Each magic item has $K$ values representing its performance, and the $j$-th $(1 \leq j \leq K)$ value of magic item $i$ $(1 \leq i \leq N)$ is $S_{i,j}$.

Koa wants to keep the cost of storing these magic items as low as possible, so
she has decided to sell all magic items $x$ $(1 \leq x \leq N)$ that satisfy the following condition.

• There exists an integer $y$ $(1 \leq y \leq N)$ different from $\boldsymbol{x}$ such that $S_{x,k} \leq S_{y,k}$ holds for every integer $k$ $(1 \leq k \leq K)$.

Find the number of magic items Koa sells.

Constraints

• $1 \leq N \leq \min(2 \times 10^{5}, 5^{K})$

• $1 \leq K \leq 8$

• $0 \leq S_{i,j} \leq 4$ $(1 \leq i \leq N \text{ and } 1 \leq j \leq K)$

• $( S_{i,1}, S_{i,2}, \dots, S_{i,K} ) \neq ( S_{j,1}, S_{j,2}, \dots, S_{j,K} )$ $(1 \leq i < j \leq N)$

• $N, K$ and $S_{i,j}$ $(1 \leq i \leq N \text{ and } 1 \leq j \leq K)$ are all integers

Input

The input is given in the following format.

$N$ $K$
$S_{1,1} S_{1,2} \cdots S_{1,K}$
$S_{2,1} S_{2,2} \cdots S_{2,K}$
 $\vdots$    $\ddots$    $\vdots$
$S_{N,1} S_{N,2} \cdots S_{N,K}$

• Line $1$ contains $N, K$ in this order, separated by a half-width space

• Line $(1 + i)$ $(1 \leq i \leq N)$ contains $S_{i,1}, S_{i,2} \dots, S_{i,K}$ in this order as a string of length $K$

Output

Print the answer on $1$ line.

Sample

3 3
210
420
004

1

2 2
40
04

0

5 1
2
3
0
1
4

4

1 8
44444444

0