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
#include<iostream>
#include<algorithm>
using namespace std;
int main(void){
	int N;
		cin >> N;
	int a,maxs=0,wa=0;
	for(int i=0;i<N;i++){
		cin >> a;
		wa+=a;
		maxs=max(maxs,a);
	}
	wa-=maxs;
	cout << (wa>maxs?"Yes":"No") << endl;
	return 0;
}