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.Collections;
import java.util.Comparator;
import java.util.LinkedList;
import java.util.Scanner;

public class Main {


	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		LinkedList<Integer> len = new LinkedList<Integer>();

		// input
		int num = scan.nextInt();
		for(int i = 0; i < num; i++){
			len.add(scan.nextInt());
		}

		// sort
		Collections.sort(len, Comparator.reverseOrder());
		int maxLen = len.poll();

		// sum & avg
		int sum = 0;
		while(len.size() > 0){
			sum += len.poll();
		}

		if(maxLen < sum){
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}


	}
}