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.

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.