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 Go (1.6) (judge verdict: Accepted)

package main

import (
  "fmt"
)

func maxInt(a ...int) int {m := a[0]; for _, x := range a {if x > m {m = x}}; return m}
func minInt(a ...int) int {m := a[0]; for _, x := range a {if x < m {m = x}}; return m}
func sumInt(a ...int) int {s := 0; for _, v := range a {s += v}; return s}

func main() {
  var n int 
  fmt.Scan(&n)
  l := make([]int, n)
  for i := 0; i < n; i++ {
    fmt.Scan(&l[i])
  }

  ans := "No"
  if sumInt(l...) > maxInt(l...) * 2 {
    ans = "Yes"
  }
  fmt.Println(ans)


}