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#include <bits/stdc++.h>
using namespace std;
typedef vector<int> VI;
typedef pair <int,int> ii;
typedef long long LL;
#define pb push_back
const int INF = 2147483647;
const int N = 100005;

int z, n, l, r, act, i, res;
VI v, v2;
char t[N];

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

int go() {
	int res = 0;
	for (int i=0;i<v2.size();i++) if (v2[i] - 1 - 4 * i >= 0) res +=  max(1, v2[i] - 1 - 4 * i);
	//printf("%d\n", res);
	return res;
}

int main() {
scanf("%d", &z);
while (z--) {
	scanf("%d", &n);
	scanf("%s", t);
	v.clear();
	l = r = 0;
	for (l=0;l<n && t[l] == '0';l++) {}
	for (r=n-1;r>=0 && t[r] == '0';r--) {}
	if (l == n) {
		printf("0\n");
		continue;
	}
	act = 0;
	for (i=l;i<=r;i++) {
		if (t[i] == '1' && act > 0) {
			v.pb(act);
			act = 0;
		} else if (t[i] == '0') act++;
	}
	r = n - r - 1;
	sort(v.begin(), v.end(), cmp);
	v2.clear();
	for (auto& w : v) v2.pb(w);
	res = go();
	if (max(l, r) >= 1) {
		v2.clear();
		for (auto& w : v) if (w > 2) v2.pb(w - 2);
		res = max(res, go() + max(l, r));
	}
	if (min(l, r) >= 1) {
		v2.clear();
		for (auto& w : v) if (w > 4) v2.pb(w - 4);
		res = max(res, go() + l + r - 1);
	}
	printf("%d\n", n - res);
}
return 0;
}