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 <bits/stdc++.h>
using namespace std;

int n, a[100010], mx, mn = 1e9;
set<int> ss;

void T_T(){ puts("No"); exit(0); }
void O_O(){ puts("Yes"); exit(0); }

int main(){
	scanf("%d", &n);
	for(int i = 1; i <= n; i++){
		scanf("%d", a + i);
		mx = max(mx, a[i]);
		mn = min(mn, a[i]);
		ss.insert(a[i]);
		if(ss.size() > 2) T_T();
	}
	if(ss.size() == 1){
		if(mx == n - 1 || mx <= n / 2) O_O();
		T_T();
	}
	else{
		if(mx - mn != 1) T_T();
		int c = 0;
		for(int i = 1; i <= n; i++) if(a[i] == mn) c++;
		if(mx - c <= 0 || (n - c) / 2 < mx - c) T_T();
		O_O();
	}
}