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#include<bits/stdc++.h>
using namespace std;
int tests,n,times,roz,Suma;
vector< pair<int,int> > vec;
vector < int > v1,one,two;
priority_queue<int> q;
int wyp;
void aktualizuj();
int aktw();
int main()
{
    ios_base::sync_with_stdio(0);
    cin >> tests;
    for (int test = 1 ; test <= tests ; test++)
    {
        cin >> n;
        int last_1 = 0;
        for (int i = 1 ; i <= n ; i++)
        {
            char c;
            cin >> c;
            if(c == '1')
            {
                v1.push_back(i);
            }
        }
        v1.push_back(n+1);
        if(v1.size() == 1)
            cout << 0<<"\n";
        else
        {
            for (int i = 0 ; i < v1.size() ; i++)
            {
                if(i == v1.size() - 1)
                {
                    if(v1[i-1] != n)
                        vec.push_back({n - v1[i-1],1});
                }
                else if(i == 0)
                {
                    if(v1[i] != 1)
                        vec.push_back({v1[i] - 1,1});
                }
                else
                {
                    if(v1[i] - v1[i-1] > 1)
                        vec.push_back({v1[i] - v1[i-1] - 1,2});
                }      
            }
            for(int i = 0 ; i < vec.size();  i++)
            {
                if(vec[i].second == 1)
                    one.push_back(vec[i].first);
                else
                    two.push_back(vec[i].first);
            }
            int Odp = INT_MAX;
            sort(two.begin(),two.end());
            for(int i = 0 ; i < one.size() ; i++)
            {
                q.push(-one[i]);
                Suma += one[i];
                roz++;
            }
            for(int i = two.size() - 1 ; i >= 0 ; i--)
            {
                aktualizuj();
                if(1 + 2*times + 2*roz <= two[i])
                {
                    Odp = min(Odp,n - (aktw() + 1));
                    Suma += (two[i] - times);
                    q.push(-(two[i] - times));
                    times++;
                    roz++;
                    Odp = min(Odp,n - aktw()); 
                }
                else
                    Odp = min(Odp,n - aktw());
            }
            if (wyp == 0)
            {
                aktualizuj();
                Odp = min(Odp,n - aktw());
            }
            cout << Odp<<"\n";
        }
        Suma = 0;
        two.clear();
        one.clear();
        v1.clear();
        vec.clear();
        while(!q.empty())
            q.pop();
        roz = 0;
        times = 0;              
    }
}
int aktw()
{
    return (Suma - times * roz - (roz * (roz-1)) / 2);
}
void aktualizuj()
{
    while(!q.empty())
    {
        if(Suma - times * roz - (roz * (roz-1)) / 2 <= Suma + q.top() - times*(roz-1) - ((roz-2) * (roz-1)) / 2)
        {
            Suma += q.top();
            q.pop();
            roz--; 
        }
        else
            break;
    }
}