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

vector<int> V;

int Ans(int t) {
  int res = 0;
  for (int i = 0; i < V.size(); i++) {
    auto v = V[i];
    int after_time = v - 2 * t;
    int add = 0;
    if (after_time > 0) {
      add = max(1, after_time - 1);
    }
    res += add;
    if (add > 1) {
      t += 2;
    } else if (add == 1) {
      t++;
    } else {
      break;
    }
  }
  return res;
}

int Solve() {
  int length;
  string temp;
  cin >> length >> temp;
  V.clear();
  V.reserve(length / 3);

  int left = 1;
  for (int i = 0; i < length; i++) {
    int right = temp[i] - '0';
    if (left == 0 && right == 0) {
      V.back()++;
    } else if (left > right) {
      V.push_back(1);
    }
    left = right;
  }

  int L = 0;
  int R = 0;

  if (temp.back() == '0' && !V.empty()) {
    R = V.back();
    V.pop_back();
  }
  if (temp[0] == '0' && !V.empty()) {
    L = V[0];
    swap(V[0], V.back());
    V.pop_back();
  }
  if (L < R) {
    swap(L, R);
  }
  if (V.empty()) {
    if (R == 0) {
      return length - L;
    }
    return length - L - R + 1;
  }

  sort(V.begin(), V.end());
  reverse(V.begin(), V.end());

  int ans1 = (L > 0 && R > 0) ? L + R - 1 + Ans(2) : 0;
  int ans2 = (L > 0) ? L + Ans(1) : 0;
  int ans3 = Ans(0);
  return length - max(ans1, max(ans2, ans3));
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int tests;
  cin >> tests;
  while (tests--) {
    cout << Solve() << "\n";
  }
}