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: Wrong Answer)

#include<stdio.h>
int max(int *A, int n) {
    int i;
    int max = 0;
    for(i = 0; i < n; i++) {
        if(max < A[i]) {
            max = A[i];
        }
        i++;
    }
    return max;
}

int min(int *A, int n) {
    int i=0;
    int min = 1000000000;
    for(i = 0; i < n; i++) {
        if(min > A[i]) {
            min = A[i];
        }
        i++;
    }
    return min;
}

int count(int *A, int n, int t) {
    int count=0;
    for(int i = 0; i < n; i++) {
        if(A[i] == t) {
            count++;
        }
    }
    return count;
}

int main(void) {
    int n;
    int i;
    scanf("%d", &n);
    int a[n];
    for(i = 0; i < n; i++) {
        scanf("%d", &a[i]);
    }
    if(max(a,n) - min(a,n) >=2) {
        printf("No");
        return 0;
    }
    if(max(a,n) - min(a,n) == 0) {
        if(a[0] == n-1 || 2*a[0] <= n) {
            printf("Yes");
        } else {
            printf("No");
        }
    }
    if(max(a,n) - min(a,n) == 1) {
        if(count(a,n,min(a,n)) < n && (max(a,n) - count(a,n,min(a,n)))*2 <= count(a,n,max(a,n))) {
            printf("Yes");
        } else {
            printf("No");
        }
    }
    return 0;
}