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 max(nums []int) int {
	max := nums[0]
	for _, v := range nums {
		if max < v {
			max = v
		}
	}
	return max
}

func sum(nums []int) int {
	sum := 0
	for _, v := range nums {
		sum += v
	}
	return sum
}

func main() {
	var n int
	fmt.Scan(&n)

	nums := make([]int, n)
	for i := range nums {
		fmt.Scan(&nums[i])
	}

	max := max(nums)
	sum := sum(nums) - max

	if max < sum {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}