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: Accepted)

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<ctime>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<cstring>
#include<map>
#include<vector>
#include<set>
#define rep(i,j,k) for(register int i = j; i <= k; i++) 
#define dow(i,j,k) for(register int i = j; i >= k; i--)
#define fi first
#define se second
//#define P pair<ull,ull>
//#define PP pair<int,pair<int,int> >
//#define mp(a,b) make_pair(a,b)
#define ll long long
#define ull unsigned long long
using namespace std;
 
inline int read() { 
	int s = 0, t = 1; char c = getchar();
	while( !isdigit(c) ) { if( c == '-' ) t = -1; c = getchar(); }
	while( isdigit(c) ) s = s * 10 + c - 48, c = getchar();
	return s * t;
}

const int N = 1e5+7, p = 1e9+7;
inline void out() { puts("No"), exit(0); }

int main() {
	int x, minl = N, maxl = 0, n1 = 0, n2 = 0, n = read();
	rep(i,1,n) { 
		x = read();
		if( x < minl ) minl = x, n1 = 1;
		else if( x == minl ) n1++;
		
		if( x > maxl ) maxl = x, n2 = 1;
		else if( x == maxl ) n2++;
	}
	
	if( maxl - minl > 1 ) out();
	if( minl == maxl ) { 
		if( minl != n - 1 && maxl > n / 2 ) out();
	} else { 
		if( n1 >= maxl ) out();
		maxl -= n1;
		if( maxl * 2 > n - n1 ) out();
	}
	puts("Yes");
	return 0; 
}