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 a[100005];
int main() {
  int n;
  scanf("%d", &n);
  int ans = 123456;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    ans = min(ans, a[i]);
  }
  int cnt = 0;
  bool ok = true;
  for (int i = 0; i < n; i++) {
    ok &= a[i] <= ans + 1;
    if (a[i] == ans) {
      cnt++;
    }
  }
  if (cnt == n) {
    if (ans == n - 1 || ans * 2 <= n) {
      printf("Yes\n");
    } else {
      printf("No\n");
    }
    return 0;
  }
  int add = ans - cnt;
  ok &= ans >= cnt;
  ok &= add <= (n - cnt) / 2;
  ok &= ans + 1 <= n - 1 - add;
  if (ok) {
    printf("Yes\n");
  } else {
    printf("No\n");
  }
  return 0;
}