Problem: Sasha is taking part in a programming competition. In one of the problems she should check if some rooted trees are isomorphic or not. She has never seen this problem before, but, being an experienced participant, she guessed that she should match trees to some sequences and then compare these sequences instead of trees. Sasha wants to match each tree with a sequence a0, a1, ..., ah, where h is the height of the tree, and ai equals to the number of vertices that are at distance of i edges from root. 

Unfortunately, this time Sasha's intuition was wrong, and there could be several trees matching the same sequence. To show it, you need to write a program that, given the sequence ai, builds two non-isomorphic rooted trees that match that sequence, or determines that there is only one such tree.

Two rooted trees are isomorphic, if you can reenumerate the vertices of the first one in such a way, that the index of the root becomes equal the index of the root of the second tree, and these two trees become equal.

The height of a rooted tree is the maximum number of edges on a path from the root to any other vertex.

Input

The first line contains a single integer h (2 ≤ h ≤ 105) — the height of the tree.

The second line contains h + 1 integers — the sequence a0, a1, ..., ah (1 ≤ ai ≤ 2·105). The sum of all ai does not exceed 2·105. It is guaranteed that there is at least one tree matching this sequence.

Output

If there is only one tree matching this sequence, print "perfect".

Otherwise print "ambiguous" in the first line. In the second and in the third line print descriptions of two trees in the following format: in one line print <image> integers, the k-th of them should be the parent of vertex k or be equal to zero, if the k-th vertex is the root.

These treese should be non-isomorphic and should match the given sequence.

Examples

Input

2
1 1 1


Output

perfect


Input

2
1 2 2


Output

ambiguous
0 1 1 3 3
0 1 1 3 2

Note

The only tree in the first example and the two printed trees from the second example are shown on the picture:

<image>

Solution (in JAVA):

Solution:
 import java.awt.Checkbox;
import java.awt.Point;
import java.io.*;
                    import java.math.*;
                    import java.util.*;
import java.util.Map.Entry;

import javax.print.attribute.SetOfIntegerSyntax;
import javax.swing.plaf.FontUIResource;


             
                    public class CODE2{
                      private static InputStream stream;
                        private static byte[] buf = new byte[1024];
                        private static int curChar,MAX;
                        private static int numChars;
                        private static SpaceCharFilter filter;
                        private static PrintWriter pw;
                        private static long count = 0,mod=1000000007;
                        static int BIT[];
                        private static boolean primer[];
                    //    private static TreeSet<Integer> ts=new TreeSet[200000];
public final static int INF = (int) 1E9;

public static void main(String args[]) {
    InputReader(System.in);
    pw = new PrintWriter(System.out); 
    new Thread(null ,new Runnable(){
       public void run(){
           try{
               solve();
               
               pw.close();
           } catch(Exception e){
               e.printStackTrace();
           }
       }
   },"1",1<<26).start();
   }
    static StringBuilder sb;
    public static void test(){
         sb=new StringBuilder();
        int t=nextInt();
        while(t-->0){
            
            solve();
           
        }
        pw.println(sb);
    }
    public static long pow(long n, long p,long mod) {
        if(p==0)
            return 1;
        if(p==1)
            return n%mod;
        if(p%2==0){
            long temp=pow(n, p/2,mod);
        return (temp*temp)%mod;
        }else{
                 long temp=pow(n,p/2,mod);
                 temp=(temp*temp)%mod;
                 return(temp*n)%mod;
                 
        }
    }
    public static long pow(long n, long p) {
        if(p==0)
            return 1;
        if(p==1)
            return n;
        if(p%2==0){
            long temp=pow(n, p/2);
        return (temp*temp);
        }else{
                 long temp=pow(n,p/2);
                 temp=(temp*temp);
                 return(temp*n);
                 
        }
    }
    public static void Merge(long a[],int p,int r){
        if(p<r){
            int q = (p+r)/2;
            Merge(a,p,q);
            Merge(a,q+1,r);
            Merge_Array(a,p,q,r);
        }
    }
    public static void Merge_Array(long a[],int p,int q,int r){
       long b[] = new long[q-p+1];
        long c[] = new long[r-q];
        for(int i=0;i<b.length;i++)
            b[i] = a[p+i];
        for(int i=0;i<c.length;i++)
            c[i] = a[q+i+1];
        int i = 0,j = 0;
        for(int k=p;k<=r;k++){
            if(i==b.length){
                a[k] = c[j];
                j++;
            }
            else if(j==c.length){
                a[k] = b[i];
                i++;
            }
            else if(b[i]<c[j]){
                a[k] = b[i];
                i++;
            }
            else{
                a[k] = c[j];
                j++;
            }
        }
    }
    
  
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd( y % x,x);
    }    
    
    public static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
 
        if (n % 2 == 0 || n % 3 == 0)
            return false;
 
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
 
        return true;
    }
    
        static LinkedList<Integer> adj[];
        static boolean Visited[];
        static HashSet<Integer> exc;
        static long oddsum[]=new long[1000001];
        static long co=0,ans=0;
        static int parent[];
        static int size[],color[],res[],k;
        static ArrayList<Integer> al[];
        static long MOD = (long)1e9 + 7;
        private static void buildgraph(int n){
            adj=new LinkedList[n+1];
            Visited=new boolean[n+1];
            levl=new int[n+1];
            
            for(int i=0;i<=n;i++){
                adj[i]=new LinkedList<Integer>();
            
            }


        }
      
       
        static int[] levl;
        static int[] eat;
      //  static int n,m;
        static int price[];
        //ind frog crab
   static  boolean check(char c)
    {
    	if(c!='a' && c!='e' && c!='i' && c!='o' && c!='u' )
    		return true;
    	else
    		return false;
    }
        public static void solve(){
       
        	int h=nextInt();
        	
        	int heights[]=new int[h+1];
        	boolean perfect=true;
        	int r=0;
        	heights[0]=nextInt();
        	
        	for(int i=1;i<=h;i++)
        	{
        		heights[i]=nextInt();
        		 if(heights[i]==1)continue;
                 if(heights[i-1]==1)continue;
                 perfect=false;
        		
        		
        	}
        	
        	if(perfect)
        	{
        		pw.println("perfect");
        	}
        	else
        	{
        		pw.println("ambiguous");
        		
        		
        		ArrayList<Integer> ll1= new ArrayList<>();
        		ArrayList<Integer> temp=new ArrayList<>();
        		ArrayList<Integer> ll2= new ArrayList<>();
        		int count=0;
        		temp.add(0);
        		int prev=1;
        		for(int i=0;i<=h;i++)
        		{
        			if(prev==1)
        			{
        				for(int j=0;j<heights[i];j++)
        				ll1.add(temp.get(0));
        				for(int j=0;j<heights[i];j++)
        				ll2.add(temp.get(0));
        				temp.clear();
        				for(int j=0;j<heights[i];j++)
        				temp.add(++count);
        			}
        			
        			else
        			{
        				
        				//System.out.println(i+" "+prev);
        				int y=temp.get(0);
        				for(int j=0;j<heights[i];j++)
        				{
        					ll1.add(y);
        					
        				}
        				
        				ll2.add(temp.get(0));int z=temp.get(1);
        				for(int j=2;j<=heights[i];j++)
        				{
        					ll2.add(z);
        				}
        				temp.clear();
        				for(int j=1;j<=heights[i];j++)
        				{
        					temp.add(++count);
        				}
        			}
        			prev=heights[i];
        		}
        		
        		for(int i=0;i<ll1.size();i++)
        			pw.print(ll1.get(i)+" ");
        		pw.println();
        		
        		for(int i=0;i<ll2.size();i++)
        			pw.print(ll2.get(i)+" ");
        	}
   
        		
    }
        
        static void seive2(int n)
        {
        	primer=new boolean[n+1];
        	Arrays.fill(primer,true);
        	primer[0]=false;
        	primer[1]=false;
        	primer[2]=true;
        	
        	for(int i=2;i*i<=n;i++)
        	{
        		if(primer[i])
        		{
        			for(int j=2*i;j<=n;j=j+i)
        			{
        				primer[j]=false;
        			}
        		}
        	}
        }
       
        
     /*   static void BITupdate(int x,int val)
        {
        	while(x<=n)
        	{
        		BIT[x]+=val;
        		x+= x & -x;
        	}
        }*/
     /*   static void update(int x,long val)
        {
      
        	val=val%MOD;
        	while(x<=n)
        	{
        		// System.out.println(x);
        	BIT[x]=(BIT[x]+val)%MOD;
        	x+=(x & -x);
        	}
        //	System.out.println("dfd");
        }*/
        static int BITsum(int x)
        		{
        	int sum=0;
        	while(x>0)
        	{
        		sum+=BIT[x];
        		x-= (x & -x);
        	}
        		return sum;
        		}
  /*      static long sum(int x)
        {
        	long sum=0;
        	while(x>0)
        	{
        		sum=(sum+BIT[x])%MOD;
        		x-=x & -x;
        	}
        	return sum;
        }*/
        static boolean union(int x,int y)
        {
        	int xr=find(x);
        	int yr=find(y);
        	if(xr==yr)
        		return false;
        	if(size[xr]<size[yr])
        	{
        		size[yr]+=size[xr];
        		parent[xr]=yr;
        	}
        	else
        	{
        		size[xr]+=size[yr];
        		parent[yr]=xr;
        		
        	}
        	return true;
        	
        }
        static int  find(int x)
        {
        	if(parent[x]==x)
        		return x;
        	else
        	{
        		parent[x]=find(parent[x]);
        		return parent[x];
        	}
        	
        }
        public static class Edge implements Comparable<Edge>
        {
        	int u, v,s;
			public Edge(int u, int v) 
			{
				this.u = u;
				this.v = v;
				//this.s = s;
			}
			public int hashCode() 
			{
				return Objects.hash();
			}
			public int compareTo(Edge other) 
			{
			//	return (Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s)):(Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u)))
				//		&((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s)):(Long.compare(u, other.v)!=0?Long.compare(u, other.v):Long.compare(v, other.u))));
				return this.u-other.u;
			}
			public String toString()
			{
				return this.u + " " + this.v;
			}
        }
       
        static int col[];
    public static boolean isVowel(char c){
        if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
            return true;
        return false;
    }
static int no_vert=0;

  private static void dfs(int start){
      Visited[start]=true;
    if(al[color[start]].size()>=k)
    {
    	res[start]=al[color[start]].get(al[color[start]].size()-k);
    }
    al[color[start]].add(start);
      for(int i:adj[start]){
          if(!Visited[i])
              {
              dfs(i);
              }
      }
      (al[color[start]]).remove(al[color[start]].size()-1);
      
  }
    
    public static String reverseString(String s) {
        StringBuilder sb = new StringBuilder(s);
        sb.reverse();
        return (sb.toString());
    }
    
  /*  
   private static void BFS(int sou){
        Queue<Integer> q=new LinkedList<Integer>();
        q.add(sou);
        Visited[sou]=true;
        levl[sou]=0;
        while(!q.isEmpty()){
            int top=q.poll();
            
            for(int i:adj[top]){
                //pw.println(i+" "+top);
            if(!Visited[i])
            {
                
                q.add(i);
                levl[i]=levl[top]+1;
            }
            
            Visited[i]=true;
            
            }
        }
    }*/
    



                  static int indeg[];
               /* private static void kahn(int n){
                    
                    PriorityQueue<Integer> q=new PriorityQueue<Integer>();
                    for(int i=1;i<=n;i++){
                        if(indeg[i]==0){
                            q.add(i);
                        }
                    }
                    while(!q.isEmpty()){
                        int top=q.poll();
                        st.push(top);
                        for(Node i:adj[top]){
                            indeg[i.to]--;
                            if(indeg[i.to]==0){
                                q.add(i.to);
                            }
                        }
                    }
                }
                    
                    static int state=1;
                    static long no_exc=0,no_vert=0;
                  static Stack<Integer> st;
                  static HashSet<Integer> inset;
                 /*   private static void topo(int curr){
                        
                        Visited[curr]=true;
                        inset.add(curr);
                        for(int x:adj[curr]){
                            if(adj[x].contains(curr) || inset.contains(x)){
                                state=0;
                                return;
                            }
                            if(state==0)
                                return;
                            
                        }
                        st.push(curr);
                        
                        inset.remove(curr);
                    }*/
                    static HashSet<Integer> hs;
                   
                 
                     static boolean prime[];
                    static int spf[];
                    public static void sieve(int n){
                        prime=new boolean[n+1];
                        spf=new int[n+1];
                        
                        Arrays.fill(spf, 1);
                        Arrays.fill(prime, true);
                    prime[1]=false;
                        spf[2]=2;
                        
                    for(int i=4;i<=n;i+=2){
                        spf[i]=2;
                    }
                    for(int i=3;i<=n;i+=2){
                        if(prime[i]){
                            spf[i]=i;
                            for(int j=2*i;j<=n;j+=i){
                                
                                prime[j]=false;
                            if(spf[j]==1){
                                spf[j]=i;
                            }
                            }
                        }
                    }
                    
                        
                    }
                     
                    // To Get Input
// Some Buffer Methods
 
                     public static void sort(long a[]){
                         Merge(a, 0, a.length-1);
                     }
                    public static void InputReader(InputStream stream1) {
                        stream = stream1;
                    }
 
                    private static boolean isWhitespace(int c) {
                        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
                    }
 
                    private static boolean isEndOfLine(int c) {
                        return c == '\n' || c == '\r' || c == -1;
                    }
 
                    private static int read() {
                        if (numChars == -1)
                            throw new InputMismatchException();
                        if (curChar >= numChars) {
                            curChar = 0;
                            try {
                                numChars = stream.read(buf);
                            } catch (IOException e) {
                                throw new InputMismatchException();
                            }
                            if (numChars <= 0)
                                return -1;
                        }
                        return buf[curChar++];
                    }
 
                    private static 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;
                    }
 
                    private static 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;
                    }
 
                    private static String nextToken() {
                        int c = read();
                        while (isSpaceChar(c))
                            c = read();
                        StringBuilder res = new StringBuilder();
                        do {
                            res.appendCodePoint(c);
                            c = read();
                        } while (!isSpaceChar(c));
                        return res.toString();
                    }
 
                    private static 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();
                    }
 
                    private static int[] nextIntArray(int n) {
                        int[] arr = new int[n];
                        for (int i = 0; i < n; i++) {
                            arr[i] = nextInt();
                        }
                        return arr;
                    }
 
                    private static long[][] next2dArray(int n, int m) {
                        long[][] arr = new long[n][m];
                        for (int i = 0; i < n; i++) {
                            for (int j = 0; j < m; j++) {
                                arr[i][j] = nextLong();
                            }
                        }
                        return arr;
                    }
                    private static char[][] nextCharArray(int n,int m){
                        char [][]c=new char[n][m];
                        for(int i=0;i<n;i++){
                            String s=nextLine();
                            for(int j=0;j<s.length();j++){
                                c[i][j]=s.charAt(j);
                            }
                        }
                        return c;
                    }
 
                    private static long[] nextLongArray(int n) {
                        long[] arr = new long[n];
                        for (int i = 0; i < n; i++) {
                            arr[i] = nextLong();
                        }
                        return arr;
                    }
 
                    private static void pArray(int[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static void pArray(long[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static void pArray(boolean[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static boolean isSpaceChar(int c) {
                        if (filter != null)
                            return filter.isSpaceChar(c);
                        return isWhitespace(c);
                    }
 
                    private interface SpaceCharFilter {
                        public boolean isSpaceChar(int ch);
                    }
                    

}