Score : 700 points
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 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.
Determine whether such a tree exists.
The input is given from Standard Input in the following format:
N a_1 a_2 ... a_N
If there exists a tree that satisfies the condition, print Possible
. Otherwise, print Impossible
.
5 3 2 2 3 3
Possible
The 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 1 1 2
Impossible
10 1 2 2 2 2 2 2 2 2 2
Possible
10 1 1 2 2 2 2 2 2 2 2
Impossible
6 1 1 1 1 1 5
Impossible
5 4 3 2 3 4
Possible