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>

#define mp make_pair
#define pb push_back

using namespace std;

typedef int32_t i32;
typedef uint32_t u32;
typedef int64_t i64;
typedef uint64_t u64;
typedef pair<int,int> pii;
typedef vector<int> vi;

const int MAX_N = 100000;
int n;
int a[MAX_N];

int main()
{
  cin >> n;
  for (int i = 0; i < n; i++)
    cin >> a[i];

  int min_a = *min_element(a, a+n);
  int max_a = *max_element(a, a+n);

  if (max_a - min_a > 1) {
    cout << "No" << endl;
  } else if (max_a - min_a == 0) {
    if (all_of(a,a+n,[](int x) { return 2*x <= n; } ))
      cout << "Yes" << endl;
    else if (all_of(a,a+n,[](int x) { return x == n-1; }))
      cout << "Yes" << endl;
    else
      cout << "No" << endl;
  } else {
    int alone = 0, not_alone = 0;
    for (int i = 0; i < n; i++)
      if (a[i] == max_a-1) alone++;
      else not_alone++;
    if (alone < max_a && 2*(max_a-alone) <= not_alone)
      cout << "Yes" << endl;
    else
      cout << "No" << endl;
  }
  return 0;
}