#include "bits/stdc++.h"

using namespace std;

using ll = long long;
using ld = long double;

#define all(x) (x).begin(), (x).end()

int main() {
  ios_base::sync_with_stdio(false);

  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    string s;
    cin >> s;

    bool has2 = false;
    for (int i = 0; i + 1 < n; ++i)
      if (s[i] == '0' && s[i + 1] == '0')
        has2 = true;

    int a = 0;
    while (a < n && s[a] == '1')
      ++a;

    int b = 0;
    while (b < n && s[n - 1 - b] == '1')
      ++b;

    int cnt1 = 0;
    for (char ch : s)
      if (ch == '1')
        cnt1++;

    int ans = 0;
    if (has2)
      ans = cnt1;
    else
      ans = cnt1 + min(a, b);

    cout << ans << "\n";
  }

  return 0;
}