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#include <bits/stdc++.h>
#ifndef ONLINE_JUDGE
# pragma GCC diagnostic warning "-Wall"
# pragma GCC diagnostic warning "-Wextra"
# pragma GCC diagnostic warning "-Wformat=2"
# pragma GCC diagnostic warning "-Wnull-dereference"
# pragma GCC diagnostic warning "-Wduplicated-branches"
# pragma GCC diagnostic warning "-Wduplicated-cond"
# pragma GCC diagnostic warning "-Wfloat-equal"
# pragma GCC diagnostic warning "-Wshadow"
# pragma GCC diagnostic warning "-Wconversion"
# pragma GCC diagnostic warning "-Wlogical-op"
# pragma GCC diagnostic warning "-Wvector-operation-performance"
# pragma GCC diagnostic warning "-Wdisabled-optimization"
# pragma GCC diagnostic warning "-Wunsafe-loop-optimizations"
# pragma GCC diagnostic warning "-Wdouble-promotion"
#endif
#pragma GCC target "arch=ivybridge", "tune=ivybridge"
#if defined(ONLINE_JUDGE) || !defined(__OPTIMIZE__)
# pragma GCC optimize "Ofast", "inline", "unroll-loops", "ipa-pta", "no-rtti", \
  "no-exceptions", "nothrow-opt", "strict-enums", "stdarg-opt", "tracer"
# pragma GCC target "inline-all-stringops"
#endif
#define rangeof(c) (c).begin(), (c).end()

using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;

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

  int qc;
  cin >> qc;
  for(int query = 0; query < qc; query++) {
#ifdef DEBUG
    clog << "teścior " << query << endl;
#endif
    int n;
    cin >> n;
    string s;
    cin >> s;
    
    vector<int> twoc_of_size(n + 1, 0), ones;
    int twoc = 0;
    int block = 0;
    bool is_all_zero = false;
    for(int i = 0; i < n; i++) {
      if(s[i] == '0') block++;
      if((i + 1 >= n || s[i + 1] == '1') && block > 0) {
        int infected_sidec = 2 - (i - block < 0) - (i == n - 1);
        if(infected_sidec == 2) {
          twoc_of_size[block]++;
          twoc++;
        } else if(infected_sidec == 1) {
          ones.push_back(block);
        } else if(infected_sidec == 0) {
          is_all_zero = true;
        } else {
          assert(false);
        }
        block = 0;
      }
    }
    if(is_all_zero) {
      cout << "0\n";
      continue;
    }
    
    sort(rangeof(ones), greater<int>()); // we know ones.size() is two at most
    vector<int> twos;
    twos.reserve(twoc);
    for(int size = n; size >= 0; size--) {
      while(twoc_of_size[size] > 0) {
        twoc_of_size[size]--;
        twos.push_back(size);
      }
    }
    
    int result = 0;
    
    auto calc_twos_val = [&](int time) {
#ifdef DEBUG
      clog << "czesc" << endl;
#endif
      int result = 0;
      for(int size: twos) {
        int actual = size - 2 * time;
        if(actual <= 0) {
          break;
        } if(actual <= 2) {
          actual = 1;
          result++;
          time++;
        } else {
          actual--;
          result += actual;
          time += 2;
        }
#ifdef DEBUG
        clog << size << " " << actual << endl;
#endif
      }
      return result;
    };
    
    result = max(calc_twos_val(0), (ones.size() < 1 ? 0 : max(ones[0] + calc_twos_val(1), (ones.size() < 2 ? 0 : max(ones[1] + calc_twos_val(1), ones[0] + ones[1] - 1 + calc_twos_val(2))))));
    
    cout << n - result << "\n";
  }
}
/*
 2  1
x+1 x

napierw lewe -> x+x-2
najpier prawe -> x-1+x

 2   2  1
x+1 x+1 x

najperw lewe -> x+x-2+x-4
nparwer prawe -> x-3+x-1+x

2  2
11 8

l,p,l,p -> 11+8 - 3 - 2 - 1 - 0
l,l,p,p -> 11+8 - 3 - 2 - 1 - 0

1 2  2
3 11 8

l,m,m,p,p ->
  3 11 8
  3 9 6 after l
  3 8 4 after m
  3 8 2 after m
  3 8 1 after p
  3 8 1 after p



*/