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#include<bits/stdc++.h>

#define maxn 100010

using namespace std;

vector<int> v[2];
int dp[maxn][3];


void dodaj(int j, int last, bool czy) {
    int x = j - last - 1;
    if (x != 0) {
        if (last == -1 || czy) {
            v[0].push_back(x);                   
        }
        else {       
           v[1].push_back(x);
        }
    }
}

bool por (int a, int b) {
    return a > b;
}

void calculate0(int i) {
    if (v[1][i-1] - 4*(i-1) == 1) {
        dp[i][0] = dp[i-1][0] + 1;
    }
    else {
        dp[i][0] = dp[i-1][0] + v[1][i-1] - 4*(i-1) - 1;
    }
}

void calculate1(int i) {
    int x = dp[i-1][1];
    if ((int)v[0].size() == 0) {
        dp[i][1] = x;
        return;
    }
    //pierwszy ostatni
    if (v[0][0] > 2 * i) {
        x = max(x, dp[i][0] + v[0][0] - 2 * i);
    }
    //i-ty ostatni
    if (v[1][i-1] > 4 * (i-1)+2) {
        if (v[1][i-1] - (4 * (i-1)+2) != 1)
            x = max(x, dp[i-1][1] + v[1][i-1] - (4 * (i-1)+2)-1);
        else
            x = max(x, dp[i-1][1] + 1);
    }
    dp[i][1] = x;
}

void calculate2(int i) {
    int x = dp[i-1][2];
    if ((int)v[0].size() < 2) {
        dp[i][2] = x;
        return;
    }
    //drugi ostatni
    if (v[0][1] > 2 * i + 1) {
        x = max(x, dp[i][1] + v[0][1] - 2 * i - 1);
    }
    //i-ty ostatni
    if (v[1][i-1] > 4 * (i-1)+4) {
        if (v[1][i-1] - (4 * (i-1)+4) != 1)
            x = max(x, dp[i-1][2] + v[1][i-1] - (4 * (i-1)+4)-1);
        else 
            x = max(x, dp[i-1][2] + 1);
    }
    dp[i][2] = x;
}

int make_dp() {
    if ((int)v[0].size() > 0) {
        dp[0][0] = 0;
        dp[0][1] = v[0][0];
        if ((int)v[0].size() > 1)
            dp[0][2] = v[0][0] + v[0][1] - 1;
        else
            dp[0][2] = 0;
    }
    else {
        dp[0][0] = dp[0][1] = dp[0][2] = 0;
    }
    for (int i = 1; i <= (int)v[1].size(); ++i) {
        if (v[1][i-1] <= 4 *(i-1)) {
            return max(dp[i-1][0], max(dp[i-1][1], dp[i-1][2]));
        }
        calculate0(i);
        calculate1(i);
        calculate2(i);
        //cout << dp[i][0] << " " << dp[i][1] << " " << dp[i][2] << endl;
    }
    int n = (int)v[1].size();
    //cout << n << endl;
    return max(dp[n][0], max(dp[n][1], dp[n][2]));
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    int t,n;
    string a;
    cin >> t;
    for (int i = 0; i < t; ++i) {
        cin >> n;
        cin >> a;
        int last = -1;
        bool check = false;
        for (int j = 0; j < n; ++j) {
            if (a[j] == '1') {
                check = true;
                dodaj(j, last, false);
                last = j;
            }
        }
        if (last != n - 1)
            dodaj(n, last, true);
        if ((int)v[0].size() != 0)
            sort(v[0].begin(), v[0].end(), por);
        if ((int)v[1].size() != 0)
            sort(v[1].begin(), v[1].end(), por);
        if (!check) {
            cout << "0\n";
        }
        else {
            //cout << make_dp() << endl;
            cout << n - make_dp() << "\n";
        }
        v[0].clear();
        v[1].clear();
    }
}