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#include <iostream>
#include<vector>
#include<string>
#include<algorithm>
using namespace std;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t,n; cin>>t; string s;
    while(t--){
        cin>>n>>s;
        vector<int>mid,kon;
        int i = 0;
        while(i<s.size() && s[i]=='0'){++i;}
        if(i==s.size()){
            cout<<0<<'\n';
            continue;
        }
        kon.push_back(i);
        i=n-1;
        while(i>=0 && s[i]=='0'){--i;}
        kon.push_back(n-1-i);
        if(kon.size()==2 && kon[1]<kon[0])swap(kon[1],kon[0]);
        for(int i = 0;i<n;++i){
            if(s[i]=='0'){
                int j = i;
                while(j<n && s[j]=='0'){++j;}
                mid.push_back(j-i);
                i=j-1;
            }
        }
        if(s[0]=='0')mid.erase(mid.begin());
        if(s[s.size()-1]=='0')mid.erase(mid.end()-1);
        sort(mid.begin(),mid.end());
        int day = 0; int ile=0;
        int imid=mid.size()-1;
        int ikon=kon.size()-1;
        while(true){
            int omid=-1, okon=-1;
            if(imid>=0)omid=mid[imid]-1-2*day;
            if(imid>=0 && omid==0 && mid[imid]==2*day+1)omid=1;
            if(ikon>=0)okon=kon[ikon]-day;
            //cout<<omid<<" "<<okon<<endl;
            if(okon<0 && omid<0)break;
            if(okon>=omid){ile+=okon;--ikon;++day;}
            else{ile+=omid;--imid;day+=2;}
        }
        int odp1=n-ile;

        day = 1; ile=kon[1];
        imid=mid.size()-1;
        ikon=0;
        while(true){
            int omid=-1, okon=-1;
            if(imid>=0)omid=mid[imid]-1-2*day;
            if(imid>=0 && omid==0 && mid[imid]==2*day+1)omid=1;
            if(ikon>=0)okon=kon[ikon]-day;
            //cout<<omid<<" "<<okon<<endl;
            if(okon<0 && omid<0)break;
            if(okon>=omid){ile+=okon;--ikon;++day;}
            else{ile+=omid;--imid;day+=2;}
        }
        int odp2=n-ile;

        day = 2; ile=kon[1]+kon[0]-1;
        imid=mid.size()-1;
        ikon=-1;
        while(true){
            int omid=-1, okon=-1;
            if(imid>=0)omid=mid[imid]-1-2*day;
            if(imid>=0 && omid==0 && mid[imid]==2*day+1)omid=1;
            if(ikon>=0)okon=kon[ikon]-day;
            //cout<<omid<<" "<<okon<<endl;
            if(okon<0 && omid<0)break;
            if(okon>=omid){ile+=okon;--ikon;++day;}
            else{ile+=omid;--imid;day+=2;}
        }
        int odp3 = n-ile;
        cout<<min(odp1,min(odp2,odp3))<<'\n';
    }
}