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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;


public class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int[] l = new int[n];
        for(int i=0;i<n;i++){
            l[i] = Integer.parseInt(sc.next());
        }
        sort(l, 0, n-1);
        int max = l[0];
        int sum = 0;
        for(int i=1;i<n;i++){
            sum += l[i];
        }
        if(max < sum){
            System.out.println("Yes");
        }else{
            System.out.println("No");
        }
    }

    

    public static void sort(int[] d, int left, int right){
        if(left>=right){return;}
        int p = d[(left + right)/2];
        int l=left, r=right;
        int tmp;
        while(l<r){
            while(d[l]>p){l++;}
            while(d[r]<p){r--;}
            if(l<=r){
                tmp=d[l];
                d[l]=d[r];
                d[r]=tmp;
                l++;r--;
            }
        }
        sort(d, left, r);
        sort(d, l, right);
    }
}