In a summer camp about Applied Maths, there are \(8m+1\) boys (with \(m > 5\)) and some girls. Every girl is friend with exactly \(3\) boys and for any \(2\) boys, there is exactly \(1\) girl who is their common friend. Let \(n\) be the greatest number of girls that can be chosen from the camp to form a group such that every boy is friend with at most \(1\) girl in the group. Prove that \(n \geq 2m+1\).