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>

int main() {
    int n, x = 1000000, y = 0;
    std::cin >> n;
    std::vector<int> a(n);
    std::map<int, int> cs;
    for (int i = 0; i < n; i++) {
        std::cin >> a[i];
        cs[a[i]]++;
        x = std::min(x, a[i]);
        y = std::max(y, a[i]);
    }

    bool ret;
    if (x == y) {
        ret = x == n - 1 || n / x > 1;
    } else if (y - x == 1) {
        ret = y > cs[x] && 2 * (n - y) >= cs[y];
    } else {
        ret = false;
    }

    std::cout << (ret ? "Yes" : "No") << std::endl;

    return 0;
}