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#include<iostream>

using namespace std;

int number[100100];

void test() {
    int n;
    cin >> n;
    for (int i = 0; i < n; i++)
        number[i] = 0;
    string a;
    cin >> a;
    int pocz = 0, kon = n;
    while(pocz < n && a[pocz] == '0') {pocz++;}
    if (pocz == n) {cout << "0\n"; return;}// nikt nie zarażony
    while(a[kon - 1] == '0') {kon--;}
    int lewo = pocz, prawo = n - kon;
    int ctr = 0;
    for (int i = pocz; i < kon; i++) {
        if (a[i] == '1') {
            number[ctr]++;
            ctr = -1;
        }
        ctr++;
    }
    int time = 0;
    int i;
    int res = 0;
    for (i = n; i >= 3 + 2 * time; i--) {
        while (number[i] && i >= 3 + 2 * time) {
            number[i]--;
            res += i - 2 * time - 1;
            time += 2;
        }
    }
    if (lewo - time > 0) {
        res+= lewo - time;
        time++;
    }
    if (prawo - time > 0) {
        res+= prawo - time;
        time++;
    }
    if (2 * time + 2 < n && (number[2 * time  + 1] || number[2 * time  + 2]))
        res++;
    cout << n - res << "\n";
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int t;
    cin >> t;
    while(t--) {test();}
    return 0;
}