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.io.*;
     
     
     
     
    import java.math.*;
    import java.util.*;    
          public class Main1
           {
            private InputStream is;
            private PrintWriter out;
            static int MOD = (int)(1e9+7);
            ArrayList<Integer>[] amp;
            public static void main(String[] args) throws Exception
            {
                new Thread(null, new Runnable()
                {
                public void run()
                {
                    try {
         } catch (Exception e)
                    {
                        System.out.println(e);
                    }
                }
            }, "1", 1 << 26).start();
                new Main1().soln();
            }
            char ch[][];
            static ArrayList<Integer>[] g;
            static ArrayList<Integer> ar[];
            static long ok[];    
            static int phi[]=new int[500005];
            void solve()
            {
               int n=ni();
               int a[]=na(n+1);
               boolean yes=false;
               for(int i=1;i<=n;i++)
               {
            	   if(a[i-1]>1&&a[i]>1)
            	   {
            		   yes=true;
            		   break;
            	   }
               }
               int sum=0;
               for(int i=0;i<=n;i++)sum+=a[i];
               if(!yes)
               {
            	   out.println("perfect");return;
               }
               out.println("ambiguous");
               int ans[]=new int[sum+1];
               ans[1]=0;
               int ans2[]=new int[1+sum];
               ans2[1]=0;
               Queue<Integer> Q=new LinkedList();Q.add(1);
               int cnt=2;
               for(int i=1;i<=n;i++)
               {
            	   if(Q.size()==1)
            	   {
            		   int p=Q.poll();
            		   for(int j=1;j<=a[i];j++)
            		   {
            			   Q.add(cnt);
            			   ans[cnt]=p;
            			   ans2[cnt++]=p;
            		   }
            	   }
            	   else if(Q.size()>1&&a[i]>1)
            	   {
            		   int lol1=Q.poll();
            		   int lol2=Q.poll();
            		   Q.clear();
            		   Q.add(cnt);
            		   int tmp=cnt;
            		   ans[cnt++]=lol1;
            		   
            		   for(int j=2;j<=a[i];j++)
            		   {
            			   Q.add(cnt);
            			   ans[cnt++]=lol2;
            		   }
            		   for(int j=1;j<=a[i];j++)
            		   {
            			   ans2[tmp++]=lol2;
            		   }
            	   }
            	   else if(Q.size()>1&&a[i]==1)
            	   {
            		   int lol1=Q.poll();
            		   Q.clear();
            		   Q.add(cnt);
            		   ans[cnt]=lol1;
            		   ans2[cnt++]=lol1;
            		  
            	   }
            	 //  System.out.println(Q+" "+cnt);
            	   
               }
               for(int i=1;i<=sum;i++)
            	   out.print(ans[i]+" ");
               out.println();
               for(int i=1;i<=sum;i++)
            	   out.print(ans2[i]+" ");
            }
            static int c[];
            static int color[]=new int[10001];
            public static int bfs(int curr)
            {
            	vi[curr]=true;
            	Queue<Integer> Q=new LinkedList();
            	Q.add(curr);
            	int ans=0;
            	while(!Q.isEmpty())
            	{
            		int count=Q.size();
            		while(count>0)
            		{
            			int p=Q.poll();
            			vi[p]=true;
            			if(color[p]==c[p])
            			{
            				for(int x:g[p])
            				{
            					if(!vi[x])
            					{
            						Q.add(x);
            					}
            				}
            				count--;
            				continue;
            			}
            			color[p]=c[p];
            			visited1=new boolean[10001];
            			dfs(p);
            			
            			for(int x:g[p])
            			{
            				if(!vi[x])
            				{
            					Q.add(x);
            				}
            			}
            			ans++;
            			count--;
            		
            		}
            	}
            	return ans;
            	
            }
            static boolean visited1[];
            public static void dfs(int curr)
            {
            	visited1[curr]=true;
            	for(int x:g[curr])
            	{
            		if(!visited1[x]&&!vi[x])
            		{
            			color[x]=color[curr];
            			dfs(x);
            		}
            	}
            }
            static boolean vi[];
            
            
            
            
			static boolean visited[][];
			static int a[][];
            public static long query(int v,int start,int end,int l,int r,int x)
            {
            	if(r < start || end < l)
                {
                    return 0;
                }
                if(l <= start && end <= r)
                {
                    return (tre[v]);
                }
                int mid = (start + end) / 2;
                long p1 = query(2*v, start, mid, l, r,x);
                long p2 = query(2*v+1, mid+1, end, l, r,x);
                return p1+p2;	
            }
            public static void update(int v,int tl,int tr,int index,long a2)
            {
            	if(tl==tr)
                {
                    tre[v]=a2;
                }
                else
                {
                    int mid=(tl+tr)/2;
                    if(tl <= index &&index <= mid)
                    {
                        update(2*v,tl, mid, index, a2);
                    }
                    else
                    {
                        update(2*v+1,mid+1,tr, index, a2);
                    }
                    tre[v]=tre[2*v]+tre[2*v+1];
                }
            }
            static long tre[]=new long[8000005];
          /* public static int find(int v,int start,int end,int l,int r)
            {
                if(r < start || end < l)
                {
                    return Integer.MIN_VALUE;
                }
                if(l <= start && end <= r)
                {
                    return (tre[v]);
                }
                int mid = (start + end) / 2;
                int p1 = find(2*v, start, mid, l, r);
                int p2 = find(2*v+1, mid+1, end, l, r);
                return Math.max(p1, p2);          
            }
            static int tre[]=new int[4000005];
            public static void Update(int v,int tl,int tr,int index,int val)
            {
                if(tl==tr)
                {
                    tre[v]=val;
                }
                else
                {
                    int mid=(tl+tr)/2;
                    if(tl <= index &&index <= mid)
                    {
                        Update(2*v,tl, mid, index, val);
                    }
                    else
                    {
                        Update(2*v+1,mid+1,tr, index, val);
                    }
                    tre[v]=(Math.max(tre[2*v],tre[2*v+1]));
                }
            }
            */
            boolean isPrime(int x)
                {
                if(x==0||x==1)
                    return false;
                for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
                return true;
            }
            int  p ;
            long modInverse(long a, long mOD2){
                return  power(a, mOD2-2, mOD2);
            }
            long power(long x, long y, long m)
            {
            if (y == 0)
            return 1;
            long p = power(x, y/2, m) % m;
            p = (p * p) % m;
        
            return (y%2 == 0)? p : (x * p) % m;
            }
            public static long gcd(long a, long b){
                if(b==0) return a;
                return gcd(b,a%b);
            }
            class Pair1 implements Comparable<Pair1>{
                long a;
                long b;
                long c;
                Pair1(long x,long y,long z){
                this.a=x;
                this.b=y;
                this.c=z;
                }
                public int hashCode() {
                    return Objects.hash();
                }
                
                @Override
                public int compareTo(Pair1 arg0) {
                    return (int)(arg0.c-c);
                }    
            }
            long power(long x, long y, int mod){
                long ans = 1;
                while(y>0){
                    if(y%2==0){
                        x = (x*x)%mod;
                        y/=2;
                    }
                    else{
                        ans = (x*ans)%mod;
                        y--;
                    }
                }
                return ans;
            }
            void soln() {
                is = System.in;
                out = new PrintWriter(System.out);
                long s = System.currentTimeMillis();
                solve();
                out.flush();
            }
             private byte[] inbuf = new byte[1024];
            public int lenbuf = 0, ptrbuf = 0;
            private int readByte() {
                if (lenbuf == -1)
                    throw new InputMismatchException();
                if (ptrbuf >= lenbuf) {
                    ptrbuf = 0;
                    try {
                        lenbuf = is.read(inbuf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (lenbuf <= 0)
                        return -1;
                }
                return inbuf[ptrbuf++];
            }
            private boolean isSpaceChar(int c) {
                return !(c >= 33 && c <= 126);
            }
            private int skip() {
                int b;
                while ((b = readByte()) != -1 && isSpaceChar(b))
                    ;
                return b;
            }
            private double nd() {
                return Double.parseDouble(ns());
            }
            private char nc() {
                return (char) skip();
            }
            private String ns() {
                int b = skip();
                StringBuilder sb = new StringBuilder();
                while (!(isSpaceChar(b))) {
                    sb.appendCodePoint(b);
                    b = readByte();
                }
                return sb.toString();
            }
            private char[] ns(int n) {
                char[] buf = new char[n];
                int b = skip(), p = 0;
                while (p < n && !(isSpaceChar(b))) {
                    buf[p++] = (char) b;
                    b = readByte();
                }
                return n == p ? buf : Arrays.copyOf(buf, p);
            }
            private int[][] nm(int n, int m) {
                int[][] map = new int[n][m];
                for (int i = 0; i < n; i++)
                {
                    for(int j=0;j<m;j++)
                        map[i][j]=ni();
                }
                return map;
            }
            private int[] na(int n) {
                int[] a = new int[n];
                for (int i = 0; i < n; i++)
                    a[i] = ni();
                return a;
            }
            private int ni() {
                int num = 0, b;
                boolean minus = false;
                while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
                    ;
                if (b == '-') {
                    minus = true;
                    b = readByte();
                }
                while (true) {
                    if (b >= '0' && b <= '9') {
                        num = num * 10 + (b - '0');
                    } else {
                        return minus ? -num : num;
                    }
                    b = readByte();
                }
            }
            private long nl() {
                long num = 0;
                int b;
                boolean minus = false;
                while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
                    ;
                if (b == '-') {
                    minus = true;
                    b = readByte();
                }
                while (true) {
                    if (b >= '0' && b <= '9') {
                        num = num * 10 + (b - '0');
                    } else {
                        return minus ? -num : num;
                    }
                    b = readByte();
                }
            }
            private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
            private void tr(Object... o) {
                if (!oj)
                    System.out.println(Arrays.deepToString(o));
            }
        }