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:
	
	
	 
	    	        			/*
	 * Author- Priyam Vora
	 * BTech 2nd Year DAIICT
	 */
	     
	     
	import java.io.*;
	        		    import java.math.*;
	        		    import java.util.*;
import java.util.regex.Pattern;
	    	     
	        		    public class Main{
	        		  	private static InputStream stream;
	        		    	private static byte[] buf = new byte[1024];
	        		    	private static int curChar;
	        		    	private static int numChars;
	        		    	private static SpaceCharFilter filter;
	        		    	private static PrintWriter pw;
	        		    	private static long count = 0,mod=(long)1e9;
	        		    //	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{
	        		
	               test();

	               pw.close();
	           } catch(Exception e){
	               e.printStackTrace();
	           }
	       }
	   },"1",1<<26).start();
	   	   }
	    static StringBuilder sb;
	    public static void test() throws IOException{
	    	 sb=new StringBuilder();
	    	int t=1;
	    	while(t-->0){
	    		
	    		solve();
	    		//pw.println();
	    		//sb.append("\n");
	    	}
	    	//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;
	    
	    	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 long d,x,y;
			static long modInverse(long A, long M)
			{
			extendedEuclid(A,M);
			return (x%M+M)%M;    //x may be negative
			}
			static void extendedEuclid(long A, long B) {
			if(B == 0) {
			d = A;
			x = 1;
			y = 0;
			}
			else {
			extendedEuclid(B, A%B);
			long temp = x;
			x = y;
			y = temp - (A/B)*y;
			}
			}
	        static double distance(int x1,int y1,int x2,int y2){
	        	return Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
	        }
	        static double area(int x1, int y1, int x2, int y2, int x3, int y3)
	        {
	           return Math.abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/2.0);
	        }
	        static boolean isInside(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y)
	        {   
	           double A = area (x1, y1, x2, y2, x3, y3);
	         
	           double A1 = area (x, y, x2, y2, x3, y3);
	         
	           double A2 = area (x1, y1, x, y, x3, y3);
	         
	           double A3 = area (x1, y1, x2, y2, x, y);
	           
	          return (A == A1 + A2 + A3);
	        }
	      
			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 long arr[], lazy[],ans[];
	static int c[];
	public static void solve() throws IOException{

		HashSet<Integer> prime=new HashSet<Integer>();
		for(int i=2;i<=1;i++){
			if(isPrime(i)){
				prime.add(i);
			}
		}
	int n=nextInt();
	int a[]=nextIntArray(n+1);
	boolean perfect=true;
	for(int i=2;i<n+1;i++){
		if(a[i]!=1 && a[i-1]!=1){
			perfect = false;
		}
	}
	if(perfect){
		pw.println("perfect");
	}else{
		pw.println("ambiguous");
		int print=1;
		pw.print(0+" ");
		for(int i=1;i<n+1;i++){
			for(int j=0;j<a[i];j++){
				pw.print(print+" ");
			}
			print+=a[i];
		}
		
		pw.println();
		pw.print(0+" ");
		print=1;
		for(int i=1;i<n+1;i++){
			if(a[i]!=1 && a[i-1]!=1){
				for(int j=0;j<a[i]-1;j++){
					pw.print(print+" ");
				}
				pw.print((print-1)+" ");
			}else{
				for(int j=0;j<a[i];j++){
					pw.print(print+" ");
				}
			}
			print+=a[i];
		}
	}
		
	}
	static int cnt=0;
	private static void df(int curr,int col){
		Visited[curr]=true;
		
		for(int i:adj[curr]){
			if(!Visited[i]){
				if(c[i]!=col){
					cnt++;
				//	pw.println(i);
				}
				df(i,c[i]);
			}
		}
	}
	static int dista[];
	private static void dfs2(int curr,int dist){
		Visited[curr]=true;
		dista[curr]=dist;
		for(int i:adj[curr]){
			if(!Visited[i]){
				dfs2(i,dist+1);
			}
		}
	}
	static long tot=0;
	static int par[]=new int[1000001];
	static long size[]=new long[1000001];
	static boolean vis[]=new boolean[1000001];
	public static void dfs1(int curr)
	{
		vis[curr]=true;
		size[curr]=1;
		for(int x:adj[curr])
		{
			if(!vis[x])
			{
				par[x]=curr;
				dfs1(x);
				size[curr]+=size[x];
			}
		}
	}
	
  
  static boolean getString (char[][] matrix, int x, int y, char[] target) {
      if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
          return false;
      }
      
      if (target == null || target.length == 0) {
          return false;
      }
      
      if (matrix[x][y] != target[0]) {
          return false;
      }
      
      int row = matrix.length;
      int column = matrix[0].length;
      
      int[] dirx = {0, 0, 1, -1, 1, 1, -1, -1}; // array, int[]!!!!
      int[] diry = {1, -1, 0, 0, 1, -1, 1, -1}; // array, int[]!!!!
      
      for (int i = 0; i < 8; i++) {
          int nextx = x;  // define !!
          int nexty = y;  // define !!
          int k = 1;
          while (k < target.length) {
              nextx += dirx[i];
              nexty += diry[i];
              
              if (nextx < 0 || nexty < 0 || nextx >= row || nexty >= column) {
                  break;
              }
              
              if (matrix[nextx][nexty] != target[k]) {
                  break;
              }
              k++;
          }
          
          if (k == target.length) {
              return true;
          }
      }
      
      return false;
  }
	
	
	
	static int no_vert=0,timer=1;
	
	private static void dfs(int s,int lev){
		Visited[s]=true;
		
		for(int x:adj[s]){
			if(!Visited[x]){
			
				dfs(x,lev+1);
			}
			
		}
		//System.out.println(lev);
		no_vert=Math.max(no_vert, lev);
	}
	
	
	    private static boolean Check(int x,int y,int n){
			if(x>=0 && x<n && y>=0 && y<n)
				return true;
			return false;
		}
	    
	    static long[][] dp;
		static long dp2[];
	    static ArrayList<Integer> pri[],pri2[];
	
	  private static void dfs3(int curr,int par,int co){
			 Visited[curr]=true;
			 for(int x:adj[curr]){
				 if(!Visited[x]){
					 dfs3(x,curr,co);
				 }
			 }
			 if(col[curr]==1){
				 dp2[curr]++;
			 }else{
				 dp2[curr]--;
			 }
			 if(dp2[curr]>0){
				 pri2[par].add(curr);
			 dp2[par]+=dp2[curr];
			 }
		  }
	    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().split(" ");
	    		    			for(int j=0;j<s.length;j++){
	    		    				c[i][j]=s[j].charAt(0);
	    		    			}
	    		    		}
	    		    		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);
	    		    	}
	    		    	
	
	}
	    		    
	    		        class Node{
	    		    	int to;
	    		    	long dist;
	    		    	Node(int to,long dist){
	    		    		this.to=to;
	    		    		this.dist=dist;
	    		    	}
	    		    	
	    		    }
	    		        class Qu{
	    		    		long a0,a1,a2,a3;
	    		    		public Qu(long a0,long a1,long a2,long a3) {
	    		    			this.a0=a0;
	    		    			this.a1=a1;
	    		    			this.a2=a2;
	    		    			this.a3=a3;
	    		    		}
	    		    }
	    		
	class Dsu{
	private int rank[], parent[] ,n;
	long str[],si[],larg[];
	long max=0;
	int cnt=0;
	private static int[] parent1;
	Dsu(int size){
		this.n=size+1;
		rank=new int[n];
		cnt=n-1;
		//parent=new int[n];
	    		    		    		parent=new int[n];
	    		    		    		str=new long[n];
	    		    		    		si=new long[n];
	    		    		
	    		    		    		larg=new long[n];
	    		    		    		makeSet();
	    		    		
	    		    		    	}
	    		    		    	
	    		    		    	void makeSet(){
	    		    		    		for(int i=0;i<n;i++){
	    		    		    			parent[i]=i;
	    		    		    			si[i]=1;
	    		    		    		}
	    		    		    	}
	    		    		    	
	    		    		    	int find(int x){
	    		    		    		if(parent[x]!=x){
	    		    		    			
	    		    		    			parent[x]=find(parent[x]);
	    		    		    		}
	    		    		    		return parent[x];
	    		    		    	}
	    		    		    	
	    		    		    	void join(int ind,long val){
	    		    		    		if(str[ind]==0){
	    		    		    			str[ind]=val;
	    		    		    			larg[ind]=val;
	    		    		    			max=Math.max(max, str[ind]);
	    		    		    		}
	    		    		    		int prev_ind=(ind-1);
	    		    		    		int next_ind=(ind+1);
	    		    		    		if(prev_ind>0 && larg[prev_ind]!=0){
	    		    		    			union(prev_ind,ind);
	    		    		    		}
	    		    		    		if(next_ind<n && larg[next_ind]!=0){
	    		    		    			union(next_ind,ind);
	    		    		    		}
	    		    		    		
	    		    		    	}
	    		    		    
	    		    		    	
	    		    		    	boolean union(int x,int y){
	    		    		    		int xRoot=find(x);
	    		    		    		int yRoot=find(y);
	    		    		    
	    		    		    	
	    		    		    		if(xRoot==yRoot)
	    		    		    			return false;
	    		    		    		if(rank[xRoot]<rank[yRoot]){
	    		    		    		parent[xRoot]=yRoot;
	    		    		    		
	    		    		    		larg[yRoot]=Math.max(larg[xRoot], larg[yRoot]);
	    		    		    		
	    		    		    		si[yRoot]+=si[xRoot];
	    		    		    		str[yRoot]=larg[yRoot]*si[yRoot];
	    		    		    			max=Math.max(str[yRoot], max);
	    		    		    		}else if(rank[yRoot]<rank[xRoot]){
	    		    		    			parent[yRoot]=xRoot;
	     
	    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
	        		    		    		
	        		    		    		si[xRoot]+=si[yRoot];
	        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
	    			    		    		max=Math.max(str[xRoot], max);
	    		    		    		}else{
	    		    		    			parent[yRoot]=xRoot;
	    		    		    			rank[xRoot]++;
	     
	    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
	        		    		    		
	        		    		    		si[xRoot]+=si[yRoot];
	        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
	    			    		    		max=Math.max(str[xRoot], max);
	    		    		    		
	    		    		    		}
	    		    		    		cnt--;
	    		    		    		return true;
	    		    		    	}
	    	
	    		    		     
	    		    		    }
class Pair1 implements Comparable<Pair1>{
		int ind;
		String v;
		@Override
		public int compareTo(Pair1 arg0) {
			if(v==arg0.v)
				return this.ind-arg0.ind;
			return this.v.compareTo(arg0.v);
			
		}
	
	
	}