CF901A.Hashing Trees

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 _a_0, _a_1, ..., a__h, where h is the height of the tree, and a__i 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 a__i, 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.

萨莎正在参加一场编程竞赛。在其中一道题目中，她需要判断一些有根树是否同构。她之前从未见过这道题，但作为一名经验丰富的参赛者，她猜测应该将每棵树映射为某个序列，然后通过比较这些序列（而非直接比较树）来判断同构性。萨莎希望将每棵树映射为一个序列 $a_0, a_1, \dots, a_h$，其中 $h$ 是该树的高度，而 $a_i$ 表示距离根节点恰好 $i$ 条边的顶点个数。

不幸的是，这次萨莎的直觉出错了：可能存在多个互不同构的有根树对应同一个序列。为了证明这一点，你需要编写一个程序：给定序列 $a_i$，构造出两棵互不同构的有根树，使得它们均对应于该序列；或者判定满足该序列的有根树唯一（即仅存在一棵，不考虑同构意义下的差异）。

两棵有根树被称为同构，当且仅当你能够对第一棵树的顶点重新编号，使得其根节点的新编号恰好等于第二棵树根节点的编号，并且重编号后两棵树完全相同（即边集完全一致）。

一棵有根树的高度定义为从根节点到任意其他顶点的路径上所含边数的最大值。

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 _a_0, _a_1, ..., a__h (1 ≤ a__i ≤ 2·105). The sum of all a__i does not exceed 2·105. It is guaranteed that there is at least one tree matching this sequence.

第一行包含一个整数 $h$（$2 \leq h \leq 10^5$）——树的高度。

第二行包含 $h+1$ 个整数——序列 $a_0,\,a_1,\,\dots,\,a_h$（$1 \leq a_i \leq 2\cdot10^5$）。所有 $a_i$ 的总和不超过 $2\cdot10^5$。保证至少存在一棵树与该序列匹配。

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 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.

如果仅存在一棵树与该序列匹配，则输出“perfect”。

否则，在第一行输出“ambiguous”。在第二行和第三行分别输出两棵树的描述，格式如下：每行输出 个整数，其中第 $k$ 个整数表示顶点 $k$ 的父节点；若顶点 $k$ 为根节点，则该整数为 $0$。

这两棵树应互不同构，且均与给定序列匹配。

The only tree in the first example and the two printed trees from the second example are shown on the picture:

第一个样例中的唯一一棵树以及第二个样例中输出的两棵树如图所示：