Problem:
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 ≦ N ≦ 100

1 ≦ a_i ≦ 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.

Sample Input 1

5
3 2 2 3 3

Sample Output 1

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.

Sample Input 2

3
1 1 2

Sample Output 2

Impossible

Sample Input 3

10
1 2 2 2 2 2 2 2 2 2

Sample Output 3

Possible

Sample Input 4

10
1 1 2 2 2 2 2 2 2 2

Sample Output 4

Impossible

Sample Input 5

6
1 1 1 1 1 5

Sample Output 5

Impossible

Sample Input 6

5
4 3 2 3 4

Sample Output 6

Possible

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn solve(n: &str) -> &str {
    let p = "Possible";
    let i = "Impossible";
    let n: usize = n.parse().unwrap();
    let mut a = String::new();
    std::io::stdin().read_line(&mut a).unwrap();
    let a: Vec<usize> = a.split_whitespace().map(|x|x.parse().unwrap()).collect();
    let &l=a.iter().min().unwrap();
    let &r=a.iter().max().unwrap();
    if n<=r { return i; }
    let mut c = vec![0;n];
    for v in a { c[v]=c[v]+1; }
    if c[l]>2 || l-c[l]+1 != r-l { return i; }
    for &v in c[l+1..r+1].iter() { if v<2 { return i; } }
    p
}
fn main() {
    loop {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right();
        if s=="" { break; }
        println!("{}",solve(&s));
    }
}