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.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using System.Collections;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var ir = new Resolver(new ConsoleReader());
            Console.WriteLine(ir.Resolve());
        }
    }

    public class Resolver
    {
        IInputReader InputReader { get; }
        public List<string> Messages { get; set; } = new List<string>();

        int n;
        int[] input;

        public void ParseLines()
        {
            n = int.Parse(InputReader.ReadLine());
            input = InputReader.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        }

        public string Resolve()
        {
            var max = input.ToList().OrderBy(x => -x).ToList();
            if (max[0] < max.GetRange(1, n - 1).Sum()) return "Yes";

            return "No";
        }


        public Resolver(IInputReader inputReader)
        {
            InputReader = inputReader;
            ParseLines();
        }

    }

    public interface IInputReader
    {
        string ReadLine();
    }

    class ConsoleReader : IInputReader
    {
        string IInputReader.ReadLine()
        {
            return Console.ReadLine();
        }
    }
}