#include<iostream>
#include<vector>
using namespace std;
int t;
int main(){
    cin >> t;
    while (t--){
        int n; cin >> n;
            int ones = 0; int odd = 0;
            for (int j = 0; j < n; ++j){
            string s; cin >> s;
            if (s.length() % 2 == 1) odd++;
            for (int i = 0; i < s.length(); ++i){
                if (s[i] == '1') ones++;
            }
        }
        if (ones % 2 == 1 && odd > 0 || ones % 2 == 0)
            cout << n << endl;
            else cout << n - 1 << endl;

    }
}