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 cxxio() {
    ios::sync_with_stdio(false);
    cin.tie(0);
}

void print(bool ok) {
    cout<<(ok? "Yes\n":"No\n");
    exit(0);
}

int main() {
    cxxio();
    int n;
    cin>>n;
    map<int, int> m;
    for (int x; cin>>x; ++m[x]);
    int lo=m.begin()->first;
    int hi=m.rbegin()->first;
    if (lo==hi) print(2*hi<=n || hi==n-1);
    else print(lo==hi-1 && m[lo]<hi && 2*hi-m[lo]<=n);
}
