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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

public class Main {
    List<Integer> g1[];
    List<Integer> g2[];

    void solve() throws IOException {
        int n = readInt() + 1;
        int[] h = readIntArray(n);
        boolean flag = false;
        for (int i = 1; i < n; i++) {
            if (h[i] != 1 && h[i - 1] != 1) {
                flag |= true;
            }
        }
        if (!flag) {
            out.println("perfect");
            return;
        }

        out.println("ambiguous");
        n = 0;
        for (int i : h) {
            n += i;
        }

        int itr = 0;
        int last = 0;
        flag = false;
        g1 = new List[n];
        g2 = new List[n];
        int[] c = h.clone();
        for (int i = 0; i < n; i++) {
            g1[i] = new ArrayList<>();
            g2[i] = new ArrayList<>();
        }
        for (int i = 0; i < n; ) {
            if (last > 1 && h[itr] > 1 && flag == false) {
                flag = true;
                int first = i - 2;
                int second = i - 1;
                boolean flag1 = false;
                while (c[itr]-- > 0) {
                    if (!flag1) {
                        flag1 = true;
                        g1[i].add(first);
                        g2[i].add(second);
                    } else {
                        g1[i].add(second);
                        g2[i].add(second);
                    }
                    i++;
                }
            } else {
                int first = i - 1;
                while (c[itr]-- > 0) {
                    g1[i].add(first);
                    g2[i].add(first);
                    i++;
                }
            }
            last = h[itr];
            itr++;
        }
        for (int i = 0; i < n; i++) {
            if (i == 0) {
                out.print(0 + " ");
                continue;
            }
            out.print(g1[i].get(0) + 1 + " ");
        }
        out.println();
        for (int i = 0; i < n; i++) {
            if (i == 0) {
                out.print(0 + " ");
                continue;
            }
            out.print(g2[i].get(0) + 1 + " ");
        }

    }


    int checkBit(int mask, int bit) {
        return (mask >> bit) & 1;
    }

    public static void main(String[] args) throws IOException {

        new Main().run();
    }

    boolean isLower(char a) {
        return ((int) a) >= 97 ? true : false;
    }

    int INF = Integer.MAX_VALUE / 10;

    int[][] STEPS = {{0, 1}, {1, 0}, {-1, 0}, {0, -1}};

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;
    Random rnd = new Random();
    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    Main() throws FileNotFoundException {

        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }

        tok = new StringTokenizer("");
    }

    long checkBit(long mask, int bit) {
        return (mask >> bit) & 1;
    }

    void run() throws IOException {
        solve();
        out.close();
    }

    char varChar;
    int varInt, varInt1, varInt2;
    long varLong;

    long sqrt(long m) {
        long l = 0;
        long r = m;
        long answer = 0;
        long mid = 0;
        while (l <= r) {
            mid = (l + r) / 2;
            if (mid * mid <= m) {
                answer = mid;
                l = mid + 1;
            } else r = mid - 1;
        }
        return answer;
    }

    int countPow(int m, int n) {
        varInt = 0;
        while (m % n == 0 && m > 0) {
            varInt++;
            m /= n;
        }
        return varInt;
    }

    long binPow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 1) {
            return a * binPow(a, b - 1);
        } else {
            varLong = binPow(a, b / 2);
            return varLong * varLong;
        }

    }

    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long pow(long x, long k) {
        varLong = 1;
        for (int i = 0; i < k; ++i) {
            varLong *= x;
        }
        return varLong;
    }

    class Fenwik {
        private long[] t;
        private int length;

        Fenwik(int[] a) {
            this.length = a.length + 100;
            this.t = new long[length];
            for (int i = 0; i < a.length; ++i) {
                this.inc(i, a[i]);
            }
        }

        void inc(int i, int delta) {
            for (; i < this.length; i = i | (i + 1)) {
                this.t[i] += delta;
            }
        }

        long getSum(int r) {
            long sum = 0;

            for (; r >= 0; r = (r & (r + 1)) - 1) {
                sum += this.t[r];
            }

            return sum;
        }

    }

    // ////////////////////////////////////////////////////////////////////

    String delimiter = " ";

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine)
                return null;

            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readIntArray(int b) {
        int a[] = new int[b];
        for (int i = 0; i < b; i++) {
            try {
                a[i] = readInt();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return a;
    }

    int[] readSortedIntArray(int size) throws IOException {
        Integer[] array = new Integer[size];

        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    int[] sortedIntArray(int size, int[] array) throws IOException {
        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) {
            min = Math.min(min, value);
        }
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) {
            max = Math.max(max, value);
        }
        return max;
    }

    long minLong(long... values) {
        long min = Long.MAX_VALUE;
        for (long value : values) {
            min = Math.min(min, value);
        }
        return min;
    }

    long maxLong(long... values) {
        long max = Long.MIN_VALUE;
        for (long value : values) {
            max = Math.max(max, value);
        }
        return max;
    }

    boolean checkIndex(int index, int size) {
        return (0 <= index && index < size);
    }

    int abs(int a) {
        return Math.abs(a);
    }
}