Help with "Guess the animal" (Bronze)

Problems and Contests
#1

Problem Link - USACO

Initially, I didn’t get this problem, but when I read the editorial, it sort of made sense to me. The only part I don’t get is why we have to add one to our count.

cin>>n;
    set<string>S[101];
    
    for(int i = 0; i < n; i++){
    	string s;
    	cin>>s>>a;
    	for(int j = 0; j < a; j++){
    		cin>>s;
    		S[i].in(s);
		}
	}
	ans = 0;
	for(int i = 0; i < n-1; i++){
		for(int j = i+1; j < n; j++){
			int cnt = 0;
			Trav(a,S[j]){
				cnt += S[i].count(a);
			}
			ans = max(ans, cnt+1)**//Why do we have to add one to count????????**;
		}
	}
	cout<<ans;```