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;

void success(){
    cout << "Yes" << endl;
    exit(0);
}
void fail(){
    cout << "No" << endl;
    exit(0);
}

int main(){
    int N;
    cin >> N;
    vector<int> A(N);
    for(int i=0; i<N; i++) cin >> A[i];
    sort(A.begin(), A.end());
    if(A[N-1] - A[0] >= 2) fail();
    if(A[0] == A[N-1] && A[0] == N-1) success();

    int one = 0;
    for(int i=0; i<N; i++) if(A[i] != A[N-1]) one++;
    int more_cat = N - one;
    int more_col = A[N-1] - one;
    if(more_col <= 0) fail();
    if(more_cat < 2*more_col) fail();
    success();
}