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

int pom(int index, const std::vector<int> &bi_intervals, int days_passed) {
    int counter = 0;
    while (index < bi_intervals.size()) {
        if (bi_intervals[index] - 2 * days_passed > 2) {
            counter += bi_intervals[index] - 2 * days_passed - 1;
            days_passed += 2;
            ++index;
        }
        else {
            break;
        }
    }

    if (bi_intervals[index] - 2 * days_passed > 0) {
        ++counter;
    }
    
    return counter;
}

int solution() {
    int n;
    std::cin >> n;
    std::string input;
    std::cin >> input;

    std::vector<int> uni_intervals;
    std::vector<int> bi_intervals;

    int begin = 0;
    for (int i = 1; i < n; ++i) {
        if (input[i] != input[i - 1]) {
            if (input[i - 1] == '0') {
                if (begin == 0) {
                    uni_intervals.push_back(i - begin);
                }
                else {
                    bi_intervals.push_back(i - begin);
                }
            }
            begin = i;
        }
    }

    if (input[n - 1] == '0') {
        uni_intervals.push_back(n - begin);
    }

    if (uni_intervals.size() == 1 && uni_intervals[0] == n) {
        return 0;
    }

    std::sort(uni_intervals.begin(), uni_intervals.end(), std::greater<int>());
    std::sort(bi_intervals.begin(), bi_intervals.end(), std::greater<int>());

    // bez alf
    int counter = pom(0, bi_intervals, 0);

    if (uni_intervals.empty()) {
        return n - counter;
    }

    // jedna alfa
    int counter2 = pom(0, bi_intervals, 1) + uni_intervals[0];
    if (counter2 > counter) {
        counter = counter2;
    }

    if (uni_intervals.size() < 2) {
        return n - counter;
    }

    // dwie alfy
    counter2 = pom(0, bi_intervals, 2) + uni_intervals[0] + uni_intervals[1] - 1;

    if (counter2 > counter) {
        counter = counter2;
    }

    return n - counter;
}

int main() {
    int t;
    std::cin >> t;
    while (t--) {
        std::cout << solution() << "\n";
    }
    return 0;
}