#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 mn = numeric_limits<int>::max();
	for(int i=0;i<n;i++) if(s[i] != '0') {
		int j = i;
		while(j + 1 < n && s[j+1] == '1') j++;
		mn = min(mn, j - i + 1);
		i = j;
	}
	cout << c1 + mn << '\n';

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

answer.code:27:9: error: expected unqualified-id before ‘for’
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |         ^~~
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:23: error: ‘n’ was not declared in this scope; did you mean ‘yn’?
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                       ^
      |                       yn
answer.code:27:21: error: ‘i’ does not name a type
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                     ^
answer.code:27:25: error: ‘i’ does not name a type
   27 |         for(int i=0;i<n;i++) if(s[i] != '0') {
      |                         ^
answer.code:33:9: error: ‘cout’ does not name a type
   33 |         cout << c1 + mn << '\n';
      |         ^~~~