Problem:
Score : 700 points

Problem Statement

There are N cats.
We number them from 1 through N.

Each of the cats wears a hat.
Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define N 100001
using namespace std;
typedef pair<int,int> P;

int A[N];
int main(){
  int n;
  cin>>n;
  for(int i=0;i<n;i++)cin>>A[i],assert(1<=A[i]&&A[i]<n);
  A[n] = 1e9;
  sort(A,A+n);

  if(A[0] == n-1)cout<<"Yes"<<endl,exit(0);
  if(A[n-1] - A[0] >=2) cout<<"No"<<endl,exit(0);

  int idx = 0;
  while(idx<n && A[idx]==A[idx+1]) idx++;
  if(idx == n-1){
    if(n/A[0] <2) cout<<"No"<<endl,exit(0);
    cout<<"Yes"<<endl,exit(0);
  }
  
  else if(A[idx]==A[idx+1]-1){
    if(idx>0&&A[0] != idx+1) cout<<"No"<<endl,exit(0);
    if(idx>0 && (n-idx-1) < 2) cout<<"No"<<endl,exit(0);
    if(idx==0 && (n-1)/A[0]<2)cout<<"No"<<endl,exit(0);
    for(int i=idx+1;i<n;i++) if(A[idx+1]!=A[i])cout<<"No"<<endl,exit(0);
    cout<<"Yes"<<endl,exit(0);
  }

  cout<<"No"<<endl;
  return 0;
}