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 Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

object Main{
  def main(args: Array[String]): Unit = {
    val sc: Scanner = new Scanner(System.in)
    sc.nextLine

    val sortedSides: Array[Int] = sc.nextLine.split(" ").map(_.toInt).sorted
    val maxSide: Int = sortedSides(sortedSides.length - 1)
    if (maxSide < sortedSides.slice(0, sortedSides.length - 1).sum) println("Yes")
    else println("No")
  }
}