#include <bits/stdc++.h>
using namespace std;
int thien, n, tt, h;
string s;
int main() {
  cin >> tt;
  for (int ii = 1; ii <= tt; ii++) {
    cin >> n;
    thien = 0;
    h = 0;
    for (int i = 1; i <= n; i++) {
      cin >> s;
      if (s.length() % 2 != 0) thien++;
      for (int j = 0; j < s.length(); j++)
        if (s[j] == '1') h++;
    }
    if (h % 2 != 0 && thien == 0)
      cout << n - 1 << endl;
    else
      cout << n << endl;
  }
}
