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;
bool f(int m, int M, int cnt, int N)
{
    if (m == M) {
        return N >= m*2 || m == N-1;
    } else if (m + 1 == M) {
        return cnt < M && cnt + (M - cnt) * 2 <= N;
    } else {
        return false;
    }
}

int main()
{
    int N; cin >> N;
    vector<int> A(N); for (auto& a : A) cin >> a;
    sort(begin(A), end(A));
    int m = A[0], M = A[N-1];
    int cnt = count(begin(A), end(A), m);
    cout << (f(m, M, cnt, N) ? "Yes" : "No") << endl;
    return 0;
}