#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define int ll
#define pb push_back
#define all(v) (v).begin(), (v).end()

void dbg_out() { cerr << endl; }
template<typename H, typename... T>
void dbg_out(H h, T... t) { cerr << ' ' << h; dbg_out(t...); }
#define dbg(...) { cerr << #__VA_ARGS__ << ':'; dbg_out(__VA_ARGS__); }

void solve() {
	int n; cin >> n;
	string s; cin >> s;
	int c1 = count(all(s), '1');
	if(s[0] == '0' || s.back() == '0') {
		cout << c1 << '\n';
		return;
	}
	for(int i=0;i+1<n;i++) if(s[i] == '0' && s[i+1] == '0') {
		cout << c1 << '\n';
		return;
	}
	int pre = 0;
	while(s[pre] == '1') pre++;
	int suf = n - 1;
	while(s[suf] == '1') suf--;
	cout << c1 + min(pre, n - 1 - suf) << '\n';
}

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