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#include <bits/stdc++.h>
using namespace std;

#define sim template <class c
#define ris return *this
#define dor > debug &operator<<
#define eni(x)                                                                    \
    sim > typename enable_if<sizeof dud<c>(0) x 1, debug &>::type operator<<(c i) \
    {
sim > struct rge
{
    c b, e;
};
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c *x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug
{
#ifdef XOX
    ~debug()
    {
        cerr << endl;
    }
    eni(!=) cerr << boolalpha << i;
    ris;
} eni(==) ris << range(begin(i), end(i));
}
sim, class b dor(pair<b, c> d)
{
    ris << "" << d.first << " --> " << d.second << "";
}
sim dor(rge<c> d)
{
    *this << "[";
    for (auto it = d.b; it != d.e; ++it)
        *this << ", " + 2 * (it == d.b) << *it;
    ris << "]";
}
#else
    sim dor(const c &)
    {
        ris;
    }
#endif
}
;
#define imie(...) "" << #__VA_ARGS__ " = " << (__VA_ARGS__) << ", "
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define f first
#define s second

#define sz(x) (x).size()
#define all(x) (x).begin(), (x).end()
#define vt vector

using ll = long long;
using pi = pair<int, int>;
using pll = pair<ll, ll>;

using vi = vt<int>;
using vvi = vt<vi>;
using vll = vt<ll>;
using vvll = vt<vll>;
using vs = vt<string>;
using vpi = vt<pi>;
using vvpi = vt<vpi>;
using vpll = vt<pll>;
using vvpll = vt<vpll>;

const int mod = 1e9 + 7;
const int nax = 1e6 + 9;
int n;
struct gap
{
    // int l, r;
    int lenght;
    int type;
    bool operator<(const gap other) const
    {
        if (lenght == other.lenght)
            return type < other.type;
        return lenght < other.lenght;
    }
};
vt<gap> gaps;
int state[nax];
void solve()
{
    gap tmp;
    gaps.clear();
    string str;
    cin >> n >> str;
    int p = 0;
    int ans = 0;
    int start = 0;
    int last = 0;
    for (int i = 1; i <= n + 1; i++)
    {
        if (i <= n)
        {
            state[i] = str[i - 1] - '0';
            ans += state[i];
        }
        if (state[i] == 1 || i == n + 1)
        {
            // debug() << imie(p) imie(i);
            // tmp.l = p;
            // tmp.r = i;
            tmp.lenght = i - p - 1;
            if (p == 0 || i == n + 1)
                tmp.type = 0, tmp.lenght *= 2;
            else
                tmp.type = 1;
            p = i;
            if (tmp.lenght)
                gaps.eb(tmp);
        }
    }
    // debug() << imie(gaps[0].l) imie(gaps[0].r) imie(gaps[0].lenght);
    sort(all(gaps));
    reverse(all(gaps));
    bool check = true;
    for (int i = 1; i <= n; i++)
        check &= !state[i];
    if (check)
    {
        cout << 0 << endl;
        return;
    }
    int day = 0;
    if (start < last)
        swap(start, last);
    for (int i = 0; i < sz(gaps); i++)
    {
        tmp = gaps[i];
        int toadd;
        int daystoadd;
        // debug() << imie(ans) imie(day) imie(toadd) imie(daystoadd) imie(tmp.lenght) imie(tmp.type);
        if (tmp.type == 0)
        {
            tmp.lenght /= 2;
            ans += min(day, tmp.lenght);
            day++;
            continue;
        }
        if (day * 2 >= tmp.lenght)
            toadd = tmp.lenght, daystoadd = 0;
        else if (2 * day + 1 == tmp.lenght)
            toadd = (2 * day), daystoadd = 1;
        else if (2 * day + 2 == tmp.lenght)
            toadd = (2 * day + 1), daystoadd = 1;
        else
            toadd = (2 * day + 1), daystoadd = 2;
        day += daystoadd;
        ans += toadd;
    }
    cout << ans << '\n';
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int tc;
    cin >> tc;
    while (tc--)
    {

        solve();
    }
}