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#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define e1 first
#define e2 second
#define pb push_back
#define OUT(x) {cout << x << "\n"; exit(0); }
#define TCOUT(x) {cout << x << "\n"; return; }
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define rep(i, l, r) for(int i = (l); i < (r); ++i)
#define boost {ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); }
#define sz(x) int(x.size())
#define trav(a, x) for(auto& a : x)
#define all(x) begin(x), end(x)
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
/*#include <atcoder/modint>
using namespace atcoder;
using mint = modint998244353;
vector <mint> fac, inv;
mint binom(int n, int k) {
	if (n < k || n < 0) return 0;
	return fac[n] * inv[k] * inv[n-k];
}

void prep(int N) {
	fac.resize(N+1, 1); inv.resize(N+1, 1);
	for (int i=1; i<=N; ++i) fac[i] = fac[i-1] * i;
	inv[N] = fac[N].inv();
	for (int i=N-1; i>0; --i) inv[i] = inv[i+1] * (i + 1);
}*/

mt19937_64 rng(time(0));
int random(int l, int r) {
	return uniform_int_distribution<int>(l, r)(rng);
}
#ifdef DEBUG
template<class T> int size(T &&x) {
	return int(x.size());
}
template<class A, class B> ostream& operator<<(ostream &out, const pair<A, B> &p) {
	return out << '(' << p.first << ", " << p.second << ')';
}
template<class T> auto operator<<(ostream &out, T &&x) -> decltype(x.begin(), out) {
	out << '{';
	for(auto it = x.begin(); it != x.end(); ++it)
		out << *it << (it == prev(x.end()) ? "" : ", ");
	return out << '}';
}
void dump() {}
template<class T, class... Args> void dump(T &&x, Args... args) {
	cerr << x << ";  ";
	dump(args...);
}
#endif
#ifdef DEBUG
  struct Nl{~Nl(){cerr << '\n';}};
# define debug(x...) cerr << (strcmp(#x, "") ? #x ":  " : ""), dump(x), Nl(), cerr << ""
#else
# define debug(...) 0 && cerr
#endif
const int maxn = 1000100;

//Did you REAALLY consider sample tests?
vi infect_cities(vi cities, vi &safe) {
	vi result = cities;
	int n = sz(cities);
	rep(i, 0, n) {
		if (safe[i]) continue;
		if (i > 0) result[i] |= cities[i - 1];
		if (i + 1 < n) result[i] |= cities[i + 1];
	}
	return result;
}

int brut(vi vec) {
	int n = sz(vec);
	vi perm(n);
	rep(i, 0, n) perm[i] = i;
	
	int best_result = INT_MAX;
	do {
		vi safe(n, 0);
		vi cities = vec;
		trav(vaccinating, perm) {
			if (!cities[vaccinating]) safe[vaccinating] = 1;
			cities = infect_cities(cities, safe);
		}
		int option = 0;
		rep(i, 0, n) option += cities[i];
		best_result = min(best_result, option);
	}while(next_permutation(all(perm)));
	
	return best_result;
}

vi compress_intervals(vi vec) {
	vec.pb(1);
	reverse(all(vec));
	vec.pb(1);
	reverse(all(vec));

	vector <int> zeroes;
	rep(i, 1, sz(vec)) {
		if (vec[i] == 0) {
			if (vec[i-1] == 1) zeroes.pb(1);
			else zeroes.back() += 1;
		}
	}
	return zeroes;
}

int wzo(vi vec) {
	auto sequences = compress_intervals(vec);
	int n = sz(vec);
	vi dwojki;
	vi jedynki;
	
	if (sequences.empty()) return n; //all virus
	if (sequences[0] == n) return 0; //no virus
	int sajz = sz(sequences);
	for (int i = 1; i + 1 < sajz; ++i) {
		dwojki.pb(sequences[i]);
	}
	
	if (sz(sequences) == 1) {
		int border = 0;
		if (vec[0] == 1) ++border;
		if (vec.back() == 1) ++border;
		assert(border > 0);
		if (border == 1) jedynki.pb(sequences[0]);
		else dwojki.pb(sequences[0]);
	}
	else {
		if (vec[0] == 1) dwojki.pb(sequences[0]);
		else jedynki.pb(sequences[0]);
	
		if (vec.back() == 1) dwojki.pb(sequences[sajz - 1]);
		else jedynki.pb(sequences[sajz - 1]);
	}

	sort(all(jedynki), greater<int>());
	sort(all(dwojki), greater<int>());
	vi cpdwojki = dwojki;
	assert(sz(jedynki) <= 2);
	//debug(dwojki); debug(jedynki);
	// may be the case that some ones are ignored completely
	int best = 0;
	for (int used_ones = 0; used_ones <= sz(jedynki); ++used_ones) {
		dwojki = cpdwojki;
		int time_passed = 0; int score = 0;
		for (int i=0; i<used_ones; ++i) {
			score += max(0, jedynki[i] - time_passed);
			time_passed += 1;
		}
		for (int i=0; i<sz(dwojki); ++i) {
			int removed_so_far = 2 * time_passed;
			if (removed_so_far >= dwojki[i]) break;
			dwojki[i] -= removed_so_far;
			assert(dwojki[i] > 0);
			score += 1; dwojki[i] -= 2; //from both ends disappear
			time_passed += 1;
			if (dwojki[i] > 0) {
				time_passed += 1;
				score += dwojki[i];
			}
		}
		best = max(best, score);
	}
	
	return n - best;
}

bool TEST = 0;

int main() {
	boost;
	int tests;
	cin >> tests;
	while (tests--) {
		int n; string s;
		if (!TEST) {
			cin >> n >> s;
		}
		else {
			//TEST GENERATION
			const int prob_zero = 80;
			n = random(1, 8);
			s = "";
			rep(i, 0, n) {
				if (random(0, 100) < prob_zero) s += '0';
				else s += '1';
			}
			//END TEST GENERATION
		}
		vi vec(n);
		rep(i, 0, n) vec[i] = (s[i] == '1') ? 1 : 0;
		if (!TEST) {
			cout << wzo(vec) << "\n";
		}
		else {
			if (tests % 100 == 0) cout << tests << endl;
			auto model = wzo(vec);
			auto slow = brut(vec);
			if (model != slow) {
				debug(vec);
				debug(model);
				debug(slow);
				OUT("WA");
			}
		}
		
		
	}
}