Note

Problem Statement

You are given $M$ strings $B_1, \cdots, B_M$, each an $N$-digit binary representation. Let $b_{m, n}$ be the $n$-th digit of $B_m$. In this problem, bitwise OR and bitwise AND are denoted by $C | D, \ C \& D$, respectively.
A subset $T$ of the set $\{0,1,...,2^N-1\}$ that satisfies the following conditions is called a good set.

• $0, B_1, \cdots, B_M, 2^N-1 \in \mathcal{T}$
• If $C,D \in \mathcal{T}$, then $C\&D, C|D \in \mathcal{T}$

Background

$\mathcal T$ forms a structure called a topology on the finite set $X = \{1, \cdots, N \}$ (Wikipedia). That is, identifying an $N$-digit binary number $b_1 \cdots b_N$ with the subset $\{ i \in X : b_i = 1 \}$ of $X$, it satisfies
$\emptyset, X \in \mathcal T,$
$U, V \in \mathcal T \Rightarrow U \cap V \in \mathcal T,$
$U, V \in \mathcal T \Rightarrow U \cup V \in \mathcal T$
.
This problem asks for the number of connected components of the topological space.

Input

$M \ N$
$b_{1, 1} b_{1, 2} \cdots b_{1, N}$
$b_{2, 1} b_{2, 2} \cdots b_{2, N}$
$\vdots$
$b_{M, 1} b_{M, 2} \cdots b_{M, N}$

$1 \leq M \leq 1024,$
$1 \leq N \leq 4096,$
$b_{i, j} \in \{ 0, 1 \} \ (1 \leq i \leq M, \ 1 \leq j \leq N).$
Note that the $B_m = b_{m, 1} b_{m, 2} \cdots b_{m, N}$ are not necessarily distinct.

Output

Print a newline at the end.

Sample

4 4
1100
1010
1001
1100

1

2 3
100
011

2

1 16
0000000000000000

1