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 static System.Console;
using static System.Math;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TemplateAlgorithm
{
    class Program
    {
        public const long Inf = (long)1e18;
        public const double eps = 1e-6;
        public const string alfa = "abcdefghijklmnopqrstuvwxyz";
        public const string ALFA = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const int MOD = 1000000007;
        
        // c ot i
        static int ToInt(char c) => c - '0';

        static void Main(string[] args)
        {
            int N = IO.ReadInt();
            int[] H = IO.ReadIntArr();
            Array.Sort(H);
            int other = H.Take(N - 1).Sum();
            int longest = H.Max();

            if (longest < other) WriteLine("Yes");
            else WriteLine("No");
        }

        #region  範囲

        public static bool InRange<T>(T begin, T end, T value) where T : IComparable<T> 
            => value.CompareTo(begin) >= 0 && value.CompareTo(end) <= 0;

        #endregion

        #region MIN,MAX

        /// <summary>
        /// 最大値を返す
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="vals"></param>
        /// <returns></returns>
        public static T MaxValue<T>(params T[] vals) => vals.Max();

        /// <summary>
        /// 最小値を返す
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="vals"></param>
        /// <returns></returns>
        public static T MinValue<T>(params T[] vals) => vals.Min();
        #endregion
    }

    #region IO

    /// <summary>
    /// IO
    /// </summary>
    public class IO
    {
        public static string ReadStr(bool isTrim = false) => (isTrim) ? ReadLine().Trim() : ReadLine();
        public static int ReadInt() => int.Parse(ReadStr());

        public static long ReadLong() => long.Parse(ReadStr());

        public static decimal ReadDecimal() => decimal.Parse(ReadStr());
        public static double ReadDouble() => double.Parse(ReadStr());
        public static string[] ReadStrArr(char separator = ' ') => ReadLine().Split(separator);
        public static int[] ReadIntArr() => Array.ConvertAll(ReadStrArr(), int.Parse);
        public static long[] ReadLongArr() => Array.ConvertAll(ReadStrArr(), long.Parse);

        public static decimal[] ReadDecimalArr() => Array.ConvertAll(ReadStrArr(), decimal.Parse);
        public static double[] ReadDoubleArr() => Array.ConvertAll(ReadStrArr(), double.Parse);        
    }

    #endregion    
}