#include <bits/stdc++.h>

using namespace std;

using i64 = long long;  

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

    int ans = count(s.begin(), s.end(), '1');
    int mx = n, cnt = 0;
    for (int i = 0;i < n;i ++){
        if (s[i] == '1'){
            cnt ++;
        }else{
            mx = min(mx, cnt);
            break;
        }
    }
    cnt = 0;
    for (int i = n - 1;i >= 0;i --){
        if (s[i] == '1'){
            cnt ++;
        }else{
            mx = min(mx, cnt);
            break;
        }
    }

    cout << ans + mx << "\n";
}

int main() {    
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

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

    return 0;
}