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:
/*
                                                                                                     
                                             `-:://:::-                                             
                                           `//:-------:/:`                                          
                                          .+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .o:--...```..---+/`                                        
                                       `/y+o/---....---:+o.                                         
                                   `...````-os+/:---:/+o/--.`                                       
              `-/+++++/:.      `...`       :h+d+oooo+/+-`   ...                                     
            `/++//:::://++-`....`         -.`//````````:`     `..`                                  
           `o+/::------://o/`           `-` -.          -`       `..`                               
 `---.-o/:./o/::-..``..-ЗАПУСКАЕМ      ..  ..            -`        `...       ``..``                
  `....o+:-++/:--.```..-://s.        `-`  .-              -`          `-o: .-//::::/:-`             
          `:s+/:--....-::/+s-`      .-   `-                -`           -///:--------:/:`           
           ./s+//:::::://oo-``..НЕЙРОННУЮ: СЕТЬ:::::::-`РАБОТЯГИ        `+:--........--:/`          
            .:ooo+++++osso-`    `.:-...`/` ./::-------:/:`   -`         :+--..``````.--:+:...-+:-`  
             `.-/+++++/+-.-`    -.   ``:so:/:--.......--:+`  `-```````o+/+--..`````..--:o/-..:s+:.  
                 ```````:``.. `-`     -` `+:--..`````..--/+-.../.`````..-o:--.......---/o.    `     
                        `:  `:-      -.  .o:--..`` ``..--:o`   `-`      `:o+:--------:+o-`          
                         `-`-...    ..   .o/--...```..--:+/`    `-`     `oy/so/////++o/.`           
                          -/`  `-` `- ``+s/o/:---...---:++.      `-`   .-../d://///:-.`             
                `.---..``-..-    .-/..`````-oo+/:::::/+o+-        `-``-`  `-.  ````                 
             `:++++/+++++-  ..``.-/:`      /y-:/++o++/:.`..`       ./.   `-                         
            -++/::::::://+/..:-``:` ..   `-.`  ```.```    `..`   `..`-` `-                          
       ``  -o//:--....-::/++` -.-`   `-`.-`                 `..`..`  `-.-                           
  -----ss+:++/:--.```..-://s.  /.     `::                    `-:.     ./`                           
  `````/:..+o/::-..``.--:/+s. ..-`   `-``-`                 ..` `-`  `-`-`                          
          `-s+/::-----::/+oo---``-` ..    .:-    ```      .-`     .-.-  `-`                         
           `:oo+//::://+os/..:`..-/:`      :y.-:::::::.`.-`        ./-`  `-`                        
            `./+oooooooo+/.`-    .-:...`.. .//:-------://`        `- `..` `:.                       
              ``.-::::-.``-/`  `-` `-  `oo:+:--.......--:/`      `-    `.:--h.``..```               
                          -.-`.-    .-   `+:--..`````..--//`    `-       /s-//::::::::.             
                         -` `/-      ..  .o:--..`` ``..--:o.```.-        `//:--------://`           
                        -` .-`.-`     -.`-o/--...```..--:+/.``-:....``:-.+:--....`...--:+`          
                       ..`-.   `-.   ``:os:o/:---...---:++.  `-     ``///+:-..``````.--:+-````-.`   
              `.:///////.-`      .:-..` -``-+o+/:::::/+o/.  `-         `:+:-..`````..--:o/:--/ys+-  
            `-++///////+o/. ``....`-.    :` `.:++++++/:.`  .-           -o/---......---/o.   `.`    
           `++//:-----::/+o:..`     .-`   :    ```````    .-           `+so+:--------:++-`          
  `````:-``:o/::-..`..--:/+o`         -.  `-             .-          `../../+o+////+o+:.`           
  -----syo/o+/:--.```..-://s.          .-` `-           .-        `...     ``-:////:-``             
       .` `/s//:--....-::/+s.            -. `-`        .-       `..`                                
           .+o+/:::--:://+s/-..`          .::+y  ```  .-     `..`                                   
            ./oo++////+oso-`   `....       :y-+:::::::/`   ...                                      
             `.:+oooooo/-`         `....-. .//:-------:/:-.`                                        
                ``...``                 /+:+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .+/--...```..--:+/`                                        
                                         `-o/:---...---:++.                                         
                                          `-+o+/:---:/+o/.                                          
                                            `.:+oooo+/-.`                                           
                                               ``````                                               
*/

#ifdef aimbot
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#endif

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <queue>
#include <ostream>
#include <istream>
#include <typeinfo>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <fstream>
#include <array>
#include <list>
#include <bitset>
#include <functional>
#include <random>
#include <cstring>
#include <chrono>

#define random escape__from__random__aetuhoetnuhshe
#define mt make_tuple
#define x first
#define y second
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define umap unordered_map
#define uset unordered_set
#define elif else if
#define len(v) ((int)v.size())
#define f(i, n) for (int i = 0; i < (n); i++)
#define rof(i, n) for (int i = ((n) - 1); i >= 0; i--)
#define apply(v, act) for (auto &x : v) { act; }
#define log(args...) {string s = #args;deque<string> deq;\
string buf = "";int bal = 0;for (char c : s) {\
if (c == '(' || c == '[' || c == '{') {bal++;\
} else if (c == ')' || c == ']' || c == '}') {\
bal--;} else {if (bal == 0) {if (c == ',') {\
deq.pb(buf);buf = "";} else {if (c != ' ') {\
buf += c;}}}}}if (!buf.empty()) {deq.pb(buf);}\
smart_io::precall_print();smart_io::_print(deq, args);}

inline int min(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^x; }
inline int max(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^y; }
inline long long min(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^x; }
inline long long max(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^y; }

#define print    \
smart_io::precall_print(); \
cout,

#define scan cin,

#ifdef fast_allocator
const int MAXMEM = 200 * 1000 * 1024;
char _memory[MAXMEM];
size_t _ptr = 0;
void* operator new(size_t _x) { _ptr += _x; assert(_ptr < MAXMEM); return _memory + _ptr - _x; }
void operator delete (void*) noexcept {}
#endif

using namespace std;

char string_in_buffer[(int)260];


void fast_scan(int &x) { scanf("%d", &x); }
void fast_scan(long long &x) { scanf("%lld", &x); }
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
void fast_scan(double &x) { scanf("%lf", &x); }
void fast_scan(long double &x) { scanf("%Lf", &x); }
void fast_scan(char &x) {
	scanf("%c", &x);
	if (x == '\n') {
		fast_scan(x);
	}
}
void fast_scan(string &x) {
	scanf("%s", string_in_buffer);
	x = string(string_in_buffer);
}

template<class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
	fast_scan(p.first);
	fast_scan(p.second);
}

template <class T>
void fast_scan(vector<T> &v) {
	for (auto &x : v) fast_scan(x);
}

void fast_print(const int &x) { printf("%d", x); }
void fast_print(const unsigned int &x) { printf("%u", x); }
void fast_print(const long long &x) { printf("%lld", x); }
void fast_print(const unsigned long long &x) { printf("%llu", x); }
void fast_print(const char &x) { printf("%c", x); };
// void fast_print(__int128 x) {
// 	if (x == 0) { fast_print('0'); return; }
// 	if (x < 0) {
// 		fast_print('-');
// 		x = -x;
// 	}
// 	__int128 p = 1;
// 	while (x / (p * 10)) p *= 10;
// 	while (p) {
// 		__int128 symb = x / p;
// 		fast_print((int)symb);
// 		x -= p * symb;
// 		p /= 10;
// 	}
// };
void fast_print(const double &x) { printf("%.15lf", x); }
void fast_print(const long double &x) { printf("%.15Lf", x); }
void fast_print(const string &x) { printf("%s", x.c_str());}
void fast_print(const char v[]) { fast_print((string)v); }

template<class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
	fast_print(p.first);
	fast_print(' ');
	fast_print(p.second);
}

template <class T>
void fast_print(const vector<T> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print(' ');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const vector<vector<T>> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print('\n');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const T &v) {
	for (const auto &x : v) {
		fast_print(x);
		fast_print(' ');
	}
}


using namespace std;


namespace smart_io {
	string print_start = "";
	string sep = " ";
	bool first_print = false;
	
	void precall_print() {
		fast_print(print_start);
		print_start = "\n";
		first_print = true;
	}
	
	void _print(deque<string>) {}
	template<class T, class... Args>
	void _print(deque<string> names, T elem, Args... args) {
		if (!first_print) {
			fast_print("\n");
		} else {
			first_print = false;
		}
		fast_print(names.front());
		fast_print(" = ");
		fast_print(elem);
		names.pop_front();
		_print(names, args...);
	}
} //namespace smart_io


template <class T>
ostream &operator,(ostream &os, const T &object) {
	if (!smart_io::first_print) {
		fast_print(smart_io::sep);
	} else {
		smart_io::first_print = false;
	}
	fast_print(object);
	return os;
}

template <class T>
istream &operator,(istream &is, T &object) {
	fast_scan(object);
	return is;
}

namespace random {
	using namespace std::chrono;
	mt19937 rng(duration_cast< milliseconds >(
											  system_clock::now().time_since_epoch()
											  ).count());
	uniform_real_distribution<> prob_dist(0.0, 1.0);
};

namespace typedefs {
	typedef long long ll;
	typedef unsigned long long ull;
	typedef pair<int, int> pii;
	typedef long double ld;
}

namespace numbers_operation {
	template<class T>
	inline T floor_mod(T a, const T &b) {
		a %= b;	
		if (a < 0) a += b;
		return a;
	}
}

using namespace numbers_operation;
using namespace typedefs;
using namespace random;

const int N = (1 << 18);
struct Node {
	int l = -1, r = -1;
	int value = -1e9;
};

Node T[(int)N * 4 + 1];
int it = 0;
int get_node() {
	return it++;	
}
int clone(int i) {
	int j = get_node();
	T[j].l = T[i].l;
	T[j].r = T[i].r;
	T[j].value = T[i].value;
	return j;
}

int query(int i, int tl, int tr, int ql, int qr) { 
	if (tr <= ql || qr <= tl) return -1e9;
	if (ql <= tl && tr <= qr) return T[i].value;
	int m = (tl + tr) / 2;
	return max(query(T[i].l, tl, m, ql, qr),
		query(T[i].r, m, tr, ql, qr));
}

void update(int i, int tl, int tr, int j, int value) {
	if (tl + 1 == tr) {
		T[i].value = value;
	} else {
		int m = (tl + tr) / 2;
		if (j < m) {
			update(T[i].l, tl, m, j, value);
		} else {
			update(T[i].r, m, tr, j, value);
		}
		T[i].value = max(T[T[i].l].value, T[T[i].r].value);
	}
}

int init(int tl, int tr) {
	int i = get_node();
	if (tl + 1 != tr) {
		int m = (tl + tr) / 2;
		T[i].l = init(tl, m);
		T[i].r = init(m, tr);
	}
	return i;
}

int n;
vector<int> p;
vector<int> recs{0};
signed main(signed argc, char *argv[]) {
	scan n;
	p.resize(n);
	scan p;
	for (int i = 1; i < n; i++) 
		if (p[i] > p[recs.back()])
			recs.pb(i);
	vector<int> O(n + 1), E(n + 1);
	int odd = init(0, n + 5);
	int even = init(0, n + 5);
	{
		update(even, 0, n + 5, n + 1, 0);
		O[n] = -1e9;
		E[n] = -1e9;
		for (int i = n - 1; ~i; i--) {
			auto it = lower_bound(recs.begin(), recs.end(), i);
			int cost = 1 + (it != recs.end() && *it == i); 
			int a, b;
			if (cost & 1) {
				a = query(even, 0, n + 5, p[i], n + 5);
				b = query(odd, 0, n + 5, p[i], n + 5);
			} else {
				a = query(odd, 0, n + 5, p[i], n + 5);
				b = query(even, 0, n + 5, p[i], n + 5);
			}
			E[i] = query(even, 0, n + 5, p[i], p[i] + 1);
			O[i] = query(odd, 0, n + 5, p[i], p[i] + 1);
			if (query(even, 0, n + 5, p[i], p[i] + 1) < b + cost)
				update(even, 0, n + 5, p[i], b + cost);
			if (query(odd, 0, n + 5, p[i], p[i] + 1) < a + cost) 
				update(odd, 0, n + 5, p[i], a + cost);
		}
	}
	int e[2];
	int c[2];
	e[0] = e[1] = 0;
	c[0] = c[1] = 0;
	string rez = "";
	for (int i = 0; i < n; i++) {
		update(even, 0, n + 5, p[i], E[i]);
		update(odd, 0, n + 5, p[i], O[i]);
		bool putz = false;
		// try 0
		{
			int et[2], ct[2];
			et[0] = e[0], et[1] = e[1];
			ct[0] = c[0], ct[1] = c[1];
			if (p[i] > et[0]) {
				et[0] = p[i];
				ct[0]++;
			}
			int H = recs.end() - lower_bound(recs.begin(), recs.end(), i + 1);
			for (int c = 0; c < 2; c++) {
				// c <--- basis
				int R = ct[1 - c] + H - ct[c];
				if (R >= 0 && query(((R & 1) ? odd : even), 0, n + 5, et[c], n + 5) >= R) {
					putz = true;
				}
			}
		}
		rez += ('0' + (1 - putz));
		if (p[i] > e[1 - putz]) {
			e[1 - putz] = p[i];
			c[1 - putz]++;
		}
	}
	if (c[0] != c[1]) {
		print -1;
	} else {
		print rez;
	}
}