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 main() {
    var n int
    fmt.Scanf("%d", &n)

    a := make([]int, n)
    for i := 0; i< n; i++ {
        fmt.Scanf("%d", &a[i])
    }

    maxValue := max(a)
    sum := sumExOneMax(a, maxValue)

    // fmt.Println(maxValue, exMaxList, exListSum)

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

}

func max(list []int) int {
    var m int
    for _, v := range list {
        if v > m {
            m = v
        }
    }
    return m
}

func sumExOneMax(list []int, max int) int {
    var s int
    ex := true
    for _, v := range list {
        // 最大値が複数ある場合を考慮。1つ目以外は加算できるようにする
        if ex && max == v {
            ex = false
            continue
        }
        s += v
    }
    return s
}