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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
using namespace std;
int main(){
  int n,i,a,c[111],ma=0,mi=111;
  for(i=0;i<n;i++)
    c[i]=0;
  for(i=0;i<n;i++){
    cin>>a;
    c[a]++;
    ma=max(ma,a);
    mi=min(mi,a);
  }
  if(ma%2==0){
    if(mi*2!=ma||c[mi]!=1){
      cout<<"Impossible"<<endl;
      return 0;
    }
    for(i=mi+1;i<=ma;i++){
      if(c[i]<2){
        cout<<"Impossible"<<endl;
      return 0;
      }
    }
    cout<<"Possible"<<endl;
  }
  else{
    if(mi*2!=ma+1||c[mi]!=2){
      cout<<"Impossible"<<endl;
      return 0;
    }
    for(i=mi;i<=ma;i++){
      if(c[i]<2){
        cout<<"Impossible"<<endl;
      return 0;
      }
    }
    cout<<"Possible"<<endl;
  }
}