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

using namespace std;

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

    string cities;
    cin >> cities;

    priority_queue<int> middle_dist;
    vector<int> edge_dist(2, -1);

    for(int i = 0; i < n; i++) {
        if(cities[i] == '1') {
            edge_dist[0] = i;
            break;
        }
    }

    if(edge_dist[0] == -1) {
        cout << "0\n";
        return;
    }

    for(int i = n - 1; i >= edge_dist[0]; i--) {
        if(cities[i] == '1') {
            edge_dist[1] = (n - 1) - i;
            break;
        }
    }

    int result = 1;
    
    int last_city = edge_dist[0];
    
    for(int i = edge_dist[0] + 1; i <= (n - 1) - edge_dist[1]; i++) {
        if(cities[i] == '1') {
            if(i - last_city - 1 > 0) middle_dist.push(i - last_city - 1);
            last_city = i;
            result++;
        }
    }

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

    for(int i = 0; i < n; i++) {
        if(middle_dist.empty() && edge_dist[0] == 0) break;
        
        if(edge_dist[0] - i >= max((middle_dist.empty() ? 0 : middle_dist.top() - 2 * i - 2), 1)) {
            result += min(edge_dist[0], i);
            edge_dist[0] = 0;
            swap(edge_dist[0], edge_dist[1]);

            continue;
        }
        
        if(!middle_dist.empty() && middle_dist.top() <= i * 2) {
            while(!middle_dist.empty()) {
                result += middle_dist.top();
                middle_dist.pop();
            }
            
        }
        
        if(!middle_dist.empty()) { 
            if(middle_dist.top() == i * 2 + 1 || middle_dist.top() == i * 2 + 2) result += middle_dist.top() - 1;
            else {
                result += i * 2 + 1;
                i++;
            }
            middle_dist.pop();
        }
    }

    result += edge_dist[0] + edge_dist[1];
    
    cout << result << "\n";
}

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    long long z;
    cin>>z;

    while(z--){
        solve();
    }

    return 0;
}