#include <bits/stdc++.h>
using namespace std;
const long long MOD = (1 << 30);
const double Exp = 1e-8;
const int maxm = 1e5 + 7;
const int maxn = 1e5 + 7;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const double pi = 3.1415926535898;
string s;
int q, n, sum1, sum2, sum3;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  cin >> q;
  while (q--) {
    cin >> n;
    sum1 = sum2 = sum3 = 0;
    for (int i = 1; i <= n; ++i) {
      cin >> s;
      if (s.size() % 2) sum3++;
      for (int j = 0; j < s.size(); ++j) {
        if (s[j] == '1')
          sum1++;
        else
          sum2++;
      }
    }
    if (sum1 % 2 && sum2 % 2 && !sum3)
      cout << n - 1 << endl;
    else
      cout << n << endl;
  }
  return 0;
}
