#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 2e5+10;
vector<int> A;
void solve() {
int n; cin >> n;
string s; cin >> s;
int oz = 0, zo = 0;
int inv = 0;
int one=0;
for(int i = 0; i < n-1; i++) {
if(s[i] != s[i+1]) inv++;
if(s[i] == '0' && s[i+1] == '1') zo++;
else if(s[i] == '1' && s[i+1] == '0') oz++;
if(s[i] == '1') one++;
}
if(s[n-1] == '1') one++;
int f1 = 0, f0 = 0;
if(s[0] == '1') f1 = 1;
if(s[n-1] == '1') f0 = 1;
if(oz >= 2 || zo >= 2) {
cout << n + inv + f1 - 2 << endl;
return;
}
if(one == n) {
cout << n+1 << endl;
return;
}
if(inv == 0) {
cout << n <<endl;
return;
}
if(inv == 1) {
cout << n+1 <<endl;
return;
}
if(f1==0) {
cout << n + inv - 1 << endl;
return;
}
cout << n + inv << endl;
}
signed main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
//freopen("Error.txt", "w", stderr);
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
int t = 1; cin >> t;
while(t--) {solve();}
}
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