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#include <algorithm>
#include <iostream>
#include <limits>
#include <utility>
#include <vector>

void another_day(std::vector<char>& cities)
{
    for (int i = 0; i < cities.size() - 1; i++) {
        if (cities[i] == '0' && cities[i + 1] == '1') {
            cities[i] = '1';
        }
        if (cities[i] == '1' && cities[i + 1] == '0') {
            cities[i + 1] = '1';
            i++;
        }
    }
}

bool is_pandemic_stable(const std::vector<char>& cities)
{
    for (int i = 0; i < cities.size() - 1; i++) {
        if (cities[i] == '1' && cities[i + 1] == '0') {
            return false;
        }
        if (cities[i] == '0' && cities[i + 1] == '1') {
            return false;
        }
    }
    return true;
}
void vaccinate(std::vector<char>& cities, int id)
{
    cities[id] = '2';
}

std::pair<int, int> find_border_city(const std::vector<char>& cities)
{
    std::vector<int> sequences(cities.size());
    int max_sequence{std::numeric_limits<int>::min()};
    int max_id{0};
    int max2_sequence{std::numeric_limits<int>::min()};
    int max2_id{0};
    bool is_2_started{false};
    for (int i = 0; i < cities.size(); ++i) {
        if (i == 0 && cities[i] == '0') {
            sequences[i] = 1;
        } else if (cities[i] == '0') {
            sequences[i] = sequences[i - 1] + 1;
        } else if (cities[i] == '2' && is_2_started) {
            sequences[i] = 0;
            max2_sequence = -1;
            max2_id = -1;
            is_2_started = false;
        } else if (cities[i] == '2') {
            sequences[i] = 0;
            is_2_started = true;
        } else {
            sequences[i] = 0;
        }
        if (!is_2_started && sequences[i] > max_sequence) {
            max_sequence = sequences[i];
            max_id = i;
        }
        if (is_2_started && sequences[i] > max2_sequence) {
            max2_sequence = sequences[i];
            max2_id = i;
        }
    }
    if (max_sequence > max2_sequence) {
        return std::make_pair(max_id - (max_sequence - 1), max_id);
    }
    return std::make_pair(max2_id - (max2_sequence - 1), max2_id);
}

int pan(std::vector<char> cities)
{
    // O(N)
    while (!is_pandemic_stable(cities)) {
        // O(N)
        const auto& [start_id, stop_id] = find_border_city(cities);
        int vaccination_id = 0;
        if (start_id == 0) {
            vaccination_id = stop_id;
        } else if (stop_id == cities.size() - 1) {
            vaccination_id = start_id;
        } else if (cities[start_id - 1] == '1') {
            vaccination_id = start_id;
        } else {
            vaccination_id = stop_id;
        }
        vaccinate(cities, vaccination_id);
        // O(N)
        another_day(cities);
    }
    // O(N)
    return std::count(cities.cbegin(), cities.cend(), '1');
}

int main()
{
    int test_cases{};
    std::cin >> test_cases;
    for (int i = 0; i < test_cases; ++i) {
        int cities_count{};
        std::cin >> cities_count;
        std::vector<char> cities(cities_count);
        for (int i = 0; i < cities_count; ++i) {
            std::cin >> cities[i];
        }
        std::cout << pan(cities) << "\n";
    }
    return 0;
}