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



void solve() {
    int n;
    cin >> n;
    string s;
    cin >> s;
    int x = 0;
    vector < int > a;
    for (int i = 0; i < n; i++) {
        if (s[i] == '1') {
            a.push_back(x);
            x = 0;
        } else x++;
    }
    if (x == n) {
        cout << "0\n";
        return;
    }
    a.push_back(x);
    int l = a[0], r = a.back();
    a.erase(a.begin());
    a.pop_back();
    bool used_l = false, used_r = false;
    sort(a.rbegin(), a.rend());
    int d = 0, ans = 0;
    for (int i = 0; i < (int)a.size(); i++) {
        if (a[i] <= d) break;
        int val = a[i] - 2 * d - 1;
        if (val <= 0) break;
        if (used_l && used_r) {
            ans += val;
            d += 2;
        } else if (!used_l && !used_r) {
            int mx = max(l - d, r - d);
            if (val >= mx) {
                ans += val;
                d += 2;
            } else if (l - d == mx) {
                ans += l - d;
                used_l = true;
                d++;
            } else {
                ans += r - d;
                used_r = true;
                d++;
            }
        } else if (used_l) {
            if (val >= l - d) {
                ans += val;
                d += 2;
            } else {
                ans += l - d;
                used_l = true;
                d++;
            }
        } else if(used_r) {
            if (val >= r - d) {
                ans += val;
                d += 2;
            } else {
                ans += r - d;
                used_r = true;
                d++;
            }
        }
    }
    if (!used_l) {
        ans += max(0, l - d);
        d++;
    }
    if (!used_r) ans += max(0, r - d);
    cout << n - ans << "\n";
}

int main() {
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int z;
    cin >> z;
    while (z--) solve();
}