{"problem":{"name":"Tree Restoring","description":{"content":"Aoki loves numerical sequences and trees. One day, Takahashi gave him an integer sequence of length $N$, $a_1, a_2, ..., a_N$, which made him want to construct a tree. Aoki wants to construct a tree w","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc005_c"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $2 ≦ N ≦ 100$\n*   $1 ≦ a_i ≦ N-1$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc005_c","tags":[],"sample_group":[["5\n3 2 2 3 3","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."],["3\n1 1 2","Impossible"],["10\n1 2 2 2 2 2 2 2 2 2","Possible"],["10\n1 1 2 2 2 2 2 2 2 2","Impossible"],["6\n1 1 1 1 1 5","Impossible"],["5\n4 3 2 3 4","Possible"]],"created_at":"2026-03-03 11:01:14"}}