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#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

/*
#pragma GCC target("avx2")
#pragma GCC optimization("Ofast")
#pragma GCC optimization("unroll-loops")
*/

using namespace __gnu_pbds;
using namespace std;

#define mp make_pair
#define eb emplace_back
#define pb push_back
#define e1 first
#define e2 second
#define vt vector
#define maxi(x,y) x=max(x,y)
#define mini(x,y) x=min(x,y)
#define size(x) (int)x.size()
#define all(r) begin(r),end(r)
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define cx real()
#define cy imag()
#define precision(x) setprecision(x)<<fixed
#define time chrono::high_resolution_clock().now().time_since_epoch().count()
#ifndef DEBUG
#define DEBUG false
#endif
#define dbg if(DEBUG)

typedef long long ll;
typedef long double ld;
typedef complex<long double> cplx;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef vt<int> vi;
typedef vt<vi> vvi;
typedef vt<bool> vb;
typedef vt<vb> vvb;
typedef vt<char> vc;
typedef vt<vc> vvc;
typedef vt<string> vs;
typedef vt<vs> vvs;
typedef vt<ll> vll;
typedef vt<vll> vvll;
typedef vt<ld> vld;
typedef vt<vld> vvld;
typedef vt<cplx> vcplx;
typedef vt<vcplx> vvcplx;

template<typename T>
using ordset=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;

template<typename T1,typename T2>
ostream& operator<<(ostream &os,pair<T1,T2>& VAR){
	os<<"("<<VAR.e1<<","<<VAR.e2<<")";
	return os;
}

template<typename T>
ostream& operator<<(ostream& os,vt<T>& VAR){
	os<<"[";
	for(int i=0;i<size(VAR)-1;i++)
		os<<VAR[i]<<",";
	if(size(VAR))
		os<<VAR.back();
	os<<"]";
	return os;
}

template<typename T>
istream& operator>>(istream& is,complex<T>& VAR){
	T value;
	is>>value;
	VAR.real(value);
	is>>value;
	VAR.imag(value);
	return is;
}

const bool TESTS=true;

void solve(){
	int n;
	cin>>n;
	string s;
	cin>>s;
	vi cnt(n+1,0);
	int lewy=0,prawy=0;
	while(lewy<n&&s[lewy]=='0')
		lewy++;
	if(lewy==n){
		cout<<"0\n";
		return;
	}
	while(prawy<n&&s[n-prawy-1]=='0')
		prawy++;
	for(int i=lewy;i<n-prawy;i++){
		if(s[i]=='1')
			continue;
		int rbound=i;
		while(s[rbound+1]=='0')
			rbound++;
		cnt[rbound-i+1]++;
		i=rbound;
	}
	if(prawy>lewy)
		swap(lewy,prawy);
	int t=0;
	int ans=n;
	for(int i=n;i>=0;i--){
		if(i<lewy*2){
			if(t<lewy){
				ans-=lewy-t;
				t++;
				lewy=0;
			}
		}
		if(i<prawy*2){
			if(t<prawy){
				ans-=prawy-t;
				t++;
				prawy=0;
			}
		}
		while(cnt[i]){
			cnt[i]--;
			if(i-2*t>=3){
				ans-=i-2*t-1;
				t+=2;
			}
			else
			if(i-2*t>0){
				ans--;
				t++;
			}
		}
	}
	if(t<lewy){
		ans-=lewy-t;
		t++;
	}
	if(t<prawy){
		ans-=prawy-t;
		t++;
	}
	cout<<ans<<'\n';
}

int32_t main(){
	fastio;
	if(TESTS){
		int TEST_COUNT;
		cin>>TEST_COUNT;
		for(int i=0;i<TEST_COUNT;i++)
			solve();
	}
	else
		solve();
	return 0;
}