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 <bits/stdc++.h>

#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define ll long long
#define INF 999999999
#define MOD 1000000007

using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

int iy[]={0, 0, 1, -1};
int ix[]={1, -1, 0, 0};

int n, a[100010], ma, cou[2];
int main(){
	cin >> n;
	for(int i=0;i<n;i++){
		cin >> a[i];
		ma = max(ma, a[i]);
	}
	for(int i=0;i<n;i++){
		if(ma==a[i]){
			cou[0]++;
		}else if(ma==a[i]+1){
			cou[1]++;
		}else{
			cout << "No" << endl;
			return 0;
		}
	}
	if(cou[1]==0){
		if(n>=ma*2||ma==n-1){
			cout << "Yes" << endl;
		}else{
			cout << "No" << endl;
		}
	}else{
		if(cou[0]>=2*(ma-cou[1])&&cou[1]<=ma-1){
			cout << "Yes" << endl;
		}else{
			cout << "No" << endl;
		}
	}

	return 0;
}