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.io.*;
import java.util.*;
import java.math.BigInteger;
public class Main {
static  Scanner sc = new Scanner(System.in);


public static void main(String[] args) {

int N=Integer.parseInt(sc.nextLine());

String[] nyu=sc.nextLine().split(" ");
int[] num=new int[nyu.length];

for(int i=0;i<nyu.length;i++){
num[i]=Integer.parseInt(nyu[i]);
}
Arrays.sort(num);
int min=0;
for(int i=0;i<nyu.length-1;i++){
min+=num[i];
}
if(num[num.length-1]<min)
System.out.println("Yes");
else
System.out.println("No");



}

}


