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//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //
namespace debug {
template <class c> struct rge { c b, e; }; template <class c> rge<c> range(c i, c j) { return rge<c>{i, j}; }
template <class c> char elo(...); template <class c> auto elo(c* a) -> decltype(cerr << *a, 0);
struct stream { ~stream() { cerr << endl; }
template <class c> typename enable_if <sizeof elo<c>(0) != 1, stream&>::type operator<<(c i) { cerr << boolalpha << i; return *this; }
template <class c> typename enable_if <sizeof elo<c>(0) == 1, stream&>::type operator<<(c i) { return *this << range(begin(i), end(i)); }
template <class a, class b> stream& operator<<(pair <a,b> p) { return *this << "(" << p.first << ", " << p.second << ")"; }
template <class c> stream& operator<<(rge<c> d) { *this << "["; for (auto it=d.b; it!=d.e; it++) *this << ", " + 2 * (it == d.b) << *it; return *this << "]"; }
stream& _dbg(const string& s, int i, int b) { return *this; } template <class c, class ... cs> stream& _dbg(const string& s, int i, int b, c arg, cs ... args) {
if (i == s.size()) return (*this << ": " << arg << ""); b += (s[i] == '(') + (s[i] == '[') + (s[i] == '{'); b -= (s[i] == ')') + (s[i] == ']') + (s[i] == '}');
if (s[i] == ',' && b == 0) return (*this << ": " << arg << "     ")._dbg(s, i+1, b, args...); return (s[i] == ' ' ? *this : *this << s[i])._dbg(s, i+1, b, arg, args...); } };}
#define dout debug::stream()
#define dbg(...) ((dout << ">> ")._dbg(#__VA_ARGS__, 0, 0, __VA_ARGS__))
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //
#define f first
#define s second
#define sc scanf
#define pr printf
#define mp make_pair
#define pb push_back
#define all(x) x.begin(),x.end()
#define ss(x) ((int)((x).size()))
#define rep0(i, b) for(int (i)=(0);i<(b);(i)++)
#define rep1(i, b) for(int (i)=(1);i<=(b);(i)++)
#define rep(i, a, b) for(int (i)=(a);i<=(b);(i)++)
#define per(i, a, b) for(int (i)=(b);i>=(a);(i)--)
#define lowb(v, x) (lower_bound(all(v),(x))-(v).begin())
#define uppb(v, x) (upper_bound(all(v),(x))-(v).begin())
#define upgrade ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define erase_duplicates(x) {sort(all(x));(x).resize(distance((x).begin(), unique(all(x))));}
template <class p, class q> pair<p,q> operator-(pair<p,q> a, pair<p,q> b) { return mp(a.f-b.f, a.s-b.s); }
template <class p, class q> pair<p,q> operator+(pair<p,q> a, pair<p,q> b) { return mp(a.f+b.f, a.s+b.s); }
template <class p, class q> void umin(p& a, const q& b) { if (a > b) a = b; }
template <class p, class q> void umax(p& a, const q& b) { if (a < b) a = b; }
using lf=long double;
using ll=long long;
using cll=const ll;
using cint=const int;
using pll=pair<ll,ll>;
using pii=pair<int,int>;
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //


const int N = 100005;
int L, R;
char s[N];
vector <int> vec;

int relax(int bl, int br){
	
	int res = 0;
	int turns = bl + br;

	if (bl == 1 && L == 0) return 0;
	if (br == 1 && R == 0) return 0;
	
	if (bl == 1 && br == 0){
		res += L;
	}
	if (bl == 0 && br == 1){
		res += R;
	}
	if (bl == 1 && br == 1){
		if (L == 1 && R == 1) return 0;
		res += L + R - 1;
	}

	for (int a : vec){
		a -= 2 * turns;
		if (a <= 0) return res;
		if (a <= 2) return res + 1;
		res += a - 1;
		turns += 2;
	}

	return res;
}

void solve (){
	int n;

	scanf("%d", &n);
	scanf("%s", s + 1);
	
	vec.clear();
	
	int now = 0;
	rep(i, 1, n){
		if (s[i] == '0'){
			now += 1;
		}
		if (s[i] == '1'){
			vec.pb(now);
			now = 0;
		}
	}

	vec.pb(now);
	
	if (ss(vec) == 1){
		printf("0\n");
		return;
	}

	R = vec.back(); vec.pop_back(); reverse(all(vec));
	L = vec.back(); vec.pop_back(); reverse(all(vec));

	sort(all(vec));
	reverse(all(vec));
	
	int out = 0;

	umax(out, relax(0, 0));
	umax(out, relax(0, 1));
	umax(out, relax(1, 0));
	umax(out, relax(1, 1));
	
	printf("%d\n", n - out);
}

int main (){
	int q = 1;
	scanf ("%d", &q);
	while (q--)
		solve();
	return 0;
}