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.List;
    		import java.io.*;
    		import java.util.*;

    		
    		
    		/*
    		 * 
    		 * daiict
    		 *
    		 * 
    		 * 
    		 */
    		
    		
    		public class prac {
    			FastScanner in;
    			PrintWriter out;
    		
    			static ArrayList[] adj;
    			
    			static int n;
    			static int m;
    			
    			static int[] dp1;
    			static int[] dp2;
    			static int color[];
    			static int visited[];
    			static long[] arr;
    			static long[] brr;
    			static long ans;
    			static int array[];
    			static int pref[];
    			static int tree[];
    			static int maxval = 32;
    		
    			static int sum = 0;
    		//for dfs do not delete
    			static int dir[][] ={{1,0},{0,1},{0,-1},{-1,0},{1,1},{1,-1},{-1,1},{-1,-1}};
    			
    		
    			static long[] seg;
    			static long count = 1;
    			static long mod = (long)1e9 + 7;
    	
    			static int parent[];
    			static int size[];
    			
    			static class Pair implements Comparable<Pair>
    		    {
    				long x;int y;
    				
    		        Pair(long l, int m) {
    		          
    		        	this.x = l;
    		            this.y = m;
    		          
    		        }
    		        
    		        public int compareTo(Pair p) {
    		            if (this.x == p.x) {
    		                return (int)(this.y-p.y);
    		            }
    		            return (int)(this.x - p.x);
    		        }
    		        
    		        public String toString(){
    		        	return x + " " + y;
    		        }
    		        
    		        public boolean equals(Object o){
    		        	if(o instanceof Pair){
    		        		Pair a = (Pair)o;
    		        		
    		        		return this.x == a.x;
    		        	}
    		        	
    		        	return false;
    		        }
    		        
    		        public int hashCode(){
    		        	return new Long(x).hashCode()*31 + new Long(y).hashCode();
    		        }
    		    
    		    }
    		    
    			
    			public static int gcd(int a, int b) {
    				if (b == 0) return a;
    				return gcd(b, a%b);
    			}
    	
    			void build(int n) {  // build the tree
    				  for (int i = n - 1; i > 0; --i) seg[i] = Math.max(seg[i<<1],seg[i<<1|1]);
    				}
     
    			public static void modify(int p, int i,long val,int n) {  // set value at position p
    					if(i == 1){
    						long temp = val;
    						val = seg[p+n] - arr[p] + val;
    						arr[p] = temp;
    					}else{
    						val = Math.min(val, p) + arr[p];
    						brr[p] = val;
    					}
    					
    				  for (seg[p += n] = val; p > 1; p >>= 1) seg[p>>1] = Math.max(seg[p],seg[p^1]);
    				}
     
    				long query(int l, int r,int n) {  // max on interval [l, r)
    				  long res = Integer.MIN_VALUE;
    				  for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
    				    if ((l&1) == 1) res = (int)Math.max(res,seg[l++]);
    				    if ((r&1) == 1) res = (int)Math.max(res,seg[--r]);
    				  }
    				  return res;
    				}
    				
    			public static void update(int x,int val){
    				while(x<=maxval){
    					tree[x] += val;
    					x = (x&-x);
    				}
    			}
    			
    			public static int read(int idx){
    				int sum = 0;
    				
    				while(idx>= 0){
    					sum += tree[idx];
    					idx -= (idx&(-idx));
    				}
    				
    				return sum;
    			}
    			
    			public static int find(int i){
    				if(parent[i] != i){
    					return find(parent[i]);
    				}
    				
    				return i;
    			}
    			
    			public static void union(int a,int b){
    				int x = find(a);
    				int y = find(b);
    				
    				if(x!=y){
    					if(size[x] > size[y]){
    						size[x] += size[y];
    						parent[y] = x;
    					}else{
    						size[y] += size[x];
    						parent[x] = y;
    					}
    				}
    			}
    			
    		    void solve() throws NumberFormatException, IOException {
    		 
    		    	//Scanner in = new Scanner(System.in);
    		    	
    		    	int n = in.nextInt();
    		    	
    		    	int arr[] = new int[n+1];
    		    	
    		    	for(int i = 0;i<=n;i++) { 
    		    		arr[i] = in.nextInt();
    		    	}
    		    	
    		    	ArrayList<Integer> list = new ArrayList();
    		    	ArrayList<Integer> list1 = new ArrayList();
    		    	
    		    	int sum = 0;
    		    	
    		    	list.add(0);
    		    	list1.add(0);
    		    	sum = 1;
    		    	int f = 0;
    		    	
    		    	for(int i = 1;i<=n;i++){
    		    		if(arr[i] > 1 && arr[i-1] > 1){
    		    			f = 1;
    		    			break;
    		    		}
    		    	}
    		    	
    		    	for(int i = 1;i<=n;i++){
    		    		if(arr[i] > 1 && arr[i-1] > 1){
    		    			for(int j = 0;j<arr[i];j++){
    		    				list.add(sum);
    		    				//list1.add(sum);
    		    			}
    		    			for(int j = 0;j<arr[i]-1;j++){
    		    				
    		    				list1.add(sum);
    		    			}
    		    			
    		    			list1.add(sum-1);
    		    		}else{
    		    			for(int j = 0;j<arr[i];j++){
    		    				list.add(sum);
    		    				list1.add(sum);
    		    			}
    		    			
    		    		}
    		    		
    		    		sum += arr[i];
    		    	}
    		    	
    		    	if(f == 0){
    		    		out.println("perfect");
    		    	}else{
    		    		out.println("ambiguous");
    		    		for(Integer s:list){
    		    			out.print(s + " ");
    		    		}
    		    		out.println();
    		    		for(Integer s:list1){
    		    			out.print(s + " ");
    		    		}
    		    	}
	    
    		    }
    		    
    		    public static void ddfss(int i,int p){
    		    	
    		    	array[i] = color[p];
    		    	
    		    	for(int j = 0;j<adj[i].size();j++){
    		    		if((int)adj[i].get(j) != p){
    		    			
    		    			ddfss((int)adj[i].get(j),i);
    		    		}
    		    	}
    		    }
    		    
    		    public static void ddfs(int i,int p){

    		    	//System.out.println(i + " " +p);
    		    	
    		    	if(color[i] != array[i]){
    		    		sum++;
    		    	//	System.out.println(i + "dd");
    		    		ddfss(i,p);
    		    		
    		    	}
	
    		    	for(int j = 0;j<adj[i].size();j++){
    		    		if((int)adj[i].get(j) != p){
    		    			ddfs((int)adj[i].get(j),i);
    		    		}
    		    	}
    		    	
    		    }
    		    
    		    public static long invcount(int arr[]){
    		    	if(arr.length<2){
    		    		return 0;
    		    	}
    		    	
    		    	int mid = (arr.length + 1)/2;
    		    	
    		    	int left[] = Arrays.copyOfRange(arr, 0,mid);
    		    	int right[] = Arrays.copyOfRange(arr, mid, arr.length);
    		    	
    		    	return invcount(left)+invcount(right)+merge(arr,left,right);
    		    	
    		    }
    		    
    		    public static long merge(int arr[],int left[],int right[]){
    		    	long count = 0;
    		    	
    		    	int i = 0;
    		    	int j = 0;
    		    	
    		    	while(i<left.length || j < right.length){
    		    		
    		    		if(i == left.length){
    		    			arr[i+j] = right[j];
    		    			j++;
    		    		}else if(j == right.length){
    		    			arr[j+i] = left[i];
    		    			i++;
    		    		}else{
    		    			if(left[i] <= right[j]){
    		    				arr[i+j] = left[i];
    		    				i++;
    		    			}else{
    		    				arr[i+j] = right[j];
    		    				j++;
    		    				count += left.length-i;
    		    			}
    		    		}
    		    		
    		    	}
    		    	
    		    	return count;
    		    }
    		    
    		  
    		    
    		    /**
    		     * 
    		     * @param div
    		     * @param left
    		     * @param right
    		     * @param value
    		     * @return the smallest index i which a[i] >= value in range [left, right) if exists, otherwise return -1
    		     */
    		    int ff(int[] div, int left, int right, int value) {
    		        int low = left;
    		        int high = right;
    		        
    		        if(value > div[right-1]){
    		        	return left;
    		        }
    		        
    		        while (low != high) {
    		            int mid = (low + high) / 2;
    		            if (div[mid] < value) {
    		                low = mid + 1;
    		            } else {
    		                high = mid;
    		            }
    		        }
    		        if (low == right) {
    		            return low;
    		        }
    		        return low;
    		    } 
    		   
    		    /**
    		     * 
    		     * @param div
    		     * @param left
    		     * @param right
    		     * @param value
    		     * @return greatest index i which a[i] <= value in range [left, right) if exists, otherwise return a number out of [left, right)
    		     */
    		    int ffff(int[] div, int left, int right, int value) {
    		        
    		    	if(value < div[left]){
    		    		return right-1;
    		    	}
    		    	
    		    	while (left != right) {
    		            int mid = (left + right) >> 1;
    		            if (div[mid] <= value) {
    		                left = mid + 1;
    		            } else {
    		                right = mid;
    		            }
    		        }
    		        if (left < 0) {
    		            left *= -1;
    		        }
    		        return --left;
    		    }
	    
    		   
    		  
    		
    		    public static String reverse(String s){
    		    	
    		    	String ans = "";
    		    	
    		    	for(int i = s.length()-1;i>=0;i--){
    		    		ans += s.charAt(i);
    		    	}
    		    	
    		    	return ans;
    		    	
    		    }
    			
    			
    		    
    		 
    		    public static long sum(long x){
    		    	return x<10?x:x%10 + sum(x/10);
    		    }
    			
    			public static long gcd(long x, long y) {
    				if (x == 0)
    					return y;
    				else
    					return gcd( y % x,x);
    			}
    			static long inv(long x , long mod)
    			{
    				long r,y;
    				for(r=1,y=mod-2;y!=0;x=x*x%mod,y>>=1)
    				{
    					if((y&1)==1)
    						r=r*x%mod;
    				
    				}
    				return r;
    			}
    			
    			public static long pow(long x,long y,long n){
    				if(y==0)
    					return 1%n;
    				if(y%2==0){
    					long z=pow(x,y/2,n);
    					return (z*z)%n;
    				}
    				return ((x%n)*pow(x,y-1,n))%n;
    			}
    			
    			
    			
    			
    			public static boolean isPrime(int n) {
    				// Corner cases
    				if (n <= 1)
    					return false;
    				if (n <= 3)
    					return true;
    		 
    				// This is checked so that we can skip 
    				// middle five numbers in below loop
    				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;
    			}
    			
    		
    			void run() throws NumberFormatException, IOException {
    				in = new FastScanner();
    				out = new PrintWriter(System.out);
    		
    				solve();
    		
    				out.close();
    			}
    		
    			class FastScanner {
    				BufferedReader br;
    				StringTokenizer st;
    		
    				public FastScanner() {
    					br = new BufferedReader(new InputStreamReader(System.in));
    				}
    		
    				String next() {
    					while (st == null || !st.hasMoreTokens()) {
    						try {
    							st = new StringTokenizer(in.br.readLine());
    						} catch (IOException e) {
    							// TODO Auto-generated catch block
    							e.printStackTrace();
    						}
    					}
    					return st.nextToken();
    				}
    		
    				int nextInt() {
    					return Integer.parseInt(next());
    				}
    		
    				long nextLong() {
    					return Long.parseLong(next());
    				}
    		
    				double nextDouble() {
    					return Double.parseDouble(next());
    				}
    			}
    			
    			
    			
    			
    		 
    		
    			public static void main(String[] args) throws NumberFormatException, IOException {
    				new prac().run();
    			}
    		}
    		class Node{
    			String s;
    			int b;
    			
    		}
    		
    		class MyComp implements Comparator<String>{
    		    
    			int c = 0;
    			
    			MyComp(int d){
    				c = d;
    			}
    			
    			@Override
    			public int compare(String a,String b) {
    				
    				// < == -1
    				
    				String arr[] = a.split(" ");
    				String brr[] = b.split(" ");
    				
    				return arr[c].compareTo(brr[c]);
    				
    				
    			}

    			
    		}
    		
    		class MyComp2 implements Comparator<Node>{
    		    
    		
    			
    			@Override
    			public int compare(Node a,Node b) {
    				
    				// < == -1

    				
    				if(a.b > b.b){
    					return -1;
    				}else{
    					return 1;
    				}
    				
    				
    			}

    			
    		}