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;

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

        var d = new int[n];
        var s = Console.ReadLine().Split(' ');
        for (int i = 0; i < n; i++)
        {
            d[i] = int.Parse(s[i]);
        }

        var max_i = 0;
        var sum = 0;
        for (int i = 0; i < n; i++)
        {
            sum += d[i];
            if (d[max_i] < d[i])
            {
                max_i = i;
            }
        }

        if (d[max_i] < sum - d[max_i]) Console.WriteLine("Yes");
        else Console.WriteLine("No");
    }
}