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<stdio.h>
int main()
{

int n,C,i,sum=0,max;
scanf("%d",&n);
int A[n];
for(i=0;i<n;i++)
{
scanf("%d",&A[i]);
sum=sum+A[i]; 
}
max=A[0];
for(i=1;i<n;i++)
{
  if(max<A[i])
  max=A[i];
}
C=sum-max;
if(C>max) printf("Yes\n");
else printf("No\n");
return 0;

}