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)

var lines =[];

var readline = require("readline");
var rl = readline.createInterface({
  input:  process.stdin,
  output: process.stdout
});

rl.on('line',function(x){
  lines.push(x);
});

rl.on('close',function(){
 var n   = Number(lines[0]);
 var tmp = lines[1].split(" ");
 var l   = Array(n);
 var sum = 0;
 
 for(var i=0;i<n;i++){
     l[i]=Number(tmp[i]);
     sum=sum+l[i];
 }

 l.sort(function(a,b){return(b-a);});
 console.log(sum-l[0]>l[0]? "Yes":"No");
});