Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  
  integer :: n,i,j,a(10) = 0,t,s=0
  
  read(*,*)n
  read(*,*)(a(i), i = 1, n)
  do i=1,N-1
     do j=i+1,N
        if(a(i) .gt. a(j))then
           t=a(i)
           a(i)=a(j)
           a(j)=t
        end if
     end do
  end do
  
  do i = 1, n-1
    s = s + a(i)
  end do
  
  if (a(n) < s) then
    write(*,*)'Yes'
  else
    write(*,*)'No'
  end if
end program main