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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

/**
 * メインクラス
 *
 */
public class Main {

	/**
	 * メインメソッド
	 * @param args
	 * @throws IOException
	 */
	public static void main(String[] args) throws IOException {

		// 標準入力を取得
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine();

		long N = Long.parseLong(line);

		List<Long> ls = new ArrayList<Long>();
		line = br.readLine();
		for (String s : line.split(" ")) {
			ls.add(Long.valueOf(s));
		}
		Collections.sort(ls);

		long max = ls.get(ls.size() - 1);
		long others = 0;

		for (int i = 0; i < ls.size() - 1; i++) {
			others += ls.get(i);
		}

		if (max < others) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}

	}
}