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// Wiktor Cupiał
// V LO Kraków
 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
 
#define mp make_pair
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define eb emplace_back
#define st first
#define nd second
#define vt vector
#define VAR(__var)  #__var << ": " << __var << " "
#define PAIR(__var) #__var << ": " << __var.first << ", " << __var.second << " "
#define FOR(__var, __start, __end)  for(int __var=__start; __var<__end; ++__var)
#define FORB(__var, __start, __end) for(int __var=__start; __var>__end; --__var)
#define maxi(__x, __y) __x = (__x>__y?__x:__y)
#define mini(__x, __y) __x = (__x<__y?__x:__y)
#define all(__var)     (__var).begin(),(__var).end()
#define rall(__var)    (__var).rbegin(),(__var).rend()
#define sz(__var)      (int)(__var).size()
#define satori         int __test; cin>>__test; while(__test--)
 
#ifndef DEBUG
#define DEBUG 0
#endif
#define debug if(DEBUG)
 
using namespace std;
 
using namespace __gnu_pbds;
template <typename T>
using ord_set = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
 
// templeos <3
typedef     int16_t i16;
typedef     int32_t i32;
typedef     int64_t i64;
typedef        void  u0;
typedef        bool  u1;
typedef        char  u8;
typedef    uint16_t u16;
typedef    uint32_t u32;
typedef    uint64_t u64;
typedef       float f32;
typedef      double f64;
typedef long double f86;
 
typedef       long long ll;
typedef     long double ld;
typedef   pair<ll, ll> pll;
typedef pair<int, int> pii;
 
const int INF = 1e9+2137;

void solve() {
	int n;
	cin >> n;

	bool sadeg = 1;
	int poczatek;
	int last = -1;
	vt<int> is_seg(n+1, 0);
	FOR(i, 0, n) {
		char x;
		cin >> x;
		if(x == '1') {
			if(sadeg) {
				sadeg = 0;
				poczatek = i;
			}
			if(last != -1)
				++is_seg[i-last-1];
			last = i;
		}
	}
	
	vt<int> ziomki;
	FORB(i, n, 0)
		FOR(j, 0, is_seg[i])
		   	ziomki.pb(i);

	int koniec = n-1-last;

	if(sadeg) {
		cout << "0\n";
		return;
	}

	vt<int> res;
	vt<int> cnt;

	res.pb(0);
	cnt.pb(0);

	if(max(koniec, poczatek) > 0) {
		res.pb(max(koniec, poczatek));
		cnt.pb(1);
	}

	if(koniec+poczatek-1 > 0) {
		res.pb(koniec+poczatek-1);
		cnt.pb(2);
	}
	
	for(auto now : ziomki) {
		FOR(j, 0, sz(res)) {
			if(now-2*cnt[j] == 1) {
				res[j]++;
				cnt[j]++;
			}
			else if(now-2*cnt[j] > 1) {
				res[j] += now-2*cnt[j]-1;
				cnt[j] += 2;
			}
		}
	}

	cout << (n-*(max_element(all(res)))) << '\n';
}
 
int32_t main() {
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

	satori
		solve();

	return 0;
}