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#include <iostream>
#include <string>
#include <algorithm>
#include <vector>

using namespace std;

int n, l, r;
vector<int> mid;

int solve_r(int& time) {
	int result =  max(r-time, 0);
	++time;
	return result;
}

int solve_l(int& time) {
	int result = max(l-time, 0);
	++time;
	return result;
}

int solve_mid(int& time) {
	int result = 0;
	for(auto el: mid) {
		if(el > 2*time) {
			if(el > 2*(time+1)) {
				result += el-2*time - 1;
				time += 2;
			} else {
				++result;
				++time;
			}
		}
	}
	return result;
}

int l_mid_r() {
	int time = 0;
	int result = solve_l(time);
	result += solve_mid(time);
	result += solve_r(time);
	return result;
}

int l_r_mid() {
	int time = 0;
	int result = 0;
	result += solve_l(time);
	result += solve_r(time);
	result += solve_mid(time);
	return result;
}

int mid_l_r() {
	int time = 0;
	int result = 0;
	result += solve_mid(time);
	result += solve_l(time);
	result += solve_r(time);
	return result;
}

int mid_r_l() {
	int time = 0;
	int result = 0;
	result += solve_mid(time);
	result += solve_r(time);
	result += solve_l(time);
	return result;
}

int r_mid_l() {
	int time = 0;
	int result = 0;
	result += solve_r(time);
	result += solve_mid(time);
	result += solve_l(time);
	return result;
}

int r_l_mid() {
	int time = 0;
	int result = 0;
	result += solve_r(time);
	result += solve_l(time);
	result += solve_mid(time);
	return result;
}

int main() {
	ios_base::sync_with_stdio(false);
	int t;
	cin >> t;
	while(t--) {
		mid.clear();
		cin >> n;
		string input;
		cin >> input;
		int ind = 0, prev;
		while(ind < input.size() && input[ind] != '1') {
			++ind;
		}
		l = ind;
		prev = ind++;
		for(; ind < input.size(); ++ind) {
			if(input[ind] == '1') {
				if(ind-prev-1 > 0) {
					mid.push_back(ind-prev-1);
				}
				prev = ind;
			}
		}
		r = ind - prev-1;
		
		// cout << l << " " << mid.size() << " " << r << endl;
		
		int time = 0;
		
		sort(mid.begin(), mid.end());
		reverse(mid.begin(), mid.end());
		
		// cout << input << ": " << solve_mid(time) << endl;
		// cout << time << endl;
		
		int res = 0;
		res = max(res, l_mid_r());
		res = max(res, l_r_mid());
		res = max(res, r_l_mid());
		res = max(res, r_mid_l());
		res = max(res, mid_l_r());
		res = max(res, mid_r_l());
		// cout << input << ": " << res << endl;
		cout << n-res << endl;
	}
	return 0;
}