#include <bits/stdc++.h>
using namespace std;
int main() {
  long long t1, n, zero, one, cnt, cnt1, i, j;
  string s;
  cin >> t1;
  while (t1--) {
    cin >> n;
    cnt = 0, zero = 0, one = 0;
    for (i = 0; i < n; i++) {
      cin >> s;
      for (j = 0; j < s.length(); j++) {
        if (s[j] == '0')
          zero++;
        else
          one++;
      }
      if (s.length() % 2 != 0) cnt++;
    }
    cnt1 = 0;
    if (zero % 2 != 0) cnt1++;
    if (one % 2 != 0) cnt1++;
    if (cnt >= cnt1)
      cout << n << endl;
    else
      cout << n - 1 << endl;
  }
}
