#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rep1(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < (t); ++i)
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define em emplace
#define pob pop_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define newline puts("")
#define vc vector
using namespace std;
template<class T> using vv = vc<vc<T>>;
template<class T> using PQ = priority_queue<T,vc<T>,greater<T>>;
using uint = unsigned; using ull = unsigned long long;
using vi = vc<int>; using vvi = vv<int>; using vvvi = vv<vi>;
using ll = long long; using vl = vc<ll>; using vvl = vv<ll>; using vvvl = vv<vl>;
using P = pair<int,int>; using vp = vc<P>; using vvp = vv<P>; using LP = pair<ll,ll>;
int geti(){int x;scanf("%d",&x);return x;}
vi pm(int n, int s=0) { vi a(n); iota(rng(a),s); return a;}
template<class T1,class T2>istream& operator>>(istream&i,pair<T1,T2>&v){return i>>v.fi>>v.se;}
template<class T1,class T2>ostream& operator<<(ostream&o,const pair<T1,T2>&v){return o<<v.fi<<","<<v.se;}
template<class T>istream& operator>>(istream&i,vc<T>&v){rep(j,sz(v))i>>v[j];return i;}
template<class T>string join(const T&v,const string&d=""){stringstream s;rep(i,sz(v))(i?s<<d:s)<<v[i];return s.str();}
template<class T>ostream& operator<<(ostream&o,const vc<T>&v){if(sz(v))o<<join(v," ");return o;}
template<class T>void vin(vc<T>&a){int n;cin>>n;a=vc<T>(n);cin>>a;}
template<class T>void vin(vv<T>&a){int n,m;cin>>n>>m;a=vv<T>(n,vc<T>(m));cin>>a;}
template<class T1,class T2>void operator--(pair<T1,T2>&a,int){a.fi--;a.se--;}
template<class T1,class T2>void operator++(pair<T1,T2>&a,int){a.fi++;a.se++;}
template<class T>void operator--(vc<T>&a,int){for(T&x:a)x--;}
template<class T>void operator++(vc<T>&a,int){for(T&x:a)x++;}
template<class T>void operator+=(vc<T>&a,T b){for(T&x:a)x+=b;}
template<class T>void operator-=(vc<T>&a,T b){for(T&x:a)x-=b;}
template<class T>void operator*=(vc<T>&a,T b){for(T&x:a)x*=b;}
template<class T>void operator/=(vc<T>&a,T b){for(T&x:a)x/=b;}
template<class T>void operator+=(vc<T>&a,const vc<T>&b){a.insert(a.end(),rng(b));}
template<class T1,class T2>pair<T1,T2>operator+(const pair<T1,T2>&a,const pair<T1,T2>&b){return {a.fi+b.fi,a.se+b.se};}
template<class T1,class T2>pair<T1,T2>operator-(const pair<T1,T2>&a,const pair<T1,T2>&b){return {a.fi-b.fi,a.se-b.se};}
template<class T>pair<T,T>operator*(const pair<T,T>&a,T b){return {a.fi*b,a.se*b};}
template<class T1,class T2>bool mins(T1& x,const T2&y){if(y<x){x=y;return true;}else return false;}
template<class T1,class T2>bool maxs(T1& x,const T2&y){if(x<y){x=y;return true;}else return false;}
template<class T>T min(const vc<T>&a){return *min_element(rng(a));}
template<class T>T max(const vc<T>&a){return *max_element(rng(a));}
template<class Tx,class Ty>Tx dup(Tx x, Ty y){return (x+y-1)/y;}
template<class T>ll suma(const vc<T>&a){ll s=0;for(auto&&x:a)s+=x;return s;}
template<class T>ll suma(const vv<T>&a){ll s=0;for(auto&&x:a)s+=suma(x);return s;}
template<class T>void uni(T&a){sort(rng(a));a.erase(unique(rng(a)),a.end());}
template<class T>void prepend(vc<T>&a,const T&x){a.insert(a.begin(),x);}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("-1"); return;}
#define yes { puts("Yes"); return;}
#define no { puts("No"); return;}
#define rtn(x) { cout<<(x)<<'\n'; return;} // flush!
#define yn {puts("Yes");}else{puts("No");}

struct Solver {
  void solve() {
    int n;
    string s;
    cin>>n>>s;
    vi dp(5,INF);
    dp[0] = 0;
    rep(i,n) {
      vi p(5,INF);
      swap(dp,p);
      mins(dp[0], min(p[2],p[4]));
      mins(dp[1], min(p[0],p[1]));
      mins(dp[2], p[2]);
      mins(dp[3], min(p[0],p[3]));
      mins(dp[4], p[4]);
      if (s[i] == '0') {
        mins(dp[0],p[0]);
        mins(dp[2],p[3]);
        mins(dp[2],p[0]);
        mins(dp[4],p[1]);
        mins(dp[4],p[0]);
      }
      dp[1] += 1;
      dp[2] += 1;
      dp[3] += 2;
      dp[4] += 2;
    }
    rtn(dp[0]);
  }
};

int main() {
  // cin.tie(nullptr); ios::sync_with_stdio(false);
  int ts = 1;
  scanf("%d",&ts);
  rep1(ti,ts) {
    Solver solver;
    solver.solve();
  }
  return 0;
}