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: Wrong Answer)

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);

		int corner = scanner.nextInt();
		List<Integer> sideLengthList = new ArrayList<Integer>();

		while(scanner.hasNext()) {
			sideLengthList.add(scanner.nextInt());
		}

		Collections.sort(sideLengthList);
		int maxSideLength = sideLengthList.get((sideLengthList.size() -1));
		sideLengthList.remove((sideLengthList.size() -1));

		int totalLength = 0;
		for(int sideLength : sideLengthList) {
			totalLength += sideLength;
		}

		String result = (maxSideLength < totalLength) ? "YES" : "NO";

		System.out.println(result);
		
		scanner.close();
	}

}