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

int t, n;
char s[100001];

void solve()
{
    scanf("%d", &n);
    scanf("%s", s);
    priority_queue<int> pq2;
    pq2.push(-1);
    int p = -1, pp1 = 0, pp2 = 0;
    for(int i=0; i^n; ++i)
    {
        if(s[i] == '0')
        {
            if(p == -1)
                p = i;
        }
        else
        {
            if(p != -1)
            {
                if(p == 0)
                {
                    pp1 = i;
                }
                else
                {
                    pq2.push(i - p);
                    //printf("%d ", i-p);
                }
                p = -1;
            }
        }
    }

    if(p != -1)
    {
        pp2 = n - p;
    }

    // printf("%d ", pq1.top());
    priority_queue<int> temp = pq2;

    int mx = 0;
    int it = 0, w = 0;
    while(pq2.top() - 2*it > 0)
    {
        if(pq2.top() - 2 * it == 1)
        {
            w += 1;
            it += 1;
        }
        else
        {
            w += pq2.top() - 2 * it - 1;
            it += 2;
        }
        pq2.pop();
    }
    mx = max(mx, w);

    pq2 = temp;
    it = 1, w = max(pp1, pp2);
    while(pq2.top() - 2 * it > 0)
    {
        if(pq2.top() - 2 * it == 1)
        {
            w += 1;
            it += 1;
        }
        else
        {
            w += pq2.top() - 2 * it - 1;
            it += 2;
        }
        pq2.pop();
    }
    mx = max(mx, w);

    pq2 = temp;
    it = 2, w = pp1 + pp2 - 1;
    while(pq2.top() - 2 * it > 0)
    {
        if(pq2.top() - 2 * it == 1)
        {
            w += 1;
            it += 1;
        }
        else
        {
            w += pq2.top() - 2 * it - 1;
            it += 2;
        }
        pq2.pop();
    }
    mx = max(mx, w);

    printf("%d\n", n-mx);
}

int main()
{
    scanf("%d", &t);
    for(int tt=0; tt^t; ++tt)
    {
        solve();
    }
}