Problem:
Score : 700 points

Problem Statement

N cells are arranged in a row.
Some of them may contain tokens.
You are given a string s that consists of 0s and 1s.
If the i-th character of s is 1, the i-th cell (from left) contains a token.
Otherwise, it doesn't contain a token.

Snuke wants to perform the following operation as many times as possible.
In each operation, he chooses three consecutive cells.
Let's call the cells X, Y, Z from left to right.
In order for the operation to be valid, both X and Z must contain tokens and Y must not contain a token.
Then, he removes these two tokens and puts a new token on Y.

How many operations can he perform if he performs operations in the optimal way?

Constraints

1 \leq N \leq 500,000

|s| = N

Each character in s is either 0 or 1.

Input

Input is given from Standard Input in the following format:

N
s

Output

Print the answer.

Sample Input 1

7
1010101

Sample Output 1

2

For example, he can perform two operations in the following way:

Perform an operation on the last three cells. Now the string that represents tokens becomes 1010010.

Perform an operation on the first three cells. Now the string that represents tokens becomes 0100010.

Note that the choice of operations matters.
For example, if he chooses three cells in the middle first, he can perform no more operations.

Sample Input 2

50
10101000010011011110001001111110000101010111100110

Sample Output 2

10

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static
#define PI  (3.1415926535)

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

struct UnionFind
{
    ull *parent, *count, *rank;

    UnionFind(ull n) {
        parent = new ull[n+1];
        count = new ull[n+1];
        rank = new ull[n+1];
        for (ull i = 0ULL; i < n+1; ++i) {
            parent[i] = i;
            count[i] = 1;
            rank[i] = 0;
        }
    }

    ~UnionFind() {
        delete rank;
        delete count;
        delete parent;
    }

    ull root(ull i) {
        if (parent[i] == i) return i;
        parent[i] = root(parent[i]);
        return parent[i];
    }

    void unite(ull i, ull j) {
        ull rooti = root(i);
        ull rootj = root(j);

        if (rooti == rootj) return;

        if (rank[rootj] < rank[rooti]) {
            parent[i] = parent[j] = parent[rootj] = rooti;
            count[rooti] += count[rootj];
        }
        else {
            parent[i] = parent[j] = parent[rooti] = rootj;
            count[rootj] += count[rooti];
            if (rank[rootj] == rank[rooti]) rank[rootj]++;
        }
    }

    bool same(ull i, ull j) {
        return root(i) == root(j);
    }
};

struct UnionFindM
{
    M<ull, ull> parent, count, rank;

    ull root(ull i) {
        ull parent_i = get_m(parent, i, i);
        if (parent_i == i) return i;
        return parent[i] = root(parent_i);
    }

    void unite(ull i, ull j) {
        ull rooti = root(i);
        ull rootj = root(j);

        if (rooti == rootj) return;

        if (get_m(rank, rootj, 0ULL) < get_m(rank, rooti, 0ULL)) {
            parent[i] = parent[j] = parent[rootj] = rooti;
            count[rooti] = get_m(count, rooti, 1ULL) + get_m(count, rootj, 1ULL);
        }
        else {
            parent[i] = parent[j] = parent[rooti] = rootj;
            count[rootj] = get_m(count, rootj, 1ULL) + get_m(count, rooti, 1ULL);
            if (get_m(rank, rootj, 0ULL) == get_m(rank, rooti, 0ULL)) rank[rootj]++;
        }
    }

    bool same(ull i, ull j) {
        return root(i) == root(j);
    }
};

struct BIT
{
    ll *tree;
    ll size;

    BIT(ll n, ll init) {
        tree = new ll[n+1];
        size = n;
        this->init(init);
    }

    void init(ll init) {
        memset(tree, 0, sizeof(ll) * (size+1));
        rep (i0, size) {
            ll idx = i0 + 1LL;
            while (idx <= size) {
                tree[idx] += init;
                idx += (idx & (-idx));
            }
        }
    }

    // idx is 1 origin
    void add(ll idx, ll x) {
        assert(idx > 0LL);
        while (idx <= size) {
            tree[idx] += x;
            idx += (idx & (-idx));
        }
    }

    // idx is 1 origin
    ll sum(ll idx) {
        assert(idx > 0LL);
        ll ret = 0LL;
        while (idx > 0LL) {
            ret += tree[idx];
            idx -= (idx & (-idx));
        }
        return ret;
    }
};

struct MaxFlow {
    V<ll> links[1005];
    ll capacities[1005][1005];
    ll nodes;

    MaxFlow(ll nodes) {
        // i == 0       --> S
        // i == nodes+1 --> T
        rep (i, nodes+2LL) links[i].clear();
        memset(capacities, 0, sizeof(capacities));
        this->nodes = nodes;
    }

    void add_path(ll a, ll b, ll capacity) {
        links[a].pb(b);
        links[b].pb(a);
        capacities[a][b] = capacity;
        capacities[b][a] = 0LL;
    }

    ll solve(void) {
        deque<V<ll> > q;
        ll ret = 0LL;

        for ( ; ; q.clear()) {

            V<ll> start;
            start.pb(0);
            q.push_front(start);

            bool checked[nodes+2];
            memset(checked, 0, sizeof(checked));

            V<ll> found;

            for ( ; !(q.empty()); ) {
                V<ll> path = q.front(); q.pop_front();
                ll last = path[path.size()-1];

                if (checked[last]) continue;
                if (last == nodes+1) {
                    found = path;
                    break;
                }

                checked[last] = true;
                for (auto next : (links[last])) {
                    if (capacities[last][next] == 0) continue;
                    V<ll> newpath(path);
                    newpath.pb(next);
                    q.push_front(newpath);
                }
            }

            if (found.size() == 0) {
                break;
            }
            else {
                ll flowcount = capacities[found[0]][found[1]];
                rep (i, found.size()-1) {
                    ll src = found[i];
                    ll dst = found[i+1];
                    flowcount = min(flowcount, capacities[src][dst]);
                }
                rep (i, found.size()-1) {
                    ll src = found[i];
                    ll dst = found[i+1];
                    capacities[src][dst] -= flowcount;
                    capacities[dst][src] += flowcount;
                }
                ret += flowcount;
            }
        }

        return ret;
    }
};

template <typename T>
struct SegmentTree {
    T *nodes;
    t2 *ranges;  // [start, end)
    ll nodecount;
    ll itemcount;
    T unit;
    T (*op)(T, T);

    SegmentTree(ll itemcount, T unit, T op(T, T)) {
        ll orig_itemcount = itemcount;
        this->itemcount = 1LL;
        while (this->itemcount < orig_itemcount) this->itemcount *= 2LL;
        nodecount = this->itemcount * 2 - 1;
        nodes = new T[nodecount];
        ranges = new t2[nodecount];
        this->unit = unit;
        this->op = op;

        ll start = 0LL;
        ll end = this->itemcount;
        ll len = this->itemcount;

        rep (i, nodecount) {
            nodes[i] = unit;
            ranges[i] = t2(start, end);
            if (end >= this->itemcount) {
                len /= 2LL;
                start = 0LL;
                end = len;
            }
            else {
                start = end;
                end = start + len;
            }
        }
    }

    void build(const T arr[]) {
        memcpy(nodes + nodecount / 2LL, arr, sizeof(T) * itemcount);
        rrep (i, nodecount / 2LL) {
            nodes[i] = op(nodes[i * 2LL + 1LL], nodes[i * 2LL + 2LL]);
        }
    }

    void update(ll k, T v) {
        ll idx = k + itemcount - 1LL;
        nodes[idx] = v;
        idx = (idx - 1LL) / 2LL;

        for ( ; idx >= 0; idx = (idx - 1LL) / 2LL) {
            nodes[idx] = op(nodes[idx * 2LL + 1LL],
                            nodes[idx * 2LL + 2LL]);
            if (!idx) break;
        }
    }

    // query to [start, end)
    virtual T query(ll start, ll end) const {
        return _query(start, end, 0LL);
    }

    virtual T _query(ll start, ll end, ll idx) const {
        ll rstart = get<0>(ranges[idx]);
        ll rend = get<1>(ranges[idx]);

        if (start <= rstart && rend <= end) {
            return nodes[idx];
        }
        if (rend <= start || end <= rstart) {
            return unit;
        }
        T left = _query(start, end, idx * 2LL + 1LL);
        T right = _query(start, end, idx * 2LL + 2LL);
        return op(left, right);
    }

    T query_fast(ll start, ll end) const {
        start += nodecount / 2LL;
        end += nodecount / 2LL;
        T lval = unit;
        T rval = unit;
        for ( ; start < end; start >>= 1LL, end >>= 1LL) {
            if (!(start & 1LL)) lval = op(lval, nodes[start]);
            if (!(end & 1LL)) rval = op(rval, nodes[end-1]);
            end--;
        }
        return op(lval, rval);
    }

};

//// update : sum / query : range sum
// ll op(ll x, ll y){ return x + y; }
// void op_upd(ll &x, ll y) { x += y; }
// ll op_div(ll x) { return x / 2LL; }
// ll op_mlt(ll x, ll y) { return x * y; }
//// update : sum / query : range max
// ll op(ll x, ll y) { return max(x, y); }
// void op_upd(ll &x, ll y) { x += y; }
// ll op_div(ll x) { return x; }
// ll op_mlt(ll x, ll y) { return x; }
//// update : substitute / query : range sum
// ll add(ll x, ll y) { return x + y; }
// void upd(ll &x, ll y) { x = y; }
// ll div(ll x) { return x / 2LL; }
// ll mlt(ll x, ll y) { return x * y; }
template <typename T>
struct SegmentTreeLazy : public SegmentTree<T> {
    T *lzvals;
    bool *lzvalids;
    ll unit_upd;
    void (*op_upd)(T&, T);
    T (*op_div)(T);
    T (*op_mlt)(T, T);

    SegmentTreeLazy(ll itemcount, T unit, T unit_upd,
                    T op(T, T), void op_upd(T&, T), T op_div(T), T op_mlt(T, T))
        : SegmentTree<T>(itemcount, unit, op) {
        this->lzvals = new T[this->nodecount];
        this->lzvalids = new bool[this->nodecount];
        this->unit_upd = unit_upd;
        this->op_upd = op_upd;
        this->op_div = op_div;
        this->op_mlt = op_mlt;
        rep (i, this->nodecount) this->lzvals[i] = unit_upd;
        memset(this->lzvalids, 0, sizeof(bool) * this->nodecount);
    }

    // newval = op_upd(oldval, lzval);
    void eval(ll nodeidx) {
        if (!lzvalids[nodeidx]) return;

        op_upd(this->nodes[nodeidx], lzvals[nodeidx]);

        if (nodeidx * 2LL + 2LL < this->nodecount) {
            ll downval = op_div(lzvals[nodeidx]);
            op_upd(lzvals[nodeidx * 2LL + 1LL], downval);
            op_upd(lzvals[nodeidx * 2LL + 2LL], downval);
            lzvalids[nodeidx * 2LL + 1LL] = lzvalids[nodeidx * 2LL + 2LL] = true;
        }

        lzvalids[nodeidx] = false;
        lzvals[nodeidx] = this->unit_upd;
    }

    void update(ll start, ll end, ll val) {
        _update(start, end, val, 0LL);
    }

    void _update(ll start, ll end, ll val, ll nodeidx) {
        eval(nodeidx);

        ll rstart = get<0>(this->ranges[nodeidx]);
        ll rend = get<1>(this->ranges[nodeidx]);
        if (end <= rstart || rend <= start) return;

        if (start <= rstart && rend <= end) {
            op_upd(lzvals[nodeidx], op_mlt(val, rend - rstart));
            lzvalids[nodeidx] = true;
            eval(nodeidx);
        }
        else {
            _update(start, end, val, nodeidx * 2LL + 1LL);
            _update(start, end, val, nodeidx * 2LL + 2LL);
            this->nodes[nodeidx] = this->op(this->nodes[nodeidx * 2LL + 1LL],
                                            this->nodes[nodeidx * 2LL + 2LL]);
        }
    }

    // query to [start, end)
    virtual T query(ll start, ll end) {
        return _query(start, end, 0LL);
    }

    virtual T _query(ll start, ll end, ll nodeidx) {
        ll rstart = get<0>(this->ranges[nodeidx]);
        ll rend = get<1>(this->ranges[nodeidx]);

        eval(nodeidx);

        if (start <= rstart && rend <= end) {
            return this->nodes[nodeidx];
        }
        if (rend <= start || end <= rstart) {
            return this->unit;
        }
        T left = _query(start, end, nodeidx * 2LL + 1LL);
        T right = _query(start, end, nodeidx * 2LL + 2LL);
        return this->op(left, right);
    }
};

void llin(ll &a)
{
    CIN(a);
}

void llinl1(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(auto &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
T min(const V<T> v)
{
    T ret = v[0];
    for (auto i : v) ret = min(ret, i);
    return ret;
}

template <typename T>
T max(const V<T> v)
{
    T ret = v[0];
    for (auto i : v) ret = max(ret, i);
    return ret;
}

ll absll(ll x)
{
    if (x < 0) return -x;
    return x;
}

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ll gcm(ll x, ll y)
{
    while (y != 0) {
        ll z = x % y;
        x = y;
        y = z;
    }
    return x;
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

void get_divisors(V<ll> &retlist, ll x)
{
    for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) {
        if (x % i == 0LL) {
            retlist.push_back(i);
            retlist.push_back(x / i);
        }
    }
}

// returns factors and 1
void get_factors(V<ll> &retlist, ll x)
{
    retlist.pb(1LL);
    for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) {
        while (x % i == 0LL) {
            retlist.pb(i);
            x /= i;
        }
    }
    retlist.pb(x);
}

bool is_prime(ll x)
{
    V<ll> factors, factors2;

    get_factors(factors, x);

    for (auto factor : factors) {
        if (factor > 1) factors2.pb(factor);
    }

    return factors2.size() == 1 && x == factors2[0];
}

template <typename T>
void intersection(const set<T> &a, const set<T> &b,
                  set<T> &result)
{
    set_intersection(ALL(a), ALL(b), inserter(result, result.end()));
}

ull combination(ll x, ll y)
{
    if (y > x / 2LL) y = x - y;

    ull ret = 1LL;
    for (ll i = 0LL; i < y; ++i) {
        ret *= x--;
        ret /= (i + 1LL);
    }

    return ret;
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
    }

    rep (i, size) {
        perm_invs[i] = mod_inv(perms[i], mod);
    }
}

#if 0
S V<ll> edgelist[n+1];
#endif
void make_edgelist(const V<t2> &srclist, V<ll> edgelist[])
{
    for (auto src : srclist) {
        ll a = get<0>(src);
        ll b = get<1>(src);
        edgelist[a].pb(b);
        edgelist[b].pb(a);
    }
}

#if 0
S ll parents[n+1];
S V<ll> children[n+1];
S ll levels[n+1];
#endif
void make_parental_relation(const V<ll> edgelist[], ll root, ll n,
                            ll parents[], V<ll> children[], ll levels[])
{
    queue<ll> q;
    bool checked[n+1];

    memset(checked, 0, sizeof(checked));

    q.push(root);
    checked[root] = true;
    parents[root] = root;
    levels[root] = 0LL;

    for ( ; !(q.empty()); ) {
        ll now = q.front(); q.pop();
        for (auto next : edgelist[now]) {
            if (checked[next]) continue;
            q.push(next);
            checked[next] = true;
            parents[next] = now;
            children[now].pb(next);
            levels[next] = levels[now] + 1LL;
        }
    }
}

void make_subtree_sizes(const ll child_count[], const ll parents[],
                        ll subtree_sizes[], ll n)
{
    ll remain_count[n+1LL];
    memcpy(remain_count, child_count, sizeof(remain_count));

    queue<ll> q;
    srep (node, 1LL, n+1LL) {
        subtree_sizes[node] = 1LL;
        if (remain_count[node] > 0) continue;
        q.push(node);
    }

    while (!q.empty()) {
        ll node = q.front(); q.pop();
        ll parent = parents[node];
        if (node == parent) continue;
        remain_count[parent]--;
        subtree_sizes[parent] += subtree_sizes[node];
        if (remain_count[parent] == 0LL) q.push(parent);
    }
}

void get_centroids(const V<ll> children[], const ll subtree_sizes[],
                   ll root, ll n, V<ll> &centroids)
{
    queue<ll> q;
    q.push(root);

    while (!q.empty()) {
        ll now = q.front(); q.pop();
        bool is_centroid = true;
        for (auto child : children[now]) {
            q.push(child);
            if (subtree_sizes[child] > n / 2LL) is_centroid = false;
        }
        if (n - subtree_sizes[now] > n / 2LL) is_centroid = false;
        if (is_centroid) centroids.pb(now);
    }

    assert(centroids.size() == 1LL || centroids.size() == 2LL);
}

#define POW_ANCESTOR_MAXSIZE   20

// preprocess for get_common_ancestor()
void make_pow_ancestor(const ll parent[], ll n,
                       ll (*pow_ancestor)[POW_ANCESTOR_MAXSIZE])
{
    rep (i, n) pow_ancestor[i+1][0] = parent[i+1];

    for (int pow2 = 1; pow(2, pow2) <= n; ++pow2) {
        rep (i0, n) {
            int i = i0+1;
            ll prev = pow_ancestor[i][pow2-1];
            pow_ancestor[i][pow2] = pow_ancestor[prev][pow2-1];
        }
    }
}

ll get_common_ancestor(ll n, ll x, ll y,
                       const ll (*pow_ancestor)[POW_ANCESTOR_MAXSIZE],
                       const ll level[])
{
    if (level[x] < level[y]) {
        ll diff = level[y] - level[x];
        for ( ; diff; ) {
            ll bit = diff & -diff;
            y = pow_ancestor[y][(int)log2(bit)];
            diff -= bit;
        }
    }
    else {
        ll diff = level[x] - level[y];
        for ( ; diff; ) {
            ll bit = diff & -diff;
            x = pow_ancestor[x][(int)log2(bit)];
            diff -= bit;
        }
    }

    if (x == y) return x;

    rrep (i, (int)log2(n)+1) {
        if (pow_ancestor[x][i] != pow_ancestor[y][i]) {
            x = pow_ancestor[x][i];
            y = pow_ancestor[y][i];
        }
    }

    return pow_ancestor[x][0];
}

void kmp_init(const string &pattern, ll kmp_next[])
{
    kmp_next[0] = -1LL;

    ll plen = pattern.size();
    ll prefix_end = -1;

    rep (suffix_end, pattern.size()) {
        while (prefix_end >= 0 && pattern[suffix_end] != pattern[prefix_end]) {
            prefix_end = kmp_next[prefix_end];
        }
        kmp_next[suffix_end+1] = ++prefix_end;
    }

    kmp_next[0] = 0LL;
}

// founds ... list of text's idx of match position. start position idx.
void kmp_search(const string &text, const string &pattern, const ll kmp_next[],
                V<ll> &founds)
{
    ll text_size = text.size();
    ll pattern_size = pattern.size();
    ll text_start = 0LL;
    ll pattern_idx = 0LL;

    assert(pattern_size <= text_size);

    for ( ; ; ) {
        if (text_start + pattern_idx >= text_size) break;
        if (pattern_idx >= pattern_size) break;

        if (text[text_start+pattern_idx] == pattern[pattern_idx]) {
            pattern_idx++;
            if (pattern_idx == pattern_size) {
                founds.pb(text_start);
                pattern_idx = kmp_next[pattern_idx];
                text_start += (pattern_size - pattern_idx);
            }
        }

        else {
            text_start += (pattern_idx - kmp_next[pattern_idx]);
            pattern_idx = kmp_next[pattern_idx];
            if (pattern_idx == 0LL && text[text_start] != pattern[0]) {
                text_start++;
            }
        }
    }
}

void z_algorithm(ll matchcounts[], const string &str)
{
    ll n = str.size();
    ll base_idx = 0LL;
    memset(matchcounts, 0, sizeof(ll) * n);

    srep (idx, 1LL, n) {

        ll checked_len = base_idx + matchcounts[base_idx];

        if (idx + matchcounts[idx-base_idx] < checked_len) {
            matchcounts[idx] = matchcounts[idx-base_idx];
            continue;
        }

        ll start = max(0LL, base_idx + matchcounts[base_idx] - idx);
        matchcounts[idx] = start;
        srep (cmp, start, n-idx) {
            if (str[cmp] == str[idx+cmp]) matchcounts[idx]++;
            else break;
        }
        base_idx = idx;

    }

    matchcounts[0] = n;
}

void _manacher(V<ll> &rlist, const string &s)
{
    ll n = s.size();
    rep (i, n) rlist.pb(1);

    ll center = -1;

    rep (i, n) {
        assert(center < i);
        if (center < 0) {
            center = 0;
            continue;
        }

        ll opi = center - (i - center);
        if (opi <= center - rlist[center]) {
            rlist[i] = 1LL;
            ll d = 1LL;
            while (i-d >= 0 && i+d < n && s[i-d] == s[i+d]) rlist[i]++, d++;
            center = i;
            continue;
        }

        if (i + rlist[opi] < center + rlist[center]) {
            rlist[i] = rlist[opi];
            continue;
        }

        rlist[i] = center + rlist[center] - i;
        ll d = center + rlist[center] - i;
        while (i-d >= 0 && i+d < n && s[i-d] == s[i+d]) rlist[i]++, d++;
        center = i;
    }
}

void manacher(V<ll> &r_oddlist, V<ll> &r_evenlist, const string &s)
{
    _manacher(r_oddlist, s);

    string ps;
    ps += s[0];
    srep (i, 1, s.size()) {
        ps += "$";
        ps += s[i];
    }

    V<ll> tmpr;
    _manacher(tmpr, ps);
    rep (i, s.size()-1) r_evenlist.pb(tmpr[i*2+1] / 2LL);
    r_evenlist.pb(0LL);
}

double xy_distance(double x1, double y1, double x2, double y2)
{
    double xx = (x1 - x2) * (x1 - x2);
    double yy = (y1 - y2) * (y1 - y2);
    return sqrt(xx + yy);
}

double heron(double a, double b, double c)
{
    double s = (a + b + c) / 2.;
    double ret = 1.;
    ret *= s;
    ret *= (s - a);
    ret *= (s - b);
    ret *= (s - c);
    ret = sqrt(ret);
    return ret;
}

double rad_normarize(double rad)
{
    while (rad < -PI) rad += 2. * PI;
    while (rad > PI) rad -= 2. * PI;
    return rad;
}

void _debug_print(auto x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
         << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
    struct tm *tm = localtime(&tv.tv_sec);
    printf("-- %s %02d:%02d:%02d.%06ld\n",
           prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}

///////////////////////////////////////////////////////////////////////////////

typedef tuple<ll, char> lc;

void f_dp(ll dp[500005], const V<ll> &cnts1)
{
    debug_printf("----------- f_dp\n");
    debug_print(cnts1);

    dp[0] = 0;

    rep (i, cnts1.size()-1) {
        dp[i+1] = (cnts1[i] - 1LL) + dp[i];
        if (i) dp[i+1] = max(dp[i+1], cnts1[i] + dp[i-1]);
        else dp[i+1] = max(dp[i+1], cnts1[i]);
    }

    debug_printf("---- dp\n");
    debug_print(dp, cnts1.size());
}

ll solve(const V<ll> &cnts1)
{
    debug_printf("---------------- solve\n");

    S ll dp_prefix[500005];
    f_dp(dp_prefix, cnts1);

    S V<ll> rcnts1;
    rcnts1 = cnts1;
    reverse(ALL(rcnts1));

    S ll dp_suffix[500005];
    f_dp(dp_suffix, rcnts1);

    ll ret = 0;
    ll n = cnts1.size();

    rep (i, n) {
        if (cnts1[i] > 1) {
            ret = max(ret, dp_prefix[i] + dp_suffix[n-i-1]);
        }
        else {
            ll cand = dp_prefix[i];
            if (i < n-1) cand += dp_suffix[n-i-2];
            ret = max(ret, cand);
        }
    }

    debug_printf("------ ret=%lld\n", ret);
    return ret;
}

void _main();
int main()
{
    cout << setprecision(12);
#if 0
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

void _main()
{
    ll n; llin(n);
    S string s; CIN(s);

    s += "$";

    S V<lc> cnts;
    ll cnt = 0;
    char prev = s[0];
    for (auto c : s) {
        if (prev == c) {
            cnt++;
        }
        else {
            cnts.pb(lc(cnt, prev));
            cnt = 1;
        }
        prev = c;
    }

    debug_printf("---- cnts\n");
    for (auto x : cnts) debug_printf("<%lld %c> ", get<0>(x), get<1>(x));
    debug_printf("\n");

    cnts.pb(lc(2, '0'));

    S V<ll> cnts1;
    ll ans = 0;

    for (auto item : cnts) {
        ll cnt = get<0>(item);
        ll c = get<1>(item);
        if (c == '0' && cnt > 1) {
            ans += solve(cnts1);
            cnts1.clear();
            continue;
        }
        if (c == '1') cnts1.pb(cnt);
    }

    debug_printf("---- ans\n");
    cout<< ans << endl;
}

///////////////////////////////////////////////////////////////////////////////