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.*;
import java.io.*;

import static java.lang.System.in;

public class Main {
    public static void main(String[] args)throws IOException{
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for(int i=0;i<n;i++) a[i]=sc.nextInt();
        Arrays.sort(a);
        int sum = 0;
        for(int w:a) sum+=w;
        sum-=a[n-1];
        String ans = a[n-1]<sum?"Yes":"No";
        System.out.println(ans);
    }
}
