Little Paul wants to learn how to play piano. He already has a melody he wants to start with. For simplicity he represented this melody as a sequence a_1, a_2, …, a_n of key numbers: the more a number is, the closer it is to the right end of the piano keyboard.

Paul is very clever and knows that the essential thing is to properly assign fingers to notes he's going to play. If he chooses an inconvenient fingering, he will then waste a lot of time trying to learn how to play the melody by these fingers and he will probably not succeed.

Let's denote the fingers of hand by numbers from 1 to 5. We call a fingering any sequence b_1, …, b_n of fingers numbers. A fingering is convenient if for all 1≤ i ≤ n - 1 the following holds:

  * if a_i < a_{i+1} then b_i < b_{i+1}, because otherwise Paul needs to take his hand off the keyboard to play the (i+1)-st note; 
  * if a_i > a_{i+1} then b_i > b_{i+1}, because of the same; 
  * if a_i = a_{i+1} then b_i≠ b_{i+1}, because using the same finger twice in a row is dumb. Please note that there is ≠, not = between b_i and b_{i+1}.



Please provide any convenient fingering or find out that there is none.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) denoting the number of notes.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 2⋅10^5) denoting the positions of notes on the keyboard.

Output

If there is no convenient fingering, print -1. Otherwise, print n numbers b_1, b_2, …, b_n, each from 1 to 5, denoting a convenient fingering, separated by spaces.

Examples

Input


5
1 1 4 2 2


Output


1 4 5 4 5 

Input


7
1 5 7 8 10 3 1


Output


1 2 3 4 5 4 3 

Input


19
3 3 7 9 8 8 8 8 7 7 7 7 5 3 3 3 3 8 8


Output


1 3 4 5 4 5 4 5 4 5 4 5 4 3 5 4 3 5 4 

Note

The third sample test is kinda "Non stop" song by Reflex.
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class codeforces 
{ 
   static class Student{
       int x,y;
        Student(int x,int y){
            this.x=x;
            this.y=y;
            //this.z=z;
        }
    }
    static int prime[];
    static void sieveOfEratosthenes(int n) 
    { 
        // Create a boolean array "prime[0..n]" and initialize 
        // all entries it as true. A value in prime[i] will 
        // finally be false if i is Not a prime, else true. 
        int pos=0;
        prime= new int[n+1]; 
        for(int p = 2; p*p <=n; p++) 
        { 
            // If prime[p] is not changed, then it is a prime 
            if(prime[p] == 0)
            { 
                // Update all multiples of p
                prime[p]=p;
                for(int i = p*p; i <= n; i += p)
                    if(prime[i]==0)
                    prime[i] = p; 
            } 
        } 
    }
static    class Sortbyroll implements Comparator<Student> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(Student c, Student b) 
    { 
        return c.y-b.y;
    } 
} 
static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
 
    static class Edge{
        int a,b;
        Edge(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
    static class Trie{
        HashMap<Character,Trie>map;
         int c;
        Trie(){
            map=new HashMap<>();
            //z=null;
            //o=null;
            c=0;
        }
    }
    //static long ans;
    static int parent[];
    static int rank[];
   // static int b[][];
    static int bo[];
    static int ho[];
    static int seg[];
    //static int pos;
     static long mod=1000000007;
    //static int dp[][];
    static HashMap<Integer,Integer>map;
    static PriorityQueue<Student>q=new PriorityQueue<>();
    //static Stack<Integer>st;
   // static ArrayList<Character>ans;
    static ArrayList<ArrayList<Integer>>adj;
    //static long ans;
    static int pos;
    static Trie root;
    static long fac[];
    static int gw,gb;
    //static long mod=(long)(998244353);
    //static int ans;
    static void solve()throws IOException{
        FastReader sc=new FastReader();
        int n,i,j,p1,p2,pos=0,k;
        n=sc.nextInt();
        int a[]=new int[n];
        for(i=0;i<n;i++)
            a[i]=sc.nextInt();
        int dp[][]=new int[n][7];
        for(i=1;i<=5;i++)
            dp[0][i]=1;
        for(i=1;i<n;i++){
            for(j=1;j<=5;j++){
                if(dp[i-1][j]==0)
                    continue;
                if(a[i]==a[i-1]){
                    for(k=j-1;k>=1&&k>0;k--)
                        dp[i][k]=1;
                    for(k=j+1;k<=5;k++)
                        dp[i][k]=1;
                }
                else if(a[i]>a[i-1]){
                    for(k=j+1;k<6;k++)
                        dp[i][k]=1;
                }
                else {
                    for(k=j-1;k>=1&&k>0;k--)
                        dp[i][k]=1;
                }
            }
        }
        for(i=1;i<=5;i++){
            if(dp[n-1][i]==1)
            {
               // System.out.print(i+ " ");
                pos=1;
                //break;
            }
        }
        //System.out.println();
        if(pos==0)
            System.out.println(-1);
        else{
            int b[]=new int[n];
            p1=Integer.MAX_VALUE;
            p2=6;
            for(i=n-1;i>=0;i--){
                    pos=0;
                    if(p1==a[i]){
                        for(j=1;j<=5;j++){
                            if(j==p2)
                                continue;
                            if(dp[i][j]==1){
                                p2=j;
                                break;
                            }
                        }
                    }
                    else if(p1<a[i]){
                        for(j=p2+1;j<=5;j++){
                            if(dp[i][j]==1){
                                p2=j;
                                pos=1;
                                break;
                            }
                        }
                    }
                    else{
                        for(j=p2-1;j>=1;j--){
                            if(dp[i][j]==1){
                                pos=1;
                                p2=j;
                                break;
                            }
                        }
                    }
                b[i]=p2;
                p1=a[i];
            }
            StringBuilder sb=new StringBuilder();
            for(i=0;i<n;i++)
                sb.append(b[i]+" ");
            System.out.println(sb.toString());
        }
    }
    static long fac(long x,long y){
        if(y==0||x==0)
            return 1;
        return x * fac(x-1,y-1);
    }
    static long nCr(long n, long r, 
                                    long p) 
    { 
        return (fac[(int)n]* modInverse(fac[(int)r], p) 
                % p * modInverse(fac[(int)(n-r)], p) 
                                    % p) % p; 
    } 
    //static int prime[];
    //static int dp[];
    public static void main(String[] args){
        //long sum=0;
        try {
                codeforces.solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
    }
       static long modInverse(long n, long p) 
    { 
        return power(n, p-(long)2,p); 
    } 
 static long power(long x, long y, long p) 
{ 
    long res = 1;      // Initialize result 
  
    x = x % p;  // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y %(long)2!=0) 
            res = (res*x) % p; 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x) % p;   
    } 
    return res%p;
 }
    /*public static long power(long x,long a) {
		if(a==0) return 1;
		if(a%2==1)return (x*1L*power(x,a-1))%mod;
		return (power((int)((x*1L*x)%mod),a/2))%mod;
	}*/
   static int find(int x) 
    { 
        // Finds the representative of the set 
        // that x is an element of 
        while(parent[x]!=x) 
        { 
            // if x is not the parent of itself 
            // Then x is not the representative of 
            // his set,
            x=parent[x];
  
            // so we recursively call Find on its parent 
            // and move i's node directly under the 
            // representative of this set 
        } 
  
        return x; 
    }
    static void union(int x, int y) 
    { 
        // Find representatives of two sets 
        int xRoot = find(x), yRoot = find(y); 
  
        // Elements are in the same set, no need 
        // to unite anything. 
        if (xRoot == yRoot) 
            return; 
  
         // If x's rank is less than y's rank 
        if (rank[xRoot] < rank[yRoot]) 
  
            // Then move x under y  so that depth 
            // of tree remains less 
            parent[xRoot] = yRoot; 
  
        // Else if y's rank is less than x's rank 
        else if (rank[yRoot] < rank[xRoot]) 
  
            // Then move y under x so that depth of 
            // tree remains less 
            parent[yRoot] = xRoot; 
  
        else // if ranks are the same 
        { 
            // Then move y under x (doesn't matter 
            // which one goes where) 
            parent[yRoot] = xRoot; 
  
            // And increment the the result tree's 
            // rank by 1 
            rank[xRoot] = rank[xRoot] + 1; 
        } 
    } 
    static long gcd(long a, long b) 
    { 
        if (a == 0){ 
             //ans+=b;
            return b;
        }
        return gcd(b % a, a); 
    }
}