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 Python (2.7.6) (judge verdict: Accepted)

p = "Possible"
imp = "Impossible"

n = int(raw_input())
a = map(int, raw_input().split())
mx = max(a)
mn = min(a)
if mx == 1 and  mn == 1:
    if n == 2:
        print p
        exit()
    else:
        print imp
        exit()
cnt = [0] * 100
for i in xrange(n):
    cnt[a[i]] += 1
if mx % 2 == 0:
    if mx / 2 != mn:
        print imp
        exit()
    if cnt[mn] != 1:
        print imp
        exit()
    for i in xrange(mn + 1, mx + 1):
        if cnt[i] < 2:
            print imp
            exit()

else:
    if mx / 2 + 1 != mn:
        print imp
        exit()
    if cnt[mn] != 2:
        print imp
        exit()
    for i in xrange(mn + 1, mx + 1):
        if cnt[i] < 2:
            print imp
            exit()
print p