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#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>

void solve() {
  long n;
  std::string b;
  std::cin >> n >> b;
  long size = 0;
  bool first = true;
  std::vector<long> R;
  long r1 = 0, r2 = 0;
  for (char c : b) {
    if (c == '0') ++size;
    else if (c == '1') {
      if (first) r1 = size;
      else R.push_back(size);
      first = false;
      size = 0;
    }
  }
  r2 = size;
  std::sort(R.begin(), R.end(), std::greater<long>());

  long max_saved = 0;
  for (int i=0;i<=3;++i) {
    long saved = 0;
    long level = 0;

    if (i&1) {
      saved += std::max(r1 - level/2, 0l);
      level += 2;
    }
    if (i&2) {
      saved += std::max(r2 - level/2, 0l);
      level += 2;
    }
    for (long r : R) {
      if (r-level == 1 || r-level == 2) {
        saved += 1;
        level += 2;
      }
      else if (level+1 < r) {
        saved += r - level - 1;
        level += 4;
      }
    }
    max_saved = std::max(saved, max_saved);
  }

  std::cout << n-max_saved << "\n";
}

int main() {
  std::ios_base::sync_with_stdio(0);
  long t;
  std::cin >> t;
  while (t--) solve();
  return 0;
}