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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtcoderTemplateForCSharp
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());

            var sides = Console.ReadLine()
                .Split(' ')
                .Select(int.Parse);

            var sortedSides = sides.OrderBy(side => side);

            // 実装1（愚直に。遅いと思ったらこっちのほうが速かった。）
            //if (sortedSides.Last() < sortedSides.Sum() - sortedSides.Last())
            //{
            //    Console.WriteLine("Yes");
            //}
            //else
            //{
            //    Console.WriteLine("No");
            //}

            // 実装2（こっちのほうが効率がいいかも？実際はこっちのほうが遅かった。範囲を足し合わせる処理があるから？）
            if (sortedSides.Last() < sortedSides.Take(sortedSides.Count() - 1).Sum())
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
        }
    }
}