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;
#define int long long
const int MOD = 1000000007;
struct edge {int from,to,cost;};

signed main() {
int n;
cin>>n;
int a[n];
for(int i=0;i<n;i++)cin>>a[i];
int amax=0;for(int i=0;i<n;i++)amax=max(amax,a[i]);
int b=0;
for(int i=0;i<n;i++){
    if(a[i]==amax){
        b++;
        continue;
    }
    if(a[i]!=amax-1){
        cout<<"No";
    return 0;
    }
    
}
if(b==1){
    cout<<"No";
    return 0;
}

if(amax>(n-b)+b/2||amax<(n-b)+1){
    if(n!=b||b!=amax+1){
        cout<<"No";
        return 0;
    }
}
cout<<"Yes";
return 0;
}
