Problem: Chouti and his classmates are going to the university soon. To say goodbye to each other, the class has planned a big farewell party in which classmates, teachers and parents sang and danced.

Chouti remembered that n persons took part in that party. To make the party funnier, each person wore one hat among n kinds of weird hats numbered 1, 2, … n. It is possible that several persons wore hats of the same kind. Some kinds of hats can remain unclaimed by anyone.

After the party, the i-th person said that there were a_i persons wearing a hat differing from his own.

It has been some days, so Chouti forgot all about others' hats, but he is curious about that. Let b_i be the number of hat type the i-th person was wearing, Chouti wants you to find any possible b_1, b_2, …, b_n that doesn't contradict with any person's statement. Because some persons might have a poor memory, there could be no solution at all.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5), the number of persons in the party.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n-1), the statements of people.

Output

If there is no solution, print a single line "Impossible".

Otherwise, print "Possible" and then n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ n).

If there are multiple answers, print any of them.

Examples

Input

3
0 0 0


Output

Possible
1 1 1 

Input

5
3 3 2 2 2


Output

Possible
1 1 2 2 2 

Input

4
0 1 2 3


Output

Impossible

Note

In the answer to the first example, all hats are the same, so every person will say that there were no persons wearing a hat different from kind 1.

In the answer to the second example, the first and the second person wore the hat with type 1 and all other wore a hat of type 2.

So the first two persons will say there were three persons with hats differing from their own. Similarly, three last persons will say there were two persons wearing a hat different from their own.

In the third example, it can be shown that no solution exists.

In the first and the second example, other possible configurations are possible.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

import javax.net.ssl.SSLContext;

public class Main
{  
   static long mod=(long)998244353;
   static long inf=1000000007;
   static int[] sieve;
   static ArrayList<Integer> primes;

   static class A
   {
	   int i;
	   int ind;
   }
   
   static class comp implements Comparator<A>
	   {

	@Override
	public int compare(A arg0, A arg1)
		{
			if(arg0.i<arg1.i) return -1;
			if(arg0.i>arg1.i) return 1;
			return 0;
		}
		   
	   }
   
   public static void main(String[] args) throws java.lang.Exception
   {	  	
	     fast s = new fast();
	     PrintWriter out=new PrintWriter(System.out);
	     Scanner sc=new Scanner(System.in);
	     StringBuilder fans = new StringBuilder();
	     
         int n=s.nextInt();
         int arr[]=new int[n];
         int output[]=new int[n];
         
         int count[]=new int[100005];
         A[] input=new A[n];
         
         Arrays.fill(count, 0);
         
         for(int i=0;i<n;i++)
        	 {
        		 arr[i]=s.nextInt();
        		 count[n-arr[i]]++;
        		 input[i]=new A();
        		 input[i].i=n-arr[i];
        		 input[i].ind=i;
        	 }
         
         int flag=1;
         
         for(int i=0;i<100005;i++)
        	 if((count[i]!=0 && count[i]%i!=0) || (count[i]!=0 && count[i]<i)) flag=0;
         
         if(flag==0) System.out.println("Impossible");
         else
        	 {
        		 Arrays.sort(input, new comp());
        		 int assign=1;
        		 for(int i=0;i<input.length;)
        			 {
        				 int counter=0;
        				 for(int j=i;j<count[input[i].i]+i;j++)
        					 {
        					    output[input[j].ind]=assign;
        					    counter++;
        					    if(counter==input[i].i) {counter=0; assign++;}
        					 }
        				 i+=count[input[i].i];
        			 }
        		 System.out.println("Possible");
        		 for(int i=0;i<output.length;i++)
        			 System.out.print(output[i]+" ");
        	 }
   }




static class fast {   
		private InputStream i;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		
		public static boolean next_permutation(int a[])
		   {
			   int i=0,j=0;int index=-1;	   
			   int n=a.length;
			   
			   for(i=0;i<n-1;i++)
				   if(a[i]<a[i+1]) index=i;
			   
			   if(index==-1) return false;
			   i=index;

			  
			   for(j=i+1;j<n && a[i]<a[j];j++);

			   int temp=a[i];
			   a[i]=a[j-1];
			   a[j-1]=temp;
			   	   
			   for(int p=i+1,q=n-1;p<q;p++,q--)
			   {
				   temp=a[p];
				   a[p]=a[q];
				   a[q]=temp;
			   }
			   
			   return true;
		   }
		   
		   
		public static void division(char ch[],int divisor)
		   {
			   int div=Character.getNumericValue(ch[0]); int mul=10;int remainder=0;
			   StringBuilder quotient=new StringBuilder("");
			   for(int i=1;i<ch.length;i++)
			   {
				   div=div*mul+Character.getNumericValue(ch[i]);	
				   if(div<divisor) {quotient.append("0");continue;}
				   quotient.append(div/divisor);
				   div=div%divisor;mul=10;
				   
			   } 
			   remainder=div;
			   while(quotient.charAt(0)=='0')quotient.deleteCharAt(0);	   
			   System.out.println(quotient+" "+remainder);	  
		   }
		
		public static void sieve(int size)
		{
			sieve=new int[size+1];
			primes=new ArrayList<Integer>();
			sieve[1]=1;
			for(int i=2;i<=Math.sqrt(size);i++)
			{
				if(sieve[i]==0)
				 {
					for(int j=i*i;j<size;j+=i) sieve[j]=1;
				 }
			}
			
			for(int i=2;i<=size;i++)
			{
				if(sieve[i]==0) primes.add(i);
			}
		}
		
		public static long pow(long n, long b, long MOD)
		   {
		       long x=1;long y=n; 
		       while(b > 0)
		       {
		           if(b%2 == 1)
		           {
		               x=x*y;
		               if(x>MOD) x=x%(MOD);
		           }
		           y = y*y;
		           if(y>MOD) y=y%(MOD); 
		           b >>= 1;
		       }
		       return x;
		   }


		public static long mod_inv(long n,long mod)
		{
			return pow(n,mod-2,mod);
		}
		
		 public static int upper(Integer[] a,int start,int end,int key)
		 {
			   int mid=(start+end)>>1;
			   if(start==end && a[mid]<key) {return -1;}
			   if(start>end) return -1;

			   if(a[mid]>=key && (((mid-1)>=0 && a[mid-1]<key) || (mid-1)==0)) return mid;
			   else if(a[mid]== key && (mid-1)>=0 && a[mid-1]==key) return lower(a,start,mid-1,key);   
			   else if(key>a[mid]) return lower(a,mid+1,end,key);
			   else return lower(a,start,mid-1,key);
		}
		 
		 public static int lower(Integer a[],int start,int end,int key)
		 {
			   int mid=(start+end)>>1;
			   if(start==end && a[mid]>key) {return -1;}
			   if(start>end) return -1;

			   if(a[mid]<=key && (((mid+1)<a.length && a[mid+1]>key) || (mid+1)==a.length)) return mid;
			   else if(a[mid]== key && (mid+1)<a.length && a[mid+1]==key) return upper(a,mid+1,end,key);   
			   else if(key>=a[mid]) return upper(a,mid+1,end,key);
			   else return upper(a,start,mid-1,key);
		} 
		   
		public int gcd(int a,int b)
		{
			if(a==0) return b;
			return gcd(b%a,a);
		}
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String nextString() {
     		int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}	
}