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.*;
class Main {
    public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	int N = sc.nextInt();
	int[] l = new int[N];
	int max = 0;
	int maxI = 0;
	for(int i = 0; i<N; i++) {
	    l[i] = sc.nextInt();
	    if(max < l[i]) {
		max = l[i];
		maxI = i;
	    }
	}
	int others = 0;
	for(int i = 0; i<N; i++) {
	    if(i == maxI) continue;
	    others += l[i];
	}
	if(others > max) {
	    System.out.println("Yes");
	}else {
	    System.out.println("No");
	}
    }
}