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#include "bits/stdc++.h" // Tomasz Nowak
using namespace std;     // University of Warsaw
using LL = long long;
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define REP(i, n) FOR(i, 0, (n) - 1)
#define ssize(x) int(x.size())
template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) {
	return o << '(' << p.first << ", " << p.second << ')';
}
template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) {
	o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}';
}
#ifdef DEBUG
#define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'
#else
#define debug(...) {}
#endif

int main() {
	cin.tie(0)->sync_with_stdio(0);

	int t;
	cin >> t;
	while(t --> 0) {
		int n;
		cin >> n;
		string s;
		cin >> s;
		assert(ssize(s) == n);

		if(*max_element(s.begin(), s.end()) == '0') {
			cout << "0\n";
			continue;
		}

		vector<pair<int, int>> gaps;
		for(int l = -1; l < n - 1; ++l)
			if((l == -1 or s[l] == '1') and s[l + 1] == '0') {
				int r = l + 1;
				while(r < n and s[r] == '0')
					++r;

				int gi = ssize(gaps);
				if(l != -1 and r != n) {
					gaps.emplace_back((r - l) / 2, gi + 1);
					gaps.emplace_back((r - l - 1) / 2, gi);
				}
				else
					gaps.emplace_back(l == -1 ? r : n - l - 1, -1);
			}
		debug(gaps);

		set<pair<int, int>> rem_gaps;

		REP(i, ssize(gaps))
			if(gaps[i].second == -1 or i < gaps[i].second) {
				int prio = 4 * gaps[i].first + 1;
				if(gaps[i].second != -1)
					prio = 2 * (gaps[i].first + gaps[gaps[i].second].first);
				rem_gaps.emplace(prio, i);
			}
		debug(rem_gaps);

		int answer = 0;
		for(char c : s)
			answer += bool(c == '1');
		debug(answer);

		for(int placed = 0; ssize(rem_gaps); ++placed) {
			int i = -1;
			while(not rem_gaps.empty()) {
				int g_len;
				tie(g_len, i) = *prev(rem_gaps.end());
				debug("considering", g_len, i);
				rem_gaps.erase(prev(rem_gaps.end()));
				if(gaps[i].first > placed)
					break;
				debug("adding", i);
				answer += gaps[i].first + (gaps[i].second == -1 ? 0 : gaps[gaps[i].second].first);
			}
			if(i == -1 or gaps[i].first <= placed)
				continue;

			answer += placed;
			int j = gaps[i].second;
			if(j != -1) {
				if(gaps[i].first == placed + 1)
					answer += gaps[j].first;
				else
					answer += ++placed;
			}
		}
		cout << answer << '\n';
	}
}