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: Accepted)

#include <bits/stdc++.h>

using namespace std;

int main() {
  int N;
  cin >> N;

  vector<int> a(N);
  for(int i = 0; i < N; i++) {
    cin >> a[i];
  }

  int mi = a[0], ma = a[0];

  for(int i = 0; i < N; i++) {
    mi = min(mi, a[i]);
    ma = max(ma, a[i]);
  }

  if(ma - mi > 1) {
    cout << "No" << endl;
    return 0;
  }

  if(ma == mi) {
    int x = ma;
    if(x == N - 1) {
      cout << "Yes" << endl;
      return 0;
    }

    if(N >= x * 2) {
      cout << "Yes" << endl;
      return 0;
    }

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

  }

  int x = ma;

  int b = 0;

  for(int i: a) {
    if(i == ma) {
      b += 1;
    }
  }

  if((N - b) + 1 <= x && x <= (N - b) + b / 2){
    cout << "Yes" << endl;
    return 0;
  }

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

}