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#if defined(EMBE_DEBUG) && !defined(NDEBUG)
#include "embe-debug.hpp"
#else
#define LOG_INDENT(...) do {} while (false)
#define LOG(...) do {} while (false)
#define DUMP(...) do {} while (false)
#endif

#include <algorithm>
#include <functional>
#include <iostream>
#include <optional>
#include <string>
#include <utility>
#include <vector>
using namespace std;

namespace {

vector<pair<int, int>> parse(string s)
{
  vector<int> lens;
  {
    auto i = s.begin();
    while (true) {
      auto j = find(i, s.end(), '1');
      lens.push_back(j - i);
      if (j == s.end()) break;
      i = find(j, s.end(), '0');
    }
  }
  int n = lens.size();
  if (n == 1) {
    return {{0, lens[0]}};
  }
  vector<pair<int, int>> res;
  res.reserve(lens.size());
  if (lens.front() > 0) res.emplace_back(1, lens.front());
  if (lens.back() > 0) res.emplace_back(1, lens.back());
  for (int i = 1; i < n - 1; ++i) {
    res.emplace_back(2, lens[i]);
  }
  return res;
}

int solve(vector<pair<int, int>> data)
{
  if (data.size() == 1 && data[0].first == 0) return data[0].second;
  vector<int> ones;
  vector<int> twos;
  for (auto const& [m, n]: data) {
    if (m == 1) ones.emplace_back(n);
    else twos.emplace_back(n);
  }
  sort(ones.begin(), ones.end(), greater<>());
  sort(twos.begin(), twos.end(), greater<>());
  int oo = ones.size();
  optional<int> res;
  for (int o = 0; o <= oo; ++o) {
    int t = 0;
    int cur = 0;
    for (int i = 0; i < o; ++i) {
      int x = ones[i];
      x -= t;
      if (x <= 0) break;
      cur += x;
      ++t;
    }
    for (auto x: twos) {
      x -= 2 * t;
      if (x <= 0) break;
      if (x <= 2) {
        ++cur;
        break;
      }
      cur += x - 1;
      t += 2;
    }
    if (!res || *res < cur) res = cur;
  }
  return *res;
}

}

int main()
{
  iostream::sync_with_stdio(false);
  cin.tie(nullptr);

  int t;
  cin >> t;

  while (t > 0) {
    --t;
    int n;
    string s;
    cin >> n >> s;
    auto tmp = parse(s);
    cout << n - solve(tmp) << endl;
  }

  return 0;
}