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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int t = 1;
  while (t--) {
    long long int n, m;
    cin >> n >> m;
    char M[n][m];
    for (long long int i = 0; i < n; i++) {
      for (long long int j = 0; j < m; j++) {
        cin >> M[i][j];
      }
    }
    int ans = 0;
    for (int i = 0; i < n; ++i) {
      bool wasBest = false;
      for (int j = 0; j < m; ++j) {
        bool isBest = true;
        for (int k = 0; k < n; ++k)
          if (M[k][j] > M[i][j]) isBest = false;
        if (isBest) wasBest = true;
      }
      if (wasBest) ans++;
    }
    cout << ans;
  }
  return 0;
}
