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, mn = 1e9, mx;
int c[100005];

int main() {
    scanf("%d", &N);
    for (int i = 0, n; i < N; i++) {
        scanf("%d", &n);
        mn = min(mn,n);
        mx = max(mx,n);
        c[n]++;
    }
    if (mx-mn>1) {
        printf("No\n");
        return 0;
    }
    if (mx-mn == 1) {
        int g = mx - c[mn];
        printf("%s\n", g > 0 && c[mx]/g > 1 ? "Yes":"No");
        return 0;
    }

    if (mn == N-1) printf("Yes\n");
    else printf("%s\n", N/mn > 1 ? "Yes":"No");
}