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: Accepted)

#include <iostream>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cassert>
#include <algorithm>
#include <iterator>
#include <string>
#include <vector>
#include <list>
#include <deque>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <queue>
#include <stack>
#include <functional>
#include <utility>
#include <complex>
#include <bitset>
#include <numeric>
using namespace std;

typedef long long LL;  typedef pair<LL, LL> PLL; typedef vector<LL> VLL;
#define REP(i,n) for(int (i)=0; (i)<(n) ;++(i))
#define REPN(i,a,n) FOR((i),(a),(a)+(n))
#define FOR(i,a,b) for(int (i)=(a); (i)<(b) ;++(i))
#define PB push_back
#define MP make_pair
#define OUT(a) cout<<(a)<<endl;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> a(n);
    int d[101]={};
    REP(i,n){
        cin >> a[i];
        d[a[i]]++;
    }

    sort(a.begin(),a.end());
    if(d[a[0]]>2){
        cout << "Impossible" <<endl;
        return 0;
    }
    if(d[a[0]]==1){
        if(a[0]*2<a[n-1]){
        cout << "Impossible" <<endl;
        return 0;
        }
        d[a[0]]--;
        FOR(i,a[0]+1,a[n-1]+1){
            d[i]-=2;
            if(d[i]<0){
                cout << "Impossible" <<endl;
                return 0;
            }
        }
    }else{
        if(a[0]*2-1<a[n-1]){
        cout << "Impossible" <<endl;
        return 0;
        }
        d[a[0]]=0;
        FOR(i,a[0]+1,a[n-1]+1){
            d[i]-=2;
            if(d[i]<0){
                cout << "Impossible" <<endl;
                return 0;
            }
        }
    }
    cout << "Possible" <<endl;

    return 0;
}