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#include <bits/stdc++.h>
#define ll long long
#define mp make_pair
#define fi first
#define se second
#define pb push_back
#define vi vector<int>
#define pi pair<int, int>
#define mod 998244353
template<typename T> bool chkmin(T &a, T b){return (b < a) ? a = b, 1 : 0;}
template<typename T> bool chkmax(T &a, T b){return (b > a) ? a = b, 1 : 0;}
ll ksm(ll a, ll b) {if (b == 0) return 1; ll ns = ksm(a, b >> 1); ns = ns * ns % mod; if (b & 1) ns = ns * a % mod; return ns;}
using namespace std;
int n;
const int maxn = 500005;
char inp[maxn];
int cal(vi a, int b) {
    int ans = 0;
    for (int i = 0; i < a.size(); i++) {
        int lst = a[i] - 2 * b;
        if (lst <= 0) continue;
        ans += 1, b += 1, lst -= 2;
        if (lst > 0) ans += lst, b += 1;
    }
    return ans;
}
int main() {    
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        scanf("%s", inp + 1);
        vi tt;
        tt.pb(0);
        for (int i = 1; i <= n; i++) 
            if (inp[i] == '1') tt.pb(i);
        tt.pb(n + 1);
        int ans = 0;
        if (tt.size() == 2) ans = 0;
        else {
            vi f, e;
            f.pb(tt[1] - tt[0] - 1);
            f.pb(tt[tt.size() - 1] - tt[tt.size() - 2] - 1);
            for (int i = 1; i < tt.size() - 2; i++)
                e.pb(tt[i + 1] - tt[i] - 1);
            sort(e.begin(), e.end());
            reverse(e.begin(), e.end());
            int mx = 0;
            for (int m = 0; m < 4; m++) {
                int st = 0;
                int cans = 0;
                for (int j = 0; j < 2; j++) 
                    if (m & (1 << j)) {
                        cans += (f[j] - st);
                        st += 1;
                    }
                cans += cal(e, st);
                chkmax(mx, cans);
            }
            ans = n - mx;
        }
        printf("%d\n", ans);
    }
    return (0-0); // <3 cxr
}