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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	static BufferedReader reader;
	
	public static void main(String[] args){
		reader = new BufferedReader(new InputStreamReader(System.in));
		String[] argA = readLine().split(" ");
		if(argA.length<1){return;}
		try{
			int N = Integer.parseInt(argA[0]);
			String[] argB = readLine().split(" ");
			if(argB.length!=N){return;}
			int[] L = new int[N];
			for(int i=0;i<N;i++){
				L[i]=Integer.parseInt(argB[i]);
			}
			for(int i=0;i<N;i++){
				int sum_other = 0;
				for(int j=0;j<N;j++){
					if(j==i){continue;}
					sum_other+=L[j];
				}
				if(L[i]>=sum_other){System.out.print("No");return;}
			}
			System.out.print("Yes");return;
		}catch(Exception e){
			e.printStackTrace();
		}
		return;
	}

	private static String readLine(){
		//BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		try{
			return reader.readLine();
		}catch(Exception e){
			return e.getMessage();
		}
	}
}