Problem Statement

 

Aoki loves numerical sequences and trees.

One day, Takahashi gave him an integer sequence of length N, a₁,a₂,…,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:

Na1 a2 … aN

Output

 

If there exists a tree that satisfies the condition, print Possible. Otherwise, print Impossible.

Sample Input 1

 

53 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

 

31 1 2

Sample Output 2

 

Impossible

Sample Input 3

 

101 2 2 2 2 2 2 2 2 2

Sample Output 3

 

Possible

Sample Input 4

 

101 1 2 2 2 2 2 2 2 2

Sample Output 4

 

Impossible

Sample Input 5

 

61 1 1 1 1 5

Sample Output 5

 

Impossible

Sample Input 6

 

54 3 2 3 4

Sample Output 6

 

Possible     把直径构造出来，然后讨论讨论就好了

#include
     
      #define ll long longusing namespace std;const int maxn=205;int cnt[maxn],n,now,M;int main(){	scanf("%d",&n);	for(int i=1;i<=n;i++){		scanf("%d",&now);		M=max(M,now);		cnt[now]++;	}		for(int i=M;i>M-i;i--) 	    if(cnt[i]<2){ puts("Impossible"); return 0;}		if(!(M&1)&&cnt[M>>1]!=1){ puts("Impossible"); return 0;}	if((M&1)&&cnt[M-(M>>1)]!=2){ puts("Impossible"); return 0;}		puts("Possible");	return 0;}