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:
// #pragma GCC target("avx")  // CPU 処理並列化
// #pragma GCC optimize("O3")  // CPU 処理並列化
// #pragma GCC optimize("unroll-loops")  // 条件処理の呼び出しを減らす
// #define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024));
// #define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_);

#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
#include<numeric>
#include<unordered_set>
#include<unordered_map>
#include<complex>
using namespace std;
const long long mod=1000000007;
const long long inf=mod*mod;
const long long d2=(mod+1)/2;
const double EPS=1e-11;
const double INF=1e+10;
const double PI=acos(-1.0);
const int C_SIZE = 11100000;
const int UF_SIZE = 3100000;
namespace{
	long long fact[C_SIZE];
	long long finv[C_SIZE];
	long long inv[C_SIZE];
	inline long long Comb(int a,int b){
	 	if(a<b||b<0)return 0;
	 	return fact[a]*finv[b]%mod*finv[a-b]%mod;
	}
	void init_C(int n){
		fact[0]=finv[0]=inv[1]=1;
		for(int i=2;i<n;i++){
			inv[i]=(mod-(mod/i)*inv[mod%i]%mod)%mod;
		}
		for(int i=1;i<n;i++){
			fact[i]=fact[i-1]*i%mod;
			finv[i]=finv[i-1]*inv[i]%mod;
		}
	}
	long long pw(long long a,long long b){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%mod;
			a=a*a%mod;
			b/=2;
		}
		return ret;
	}
	long long pw_mod(long long a,long long b,long long M){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%M;
			a=a*a%M;
			b/=2;
		}
		return ret;
	}
	int pw_mod_int(int a,int b,int M){
		if(a<0)return 0;
		if(b<0)return 0;
		int ret=1;
		while(b){
			if(b%2)ret=(long long)ret*a%M;
			a=(long long)a*a%M;
			b/=2;
		}
		return ret;
	}
	int ABS(int a){return max(a,-a);}
	long long ABS(long long a){return max(a,-a);}
	double ABS(double a){return max(a,-a);}
	int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; }
	int UF[UF_SIZE];
	void init_UF(int n){
		for(int i=0;i<n;i++)UF[i]=-1;
	}
	int FIND(int a){
		if(UF[a]<0)return a;
		return UF[a]=FIND(UF[a]);
	}
	void UNION(int a,int b){
		a=FIND(a);b=FIND(b);if(a==b)return;
		if(UF[a]>UF[b])swap(a,b);
		UF[a]+=UF[b];UF[b]=a;
	}
}
// ここから編集しろ
int p[210000];
int x[210000][2];
int t[210000];
int segtree[2][524288];

int query(int a,int b,int c,int d,int e,int f){
	if(d<a||b<c)return -mod;
	if(c<=a&&b<=d)return segtree[f][e];
	return max(query(a,(a+b)/2,c,d,e*2,f),query((a+b)/2+1,b,c,d,e*2+1,f));
}
void update(int a,int b,int c){
	a+=262144;
	segtree[c][a]=b;
	a/=2;
	while(a){
		segtree[c][a]=max(segtree[c][a*2],segtree[c][a*2+1]);
		a/=2;
	}
}
char ans[210000];
int R[210000][18];
int Q;
int n;
bool chk(int a,int b,int c,int d,int e){

	int V,at;
	V=Q+b-c;

	// printf("A %d %d\n",V,query(0,262143,e+1,n,1,ABS(V)%2));
	if(V>=0&&V<=query(0,262143,e+1,n,1,ABS(V)%2))return true;

	V=Q+c-b;

	// printf("B %d %d\n",V,query(0,262143,d+1,n,1,ABS(V)%2));
	if(V>=0&&V<=query(0,262143,d+1,n,1,ABS(V)%2))return true;

	return false;
}
int main(){
	int a;scanf("%d",&a);n=a;
	for(int i=0;i<a;i++){
		scanf("%d",p+i);p[i]--;
	}
	int mh=-1;
	for(int i=0;i<a;i++){
		if(mh<p[i]){
			mh=p[i];
			t[i]=1;
			Q++;
		}
	}
	for(int i=0;i<524288;i++){
		segtree[0][i]=segtree[1][i]=-mod;
	}
	update(a,0,0);
	
	for(int i=0;i<a;i++){
		R[i][0]=p[i];
	}
	for(int i=1;i<18;i++){
		for(int j=0;j<a;j++){
			R[j][i]=max(R[j][i-1],R[min(j+(1<<(i-1)),a)][i-1]);
		}
	}
	x[a][0]=0;
	x[a][1]=-mod;
	for(int i=a-1;i>=0;i--){
		if(t[i]){
			x[i][0]=query(0,262143,p[i],a,1,0)+2;
			x[i][1]=query(0,262143,p[i],a,1,1)+2;
		}else{
			x[i][1]=query(0,262143,p[i],a,1,0)+1;
			x[i][0]=query(0,262143,p[i],a,1,1)+1;
		}
		update(p[i],x[i][0],0);
		update(p[i],x[i][1],1);
		// x[i][0]=max(x[i][0],x[i+1][0]);
		// x[i][1]=max(x[i][1],x[i+1][1]);
		
	}
	for(int i=0;i<2;i++)for(int j=0;j<524288;j++)segtree[i][j]=-mod;

	for(int i=0;i<a;i++){
		update(p[i],x[i][0],0);
		update(p[i],x[i][1],1);
	}
	update(a,0,0);
	if(!chk(0,0,0,-1,-1)){
		printf("-1\n");return 0;
	}
	int A1=0;
	int A2=0;
	int L1=-1;
	int L2=-1;
	for(int i=0;i<a;i++){
		if(t[i])Q--;
		update(p[i],-mod,0);
		update(p[i],-mod,1);
		if(chk(i+1,A1+((L1<p[i])?1:0),A2,max(L1,p[i]),L2)){
			ans[i]='0';
			if(L1<p[i]){
				A1++;
				L1=p[i];
			}
		}else{
			ans[i]='1';
			if(L2<p[i]){
				A2++;
				L2=p[i];
			}
		}
	}
	printf("%s\n",ans);
}