{"raw_statement":[{"iden":"problem statement","content":"Aoki loves numerical sequences and trees.\nOne day, Takahashi gave him an integer sequence of length $N$, $a_1, a_2, ..., a_N$, which made him want to construct a tree.\nAoki wants to construct a tree with $N$ vertices numbered $1$ through $N$, such that for each $i = 1,2,...,N$, the distance between vertex $i$ and the farthest vertex from it is $a_i$, assuming that the length of each edge is $1$.\nDetermine whether such a tree exists."},{"iden":"constraints","content":"*   $2 ≦ N ≦ 100$\n*   $1 ≦ a_i ≦ N-1$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_N$"},{"iden":"sample input 1","content":"5\n3 2 2 3 3"},{"iden":"sample output 1","content":"Possible\n\n![image](https://atcoder.jp/img/agc005/cda0380bb5cd1b9502cfceaf2526d91e.png)\nThe diagram above shows an example of a tree that satisfies the conditions. The red arrows show paths from each vertex to the farthest vertex from it."},{"iden":"sample input 2","content":"3\n1 1 2"},{"iden":"sample output 2","content":"Impossible"},{"iden":"sample input 3","content":"10\n1 2 2 2 2 2 2 2 2 2"},{"iden":"sample output 3","content":"Possible"},{"iden":"sample input 4","content":"10\n1 1 2 2 2 2 2 2 2 2"},{"iden":"sample output 4","content":"Impossible"},{"iden":"sample input 5","content":"6\n1 1 1 1 1 5"},{"iden":"sample output 5","content":"Impossible"},{"iden":"sample input 6","content":"5\n4 3 2 3 4"},{"iden":"sample output 6","content":"Possible"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}