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>

int main(void)
{
	int N;
	int a[100000];

	int max;
	int cnt, mcnt;

	int i;

	scanf("%d", &N);
	for (i = 0; i < N; i++){
		scanf("%d", &a[i]);
	}
	
	max = 1;
	for (i = 0; i < N; i++){
		if (a[i] > max) max = a[i];
	}

	cnt = 0;
	mcnt = 0;
	for (i = 0; i < N; i++){
		if (a[i] < max - 1) break;
		if (a[i] == max - 1) cnt++;
		else mcnt++;
	}

	if (i < N) {
		puts("No");
	} else if (max == N - 1 && mcnt == N){
		puts("Yes");
	} else if (cnt <= max - 1 && cnt >= max * 2 - N){
		puts("Yes");
	} else {
		puts("No");
	}

	return 0;
}