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 REP(i,n) for(int i=0;i<n;i++)
#define REPP(i,n) for(int i=1;i<=n;i++)
const double PI = acos(-1);
const double EPS = 1e-15;
long long INF=(long long)1E17;
#define i_7 (long long)(1E9+7)
long mod(long a){
    long long c=a%i_7;
    if(c>=0)return c;
    return c+i_7;
}
using namespace std;
bool prime_(int n){
  if(n==1){
    return false;
  }else if(n==2){
    return true;
  }else{
    for(int i=2;i<=sqrt(n);i++){
      if(n%i==0){
        return false;
      }
    }
    return true;
  }
}

long long gcd_(long long a, long long b){
  if(a<b){
    swap(a,b);
  }
  if(a%b==0){
    return b;
  }else{
    return gcd_(b,a%b);
  }
}
 
long long lcm_(long long x, long long y){
  return (x/gcd_(x,y))*y;
}
 
class UnionFind {
    public:
    //各頂点の親の番号を格納する。その頂点自身が親だった場合は-(その集合のサイズ)を入れる。
    vector<int> Parent;
    
    //クラスを作るときは、Parentの値を全て-1にする。
    //以下のようにすると全てバラバラの頂点として解釈できる。
    UnionFind(int N) {
        Parent = vector<int>(N, -1);
    }
    
    //Aがどのグループに属しているか調べる
    int root(int A) {
        if (Parent[A] < 0) return A;
        return Parent[A] = root(Parent[A]);
    }
    
    //自分のいるグループの頂点数を調べる
    int size(int A) {
        return -Parent[root(A)];//先祖をrootで取っておきたい。
    }
    
    //AとBをくっ付ける
    bool connect(int A, int B) {
        //AとBを直接つなぐのではなく、root(A)にroot(B)をくっつける
        A = root(A);
        B = root(B);
        if (A == B) {
            //すでにくっついてるからくっ付けない
            return false;
        }
        
        //大きい方(A)に小さいほう(B)をくっ付けたい
        //大小が逆だったらAとBをひっくり返す。
        if (size(A) < size(B)) swap(A, B);
        
        //Aのサイズを更新する
        Parent[A] += Parent[B];
        //Bの親をAに変更する
        Parent[B] = A;
        
        return true;
    }
};

int main(){
  
  int n;
  cin>>n;
  int a[n];
  int min_v=100'000;
  int max_v=0;
  REP(i,n){
    cin>>a[i];
    min_v = min(min_v, a[i]);
    max_v = max(max_v, a[i]);
  }
  if(max_v-min_v>1){
    cout<<"No"<<endl;
    return 0;
  }
  //max_v-min_vは、0か1
  if(max_v==min_v){
    if(1<=max_v && max_v<=n/2){
      cout<<"Yes"<<endl;
    }else if(max_v==n-1){
      cout<<"Yes"<<endl;
    }else{
      cout<<"No"<<endl;
    }
    return 0;
  }
  //以下max_v-min_vは、1
  int p=0;//唯一の色の帽子をかぶっている猫の数
  int q;
  REP(i,n){
    if(a[i]==min_v){
      p++;
    }
  }
  q = max_v - p;
  if(n-p>=2*q){
    cout<<"Yes"<<endl;
  }else{
    cout<<"No"<<endl;
  }
  return 0;
}