152_A. Marks_34901
Vasya, or Mr. Vasily Petrov is a dean of a department in a local university. After the winter exams he got his hands on a group's gradebook.

Overall the group has n students. They received marks for m subjects. Each student got a mark from 1 to 9 (inclusive) for each subject.

Let's consider a student the best at some subject, if there is no student who got a higher mark for this subject. Let's consider a student successful, if there exists a subject he is the best at.

Your task is to find the number of successful students in the group.

Input

The first input line contains two integers n and m (1 ≤ n, m ≤ 100) — the number of students and the number of subjects, correspondingly. Next n lines each containing m characters describe the gradebook. Each character in the gradebook is a number from 1 to 9. Note that the marks in a rows are not sepatated by spaces.

Output

Print the single number — the number of successful students in the given group.

Examples

Input

3 3
223
232
112


Output

2


Input

3 5
91728
11828
11111


Output

3

Note

In the first sample test the student number 1 is the best at subjects 1 and 3, student 2 is the best at subjects 1 and 2, but student 3 isn't the best at any subject.

In the second sample test each student is the best at at least one subject.
n,m=map(int,input().split())
a=list()
b=list()
c=list()
for i in range(n):
    a.append([int(i) for i in list(input())])
for i in range(m):
    x=0
    for j in range(n):
        if(a[j][i]>x):
            x=a[j][i]
            b=list()
            b.append(j)
        elif(a[j][i]==x):
            b.append(j)
    c+=b
print(len(set(c)))