Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input){
	input = input.split("\n");
  var a = ~~input[0];
  var b = input[1].split(" ").map((a)=>~~a);
  var max = b[0];
  var sum = 0;
  for(var i = 0; i < a ; i++){
  	var c = b[i];
  	if(max < c){max = c}
    sum += c;
  }
  if(max * 2 < sum){return "Yes"}
  return "No"
}

// If you are interested in the algorithms I used, 
// there is no need to read down from this line.

((b,c,d)=>"undefined"!=typeof require?console.log(Main(require("fs").readFileSync("/dev/stdin","utf8"))):[b=b.split("\n").slice(1,-1).join("\n"),c=function(){try{return Main(b)}catch(f){return f.stack||f.message}}(),d=typeof c,"string"==d||(c=JSON.stringify(c)),$("<form>").append([[10,b],0,[1,d],0,[10,c]].map(f=>$(f?"<textarea>":"<br>",f&&{rows:f[0],cols:40,text:f[1]}))).appendTo("body")])(`
4
3 8 4 1
`);