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//Konrad Paluszek,University of Warsaw(former XIV LO Staszic)
//#STAY AT HOME
#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#define TIME (chrono::steady_clock::now().time_since_epoch().count())
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define xfm(a,b)a##b
#define xwb(a,b)xfm(a,b)
#define _ xwb(nvj,__LINE__)
#define __ xwb(kjy,__LINE__)
#define ___ xwb(cjm,__LINE__)
#define REP(i,n)for(urs(n)i=0;i<(n);++i)
#define PER(r...)for(bool _=1;_||next_permutation(r);_=false)
#define FS(r)r.first,r.second
#define ALL(r)(r).begin(),(r).end()
#define M0(r) memset(r,0,sizeof(r))
#define sim template<class c
#define forbits(i,m)if(m)for(urs(m)i=ctz(m),i##nvj=m;i##nvj;i##nvj^=((urs(m))1<<i),i=i##nvj?ctz(i##nvj):0)
#define fordbits(i,m)if(m)for(urs(m)i=8*sizeof(m)-clz(m)-1,i##nxd=m;i##nxd;i##nxd^=((urs(m))1<<i),i=i##nxd?8*sizeof(m)-clz(i##nxd)-1:0)
#define ksets(t, m, k, n)for(t m=(((t)1<<(k))-1);m<((t)1<<(n));m=nux(m))
#define urs(r...)typename decay<decltype(r)>::type
#define hur(f,g)sim>int f(c a){if(sizeof(c)==8)return g##ll(a);return g(a);}
using namespace __gnu_pbds;using namespace std;using ll=long long;using ld=long double;using ull=unsigned long long;using vi=vector<int>;using vll=vector<ll>;using pii=pair<int,int>;using pll=pair<ll,ll>;using vpii=vector<pii>;using unt=unsigned int;sim>using min_queue=priority_queue<c,vector<c>,greater<>>;sim,class b,class cmp=less<c>>using ordered_map=tree<c,b,cmp,rb_tree_tag,tree_order_statistics_node_update>;sim,class cmp=less<c>>using ordered_set=ordered_map<c,null_type,cmp>;hur(popc,__builtin_popcount)hur(ctz,__builtin_ctz)hur(clz,__builtin_clz)sim,class N>bool mini(c&o,const N&h){if(o>h)return o=h,1;return 0;}sim,class N>bool maxi(c&o,const N&h){if(o<h)return o=h,1;return 0;}
#ifdef LOCAL
#include </home/konrad/cp/headers/debuglib.hpp>
#else
#define loc(...)
#define onl(r...)r
#define debug(...)
#define print_stack(...)
#define mark_stack(...)
#define set_pre(...)
#define reg_it(...)
#define def_op(...) struct _{};
#define mask_set(...)
#define exit my_exit
void __resources();
void my_exit(int x) {fflush(stdout);
#ifdef LOCAL2
__resources();
#endif
_Exit(x);}
#endif
#define next nexT
#define prev preV
#define tree trEE
#define left lefT
#define right righT
#define div diV
#define y1 y_1
#define pow don't'
ull mix(ull o){o+=0x9e3779b97f4a7c15;o=(o^(o>>30))*0xbf58476d1ce4e5b9;o=(o^(o>>27))*0x94d049bb133111eb;return o^(o>>31);}ull SALT=0x7a14a4b0881ebf9,tqu=0x7a14a4b0881ebf9;ull my_rand(){return tqu=mix(tqu);}void my_srand(ull x){SALT=tqu=x;}const int inf=1023400000;const ll llinf=1234567890000000000ll;ll fix(ll o, ll m){o%=m;if(o<0)o+=m;return o;}
#define rand my_rand
#define srand my_srand
#define random_shuffle(r...)random_shuffle(r,[](int _){return my_rand()%_;})
sim>inline c nux(c m){if(!m)return numeric_limits<c>::max();c A=m&-m;c B=~((A-1)^m);c C=B&-B;c D=(C>>(1+ctz(A)))-1;return C|(m&~(C-1))|D;}sim>void unq(c&x){x.resize(unique(ALL(x))-x.begin());}
//#STAY AT HOME
int run(const vpii &input) {
	static unordered_map<ll, int> cache;
	if (input.empty()) return 0;
	ull hash = 0;
	for (auto [a, b] : input) hash += mix(a ^ mix(b));
	auto it = cache.find(hash);
	if (it != cache.end()) return it->second;
	int ans = numeric_limits<int>::max();
	int len = input.size();
	REP(i, len) {
		vpii rest;
		int lost = 0;
		REP(j, len) {
			auto [len, dirs] = input[j];
			if (i == j) {
				dirs--;
				len--;
			}
			int take = min(len, dirs);
			lost += take;
			len -= take;
			if (len && dirs) rest.emplace_back(len, dirs);
		}
		mini(ans, run(rest) + lost);
	}
	return cache[hash] = ans;
}
int ord(pii x) {
	auto [len, dirs] = x;
	if (dirs == 1) return len * 2;
	else return len;
	// return len - dirs;
	// return dirs == 1 ? len * 2 : len;
}
int calc_per(const vpii &input) {
	int saved = 0, sum = 0;
	int timer = 0;
	REP(i, (int)input.size()) {
		auto [len, dirs] = input[i];
		sum += len;
		int left_len = len - dirs * timer;
		// debug(imie(left_len), imie(dirs));
		if (left_len > 0) {
			if (left_len == 1 || (left_len == 2 && dirs == 2)) {
				timer++;
				saved++;
			}
			else {
				if (dirs == 1) saved += left_len;
				else saved += left_len - 1;
				timer += dirs;
			}
		}
		// debug(imie(sum), imie(timer), imie(saved));
	}
	// debug(imie(input), imie(saved), imie(sum));
	return sum - saved;
}
int per_run(vpii input) {
	sort(ALL(input));
	int ans = numeric_limits<int>::max();
	PER(ALL(input)) {
		mini(ans, calc_per(input));
	}
	return ans;
}
int greedy_run(vpii input) {
	sort(ALL(input), [](pii a, pii b){return ord(a) > ord(b);});
	return calc_per(input);
}
void solve() {
	const int nax = 1e5 + 44;
	int n;
	// int n = 1 + rand() % 100;
	static char input[nax];
	scanf("%d%s", &n, input);
	// auto p = rand();
	// REP(i, n) input[i] = rand() < p ? '1' : '0';
	// input[n] = 0;
	vi ones;
	REP(i, n) if (input[i] == '1') ones.push_back(i);
	if (ones.empty()) {
		puts("0");
	}
	else {
		vpii blocks;
		if (ones[0]) blocks.emplace_back(ones[0], 1);
		if (ones.back() < n - 1) blocks.emplace_back(n - 1 - ones.back(), 1);
		REP(i, (int) ones.size() - 1) {
			int l = ones[i + 1] - ones[i] - 1;
			if (l) blocks.emplace_back(l, 2);
		}
		debug(imie(input), imie(blocks));
		int v1 = greedy_run(blocks);
		constexpr bool test = false;//true;
		if (test) {
			int v2 = run(blocks);
			if (v1 != v2) {
				debug(imie(blocks), imie(v1), imie(v2));
				abort();
			}
		}
		printf("%d\n", (int)ones.size() + v1);
	}
}
int main() {
	// unt seed = TIME; debug(imie(seed));srand(seed);
	int t = 1;
	scanf("%d", &t);
	REP(_, t) solve();
	// while (true) solve();
	exit(0);
}
//#STAY AT HOME