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: Runtime Error)

/*
* Author. Silviase(@silviasetitech)
* For AtCoder
*/

import java.util.*;
import java.lang.*;
import java.math.*;


public class Main {
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
        int[] ar = new int[n];
        intArrayScan(ar);
        Arrays.sort(ar);
        int sum = 0;
        for (int i = 0; i < n-1; i++) {
            sum += ar[i];
        }
        if (sum > ar[n-1]) {
            System.out.println("Yes"); 
        } else {
            System.out.println("No");
        }

        sc.close();

    }

    public static void intArrayScan(int[] array) {
        Scanner sc = new Scanner(System.in);
        for (int i = 0; i < array.length; i++) {
            array[i] = sc.nextInt();
        }
        sc.close();
    }

    public static void intArrayPrint(int[] array) {
        for (int i = 0; i < array.length; i++) {
            System.out.println(array[i]);
        }
    }

    public static void intSquareArrayScan(int[][] array, int h, int w) {
        Scanner sc = new Scanner(System.in);
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                array[i][j] = sc.nextInt();
            }
        }
        sc.close();
    }

    public static void intArrayListScan(List<Integer> list, int n) {
        Scanner sc = new Scanner(System.in);
        for (int i = 0; i < n; i++) {
            list.add(sc.nextInt());
        }
        sc.close();
    }

    public static void intArrayListPrint(List<Integer> list) {
        for (int i = 0; i < list.size(); i++) {
            System.out.println(list.get(i));  
        }
    }
}