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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;

int a[100000];
int main() {
	int n; scanf("%d", &n);
	int Min = INT_MAX, Max = 0;
	rep(i, n) {
		scanf("%d", &a[i]);
		Min = min(Min, a[i]);
		Max = max(Max, a[i]);
	}
	if (Min != Max) {
		if (Max - Min > 1) {
			puts("No"); return 0;
		}
		int cnt = 0;
		rep(i, n) {
			if (Min == a[i])cnt++;
		}
		//色の数はcnt+b
		if(Max-cnt&&(n-cnt)/(Max-cnt)>=2)puts("Yes");
		else puts("No");
		return 0;
	}
	if (n / a[0] >= 2) {
		puts("Yes"); return 0;
	}
	if (n == a[0] + 1) {
		puts("Yes"); return 0;
	}
	puts("No");
}