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 = 100 * 1000 + 23;








int n, a[MAXN];


int main() {
    cin >> n;
    for (int i = 0; i < n; i++) cin >> a[i];
    int mx = *max_element(a, a + n), mn = *min_element(a, a + n), x = count(a, a + n, mx), y = count(a, a + n, mn);
    if (mx - mn > 1) return cout << "No", 0;
    if (mx == mn) return cout << ((mx <= n / 2 || mx == n - 1)? "Yes": "No"), 0;
    if (mx >= y + 1 && mx <= y + x / 2)
        return cout << "Yes", 0;
    cout << "No";
    return 0;
}