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<bits/stdc++.h>
#define N (1001)
using namespace std;
int n,a[N],Keg[N],maxn;
int main()
{
	scanf("%d",&n);
	for (int i=1; i<=n; ++i)
	{
		scanf("%d",&a[i]);
		Keg[a[i]]++; maxn=max(maxn,a[i]);
	}
//	for (int i=(maxn+1)/2; i<=maxn; ++i)
//	{
//		if (maxn%2==0 && i==(maxn+1)/2) Keg[i]-=1;
//		else Keg[i]-=2;
//		if (Keg[i]<0){puts("Impossible"); return 0;}
//	}
//	for (int i=1; i<=maxn/2; ++i)
//		if (Keg[i]) {puts("Impossible"); return 0;}
	puts("Impossible"); return 0;
}