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Description

You have taken the graduation picture of graduates. The picture could be regarded as a matrix A of $n \times n$, each element in A is 0 or 1, representing a blank background or a student, respectively.

However, teachers are too busy to take photos with students and only took a group photo themselves. The photo could be regarded as a matrix B of $1 \times m$ where each element is 2 representing a teacher.

As a master of photoshop, your job is to put photo B into photo A with the following constraints:

• you are not allowed to split, rotate or scale the picture, but only translation.
• each element in matrix B should overlap with an element in A completely, and each teacher should overlap with a blank background, not shelter from a student.

Please calculate the possible ways that you can put photo B into photo A.

Format

Input

The first line contains two integers$n,m(1 \le n,m \le 2000)$ indicating the size of photos A and B.

In the next $n$ lines,each line contains ${n}$ characters of '0' or '1',representing the matrix A.

The last line contains ${m}$ characters of '2', representing matrix B.

Output

Output one integer in a line, indicating the answer.

Samples

5 3
00000
01110
01110
01110
00000
222

6

3 2
101
010
101
22

0

3 1
101
010
101
2

4

Limitation

1s, 1024KiB for each test case.