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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.stream.Collectors;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    try {
            int numberOfSides = Integer.parseInt(br.readLine());
            List<Integer> sides = new ArrayList<Integer>();
            if (3 <= numberOfSides && numberOfSides <= 10) {
            	List<String> sidesStr = Arrays.asList(br.readLine().split(" ")).stream().collect(Collectors.toList());
            	for(String s : sidesStr) {
            		sides.add(Integer.parseInt(s));
            	}
            	if(sides.size() == numberOfSides && 1 <= sides.iterator().next() && sides.iterator().next() <= 100) {
            	    Collections.sort(sides, Comparator.reverseOrder());
            	    int max = sides.stream().findFirst().get();
            	    int sum = sides.stream().mapToInt(v -> v).filter(v -> v != max).sum();
            	    if(max < sum) {
            	    	System.out.println("Yes");
            	    } else {
            	    	System.out.println("No");
            	    }
            	} else {
                	System.exit(1);
            	}
            } else {
            	System.exit(1);
        	}
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		} catch (NumberFormatException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
}