Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.

You can use the following theorem:

Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.

Constraints

* All values in input are integers.
* 3 \leq N \leq 10
* 1 \leq L_i \leq 100

Input

Input is given from Standard Input in the following format:


N
L_1 L_2 ... L_N


Output

If an N-sided polygon satisfying the condition can be drawn, print `Yes`; otherwise, print `No`.

Examples

Input

4
3 8 5 1


Output

Yes


Input

4
3 8 4 1


Output

No


Input

10
1 8 10 5 8 12 34 100 11 3


Output

No
#include<bits/stdc++.h>
using namespace std;
int main(){
  int i,N;
  cin>>N;
  vector<int> v(N);
  for(i=0;i<N;i++)cin>>v[i];
  if(*max_element(v.begin(),v.end())*2<accumulate(v.begin(),v.end(),0)){
    cout<<"Yes"<<endl;
  }else{
    cout<<"No"<<endl;
  }
}