Exam Manipulation

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Time limit1sMemory limit512 MB

Summary

Given n students' True/False answer strings of length k, choose an answer key to maximize the minimum score across all students.

Level: Medium5 of 10
Topics: Brute force, Bit manipulation, Implementation, Array
Solved: No attempts yet

Problem

A group of students is taking a True/False exam. Each question is worth one point. You, as their teacher, want to make your students look as good as possible, so you cheat! (I know, you would never actually do that.) To cheat, you manipulate the answer key so that the lowest score in the class is as high as possible.

What is the best possible lowest score you can achieve?

Input

The first line of input contains two integers $n$ ( $1 \le n \le 1,000$ ) and $k$ ( $1 \le k \le 10$ ), where $n$ is the number of students, and $k$ is the number of True/False questions on the exam.

Each of the next $n$ lines contains a string of length $k$ , consisting only of upper-case ‘T’ and uppercase ‘F’. This string represents the answers that a student submitted, in the order the questions were given.

Output

Output, on a single line, the best possible lowest score in the class.

Examples2

Example 1
Input
```
5 4
TFTF
TFFF
TFTT
TFFT
TFTF
```
Expected output
```
2
```
Example 2
Input
```
3 5
TFTFT
TFTFT
TFTFT
```
Expected output
```
5
```