#include <bits/stdc++.h>

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;
using u128 = unsigned __int128;

void solve() {
    int n;
    std::cin >> n;
    
    std::string s;
    std::cin >> s;
    
    int ans = n;
    for (int i = 0, j = -1; i <= n; i++) {
        if (i == n || s[i] == '0') {
            ans = std::min(ans, i - j - 1);
            j = i;
        }
    }
    ans += std::count(s.begin(), s.end(), '1');
    std::cout << ans << "\n";
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int t;
    std::cin >> t;
    
    while (t--) {
        solve();
    }
    
    return 0;
}