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#include <bits/stdc++.h>
#define PB push_back
#define ST first
#define ND second

//#pragma GCC optimize ("O3")
//#pragma GCC target("tune=native")

//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

using namespace std;
using ll = long long;
using pi = pair<int, int>;
using vi = vector<int>;

int t, n;
const int nax = 1e5 + 10;
string s;
int oneside[5];
int r[nax];
int dp[nax][5];

void solve() {
	cin >> n >> s;
	int any = 0;
	for(auto c : s) any |= ('1' == c);
	if(!any) {
		cout << "0\n";
		return;
	}
	int g = 0; any = 0;
	int ptr = 0;
	for(int i = 0; i < n; ++i) {
		r[i] = 0;
	}
	oneside[0] = oneside[1] = 0;
	for(int i = 0; i < n; ++i) {
		if(s[i] == '0') {
			g++;
		} else {
			if(!any) {
				oneside[0] = g;
			} else {
				r[ptr++] = g;
			}
			g = 0;
			any = 1;
		}
	}
	oneside[1] = g;
	sort(r, r + n);
	reverse(r, r + n);
	int ans = 0;
	for(int i = 1; i <= n; ++i) {
		// poczatek i-tego dnia
		for(int mask = 0; mask < (1 << 2); ++mask) {
			// maska odwiedzonych oneside
			dp[i][mask] = dp[i - 1][mask];
			int cnt = 0;
			for(int j = 0; j < 2; ++j) {
				if((1 << j) & mask) {
					dp[i][mask] = max(dp[i][mask], dp[i - 1][mask ^ (1 << j)] + oneside[j] - (i-1));
					cnt++;
				}
			}
			//nie biore z maski, to
			int id = (i - cnt - 1) / 2;
			if(id >= 0 && (i - cnt - 1) % 2 == 1) {
				if(i >= 2) {
					dp[i][mask] = max(dp[i][mask], dp[i - 2][mask] + r[id] - 2*(i-2) - 1);
				}
			}
			if(id >= 0 && r[id] > 2 * (i - 1) && (i - cnt - 1)%2==0) {
				ans = max(ans, dp[i - 1][mask] + 1);
			}
			//cout << i << " " << mask << ": " << dp[i][mask] << "\n";
		}
	}
	for(int mask = 0; mask < (1 << 2); ++mask) {
		ans = max(ans, dp[n][mask]);
	}
	cout << n - ans << "\n";
}
	

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cin >> t;
	while(t--) {
		solve();
	}
}