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#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;

#define FOR(i,a,b) for(int (i)=(int)(a); (i)!=(int)(b); ++(i))

int t, n;
char S[100005];

int solve() {
    int occupied = 0;
    FOR(i,0,n) if (S[i] == '1') ++occupied;
    if (occupied == 0) return 0;
    if (occupied == n) return n;

    vector<int> P1;
    int L = 0, R = 0;
    while (S[L] != '1') ++L;
    while (S[n-1-R] != '1') ++R;
    if (L>0) P1.push_back(L);
    if (R>0) P1.push_back(R);
    if (P1.size() == 2 && P1[0] < P1[1]) swap(P1[0], P1[1]);

    vector<int> P2;
    int len = 0;
    FOR(i,0,n-L-R) {
        if (S[L+i] == '1') {
            if (len > 0) P2.push_back(len);
            len = 0;
        } else ++len;
    }
    sort(P2.begin(), P2.end());
    reverse(P2.begin(), P2.end());

    if (P2.size() == 0) {
        if (P1.size() == 1) return occupied;
        return occupied + 1;
    }

    int result = 0;
    int res_2 = 0;
    FOR(i,0,P2.size()+1){
        int res_1 = 0;
        if (P1.size() >= 1) res_1 += max(0, P1[0] - 2*i);
        if (P1.size() == 2) res_1 += max(0, P1[1] - 2*i - 1);

        if (i>0) {
            int val = max(0, P2[i-1] - 1 - 4*(i-1));
            res_2 += val;
        }

        result = max(result, res_1 + res_2);
    }

    return n - result;
}

int main() {
    scanf("%d", &t);
    while (t--) {
        scanf("%d", &n);
        scanf("%s", &S);
        printf("%d\n", solve());
    }
}