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#include <bits/stdc++.h>

#define ll long long
#define str string
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second

#define vc vector<char>
#define vvc vector<vc>
#define vi vector<int>
#define vvi vector<vi>
#define vvvi vector<vvi>
#define vvvvi vector<vvvi>
#define vll vector<ll>
#define vvll vector<vll>
#define vvvll vector<vvll>
#define vvvvll vector<vvvll>
#define vs vector<str>
#define vvs vector<vs>
#define vpii vector<pii>
#define vvpii vector<vpii>
#define vpll vector<pll>
#define vvpll vector<vpll>
#define vb vector<bool>
#define vvb vector<vb>
#define rep(i, a, b) for (int i = (a); i < int(b); i++)
#define repi(i, a, b) for (int i = (a); i <= int(b); i++)

using namespace std;

int inf = 1e7;

void solve() {
    int n; cin >> n;
    str s; cin >> s;
    vpii sticks;

    int ix = 0;
    while (ix < n && s[ix] == '0') {
        ix++;
    }

    if (ix == n) {
        cout << 0 << '\n';
        return;
    }

    sticks.emplace_back(ix, inf);

    int jx = 0;
    while (n - 1 - jx >= 0 && s[n - 1 - jx] == '0') {
        jx++;
    }

    sticks.emplace_back(jx, inf);


    int i = ix;
    while (i <= n - 1 - jx) {
        if (s[i] == '1') {
            i++;
            continue;
        }

        int j = i;
        while (j <= n - 1 - jx && s[j] == '0') {
            j++;
        }

        int cnt = j - i;
        sticks.emplace_back(cnt - (cnt / 2), cnt / 2);

        i = j;
    }

    /*for (auto & [x, y] : sticks) {
        cerr << x << " " << y << endl;
    }*/

    sort(sticks.begin(), sticks.end(), greater<>());

    int k = 0;
    int ans = 0;

    for (auto p : sticks) {

        int x = p.fi;
        int y = p.se;

        if (y == inf) y = 0;

        if (x - k <= 0) {
            break;
        }

        if (x - k == 1 && y - k == 0) {
            ans++;
            k++;
            continue;
        }

        if (x - k == 1 && y - k == 1) {
            ans++;
            k++;
            continue;
        }

        if (x - k == 2 && y - k == 1) {
            ans += 2;
            k += 2;
            continue;
        }

        ans += x - k;
        k++;
        if (y - k > 0) {
            ans += y - k;
            k++;
        }
    }

    cout << n - ans << '\n';
}


int main() {

    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    bool _multipleTestCases = true;

    if (_multipleTestCases) {
        ll t; cin >> t;
        while (t--)
            solve();
    }
    else {
        solve();
    }

    return 0;
}