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

#define pb push_back

int calc(const vector<int>& v, int t) {
    int ans = 0; 
    for (int x : v) {
        int left = x - 2 * t;
        if (left <= 0)
            continue;
        if (left == 1) {
            ans += 1;
            t += 1;
        }
        else {
            ans += left - 1;
            t += 2;
        }
    }
    return ans;
}

int solve() {
    int n;
    string s;
    cin >> n >> s;

    size_t b = s.find('1');
    if (b == s.npos)
        return 0;

    int e = s.rfind('1');
    vector<int> v;
    int c = 0;
    for (int i = b + 1; i <= e; ++i)
        if (s[i] == '0')
            ++c;
        else if (c) {
            v.pb(c);
            c = 0;
        }

    sort(v.begin(), v.end(), greater<int>());
    int l = b, r = n - 1 - e;
    if (l < r)
        swap(l, r);

    return n - max({
            calc(v, 0),
            calc(v, 1) + l,
            calc(v, 2) + l + r - 1});
}

int main() {
    ios_base::sync_with_stdio(false);

    int t;
    cin >> t;
    while (t--)
        cout << solve() << '\n';

    return 0;
}