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

#include<bits/stdc++.h>
using namespace std;
int read(){
	int c=0,nx,sign=1;
	do{
		nx=getchar()-'0';
		if(nx=='-'-'0')
			sign=-1;
	}while(nx<0 or nx>9);
	while(nx>=0 and nx<=9){
		c=c*10+nx;
		nx=getchar()-'0';
	}
	return sign*c;
}
const int N=200;
int a[N],len,cnt[N];
char s[2][30]={"Possible","Impossible"};
int main(){
	int n=read();
	for(int i=1;i<=n;i++){
		a[i]=read();
		len=max(len,a[i]);
		++cnt[a[i]];
	}
	if(len%2==0){
		if(cnt[len>>1]!=1){
			puts(s[1]);
			return 0;
		}
	}else if(cnt[len>>1]){
		puts(s[1]);
		return 0;
	}
	for(int i=len;i>len/2;i--)
		if(cnt[i]<2){
			puts(s[1]);
			return 0;
		}
	for(int i=1;i<len>>1;i++)
		if(cnt[i]){
			puts(s[1]);
			return 0;
		}
	puts(s[0]);
}