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;
#define ll long long
int main()
{
ll a,b,c,d=0,e=0;
 cin>>a;
    for(ll i=1;i<=a;i++)
    {
    cin>>b;e+=b;d=max(d,b);
    
  }
  e=e-d;
 if(e>d){cout<<"Yes\n";}
    else cout<<"No\n";

}