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

typedef long long int LL;

struct Fragment
{
    int len, freeSides, id;
};

bool operator<(const Fragment& a, const Fragment& b)
{
    const int calcLenA = a.len * (a.freeSides+1);
    const int calcLenB = b.len * (b.freeSides+1);

    if(calcLenA == calcLenB)
    {
        if(a.freeSides == b.freeSides)
        {
            return a.id < b.id;
        }
        return a.freeSides < b.freeSides;
    }
    return calcLenA > calcLenB;
}

ostream& operator<<(ostream& os, const Fragment& f)
{
    os << "len: " << f.len << ", freeSides: " << f.freeSides << ", id: " << f.id;
    return os;
}

void print(const string& comment, const set<Fragment>& fragments)
{
    cout << comment << endl;
    for(const auto x : fragments)
    {
        cout << x << endl;
    }
    cout << "-----" << endl;
}

int infectedCount;

set<Fragment> prepareFragments(const string& s)
{
    int id = 0, freeSides = 2;
    Fragment curr = {0, freeSides, id++};
    set<Fragment> fragments;
    vector<Fragment> fragmentVec;
    bool wasInfected = false;

    for(const char c : s)
    {
        if(c == '0')
        {
            ++curr.len;
            continue;
        }

        ++infectedCount;

        if(curr.len > 0)
        {
            curr.freeSides = freeSides-1;
            fragmentVec.push_back(curr);
            curr = {0, freeSides-1, id++};
        }

        if(freeSides == 2)
        {
            freeSides = 1;
        }
    }

    if(curr.len > 0)
    {
        curr.freeSides = freeSides;
        fragmentVec.push_back(curr);
        curr = {0, freeSides, id++};
    }

    for(const auto& f : fragmentVec)
    {
        fragments.insert(f);
    }

    return fragments;
}

void vaccine(set<Fragment>& fragments)
{
    if(fragments.empty())
    {
        return;
    }

    while(!fragments.empty())
    {
        auto toVaccine = *fragments.begin();
        fragments.erase(fragments.begin());

        if(toVaccine.len == 0 || toVaccine.freeSides == 2)
        {
            continue;
        }

        if(toVaccine.len == 1 || toVaccine.freeSides == 1)
        {
            break;
        }

        fragments.insert({toVaccine.len-1, toVaccine.freeSides+1, toVaccine.id});
        break;
    }
}

set<Fragment> infect(const set<Fragment>& fragments)
{
    if(fragments.empty())
    {
        return fragments;
    }

    set<Fragment> newFragments;
    for(const auto& f : fragments)
    {
        if(f.freeSides == 2 || f.len == 0)
        {
            continue;
        }

        const int toInfectCount = min(f.len, 2-f.freeSides);
        infectedCount += toInfectCount;
        const int newLen = f.len - toInfectCount;

        if(f.len > 0)
        {
            newFragments.insert({newLen, f.freeSides, f.id});
        }
    }

    return newFragments;
}

int t;

int main()
{
    ios_base::sync_with_stdio(0);

    cin >> t;
    while(t--)
    {
        infectedCount = 0;

        int n;
        cin >> n;

        string s;
        cin >> s;

        auto fragments = prepareFragments(s);
        //print("initial: ", fragments);

        while(!fragments.empty())
        {
            vaccine(fragments);
            //print("vaccined: ", fragments);

            fragments = infect(fragments);
            //print("infected: ", fragments);
            //cout << "infected count: " << infectedCount << endl;
        }

        cout << infectedCount << endl;
    }

    return 0;
}