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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

bool check(const vector<int>& a){
    const int N = a.size();
    int m = *min_element(a.begin(), a.end());
    int M = *max_element(a.begin(), a.end());
    if(M - m > 1) return false;
    if(M == m){
        return M == N-1 || 2*M <= N;
    }
    auto c = count_if(a.begin(), a.end(), [&](int t){ return t == m; });
    return c <= m && c + 2 * (M-c) <= N;
}

int main(){
    int N; cin >> N;
    vector<int> a(N);
    for(auto& t : a) cin >> t;
    cout << (check(a) ? "Yes" : "No") << endl;
}