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#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>

using namespace std;

typedef vector<int> VI;
typedef long long LL;

#define FOR(x, b, e) for(int x=b; x<=(e); ++x)
#define FORD(x, b, e) for(int x=b; x>=(e); --x)
#define REP(x, n) for(int x=0; x<(n); ++x)
#define VAR(v, n) __typeof(n) v = (n)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(x) ((int)(x).size())
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define PB push_back
#define ST first
#define ND second

int main() {
	ios_base::sync_with_stdio(0);
    int t;
    cin >> t;
    while(t--) {
        int n;
        string cities;
        cin >> n >> cities;
        int i = 0;
        while(i < n && cities[i] == '0') i++;
        if(i == n) {
            cout << "0\n";
        } else {
            int j = n - 1;
            while(cities[j] == '0') j--;
            VI lengths;
            int k = i + 1;
            while(k < j) {
                while(cities[k] == '1' && k < j) k++;
                int l = k + 1;
                while(cities[l] == '0' && l < j) l++;
                if(cities[k] == '0') lengths.PB(l - k);
                k = l + 1;
            }
            sort(lengths.rbegin(), lengths.rend());
            int first = 0, second = 0, third = 0;
            int days = 0, days2 = 0;
            REP(x, lengths.size()) {
                int tmp = lengths[x] - 4 * x - 1;
                if(tmp < 0) break;
                if(tmp == 0) {
                    tmp = 1;
                    days++;
                } else days += 2;
                first += tmp;
                if(tmp - 2 == 0) days2++; else if(tmp - 2 > 0) days2 += 2;
                second += max(0, tmp - 2 == 0 ? 1 : tmp - 2);
                third += max(0, tmp - 4 == 0 ? 1 : tmp - 4);
            }
            int prefix = i - days;
            int case1 = prefix > 0 ? first + prefix + max(0, n - j - days - 2) : first + max(0, n - j - 1 - days);
            int case2 = i > 0 ? i + second + max(0, n - j - 2 - days2) : 0;
            int case3 = n != j ? n - j - 1 + second + max(0, i - days2 - 1) : 0;
            int case4 = i > 0 && n != j ? i + n - j - 2 + third : 0;
            cout << n - max(max(case1, case2), max(case3, case4)) << '\n';
        }
    }
    return 0;
}