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;
const int maxn = 1e5 + 100;

int cnt[maxn];

int main() {
    //freopen("input.txt", "r", stdin);
    int n;
    cin >> n;
    int x, m = -1;
    for (int i = 0; i < n; i++) {
        cin >> x;
        cnt[x]++;
        m = max(m, x);
    }
    if ((cnt[m] == n && m == n - 1) ||
        (cnt[m] + cnt[m - 1] == n && cnt[m - 1] <m &&
         (m - cnt[m - 1]) * 2 <= cnt[m]))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}