Contest Duration: - (local time) (110 minutes) Back to Home
C - Tree Restoring /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

これを満たす木が存在するか判定してください。

### 制約

• 2 ≦ N ≦ 100
• 1 ≦ a_i ≦ N-1

### 入力

N
a_1 a_2 ... a_N


### 入力例 1

5
3 2 2 3 3


### 出力例 1

Possible


### 入力例 2

3
1 1 2


### 出力例 2

Impossible


### 入力例 3

10
1 2 2 2 2 2 2 2 2 2


### 出力例 3

Possible


### 入力例 4

10
1 1 2 2 2 2 2 2 2 2


### 出力例 4

Impossible


### 入力例 5

6
1 1 1 1 1 5


### 出力例 5

Impossible


### 入力例 6

5
4 3 2 3 4


### 出力例 6

Possible


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