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: Runtime Error)

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {

  long long int n;
  cin >> n;

  vector< long long int > a;
  for ( long long int i = 0; i < n; i++ ) {
    long long int in;
    cin >> in;
    a.push_back( in );
  }

  sort( a.begin(), a.end() );

  if ( a[n-1] - a[0] >= 2 ) {
    cout << "No" << endl;
    return 0;
  }

  if ( a[n-1] - a[0] == 0 ) {
    if ( n == a[0] + 1 ) {
      cout << "Yes" << endl;
      return 0;
    }
    if ( n >= a[0] * 2 ) {
      cout << "Yes" << endl;
      return 0;
    }
    cout << "No" << endl;
    return 0;
  }
  a[-1] = 0;
  long long int cnt = 0;
  for ( long long int i = 0; i < n; i++ ) {
    if ( a[i] != a[0] ) break;
    cnt++;
  }

  if ( cnt >= 2 ) {
    cout << "No" << endl;
    return 0;
  }
  if ( n <= a[0] * 2 ) {
    cout << "No" << endl;
    return 0;
  }

  cout << "Yes" << endl;
  return 0;

}