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.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#include <iostream>
#include <vector>
#include <string>
#include <queue>

using namespace std;

bool solve(const vector<int>& a){
	const int N = a.size();
	vector<int> cnt(N+1, 0);
	for(auto& t : a) ++cnt[t];
	for(int c=1;c<=N;c++){
		if(cnt[c]+cnt[c-1] != N) continue;
		int restColor = c - cnt[c-1];
		if(restColor < 0) continue;
		if(cnt[c] > 0){
			if(restColor == 0) continue;
			if(cnt[c] < 2 * restColor) continue;
		}
		return true;
	}
	return false;
}

int main(){
	int N;
	while(cin >> N){
		vector<int> a(N);
		for(auto& t : a) cin >> t;
		cout << (solve(a) ? "Yes" : "No") << endl;
	}
}
