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#include <bits/stdc++.h>
using namespace std;
#define PII pair<int, int>
#define VI vector<int>
#define VPII vector<PII>
#define LL long long
#define LD long double
#define f first
#define s second
#define MP make_pair
#define PB push_back
#define endl '\n'
#define ALL(c) (c).begin(), (c).end()
#define SIZ(c) (int)(c).size()
#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i, b, e) for(int i = (b); i <= (int)(e); ++i)
#define FORD(i, b, e) for(int i = (b); i >= (int)(e); --i)
 
#define sim template<class n
sim, class s> ostream & operator << (ostream &p, pair<n, s> x)
{return p << "<" << x.f << ", " << x.s << ">";}
sim> auto operator << (ostream &p, n y) ->
typename enable_if<!is_same<n, string>::value, decltype(y.begin(), p)>::type 
{int o = 0; p << "{"; for(auto c: y) {if(o++) p << ", "; p << c;} return p << "}";}
void dor() {cerr << endl;}
sim, class...s> void dor(n p, s...y) {cerr << p << " "; dor(y...);}
sim, class s> void mini(n &p, s y) {if(p>y) p = y;}
sim, class s> void maxi(n &p, s y) {if(p<y) p = y;}
// #ifdef DEB
#define debug(...) dor(__FUNCTION__, ":", __LINE__, ": ", __VA_ARGS__)
// #else
// #define debug(...)
// #endif 
 
#define I(x) #x " =", (x), " "
#define A(a, i) #a "[" #i " =", i, "] =", a[i], " "

using namespace std;

const int MXN = 1e5+5;
char in[MXN];
int n;
int dp[MXN][3];
int cost2(int val, int turn)
    {
    return max(max(0, val - 2 * turn - 1), 2 * turn + 1 <= val ? 1 : 0);
    }
int cost1(int val, int turn)
    {
    return max(0, val - turn);
    }
int solve() 
    {
    int prev = -1;
    int first = 0;
    int last = 0;
    VI rest;
    for(int i = 0; i < n; i++)
        {
        if(in[i] == '1')
            {
            if(prev == -1)first = i;
            else rest.PB(i - prev - 1);
            prev = i;
            }
        }
    last = n - 1 - prev;
    if(prev == -1)return 0;
    sort(ALL(rest));
    reverse(ALL(rest));
    int res = 0;
    int turn = 0;
    if(first < last)swap(last, first);
    REP(i, rest.size() + 1)
        dp[i][0] = dp[i][1] = dp[i][2] = 0;
    
    dp[0][0] = 0;
    dp[0][1] = cost1(first, 0);
    dp[0][2] = cost1(first, 0) + cost1(last, 1);
    REP(i, rest.size())
        {
        maxi(dp[i+1][0], dp[i][0] + cost2(rest[i], 2 * i));
        maxi(dp[i+1][1], dp[i][1] + cost2(rest[i], 2 * i + 1));
        maxi(dp[i+1][2], dp[i][2] + cost2(rest[i], 2 * i + 2));
        maxi(dp[i+1][1], dp[i+1][0] + cost1(first, 2 * i + 2));
        maxi(dp[i+1][2], dp[i+1][1] + cost1(last, 2 * i + 3));
        }
    int result = max(dp[rest.size()][0], max(dp[rest.size()][1], dp[rest.size()][2]));
    return n - result;
    }

int main()
    {
    ios_base::sync_with_stdio(0);
    int z;
    cin >> z;
    while(z--)
        {
        cin >> n;
        cin >> in;
        
        cout << solve() << endl;
        }

    }