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

#define boost                     \
    ios_base::sync_with_stdio(0); \
    cin.tie(0);                   \
    cout.tie(0)

pair<int, int> middle(const vector<int> &segments, int time) {
    int saved = 0;
    for (int x : segments) {
        int possible_to_save = x - 2*time;
        if (possible_to_save > 0) {
            saved += possible_to_save - (possible_to_save > 1);
            time += min(2, possible_to_save);
        }
        else {
            break;
        }
    }
    return {saved, time};
}

pair<int, int> boundary(int bound_val, int time) {
    return {max(0, bound_val - time), time + max(0, min(bound_val - time, 1))};
}

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

    string s; cin >> s;
    vector<int> segments;
    vector<int> boundaries;
    int seg_len = 0;
    bool first_zero = (s[0] == '0');

    for (char c : s) {
        if (c == '0') {
            seg_len += 1;
        } else {
            if (seg_len > 0) {
                if (first_zero && segments.empty()) {
                    boundaries.push_back(seg_len);
                    first_zero = false;
                } else {
                    segments.push_back(seg_len);
                }
                seg_len = 0;
            }
        }
    }
    if (seg_len == n)
        return 0;

    if (seg_len > 0) boundaries.push_back(seg_len);

    sort(segments.begin(), segments.end(), greater<>());
    sort(boundaries.begin(), boundaries.end(), greater<>());

    int res = n;
    for (int i = -1; i < int(boundaries.size()); ++i) {
        int saved = 0, time = 0;
        for (int j = 0; j <= i; ++j) {
            auto b = boundary(boundaries[j], time);
            saved += b.first, time = b.second;
        }
        auto b = middle(segments, time);
        saved += b.first, time = b.second;
        for (int j = i + 1; j < boundaries.size(); ++j) {
            b = boundary(boundaries[j], time);
            saved += b.first, time = b.second;
        }
        res = min(res, n - saved);
    }
    return res;
}

int main() {
    boost;

    int t;cin >> t;
    for(int i = 0; i < t; ++i) {
        cout << solve() << '\n';
    }

    return 0;
}

/**
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4
1000
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0100
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0010
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0001
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1111


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00001111001001111000

1
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00011000000000001000

1
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00101000101100100010

1
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00000100000010000010


*/