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#include<bits/stdc++.h>

using namespace std;

const int N = 1e5+3;

int n,L=0,R=0;
int T[N+3],T2[N+3];
string inp;
vector<int> v;

void zeruj(){
	v.clear();
	L = 0;
	R = 0;
	inp = "";
	for(int i = 1;i<=n;i++){
		T2[i]=0;
		T[i]=0;
	}
}

int main(){
	
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	int zap;
	cin>>zap;
	
	while(zap--){
	
		zeruj();
		cin>>n;
		cin>>inp;
		bool flag = true;
		for(int i = 1;i<=n;i++){
			T[i] = (inp[i-1]=='1');
			if(T[i]){
				flag = false;
			}
		}
		if(flag){
			cout<<0<<endl;
			continue;
		}
		while(T[L+1]!=1){
			L += 1;
		}
		R = n+1;
		while(T[R-1]!=1){
			R -= 1;
		}
		int ost = R;
		ost -= 1;
		R = n-R + 1;
		int p = L+1;
		for(int k = p;k<=ost;k++){
			if(T[k]==1){
				if(T[p]==0)
				v.push_back(k-p);
				p = k+1;
			}
		}
		sort(v.begin(),v.end());
		reverse(v.begin(),v.end());
		int n2 = v.size();
		if(n2==0){
			cout<<n - (L+R-(L !=0 && R != 0))<<endl;
			continue;
		}
		int suma1 = 0;
		for(int i = 0;i<v.size();i++){
			T2[i+1] = v[i];
		}
		for(int i = 1;i<=n2;i++){
			int d = T2[i] - (i-1)*4;
			if(d <= 0){
				break;
			}
			if(d == 1 || d == 2){
				suma1 += 1;
			}else{
				suma1 += d-1;
			}
		}
		if(L < R){
			swap(L,R);
		}
		int suma = L;
		for(int i = 1;i<=n2;i++){
			int x = T2[i] - 2 - 4*(i-1);
			if(x <= 0){
				break;
			}
			if(x == 1 || x == 2){
				suma += 1;
				continue;
			}
			suma += x-1;
		}
		
		int suma2 = L+R-1;
		for(int i = 1;i<=n2;i++){
			int x = T2[i] - 4 - 4*(i-1);
			if(x <= 0){
				break;
			}
			if(x == 1 || x == 2){
				suma2 += 1;
				continue;
			}
			suma2 += x-1;
		}
		int best = max({suma,suma2,suma1});
		cout<<n-best<<endl;
	}
	
	return 0;
	
}