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:
/*
ID: abdelra29
LANG: JAVA
TASK: skidesign
*/
import java.util.*;
import java.math.*;
import java.io.*; 
 public class B{
static int[] dx = new int[]{-1,0,1,0};
    static int[] dy = new int[]{0,1,0,-1};
    static FastReader scan=new FastReader();
   public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  static ArrayList<Pair>es;
  static LinkedList<Integer>edges[];
  static Set<Pair>edges2[][];

   static boolean prime[];
   static void sieve(int n) 
    { 
        
        prime = new boolean[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
           
            if(prime[p] == true) 
            { 
                
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
          
        
    }      
     public static int lowerBound(int[] array, int length, int value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            //checks if the value is less than middle element of the array
            if (value <= array[mid]) {
                high = mid;
            } else {
                low = mid+1 ;
            }
        }
        return low;
    }
    public static int upperBound(int[] array, int length, int value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = low+(high-low) / 2;
            if ( array[mid]>value) {
                high = mid ;
            } else {
                low = mid+1;
            }
        }
        return low;
    }
static long mod(long x,long y)
    {
        if(x<0)
            x=x+(-x/y+1)*y;
        return x%y;
    }    
     static boolean isPowerOfTwo(long n) 
    { 
        if (n == 0) 
            return false; 
  
        while (n != 1) { 
            if (n % 2 != 0) 
                return false; 
            n = n / 2; 
        } 
        return true; 
    } 

  
   
static boolean isprime(long x)
           {
            for(long i=2;i*i<=x;i++)
                if(x%i==0)
                    return false;
                return true;
           }


static int dist(int x1,int y1,int x2,int y2){
return Math.abs(x1-x2)+Math.abs(y1-y2);
}


    static long cuberoot(long x)
    {
        long lo = 0, hi = 1000005;
        while(lo<hi)
        {
            long m = (lo+hi+1)/2;
            if(m*m*m>x)
                hi = m-1;
            else
                lo = m;
        }
        return lo;
    }
     public static int log2(int N) 
    { 
  
        // calculate log2 N indirectly 
        // using log() method 
        int result = (int)(Math.log(N) / Math.log(2)); 
  
        return result; 
    } 
  
    
   
       static long gcd(long a, long b) {
    if(a!=0&&b!=0)
        while((a%=b)!=0&&(b%=a)!=0);
    return a^b;
}
    static long LCM(long a,long b){
    return (Math.abs(a*b))/gcd(a,b);
   }
   static int mid;
   public static class comp1 implements Comparator<Pair>{  
public int compare(Pair o1,Pair o2){
    return (int)(o1.y-o2.y);
}
  }

     public static class comp2 implements Comparator<Pair>{  
public int compare(Pair o1,Pair o2){
 
return (int)((o1.x+o1.y*mid)-(o2.x+o2.y*mid));
}
  }
 static boolean can(int m,int s)
 {
    return (s>=0&&s<=m*9);
 }
   static boolean collinear(long x1, long y1, long x2,  
                          long y2, long x3, long y3) 
{
    long a = x1 * (y2 - y3) +  
                x2 * (y3 - y1) +  
                x3 * (y1 - y2); 
                if(a==0)
                    return true;
                return false;
}

static int ceil(int a,int b)
{
    if(a%b!=0)
        return (a/b)+1;
    else return a/b;
}
static boolean vis[]=new boolean[(int)1e5+5];
static int cnt=0;
static int count1[];
 static void numberOfNodes(int s, int e) 
    { 
        count1[s] = 1; 
        for(Integer u: edges[s]) 
        { 
            // condition to omit reverse path 
            // path from children to parent 
            if(u == e) 
                continue; 
              
            // recursive call for DFS 
            numberOfNodes(u ,s); 
              
            // update count[] value of parent using  
            // its children 
            count1[s] += count1[u]; 
        } 
    } 
    static int res=0;
static void dfs(int x)
{
    vis[x]=true;
    cnt++;
    for(int v:edges[x])
        if(!vis[v]){
            if(count1[v]%2==0)
                res++;
            dfs(v);
        }
}

public static void main(String[] args)  throws Exception 
{
    /*int xx=253;
    for(int i=1;i*i<=xx;i++)
    {
        if(xx%i==0)
        {
            System.out.println(i);
            System.out.println(xx/i);
        }
    }*/
//java.util.Scanner scan=new java.util.Scanner(new File("mootube.in"));
// PrintWriter out = new PrintWriter (new FileWriter("mootube.out"));
//scan=new FastReader("skidesign.in");
//out = new PrintWriter ("skidesign.out");
//System.out.println(3^2);
//System.out.println(19%4);
   //StringBuilder news=new StringBuilder("ab");
   //news.deleteCharAt(1);
   //news.insert(0,'c');
   //news.deleteCharAt(0);
   //System.out.println(news);
   //System.out.println(can(2,15));
    //System.out.println(LCM(2,2));
  // System.out.println(31^15);
 //System.out.println("");
   //System.out.println(824924296372176000L>(long)1e16);
int tt=1;
//rec(2020);

//int st=scan.nextInt();
//System.out.println(calc(91));
//sieve(21000);

//SNWNSENSNNSWNNW

   // System.out.println(set.remove(new Pair(1,1)));
//System.out.println(count("cccccccccccccccccccccccccooooooooooooooooooooooooodddddddddddddeeeeeeeeeeeeeeeeeeeeeeeeeffffffffffffforrrrrrrrrrrrrcesssssssssssss","codeforces"));
  //S0ystem.out.println(isPowerOfTwo(446265625L));
//System.out.println("daaa".compareTo("bccc"));
//System.out.println(2999000999L>1999982505L);
//System.out.println("?bac?bac??a?a?a?abac????abacab?ca?a".length());
 //tt=scan.nextInt();
//String ok="ABDC";
//System.out.println(ok.substring(2));
//System.out.println(2000000000/2);
//tt=scan.nextInt();
//System.out.println(isprime(23335));
int T=1;
  outer:while(tt-->0)
 {
    int n=scan.nextInt();
    int arr[]=new int[n];
    ArrayList<Integer>gotya[]=new ArrayList[n+1];
    for(int i=0;i<n+1;i++)
        gotya[i]=new ArrayList();
    int cnt2[]=new int[n+1];
    for(int i=0;i<n;i++){
        arr[i]=scan.nextInt();
        cnt2[arr[i]]++;
        gotya[n-arr[i]].add(i);
    }
    //out.println(2%1);
    for(int i=1;i<n+1;i++)
    {
        //out.println(gotya[i].size()+" "+i);
        if(gotya[i].size()>0&&(gotya[i].size())%i!=0)
        {
            //out.println(i);
            out.println("Impossible");
            out.close();
            return;
        }
    }
    int k=1;
    int res[]=new int[n];
    for(int i=0;i<n+1;i++)
    {
        int lk=0;
        for(int l=0;l<gotya[i].size();l++,lk++){
           
            res[gotya[i].get(l)]=k;
             if((l+1)%i==0){
                k++;
            }
        }
        //if(k==2&&i==1)
           // out.println(lk);
     
        
    }
    int cnt[]=new int[n+100];
   
    for(int i=0;i<n;i++)
        cnt[res[i]]++;
    int all=0;
    for(int i=0;i<n+1;i++)
        all+=cnt[i];


   
    out.println("Possible");
    for(int i=0;i<n;i++)
        out.print(res[i]+" ");



  

}
out.close();

}

static class dsu{
    static int id[]=new int[101];
    dsu()
    {
        for(int i=0;i<101;i++)
            id[i]=i;
    }
    static int find(int x)
    {
        if(x==id[x])
            return x;
        return find(id[x]);
    }
    static void connect(int i,int j)
    {
        i=find(i);
        j=find(j);
        id[i]=j;
    }
    static boolean is(int i,int j)
    {
        return find(i)==find(j);
    }
}
static long binexp(long a,long n,long mod)
{
    if(n==0)
       return 1;
    long res=binexp(a,n/2,mod)%mod;
    res=res*res;
    if(n%2==1)
        return (res*a)%mod;
    else 
        return res%mod;
}
static class special{
    Pair x;
    Pair y;
    special(Pair x,Pair y)
    {
      this.x=new Pair(x.x,x.y);
      this.y=new Pair(y.x,y.y);
    }   
      @Override
        public int hashCode() {
            return (int)(x.x + 31 * y.y);
        }
        public boolean equals(Object other)
    {
        if(other instanceof special)
        {
            special e =(special)other;
            return this.x.x==e.x.x && this.x.y==e.x.y && this.y.x==e.y.x && this.y.y==e.y.y;
        }
        else return false;
    }
}
static long powMod(long base, long exp, long mod) {
       if (base == 0 || base == 1) return base;
       if (exp == 0) return 1;
       if (exp == 1) return base % mod;
       long R = powMod(base, exp/2, mod) % mod;
       R *= R;
       R %= mod;
       if ((exp & 1) == 1) {
           return base * R % mod;
       }
       else return R % mod;
   }
 public static  long pow(long b, long e) {
            long r = 1;
            while (e > 0) {
                if (e % 2 == 1) r = r * b ;
                b = b * b;
                e >>= 1;
            }
            return r;
        }

private static void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
 public static class FastReader {
        BufferedReader br;
        StringTokenizer root;
        
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        FastReader(String filename)throws Exception
        {

            br=new BufferedReader(new FileReader(filename));
        }
 
        String next() {
            while (root == null || !root.hasMoreTokens()) {
                try {
                    root = new StringTokenizer(br.readLine());
                } catch (Exception addd) {
                    addd.printStackTrace();
                }
            }
            return root.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception addd) {
                addd.printStackTrace();
            }
            return str;
        }
         public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }
 
            return array;
        }
}
public static class Pair implements Comparable<Pair>{
         long x;
         long y;
         long ab;
        
        long z;
        public Pair(){}
        public Pair(long x1, long y1,long z) {
            x=x1;
            y=y1;
            this.z=z;
        }
        public Pair(long x1, long y1) {
            x=x1;
            y=y1;
            this.ab=x+y;
        
        }
        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result +(int) x;
            result = prime * result + (int)y;
            return result;
        }
        public String toString() {
            return x + " " + y;
        }
        @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if(o==null)
                return false;
            if (o.getClass() != getClass()) return false;
            Pair t = (Pair)o;
            return t.x == x && t.y == y;
        }
        public  int compareTo(Pair o)
        {
            return (int)(y-o.y);
        }
}

}