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#include <bits/stdc++.h>
#define fi first
#define sc second
#define forn(i,p,k) for(int i=(p);i<=(k);++i)
#define pb push_back
#define mp make_pair
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
vector<int> W;

int simulate(vector<int> P) {
    int wyn = 0, mx;
    while(!P.empty()) {
        mx = 0;
        for(const int &v:P) if(v > mx)  mx = v;
        if (mx <= 2) {
            ++wyn;
            return wyn;
        }
        wyn += mx - 1;
        W.clear();
        for(const int &v:P) {
            if(v != mx) {
                if (v > 4)  W.push_back(v-4);
            } else    mx = -1;
        }
        P.swap(W);
    }
    return wyn;
}

vector<int> V;

void MAIN()
{
    int n,cnt = 0, first = -1, last = -1, total = 0;
    V.clear();
    W.clear();
    cin>>n;
    string Z;
    cin>>Z;
    forn(i,0,n-1) {
        if (Z[i] == '0') {
            cnt++;
        } else {
            total++;
            if(first == -1) {
                first = cnt;
            } else {
                if (cnt != 0)   V.push_back(cnt);
            }
            cnt = 0;
        }
    }
    last = cnt;
    if (total == 0) return void(cout<<0<<"\n");
    if (total == n) return void(cout<<n<<"\n");
    if (first == 0 && last == 0)    cout<<n - simulate(V)<<"\n";
    else {
        if(first == 0 || last == 0) {
            int tmp1 = first + last;
            for(const int &v:V) if(v > 2)   W.push_back(v-2);
            tmp1 += simulate(W);
            int tmp2 = simulate(V);
            cout<<n - max(tmp1, tmp2)<<"\n";
            return;
        } else {
            int tmp1 = first + last - 1;
            for(const int &v:V) if(v > 4)   W.push_back(v-4);
            tmp1 += simulate(W);
            W.clear();
            for(const int &v:V) if(v > 2)   W.push_back(v-2);
            int tmp2 = max(first, last);
            tmp2 += simulate(W);
            int tmp3 = simulate(V);
            cout<<n - max(tmp1,max(tmp2,tmp3))<<"\n";
        }
    }
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int Z;cin>>Z;
    while(Z--) MAIN();
    return 0;
}