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#include<bits/stdc++.h>

#define st first
#define nd second
#define pb(x) push_back(x)
#define pp(x) pop_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) (x).begin(), (x).end()
#define rev(x) reverse(all(x))
#define sor(x) sort(all(x))
#define sz(x) (int)(x).size()
#define rsz(x) resize(x)

using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii > vii;
typedef vector<ll> vl;
typedef vector<pll> vll;
typedef string str;
#define BOOST ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);

const int mx_N = 1e5+10;
char T[mx_N];
int main()
{
    BOOST
    int test, n;
    cin>>test;
    for(int i = 0 ; i < test ; i++)
    {
        cin>>n;
        for(int j = 0 ; j < n; j++)
            cin>>T[j];
        int lef = -1, rig = n;
        while(lef < n-1 && T[lef+1] == '0')
            lef++;
        while(rig > 0 && T[rig-1] == '0')
            rig--;
        if(lef == n-1)
        {
            cout<<0<<'\n';
            continue;
        }
        int side1 = lef+1, side2 = n-rig;//do wywalenia

        priority_queue<pii>Q;// 1 - np, 2 - p, 3 - drugie
        Q.push({lef+1 , 3});
        Q.push({n-rig , 3});
        int dl = 0;
        for(int j = lef + 1 ; j < rig ; j++)
        {
            if(T[j] == '0')
            {
                dl++;
            }
            else
            {
                if(dl>0)
                {
                    Q.push({(dl+1)/2,(dl&1 ? 1:2)});
                    dl = 0;
                }
            }
        }
        int T = Q.top().st;
        int t = 0;
        pii temp;
        int saved = 0;
        while(!Q.empty() && t < T)
        {
            temp = Q.top();
            Q.pop();
            if(temp.st - t <= 0)
                break;
            if(temp.nd == 3)
                saved+=(temp.st - t);
            else
            {
                saved++;
                if(temp.nd == 2)
                    Q.push({2*temp.st -t - 1, 3});
                else
                    Q.push({2*temp.st - 2 - t , 3});
            }


            t++;
        }
        cout<<n-saved<<'\n';





    }
    return 0;
}