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`.

Examples

Input

4
3 8 5 1


Output

Yes


Input

4
3 8 4 1


Output

No


Input

10
1 8 10 5 8 12 34 100 11 3


Output

No

import java.util.Arrays;
import java.util.Scanner;

public class Main {

	static Scanner in = new Scanner(System.in);

	public static void main(String[] args) {
		int N = in.nextInt();
		int[] L = new int[N];
		for (int i = 0; i < N; i++) {
			L[i] = in.nextInt();
		}
		int max = Arrays.stream(L).max().getAsInt();
		int sum = Arrays.stream(L).sum();
		String ans = max < (sum - max) ? "Yes" : "No";
		System.out.println(ans);
	}
}
