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, mx, mn = INT_MAX;
vector<int> a;
bool check() {
	if(mx == mn) return mx <= n/2 || mx == n-1;
	int cntmx = 0, cntmn = 0;
	for(int i = 0; i < n; i++) {
		cntmx += a[i] == mx;
		cntmn += a[i] == mn;
	}
	int mx_groups = cntmx >> 1;
	return mx_groups+cntmn >= mx && !(cntmx && mx-cntmn <= 0);
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n;
	for(int i = 0, x; i < n; i++) {
		cin >> x;
		mx = max(x, mx);
		mn = min(x, mn);
		a.push_back(x);
	}
	if(mx-mn > 1) cout << "No", exit(0);
	else cout << (check() ? "Yes" : "No");
}
