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>

using namespace std;

int n, k;
int a[212345];
int cnt[212345];

int main() {
                                               

	cin >> n;                                                                         
	for(int i = 1; i <= n; i++) {
	cin >> a[i]; 
	cnt[a[i]]++;
	}

	sort(a + 1, a + n + 1);
	if(a[1] * 2 < a[n]) return cout << "Impossible", 0;

	if(cnt[1]>1)return cout << "Impossible", 0;

	for(int i = n; i <= n; i++)
		if(a[i]!=1&&cnt[a[i]]<2)return cout << "Impossible", 0;
	if(a[1] == a[n] && n > 2) return cout << "Impossible", 0;
	cout << "Possible";
	return 0;
}