# HackerRank: ACM ICPC Team

### Problem

You are given a list of N people who are attending ACM-ICPC World Finals. Each of them are either well versed in a topic or they are not. Find out the maximum number of topics a 2-person team can know. And also find out how many teams can know that maximum number of topics.

Note Suppose a, b, and c are three different people, then (a,b) and (b,c) are counted as two different teams.

Input Format

The first line contains two integers, N and M, separated by a single space, where N represents the number of people, and M represents the number of topics. N lines follow.
Each line contains a binary string of length M. If the ith line’s jth character is 11, then the ith person knows the jth topic; otherwise, he doesn’t know the topic.

Constraints
2N500
1M500

Output Format

On the first line, print the maximum number of topics a 2-person team can know.
On the second line, print the number of 2-person teams that can know the maximum number of topics.

Sample Input

4 5
10101
11100
11010
00101


Sample Output

5
2


Explanation

(1, 3) and (3, 4) know all the 5 topics. So the maximal topics a 2-person team knows is 5, and only 2 teams can achieve this.

### Solution

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