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>
#include <stdlib.h>
#include <math.h>
#include <string.h>

#define mod 1e9+7
#define ll long long int
#define epsilon 1e-7

int compare_int(const void *a, const void *b){
	int *A = (int *)a;
	int *B = (int *)b;
    return *A - *B;
}

int main(void){
    int n;
    scanf("%d", &n);
    int a[n];
    for(int i = 0;i < n;i++)scanf("%d", &a[i]);
    qsort(a, n, sizeof(int), compare_int);
    int small = a[0];
    int big = a[n-1];
    if(big - small > 1)printf("No\n");
    else if(big - small == 0){
        if(small == n-1 || n/2 >= small)printf("Yes\n");
        else printf("No\n");
    }else{
        int count = 0;
        while(1){
            count++;
            if(a[count] != small){
                break;
            }
        }
        if(count > small || (n-count)/2 + count < big)printf("No\n");
        else printf("Yes\n");
    }
    return 0;
}