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#include <bits/stdc++.h>
#define rep(i, a, b) for (int i = a; i <= b; i++)
#define per(i, a, b) for (int i = b; a <= i; i--)
#define cat(x) cerr << #x << " = " << x << '\n';
using ll = long long;
using namespace std;

const int N = 111000;

int n, dp[N][3];
string s;
vector<int> v;

void solve() {
	cin >> n >> s;

	v.clear();
	int last = -1;
	rep(i, 0, n - 1) {
		if (s[i] == '1') {
			if (last >= 0) {
				v.push_back(i - last - 1);
			}
			last = i;
		}
	}

	if (last == -1) {
		cout << 0 << '\n';
		return;
	}

	sort(v.rbegin(), v.rend());

	int w[2]{};
	for (int i = 0; s[i] == '0'; w[0]++, i++);
	for (int i = n - 1; s[i] == '0'; w[1]++, i--);

	if (w[0] < w[1]) swap(w[0], w[1]);

	int m = int(v.size());
	rep(i, 0, m)
		rep(j, 0, 2)
			dp[i][j] = 0;

	auto upd = [&](int &a, int b) {
		a = max(a, b);
	};

	auto f1 = [&](int x, int tim) {
		return max(0, x - tim);
	};

	auto f2 = [&](int x, int tim) {
		x -= 2 * tim;
		if (x <= 0) return 0;
		if (x == 1) return 1;
		return x - 1;
	};

	// bigger segments go before smallers
	rep(i, 0, m) {
		// outside segments
		upd(dp[i][1], dp[i][0] + f1(w[0], 2 * i));
		upd(dp[i][2], dp[i][1] + f1(w[1], 2 * i + 1));
		// inside segment
		if (i < m) {
			rep(j, 0, 2) {
				upd(dp[i + 1][j], dp[i][j] + f2(v[i], 2 * i + j));
			}
		}
	}
	
	cout << n - dp[m][2] << '\n';
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	int t;
	cin >> t;
	while (t--) {
		solve();
	}

	return 0;
}