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.util.*; 
import java.math.*;
import java.io.*;
import java.text.DecimalFormat;
import java.math.BigInteger;
public class Main{
    //static int d=20;
    static long mod=1000000007 ;
    
    static ArrayList<ArrayList<Integer>> arr;
   // static long[] dp1,dp2;
    static int[] a;
    static int[][][] vis;
    static long max;
    static HashSet<String> hs;
    static int flag,ans;
    static long max1,max2,ans1;
    
    static int total,possible=0;
    static int[] tin,tout,parent,level;
    static int[][] reach;
    static HashMap<Long,Integer> hm;
    static long[] dp1,dp2,dp3,dp4;
    static int[] c ;
       
    public static void main(String[] args)  throws IOException {
        ///long start=System.currentTimeMillis();
        boolean online = false  ;
        String fileName = "A-small-attempt0 (1).in";
        PrintWriter out; 
        if (online) {
            s.init(new FileInputStream(new File("Downloads/"+fileName)));
             out= new PrintWriter(new FileWriter(fileName + "out.txt"));
        }
         else {
            s.init(System.in);   
        
            out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        }
        int n=s.ni();
        int[] a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=s.ni();

        }

        int[] b=new int[n];
        int[] c=new int[n];
        int[] d=new int[n];
        Arrays.fill(c,-1);
        Arrays.fill(b,-1);
        int flag=0;
        int count=0;
        HashSet<Integer> hs=new HashSet<>();
        hs.add(0);
        int last =0;
        for(int i=0;i<n;i++){
            int x=a[i];
            int y=n-x;
            if(flag==1)
                break;
            HashSet<Integer> hs2=new HashSet<Integer>(hs);
            for(int z:hs2){
                if((z>=n) || (c[z] > (n-i))){
                    flag=1;
                    break;
                }
                if(c[z]==-1){
                    b[i]=z;
                    c[z]=y-1;
                    d[z]=y;
                    if(c[z]==0){
                        hs2.remove(z);
                        // hs.add(z++);
                    }
                    break;
                }

                else if(y==d[z]){
                    b[i]=z;
                    c[z]--;
                    if(c[z]==0){
                        hs2.remove(z);
                        // hs.add(z++);
                    }
                    break;
                }
                
                
            
            }
            hs = new HashSet<Integer>(hs2);
            if(flag==1)
                break;
            int w=0;
            if(b[i]==-1){
                w=1;
                last++;
                if(last>=n){
                    flag=1;
                    break;
                }
                c[last]=y-1;
                d[last]=y;
                b[i]=last;
                if(c[last]==0)
                    w=0;
            }
            if(hs.size()==0 || w==1){
                if(w==0)
                    last++;
                hs.add(last);
            }
        }
        int sum=0;
        for(int i=0;i<n;i++){
            if(c[i]>0){
                flag=1;
                break;
            }
            sum+=d[i];
        }
        if(sum!=n){
            flag=1;
        }
        if(flag==1){
            out.println("Impossible");

        }
        else {
            out.println("Possible");
            for(int x:b)
                out.print((x+1)+" ");
            out.println();
        }
        out.close();      
            

    }

    public static boolean mazedfs(int[] c, int[]a, int[] b, int flag, int index){
        int n=c.length-1;
        if(index==n)
            return true;
        for(int i=index;i<n;i++){
            if(a[i]==b[i])
                continue;
            if(a[i]<b[i])
                return false;

            boolean currentFlag=true;
            for(int u=0;u<=3;u++){
                for(int v=0;v<=3;v++){
                    if((u|v)!=a[i] )
                        continue;
                    if((u&v)!=b[i])
                        continue;

                    if(c[i]==-1 && c[i+1]==-1){
                c[i]=u;
                c[i+1]=v;
                if(!mazedfs(c, a,b,flag,index+1)){
                    c[i]=v;
                    c[i+1]=u;
                    if(mazedfs(c, a,b,flag,index+1))
                        return true;
                    else
                        currentFlag=false;

                }
                else
                    return true;
                c[i]=c[i+1]=-1;

            }
            else if(c[i]!=-1 && c[i+1]!=-1){
                    if((c[i]|c[i+1])!=a[i]){
                        flag=1;
                        return false;
                    }
                    if((c[i] & c[i+1]) !=b[i]){
                        flag=1;
                        return false;
                    }
                }
                else{
                    if(c[i]!=-1){
                        int store=c[i];
                        if(c[i]==u){
                            c[i+1]=v;
                        }
                        else if(c[i]==v){
                            c[i+1]=u;
                        }
                        else{
                            flag=1;
                            currentFlag=false;
                        }
                        if(mazedfs(c, a,b,flag,index+1))
                            return true;
                        
                        c[i]=store;
                        c[i+1]=-1;

                    }
                    else if(c[i+1]!=-1){
                        int store=c[i+1];
                        if(c[i+1]==u){
                            c[i]=v;
                        }
                        else if(c[i+1]==v){
                            c[i]=u;
                        }
                        else{
                            flag=1;
                            currentFlag=false;
                        }
                         if(mazedfs(c, a,b,flag,index+1))
                            return true;
                        c[i+1]=store;
                        c[i]=-1;

                    }
                }
                }
            }

            if(currentFlag==false)
                return false;
            
            }
        return true;

    }
   
    

    public static void union(int[] a,int x,int y){
        int u=find(a,x);
        int v=find(a,y);
        a[v]=u;

    }
    public static int find(int[] a,int x){
        if(a[x]!=x){
            a[x]=find(a,a[x]);
        }
        return a[x];
    }
    public static int gcd(int a, int b){
            if (a == 0) return b;
            return gcd(b % a, a);
    }
        
    public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
        vis[c]=1;
        if(g!=-1){
            if(!arr.get(c).contains(g)){
                flag=1;
                return;
            }
        }
        for(int x:arr.get(c)){
            if(x!=p && x!=g && vis[x]==0 ){
                cfs(arr,x,c,p,vis);
            }
        }

    }
                          //   public static void dfs(int u,int p){
//                            //       if(p>=0)
//                            //           tin[u]=tout[u]=tt++;
//                            //       if(p>=0)
//                            //           level[u]=level[p]+1;
//                            //       parent[u]=p;
//                            //       for(int x:arr.get(u)){
//                            //           if(x!=p){
//                            //               dfs(x,u);
//                            //               tout[u]=Math.max(tout[u],tout[x]);
//                            //           }
//                            //       }
//                            //       
//
//
 //   }
    public static int lca(int[][] p,int a,int b){
        if(level[a]<level[b]){
            int x=a;
            a=b;
            b=x;
        }
        int log=p[0].length;
        for(int i=log-1;i>=0;i--){
            if(1<<i<=level[a]-level[b]){
                a=p[a][i];
            }
        }
        if(a==b)
            return a;
        for(int i=log-1;i>=0;i--){
            if(p[a][i]!=p[b][i]){
                a=p[a][i];
                b=p[b][i];
            }
        }
        return p[a][0];

    }
    public static int[][] par(int[] parent){
        int n=arr.size();
        int[][] p=new int[n][17];
        for(int i=0;i<n;i++)
            p[i][0]=parent[i];
        for(int k=1;k<17;k++){
            for(int i=0;i<n;i++){
                if(p[i][k-1]>-1)
                    p[i][k]=p[p[i][k-1]][k-1];
                else
                    p[i][k]=-1;
            }
        }
        return p;
    }
    static class Edge implements Comparable<Edge>{
           int from;
            int to;
            long cost;
    
           public Edge(int from, int to, long weight) {
               this.from = from;
               this.to = to;
               this.cost= weight;
           }
           public int compareTo(Edge o){
                return (int)Math.signum(cost-o.cost); 
           }

    }                               
    static class Node {
        int start;
        int end;

        int cost;
        int updated;

        Node[] nodes;

        public Node(int start, int end) {
            this.start = start;
            this.end = end;

            if (start < end) {
                int[] pos = {start, (start + end) / 2, end};
                nodes = new Node[2];
                for (int i = 0; i < 2; i++) {
                    nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                }
            }
        }

        public void update(int queryStart, int queryEnd, int value) {
            if (queryEnd < start || end < queryStart) {
                return;
            }

            if (queryStart <= start && end <= queryEnd) {
                cost += value;
                updated += value;
                return;
            }

            propagate();
            for (Node node: nodes) {
                node.update(queryStart, queryEnd, value);
            }
        }

        public int query(int pos) {
            if (pos < start || end < pos) {
                return 0;
            }

            if (start == end) {
                return cost;
            }

            propagate();
            int ans = 0;
            for (Node node: nodes) {
                ans = Math.max(ans, node.query(pos));
            }
            return ans;
        }

        public void propagate() {
            if (updated != 0 && start < end) {
                for (Node node: nodes) {
                    node.cost += updated;
                    node.updated += updated;
                }
                updated = 0;
            }
        }
    }
    public static double nthroot(int n, double A) {
        return nthroot(n, A, 0.0000001);
    }
    public static double nthroot(int n, double A, double p) {
        if(A < 0) {
            System.err.println("A < 0");// we handle only real positive numbers
            return -1;
        } else if(A == 0) {
            return 0;
        }
        double x_prev = A;
        double x = A / n;  // starting "guessed" value...
        while(Math.abs(x - x_prev) > p) {
            x_prev = x;
            x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
        }
        return x;
    }
    
    static class item implements Comparable<item> {
        int from,to,cost;
        public item(int x,int y){
            from=x;
            to=y;
            
        }
        public int compareTo(item o){
            
            return  o.cost-cost;
        }
        
    }
   
    public static void dfs2(int c,int p,int[] a){
        //System.out.println(c+" "+p);
       
        
        

    }
//public static void dfs(int x,int[] vis,Stack<Integer> st){
    //    vis[x]=1;
    //    ArrayList<Integer> arr2=arr.get(x);
    //    Collections.sort(arr2);
    //    for(int i=arr2.size()-1;i>=0;i--){
    //        int z=arr2.get(i);
    //        if(vis[z]==0)
    //            dfs(z,vis,st);
    //    }
    //    st.push(x);
//
    //}
    public static long gcd2(long a, long b){
            if (a == 0) return b;
            return gcd2(b % a, a);
    }
        
    public static boolean check(long x){
        if(x%4==0 || x%7==0 || x%11==0)
            return true;
        if(x<4 || x<7 || x<11)
            return false;
        if(x%2==0){
            return check(x/2);
        }
        else
            return check(x/2) && check((x+1)/2);
    }
    public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
        long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
        if(val<0)
            return 1;
        else if(val>0)
            return -1;
        else
            return 0;
    }
    
    static class BIT{
    
        int N;
        long tree[];
        
        BIT(int N){
            this.N = N;
            tree = new long[N + 1];
        }
        
        void update(int idx,long val){
            while(idx <= N){
                tree[idx]+=val;
                idx += (idx & -idx);
            }
        }
        
        long query(int l,int r){
            if(l == 1)
                return read(r);
            else
                return read(r) - read(l-1);
        }
        
        long read(int idx){
            long sum = 0;
            while(idx > 0){
                sum += tree[idx];
                idx -= (idx & -idx);
            }
            return sum;
        }
    }
    public static boolean pal(String a){
        int i=0;
        int j=a.length()-1;
        while(i<j){
            if(a.charAt(i)!=a.charAt(j)){
                return false;
            }
            i++;
            j--;
        }
        return true;
            
    }
    public static long find(long n,long k){
        if(n==2){
            if(k==1 || k==3)
                return 1;
            else
                return 2;
        }
        long t=pow2(2,n,mod)-1;
        long z=(t+1)/2;
        if(k==z)
            return n;
        if(k<z)
            return find(n-1,k);
        else
            return find(n-1,k-z);
    }
    public static long pow2(long a,long b,long mod){
            
            long ans=1;
           // long z=b;
            while(b>0){
               
                if(b%2==1)
                    ans=(a*ans)%mod;
                a=(a*a)%mod;
                b/=2;
            }
          
            return  ans;
    }
     public static long pow3(long a,long b){
            
            long ans=1;
           // long z=b;
            while(b>0){
               
                if(b%2==1)
                    ans=(a*ans);
                a=(a*a);
                b/=2;
            }
          
            return  ans;
    }
    public static long fib(long n){
        long[][]    f=new long[][]{{1L,1L},{1L,0}};
        if(n==0)
            return 0;
        f=arrpow(f,n-1);
        return f[0][0];
    }
    public static long[][] arrpow(long[][] a,long b){
       
            int n=a.length;
          //  long z=b;
            long[][] ans=new long[n][n];
            for(int i=0;i<n;i++)
                ans[i][i]=1L;
            while(b>0){
                
                if(b%2==1)
                    ans=mul(a,ans);
                a=mul(a,a);
                b/=2;
            }
            
            return  ans;
    }
    public static long[][] mul(long[][] a,long[][] b){
        int n=a.length;
        int m=b[0].length;
        long[][] ans=new long[n][m];
        if(n==2 && m==2 && b.length==2){
            ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
            ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
            ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
            ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
            return ans;

        }
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                for(int k=0;k<b.length;k++){
                    ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                }
            }
        }
        return ans; 
    }
     static class name implements Comparable<name> {
        long l,b,h;
        public name(long   x,long y,long z){
            {
                l=x;
                b=y;        
            }
            
            
            h=z;
        }
        public int compareTo(name o){
            return -(int)(l*b-o.l*o.b);
        }
        
    }
    public static class s {
        static BufferedReader reader;
        static StringTokenizer tokenizer;
    
        /** call this method to initialize reader for InputStream */
        static void init(InputStream input) {
            reader = new BufferedReader(
                        new InputStreamReader(input) );
            tokenizer = new StringTokenizer("");
        }   
    
        /** get next word */
        static String ns() throws IOException {
            while ( ! tokenizer.hasMoreTokens() ) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                    reader.readLine() );
            }
            return tokenizer.nextToken();
        }
    
        static int ni() throws IOException {
            return Integer.parseInt( ns() );
        }
    
        static double nd() throws IOException {
            return Double.parseDouble( ns() );
        }
        static long nl() throws IOException {
            return Long.parseLong( ns() );
        }
    }
}