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#include <bits/stdc++.h>
#include <chrono>
#include <math.h>
using namespace std;
#define endl "\n"
#define mp make_pair
#define st first
#define nd second
#define pii pair<int, int>
#define pb push_back
#define _upgrade ios_base::sync_with_stdio(0), cout.setf(ios::fixed), cout.precision(10), cin.tie(0), cout.tie(0);
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define fwd(i, a, b) for (int i = (a); i < (b); ++i)
#define trav(a, x) for (auto &a : x)
#define all(c) (c).begin(), (c).end()
#define sz(X) (int)((X).size())
typedef long double ld;
typedef unsigned long long ull;
typedef long long ll;
// mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());uniform_int_distribution<int> distr(0, 1e9);auto my_rand = bind(distr, gen); // my_rand() zwraca teraz liczbe z przedzialu [a, b]
#ifdef LOCAL
ostream &operator<<(ostream &out, string str) {
   for (char c : str)
      out << c;
   return out;
}
template <class L, class R> ostream &operator<<(ostream &out, pair<L, R> p) { return out << "(" << p.st << ", " << p.nd << ")"; }
template <class L, class R, class S> ostream &operator<<(ostream &out, tuple<L, R, S> p) {
   auto &[a, b, c] = p;
   return out << "(" << a << ", " << b << ", " << c << ")";
}
template <class T> auto operator<<(ostream &out, T a) -> decltype(a.begin(), out) {
   out << '{';
   for (auto it = a.begin(); it != a.end(); it = next(it))
      out << (it != a.begin() ? ", " : "") << *it;
   return out << '}';
}
void dump() { cerr << "\n"; }
template <class T, class... Ts> void dump(T a, Ts... x) {
   cerr << a << ", ";
   dump(x...);
}
#define debug(...) cerr << "[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__)
#else
#define debug(...) 42
#endif

int solve(deque<int> &A, int t) {
   if (sz(A) == 0)
      return 0;
   int res = A[0] == (2 * t + 1) ? 1 : max(0, A[0] - (2 * t + 1));
   A.pop_front();
   debug(res);
   return solve(A, t + 2) + res;
}

int solve(deque<int> A, int a, int b) {
   auto P = A, Q = A, R = A;
   return max({solve(P, 0), solve(Q, 1) + max(a, b), solve(R, 2) + a + b - 1});
}

int solve(string S, int n) {
   vector<int> X = {0};
   for (char c : S)
      if (c == '1')
         X.push_back(0);
      else
         X.back()++;

   if (sz(X) == 1)
      return 0;

   debug(X);

   int a = X[0];
   int b = X.back();
   debug(a, b);

   deque<int> A(X.begin() + 1, X.end() - 1);
   sort(all(A), greater<int>());
   debug(A);

   return n - solve(A, a, b);
}

void solve() {
   int n;
   string S;
   cin >> n >> S;
   cout << solve(S, n) << endl;
}

int32_t main() {
   _upgrade;
   int Z;
   cin >> Z;
   while (Z--)
      solve();
}