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 Ruby (2.3.3) (judge verdict: Accepted)

#!/usr/bin/ruby

def solve(_, ls)
  max = -1
  sum = 0
  ls.each do |l|
    sum += l
    if l > max
      max = l
    end
  end
  sum -= max
  if max < sum
    "Yes"
  else
    "No"
  end
end

def each_case(sin)
  while ln = sin.gets
    n = ln.chomp.to_i
    ls = sin.gets.chomp.split(" ").map(&:to_i)
    yield n, ls
  end
end

each_case(STDIN) do |n, ls|
  puts solve(n, ls)
end