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: Accepted)

#include <bits/stdc++.h>
using namespace std;

int n,m,a[100010];

void work()
{
	scanf("%d",&n);
	for (int i=1,x; i<=n; i++)
		scanf("%d",&x),m=max(m,x),a[x]++;
	for (int i=m/2+1; i<=m; i++)
		if (a[i]<2)  puts("Impossible"),exit(0);
		else  a[i]-=2;
	if (!(m&1))
		{
			if (a[m/2]!=1)  puts("Impossible"),exit(0);
			a[m/2]=0;
		}
	for (int i=1; i<=(m+1)/2; i++)  if (a[i])  puts("Impossible"),exit(0);
	puts("Possible");
}

int main()
{
	work();
	return 0;
}