Binary Matrix
Description
You are given a matrix of size n × m. Each element of the matrix is either 1 or 0. You have to determine the number of connected components consisting of 1's. Two cells belong to the same component if they have a common border, and both elements in these cells are 1's.
Note that the memory limit is unusual!
The first line contains two numbers n and m (1 ≤ n ≤ 212, 4 ≤ m ≤ 214) — the number of rows and columns, respectively. It is guaranteed that m is divisible by 4.
Then the representation of matrix follows. Each of n next lines contains 
one-digit hexadecimal numbers (that is, these numbers can be represented either as digits from 0 to 9 or as uppercase Latin letters from A to F). Binary representation of each of these numbers denotes next 4 elements of the matrix in the corresponding row. For example, if the number B is given, then the corresponding elements are 1011, and if the number is 5, then the corresponding elements are 0101.
Elements are not separated by whitespaces.
Print the number of connected components consisting of 1's.
Input
The first line contains two numbers n and m (1 ≤ n ≤ 212, 4 ≤ m ≤ 214) — the number of rows and columns, respectively. It is guaranteed that m is divisible by 4.
Then the representation of matrix follows. Each of n next lines contains one-digit hexadecimal numbers (that is, these numbers can be represented either as digits from 0 to 9 or as uppercase Latin letters from A to F). Binary representation of each of these numbers denotes next 4 elements of the matrix in the corresponding row. For example, if the number B is given, then the corresponding elements are 1011, and if the number is 5, then the corresponding elements are 0101.
Elements are not separated by whitespaces.
Output
Print the number of connected components consisting of 1's.
Samples
3 4
1
A
8
3
2 8
5F
E3
2
1 4
0
0
Note
In the first example the matrix is:
0001
1010
1000
It is clear that it has three components.
The second example:
01011111
11100011
It is clear that the number of components is 2.
There are no 1's in the third example, so the answer is 0.