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.BigInteger;
	import java.util.*;
	
	import javax.sound.midi.Synthesizer;

	
	
	public class Main
	{
		private InputStream is;
		private PrintWriter out;
		int time = 0, freq[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7), arr[], weight[][], x[], y[], parent[];
		int MAX = 1000001, N, K;
		long red[], ans = Long.MAX_VALUE;
	
		ArrayList<Integer>[] amp;
		ArrayList<Pair>[] pmp;
		boolean b[];
		boolean boo[][], b1[];
		Pair prr[];
		HashMap<Pair, Integer> hm = new HashMap();
		int Dp[][] = new int[1100][1100];
	
		void soln() 
		{
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
	
			// out.close();
			out.flush();
			// tr(System.currentTimeMillis() - s + "ms");
		}
		
		 class ST1 // min ST
		{
			int arr[], st[];
			int size;
	
			ST1(int a[]) {
				arr = a.clone();
				size = 10 * arr.length;
				st = new int[size];
				build(0, arr.length - 1, 1);
			}
	
			void build(int ss, int se, int si) {
				if (ss == se) {
					st[si] = arr[ss];
					return;
				}
				int mid = (ss + se) / 2;
				int val = 2 * si;
				build(ss, mid, val);
				build(mid + 1, se, val + 1);
				st[si] = gcd(st[val], st[val + 1]);
			}
	
			/*void update(int ss, int se, int idx, long val, int si) {
				if (ss == se) {
					// if(si==idx+1)
					st[si] = val;
					return;
				}
				int mid = (ss + se) / 2;
				if (ss <= idx && idx <= mid) {
					update(ss, mid, idx, val, 2 * si);
				} else {
					update(mid + 1, se, idx, val, 2 * si + 1);
				}
				int v = 2 * si;
				st[si] = Math.min(st[v], st[v + 1]);
			}*/
	
			int get(int ss, int se, int l, int r, int si) {
				if (l > se || r < ss || l > r)
					return 0;
				if (l <= ss && r >= se)
					return st[si];
				int mid = (ss + se) / 2;
				int val = 2 * si;
				return gcd(get(ss, mid, l, r, val), get(mid + 1, se, l, r, val + 1));
			}
		}
	
		public static void main(String[] args) throws Exception
		{
			new Thread(null, new Runnable() 
			{
				public void run() 
				{
					try 
					{
						// new Main().soln();
					} catch (Exception e) 
					{
						System.out.println(e);
					}
				}
			}, "1", 1 << 26).start();
			new Main().soln();
		}
	
		int D[][];
		char ch[][], ch1[];
		int hash = 29;
		int x2, y2;
		HashSet<Integer>[] hs = (HashSet<Integer>[]) new HashSet[110];
		cell[] c;
		 boolean ar[] = new boolean[1000];
		Pair[] p = new Pair[4];
		 int a1[] = new int[7];
		 int a2[] = new int[7];
		 int a3[] = new int[7];
		 int a4[] = new int[7];
		 private static class Comp implements Comparable<Comp>{
				int ind;
				BigInteger v;

				@Override
				public int compareTo(Comp arg0) {
					if(v==arg0.v)
						return this.ind-arg0.ind;
					return this.v.compareTo(arg0.v);
				}
			}
		 private static class Comp1 implements Comparable<Comp1>{
				int ind;
				String v;

				@Override
				public int compareTo(Comp1 arg0) {
					if(v.equals(arg0.v))
						return this.ind-arg0.ind;
					return this.v.compareTo(arg0.v);
				}
			}
		 void solve()
		 {
			int h = ni();
			int arr[] = na(h+1);
			boolean b = true;
			int j = 0;
			for(int i = 1; i<=h; i++) {
				if(arr[i]!=1 && arr[i-1]!=1) {
					b = false; 
					j = i-1;
				}
			}
			if(b) {
				out.println("perfect");
			}
			else {
				out.println("ambiguous");
				int k = 1;
				out.print(0+" ");
				for(int i = 1; i<=h;i++) {
					for(int v = 0;v<arr[i];v++) {
						out.print(k+" ");
					}
					k+=arr[i];
				}
				out.println();
				out.print(0+" ");
				k = 1;
				for(int i = 1; i<=j;i++) {
					for(int v = 0;v<arr[i];v++) {
						out.print(k+" ");
					}
					k+=arr[i];
				}
				out.print(k-1+" ");
				//out.println(k+"*");
				for(int v = 1;v<arr[j+1];v++) {
					out.print(k+" ");
				}
				//out.println(k+"*");
				k+=arr[j+1];
				//out.println(k+"*");
				for(int i = j+2; i<=h;i++) {
					for(int v = 0;v<arr[i];v++) {
						out.print(k+" ");
					}
					k+=arr[i];
				}
			}
		 }
		 void dfs(int v, int col) {
			 if(col!=arr[v]) {
				 ans++;
				 col = arr[v];
			 }
			 for(int i : amp[v]) {
				 dfs(i,col);
			 }
		 }
		 String check(String[] s) {
			 char ch[] = new char[] {'a','a','a','a'};
			 boolean b = false;
			 for(int i = 0;i<4;i++) {
				 if(i>0) {
					 if(ch[i]=='a') continue;
				 }
				 for(int j = i+1;j<4;j++) {
					 if(!s[i].equals(s[j])) {
						 if(ch[i] == 'a' && ch[j]=='a') ch[j] = 'b';
						 else if(ch[j]=='a') continue;
						 else {
							 System.out.println("NO");
							 System.exit(0);
						 }
					 }
					 else b = true;
				 }
			 }
			 return new String(ch);
		 }
		 boolean isVowel(char c) {
			 if(c=='a' || c=='e' ||c=='i' ||c=='o' ||c=='u' ) return true;
					 return false;
		 }
		 void recur1(int[] a1, int[] a2) {
			 for(int i = 1; i< 7;i++) {
				 for(int j = 1; j< 7;j++) {
					 ar[a1[i]*10+a2[j]] = true;
					 ar[a2[j]*10+a1[i]] = true;
				 }
			 }
		 }
		 int dfs(int x) {
			 b[x] = true;
			 for(int i : amp[x]) {
				 if(!b[i]) {
					 dist[i] = dist[x]+1;
					 arr[x] += dfs(i);
				 }
			 }
			 return ++arr[x];
		 }
		boolean binaryS(int a, int b, int c, int d) {
			double l = 0, r = 90;
			for(int count = 0;count<=300;count++)
			{
				double mid = (l + r) / 2;
				double temp = mid * Math.PI / 180;
				double x1 = Math.cos(temp) * c;
				double x2 = Math.sin(temp) * c;
				temp = Math.PI / 2 - temp;
				double y1 = Math.cos(temp) * d;
				double y2 = Math.sin(temp) * d;
				if ((x1 + y1 <= a) && (x2 + y2 <= b)) return true;
				else if (x1 + y1 > a) l = mid;
				else r = mid;
			}
			return false;
		}
		/*void bfs(int s, int n) {
			b = new boolean[n];
			dist = new int[n];
			Arrays.fill(dist, 1000000);
			dist[s] = 0;
			b[s] = true;
			Queue<Integer> q = new LinkedList<>();
			q.add(s);
			while(!q.isEmpty()) {
				int y = q.poll();
				for(int i : amp[y]) {
					dist[i] = min(dist[i],dist[y]+1);
					if(!b[i]) {
						b[i] = true;
						q.add(i);
					}
				}
			}
		}*/
		boolean check(String s, String s1) {
			char ch1[] = s.toCharArray(), ch2[] = s1.toCharArray();
			int arr[] = new int[10];
			for(char c : ch1) {
				arr[c-'0']++;
			}
			int ans = 0;
			for(char c:ch2) {
				arr[c-'0']--;
			}
			
			for(int i:arr) ans += ((i>0)?i:0);
			return ans==3;
		}
		void seive(int n)
		{
			start = new int[n];
			for(int i = 2;i<n;i++) {
				if(start[i]==0) {
					for(int j = 2*i;j<n;j+=i) {
						start[j] = i;
					}
				}
			}
		}
		void print(int[][] arr) 
		{
			int seed = 110, n = arr.length - 220;
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					System.out.print(arr[i + seed][j + seed] + " ");
				}
				System.out.println();
			}
			System.out.println();
		}
	
		 class cell implements Comparable<cell>
		 {
			int s, d, p, i;
	
			cell(int t, int d, int p, int i) {
				this.s = t;
				this.p = p;
				this.d = d;
				this.i = i;
			}
	
			public int compareTo(cell other) {
				// return Integer.compare(val, other.val);
				return Long.compare(d, other.d) != 0 ? (Long.compare(d, other.d)): (Long.compare(i,other.i));
												// other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)):
												// (Long.compare(v, other.v)))
				// &(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)):
				// (Long.compare(v, other.u))));
			}
	
			public String toString() {
				return this.d + " " + this.s +" "+this.p+" "+this.i;
			}
		}
	
		int abs(int x)
		{
			return ((x > 0) ? x : -x);
		}
	
		long ret(int p) 
		{
			if (p >= 0)
				return 0;
			else
				return 1;
		}
	
		long val(int p, int a, int b) 
		{
			if (p >= 0) {
				return (a * 1l * p);
			}
			return (b * 1l * p);
		}
	
		
	
	
		public int getParent(int x) 
		{
			while (parent[x] != x) {
				parent[x] = parent[parent[x]];
				x = parent[x];
			}
			return x;
		}
	
		void getFactors(int n, int x)
		{
			for (int i = 1; i * i <= n; i++) {
				if (n % i == 0) {
					hs[x].add(i);
					hs[x].add(n / i);
				}
			}
		}
	
		void recur(int a, int b, int k) 
		{
			if (k == 0) {
				if (a == x2 && b == y2)
					ans++;
				return;
			}
			recur(a, b + 1, k - 1);
			recur(a, b - 1, k - 1);
			recur(a + 1, b, k - 1);
			recur(a - 1, b, k - 1);
		}
	
		int min(int a, int b) 
		{
			return (a < b) ? a : b;
		}
	
		/*private class Cell implements Comparable<Cell> {
			int u, v, s;
	
			public Cell(int u, int v, int s) {
				this.u = u;
				this.v = v;
				this.s = s;
			}
	
			public int hashCode() {
				return Objects.hash();
			}
	
			public int compareTo(Cell 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))));
			}
	
			public String toString() {
				return this.u + " " + this.v;
			}
		}*/

		
		class Pair implements Comparable<Pair>
		{
			int u ,v,i;
	
			Pair(int u, int v) {
				this.u = u;
				this.i = v;
			}
	
			Pair(int u, int v, int i) {
				this.u = u;
				this.v = v;
				this.i = i;
			}
	
			public int hashCode() {
				return Objects.hash();
			}
	
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v));
			}
	
			public int compareTo(Pair other) {
				// return Integer.compare(val, other.val);
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(i, other.i));// ((Long.compare(u,
			
			}									
			public String toString() {
				return this.u + " " + this.v +" "+this.i;
			}
		}
	
		long max(long a, long b) 
		{
			if (a > b)
				return a;
			return b;
		}
	
		static class FenwickTree 
		{
	
			int[] array; // 1-indexed array, In this array We save cumulative
							// information to perform efficient range queries and
							// updates
	
			public FenwickTree(int size) {
				array = new int[size + 1];
			}
	
			public int rsq(int ind) {
				assert ind > 0;
				int sum = 0;
				while (ind > 0) {
					sum += array[ind];
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and decrementing ind by that
					// number
					ind -= ind & (-ind);
				}
				return sum;
			}
	
			public int rsq(int a, int b) {
				assert b >= a && a > 0 && b > 0;
				return rsq(b) - rsq(a - 1);
			}
	
			public void update(int ind, int value) {
				assert ind > 0;
				while (ind < array.length) {
					array[ind] += value;
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and incrementing ind by that
					// number
					ind += ind & (-ind);
				}
			}
	
			public int size() {
				return array.length - 1;
			}
		}
		void buildGraph(int n)
		{
			for (int i = 0; i < n; i++) {
				int x1 = ni(), y1 = ni();
				amp[x1-1].add(y1-1);
				amp[y1-1].add(x1-1);
			}
		}
		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 int gcd(int a, int b)
		{
			if (b == 0)
				return a;
			return gcd(b, a % b);
		}
	
		/*static class ST
		{
			int arr[], lazy[], n;
	
			ST(int a) {
				n = a;
				arr = new int[10 * n];
				lazy = new int[10 * n];
			}
	
			void up(int l, int r, int val) {
				update(0, n - 1, 0, l, r, val);
			}
	
			void update(int l, int r, int c, int x, int y, int val) {
				if (lazy[c] != 0) {
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l > r || x > y || l > y || x > r)
					return;
				if (x <= l && y >= r)
	
				{
					lazy[c] += val;
					return;
				}
				int mid = l + r >> 1;
				update(l, mid, 2 * c + 1, x, y, val);
				update(mid + 1, r, 2 * c + 2, x, y, val);
				arr[c] = Math.max(arr[2 * c + 1], arr[2 * c + 2]);
			}
	
			int an(int ind) {
				return ans(0, n - 1, 0, ind);
			}
	
			int ans(int l, int r, int c, int ind) {
				if (lazy[c] != 0) {
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l == r)
					return arr[c];
				int mid = l + r >> 1;
				if (mid >= ind)
					return ans(l, mid, 2 * c + 1, ind);
				return ans(mid + 1, r, 2 * c + 2, ind);
			}
		}*/
	
		public static int[] shuffle(int[] a, Random gen)
		{
			for (int i = 0, n = a.length; i < n; i++) {
				int ind = gen.nextInt(n - i) + i;
				int d = a[i];
				a[i] = a[ind];
				a[ind] = d;
			}
			return a;
		}
	
		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;
		}
	
		// To Get Input
		// Some Buffer Methods
		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) && b!=' ')) { // when nextLine, (isSpaceChar(b) && 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 char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			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));
		}
	}