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#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using ll   = long long;
using ull  = unsigned long long;
using ld   = long double;
using pii  = pair<int,int>;
using pll  = pair<ll,ll>;
using vi   = vector<int>;
using vb   = vector<bool>;
using vc   = vector<char>;
using vvc  = vector<vc>;
using vvi  = vector<vi>;
using vvb  = vector<vb>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vll  = vector<ll>;
using vull = vector<ull>;
using vvll = vector<vll>;
using namespace __gnu_pbds;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define f first
#define s second
#define pb emplace_back
#define rep(i, begin, end) for(auto i = (begin); i <= (end); ++i)
#define repr(i, begin, end) for(auto i = (begin); i >= (end); --i)
#define bend(X) X.begin(), X.end()
#ifdef LOCAL
#define deb(...) cout << #__VA_ARGS__ << " = " << __VA_ARGS__ << endl
#define say(...) cout << __VA_ARGS__ << endl
#else
#define deb(x)
#define say(x)
#define endl '\n'
#endif
constexpr int INF = 1e9+1e7;
constexpr ll INFl = INF;
constexpr ll INFll = 1e18+1e16;
void print() { cout << '\n'; }
template <typename T, typename... Args> void print(T x, Args... args) { cout << x << ' '; print(args...); }
template <typename T1, typename T2> ostream& operator<<(ostream& os, pair<T1,T2> x) { os << x.f << ' ' << x.s; return os; }
template <typename T1, typename T2> istream& operator>>(istream& is, pair<T1,T2>& x) { is >> x.f >> x.s; return is; }
template <typename Ch, typename Tr, typename T> ostream& operator<<(basic_ostream<Ch,Tr>& os, T x) { for(auto i : x) os << i << ' '; return os; }
template <typename T> istream& operator>>(istream& is, vector<T>& x) { for(T& i : x) is >> i; return is; }
template <typename T1, typename T2> pair<T1,T2> operator+(const pair<T1,T2>& A, const pair<T1,T2>& B) { return {A.f+B.f, A.s+B.s}; }
template <typename T1, typename T2> pair<T1,T2> operator-(const pair<T1,T2>& A, const pair<T1,T2>& B) { return {A.f-B.f, A.s-B.s}; }
template <typename T1, typename T2> pair<T1,T2>& operator+=(pair<T1,T2>& A, const pair<T1,T2>& B) { A.f += B.f; A.s += B.s; return A; }
template <typename T1, typename T2> pair<T1,T2>& operator-=(pair<T1,T2>& A, const pair<T1,T2>& B) { A.f -= B.f; A.s -= B.s; return A; }
template <typename T1, typename T2> pair<T1,T2> operator-(const pair<T1,T2>& A) { return {-A.f, -A.s}; }
template <typename T1, typename T2> bool maxe(T1& A, const T2& B) { if(B>A) { A=B; return 1; } return 0; }
template <typename T1, typename T2> bool mine(T1& A, const T2& B) { if(B<A) { A=B; return 1; } return 0; }
class Nic{} nic;
template <typename T> Nic operator<<(Nic, T) { return nic; }
Nic operator<<(ostream&, Nic) { return nic; }

//////////////////////////////////////////////////

int saved(const vi& T, int t) {
    int R = 0;
    for (int x : T) {
        x -= 2*t;
        if (x <= 0) return R;
        if (x == 1) return R+1;
        R += x-1;
        t += 2;
    }
    return R;
}

auto solve() {
    int n;
    cin >> n;
    vpii T;
    rep (i, 1, n) {
        char c;
        cin >> c;
        if (T.empty() || T.back().f != c-'0')
            T.pb(c-'0', 0);
        T.back().s++;
    }
    if (T.size() == 1) return T[0].f ? n : 0;
    if (T.size() == 2) return T[0].f ? T[0].s : T[1].s;
    if (T.size() == 3) return T[1].f ? T[1].s + 1 : T[1].s == 1 ? n-1 : T[0].s + T[2].s + 1;
    int l = T[0].f ? 0 : T[0].s;
    int r = T.back().f ? 0 : T.back().s;
    if (l < r) swap(l,r);
    vi U;
    for (int i = 1; i+1 < T.size(); i++)
        if (T[i].f == 0)
            U.pb(T[i].s);
    sort(bend(U), greater<int>());
    return n-max({l+r-1+saved(U,2), l+saved(U,1), saved(U,0)});
}



int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int noOfTests = 1;
    cin >> noOfTests;

    while(noOfTests --> 0)
        cout << solve() << '\n';

    return 0;
}