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 <iostream>
#include <algorithm>
using namespace std;
#define MAX (int)1e5
#define FAIL { cout << "No\n"; return 0; }
int a[MAX], N;

int solve(int k) {
    int comp = 0, rem = 0, i;
    for (i = 0; i < N; i++) {
        if (a[i] < k) comp++;
        else rem++;
    }
    k -= comp;
    if (rem/2 < k || rem == 1) return 0;
    return (k >= 0 && !(k == 0 && rem > 0));

}

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

    int diff = a[N-1]-a[0];
    if (diff > 1) FAIL;
        
    int res;
    if (diff == 1) res = solve(a[N-1]);
    else res = max(solve(a[N-1]), solve(a[N-1]+1));
    cout << (res ? "Yes\n" : "No\n");
}