Score : $700$ points

Problem Statement

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.

Constraints

• $2 \leq N \leq 100$
• $1 \leq a_i \leq N-1$

Input

The input is given from Standard Input in the following format:

$N$

$a_1$ $a_2$ $...$ $a_N$

Output

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