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#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
const ll mod=1000000007;

mt19937 mrand(chrono::high_resolution_clock::now().time_since_epoch().count());
int rnd(int x) { return mrand() % x;}

ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

const int N=1010000;
int n,_;
char s[N];
int len[N];
void solve() {
	scanf("%d",&n);
	scanf("%s",s);
	int t=0;
	int L=0, R=0;
	rep(i,0,n) if (s[i]=='0'&&(i==0||s[i-1]=='1')) {
		int x=i;
		while (x<n&&s[x]=='0') ++x;
		int ed=(i!=0)+(x!=n);
		if (ed==0) {
			puts("0");
			return;
		}
		if (ed==1) {
			if (i==0) L=x-i;
			else R=x-i;
		} else {
			len[t++]=x-i;
		}
	}
	sort(len,len+t);
	reverse(len,len+t);
	auto gao=[&]() {
		int ans=0,tt=0;
		rep(i,0,t) {
			if (len[i]-2*tt>=3) {
				ans+=len[i]-2*tt-1;
				tt+=2;
			} else if (len[i]-2*tt>=1) {
				ans+=1;
				tt+=1;
			}
		}
		return ans;
	};
	int ans=gao();
	rep(i,0,t) len[i]-=2;
	ans=max(ans,max(L,R)+gao());
	rep(i,0,t) len[i]-=2;
	ans=max(ans,max(L+max(R-1,0),R+max(L-1,0))+gao());
	printf("%d\n",n-ans);
}

int main() {
	for (scanf("%d",&_);_;_--) {
		solve();
	}
}