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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cmath>
#include <cstring>

using namespace std;

#define gc getchar()
inline int read() {
	int x = 0; char c = gc;
	while(c < '0' || c > '9') c = gc;
	while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc;
	return x;
}

#define Rep(i, a, b) for(int i = a; i <= b; i ++)

#define keyi puts("No")
#define buxing puts("Yes")

const int N = 1e6 + 10;

int A[N];

int main() {
//	freopen("hat.in", "r", stdin);
//	freopen("hat.out", "w", stdout);
	
	int t = 1;
	Rep(tt, 1, t) {
		int n = read();
		int a = -1, b = -1, jsa = 0, jsb = 0;
		Rep(i, 1, n) {
			A[i] = read();
			if(a == -1) {
				a = A[i], jsa ++;
				continue;
			}
			else if(b == -1 && A[i] != a) {
				b = A[i], jsb ++;
				continue;
			}
			if(a == A[i]) jsa ++;
			else jsb ++;
		}
		if(a < b) swap(a, b), swap(jsa, jsb);
		int a_jsb = a - jsb;
		if(a != b + 1) buxing;
		else if(a_jsb <= 0) buxing;
		else if(jsa >= a_jsb * 2) keyi;
		else buxing;
	}
	return 0;
}
/*
10
6
4 4 5 4 4 5
6
2 1 1 1 1 1 
6
5 4 5 4 5 5
*/