Problem: You are given P, a permutation of (1,\ 2,\ ...\ N).

A string S of length N consisting of `0` and `1` is a good string when it meets the following criterion:

* The sequences X and Y are constructed as follows:
* First, let X and Y be empty sequences.
* For each i=1,\ 2,\ ...\ N, in this order, append P_i to the end of X if S_i= `0`, and append it to the end of Y if S_i= `1`.
* If X and Y have the same number of high elements, S is a good string. Here, the i-th element of a sequence is called high when that element is the largest among the elements from the 1-st to i-th element in the sequence.



Determine if there exists a good string. If it exists, find the lexicographically smallest such string.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq P_i \leq N
* P_1,\ P_2,\ ...\ P_N are all distinct.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
P_1 P_2 ... P_N


Output

If a good string does not exist, print `-1`. If it exists, print the lexicographically smallest such string.

Examples

Input

6
3 1 4 6 2 5


Output

001001


Input

5
1 2 3 4 5


Output

-1


Input

7
1 3 2 5 6 4 7


Output

0001101


Input

30
1 2 6 3 5 7 9 8 11 12 10 13 16 23 15 18 14 24 22 26 19 21 28 17 4 27 29 25 20 30


Output

000000000001100101010010011101

Solution (in CPP):

Solution:
/**
 *    author:  tourist
 *    created: 08.12.2019 04:23:25       
**/
#include <bits/stdc++.h>

using namespace std;

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char* s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

class segtree {
 public:
  struct node {
    // don't forget to set default value (used for leaves)
    // not necessarily neutral element!
    int mx = 0;

    void apply(int l, int r, int v) {
      mx = v;
    }
  };

  node unite(const node &a, const node &b) const {
    node res;
    res.mx = max(a.mx, b.mx);
    return res;
  }

  inline void push(int x, int l, int r) {
  }

  inline void pull(int x, int z) {
    tree[x] = unite(tree[x + 1], tree[z]);
  }

  int n;
  vector<node> tree;

  void build(int x, int l, int r) {
    if (l == r) {
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    build(x + 1, l, y);
    build(z, y + 1, r);
    pull(x, z);
  }

  template <typename M>
  void build(int x, int l, int r, const vector<M> &v) {
    if (l == r) {
      tree[x].apply(l, r, v[l]);
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    build(x + 1, l, y, v);
    build(z, y + 1, r, v);
    pull(x, z);
  }

  node get(int x, int l, int r, int ll, int rr) {
    if (ll <= l && r <= rr) {
      return tree[x];
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    push(x, l, r);
    node res{};
    if (rr <= y) {
      res = get(x + 1, l, y, ll, rr);
    } else {
      if (ll > y) {
        res = get(z, y + 1, r, ll, rr);
      } else {
        res = unite(get(x + 1, l, y, ll, rr), get(z, y + 1, r, ll, rr));
      }
    }
    pull(x, z);
    return res;
  }

  template <typename... M>
  void modify(int x, int l, int r, int ll, int rr, const M&... v) {
    if (ll <= l && r <= rr) {
      tree[x].apply(l, r, v...);
      return;
    }
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    push(x, l, r);
    if (ll <= y) {
      modify(x + 1, l, y, ll, rr, v...);
    }
    if (rr > y) {
      modify(z, y + 1, r, ll, rr, v...);
    }
    pull(x, z);
  }

  int find_first_knowingly(int x, int l, int r, const function<bool(const node&)> &f) {
    if (l == r) {
      return l;
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res;
    if (f(tree[x + 1])) {
      res = find_first_knowingly(x + 1, l, y, f);
    } else {
      res = find_first_knowingly(z, y + 1, r, f);
    }
    pull(x, z);
    return res;
  }

  int find_first(int x, int l, int r, int ll, int rr, const function<bool(const node&)> &f) {
    if (ll <= l && r <= rr) {
      if (!f(tree[x])) {
        return -1;
      }
      return find_first_knowingly(x, l, r, f);
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res = -1;
    if (ll <= y) {
      res = find_first(x + 1, l, y, ll, rr, f);
    }
    if (rr > y && res == -1) {
      res = find_first(z, y + 1, r, ll, rr, f);
    }
    pull(x, z);
    return res;
  }

  int find_last_knowingly(int x, int l, int r, const function<bool(const node&)> &f) {
    if (l == r) {
      return l;
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res;
    if (f(tree[z])) {
      res = find_last_knowingly(z, y + 1, r, f);
    } else {
      res = find_last_knowingly(x + 1, l, y, f);
    }
    pull(x, z);
    return res;
  }

  int find_last(int x, int l, int r, int ll, int rr, const function<bool(const node&)> &f) {
    if (ll <= l && r <= rr) {
      if (!f(tree[x])) {
        return -1;
      }
      return find_last_knowingly(x, l, r, f);
    }
    push(x, l, r);
    int y = (l + r) >> 1;
    int z = x + ((y - l + 1) << 1);
    int res = -1;
    if (rr > y) {
      res = find_last(z, y + 1, r, ll, rr, f);
    }
    if (ll <= y && res == -1) {
      res = find_last(x + 1, l, y, ll, rr, f);
    }
    pull(x, z);
    return res;
  }

  segtree(int _n) : n(_n) {
    assert(n > 0);
    tree.resize(2 * n - 1);
    build(0, 0, n - 1);
  }

  template <typename M>
  segtree(const vector<M> &v) {
    n = v.size();
    assert(n > 0);
    tree.resize(2 * n - 1);
    build(0, 0, n - 1, v);
  }

  node get(int ll, int rr) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    return get(0, 0, n - 1, ll, rr);
  }

  node get(int p) {
    assert(0 <= p && p <= n - 1);
    return get(0, 0, n - 1, p, p);
  }

  template <typename... M>
  void modify(int ll, int rr, const M&... v) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    modify(0, 0, n - 1, ll, rr, v...);
  }

  // find_first and find_last call all FALSE elements
  // to the left (right) of the sought position exactly once

  int find_first(int ll, int rr, const function<bool(const node&)> &f) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    return find_first(0, 0, n - 1, ll, rr, f);
  }

  int find_last(int ll, int rr, const function<bool(const node&)> &f) {
    assert(0 <= ll && ll <= rr && rr <= n - 1);
    return find_last(0, 0, n - 1, ll, rr, f);
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<int> p(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
    --p[i];
  }
  vector<int> is_high(n, 0);
  {
    int mx = -1;
    for (int i = 0; i < n; i++) {
      if (p[i] > mx) {
        is_high[i] = 1;
        mx = p[i];
      }
    }
  }
  int cnt_high = accumulate(is_high.begin(), is_high.end(), 0);
  const int inf = 123456789;
  vector<segtree> st(2, segtree(n));
  for (int i = 0; i < n; i++) {
    st[1].modify(i, i, -inf);
  }
  for (int i = n - 1; i >= 0; i--) {
    int val0;
    int val1;
    if (is_high[i]) {
      val0 = 2 + st[0].get(p[i], n - 1).mx;
      val1 = 2 + st[1].get(p[i], n - 1).mx;
    } else {
      val0 = 1 + st[1].get(p[i], n - 1).mx;
      val1 = 1 + st[0].get(p[i], n - 1).mx;
    }
    st[0].modify(p[i], p[i], val0);
    st[1].modify(p[i], p[i], val1);
  }
  if (st[cnt_high % 2].get(0, n - 1).mx < cnt_high) {
    cout << -1 << '\n';
    return 0;
  }
  vector<int> mx(2, -1);
  vector<int> res(2, 0);
  for (int i = 0; i < n; i++) {
    st[0].modify(p[i], p[i], -inf);
    st[1].modify(p[i], p[i], -inf);
    int diff = res[0] + (p[i] > mx[0]) + (cnt_high - is_high[i]) - res[1];
    int cur = max(0, st[diff & 1].get(max(0, mx[1]), n - 1).mx);
    int diff2 = res[1] + (cnt_high - is_high[i]) - res[0] - (p[i] > mx[0]);
    int cur2 = max(0, st[diff2 & 1].get(max(p[i], mx[0]), n - 1).mx);
    int q = ((cur < diff || diff < 0) && (cur2 < diff2 || diff2 < 0));
    cout << q;
    if (p[i] > mx[q]) {
      mx[q] = p[i];
      ++res[q];
    }
    cnt_high -= is_high[i];
  }
  cout << '\n';
  return 0;
}