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#include <bits/stdc++.h>

#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define debug std::cout << "hmm" << std::endl;
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll, ll> pll;
typedef std::vector<int> vi;
typedef std::vector<ll> vl;

template <typename T>
void print(T t)
{
    std::cout << t << ' ';
}
template <typename T1, typename T2>
void print(std::pair<T1, T2> t)
{
    std::cout << '{' << t.first << ' ' << t.second << '}';
}
template <typename T>
void print(std::vector<T> t)
{
    for (auto a : t)
        print(a);
    std::cout << std::endl;
}

void solve(int &ans, int t, vi &V)
{
    int it = 0;
    while (it < V.size() && V[it] - t * 2 > 0)
    {
        if (V[it] - t * 2 == 1)
            ans++;
        else
            ans += V[it] - t * 2 - 1;
        t += 2;
        it++;
    }
}

main()
{
    std::cin.tie(0)->sync_with_stdio(0);
    std::cin.exceptions(std::cin.failbit);

    int Z = 1;
    std::cin >> Z;
    while (Z--)
    {
        int n;
        std::cin >> n;
        std::string S;
        std::cin >> S;
        vi V(1, 0);
        for (int i = 0; i < n; i++)
            if (S[i] == '0')
                V.back()++;
            else
                V.push_back(0);
        if (V.size() == 1)
        {
            if (V.back())
                std::cout << 0 << std::endl;
            else
                std::cout << n << std::endl;
            continue;
        }
        int end = V.back();
        int start = V[0];
        for (int i = 0; i < V.size() - 1; i++)
            V[i] = V[i + 1];
        V.resize(V.size() - 2);
        if (V.size())
        {
            std::sort(V.begin(), V.end());
            std::reverse(V.begin(), V.end());
        }
        int ans1 = 0, ans2 = 0, ans3 = 0;
        if (start < end)
            std::swap(start, end);
        if (start)
        {
            if (end && start + end > 2)
            {
                ans1 = start + end - 1;
                solve(ans1, 2, V);
            }
            ans2 = start;
            solve(ans2, 1, V);
        }
        solve(ans3, 0, V);
        std::cout << n - std::max(std::max(ans1, ans2), ans3) << std::endl;
    }
}