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 main() {
	int max=0, min=1000000,maxnum=0,minnum=0;
	int n;
	int s[100005];
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d", &s[i]);
		if (max < s[i])max = s[i];
		if (min > s[i])min = s[i];
	}
	if (max - min >= 2) { printf("No"); return 0; }
	
	for (int i = 0; i < n; i++) {
		if (max == s[i])maxnum++;
		if (min == s[i])minnum++;
	}
	if (max == min && n - maxnum + 1 <= max && (max <= n - maxnum + maxnum / 2 && max + 1 != n)) { printf("No"); return 0; }
	else if (max == min ) { printf("Yes"); return 0; }

	if (n - maxnum + 1 <= max && max <= n - maxnum + maxnum / 2) { printf("Yes"); return 0; }
	else {
		printf("Yes");
	}
}