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>
using namespace std;

int main(){
  int N;
  cin >> N;
  vector<int> a(N);
  int loop,isTrue=1;
  cin >> a[0];
  int Max=a[0],Min=a[0];
  for(loop=1;loop<N;loop++){
    cin >> a[loop];
    if(Max<a[loop]){
      Max=a[loop];
    }else if(Min>a[loop]){
      Min=a[loop];
    }
  }
  if(Max-Min>1){
    isTrue=0;
  }else if(Max-Min){
    int colorable=Max-1;
    //人と完全に違う色を被った猫はMax-1匹以下であることが保証される
    //countの値はcolorable以下でなければならない
    int count=0;
    for(loop=0;loop<N;loop++){
      if(a[loop]==Min)
        count++;
    }
    if(colorable<count)
      isTrue=0;
  }else{
    if(N-Max!=1&&N/2<Max){
      isTrue=0;
    }
  }
  if(isTrue){
    cout << "Yes" << endl;
  }else{
    cout << "No" << endl;
  }
  return 0;
}