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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#define trade(a,b)      (a)+=(b);(b)=(a)-(b);(a)-=(b);
main(){
        int N,ln=1,hn=1,l=-1,h=-1,tmp,i;
        scanf("%d",&N);
        for(i=0;i<N;i++){
                scanf("%d",&tmp);
                if(tmp==l)
                        ln++;
                else{
                        if(tmp==h)
                                hn++;
                        else if(l==-1)
                                l=tmp;
                        else if(h==-1){
                                h=tmp;
                                if(h<l){
                                        trade(h,l);
                                        trade(hn,ln);
                                }
                        }else{
                                puts("No");
                                return 0;
                        }
                }
        }
        if(l+1==h && ln+1<=h && h<=ln+hn/2){
                puts("Yes");
        }else if(ln==N && (l<=N/2 || l==N-1)){
                puts("Yes");
        }else{
                puts("No");
        }
        return 0;
}