For technical reasons, some programming languages (Kotlin, C #) will not be available during round 877.
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A. Marks

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya, 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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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