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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::cmp;

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

#[allow(dead_code)]
fn find_min(x: &[u32]) -> u32 {
    let mut min: u32 = x[0];
    let mut x_iter = x.iter();
    while let Some(i) = x_iter.next() {
        min = cmp::min(*i, min);
    }
    return min;
}

#[allow(dead_code)]
fn find_max(x: &[u32]) -> u32 {
    let mut max: u32 = x[0];
    let mut x_iter = x.iter();
    while let Some(i) = x_iter.next() {
        max = cmp::max(*i, max);
    }
    return max;
}

fn main() {
    let _n: usize = read();
    let length: Vec<u32> = read_vec();

    let max = find_max(&length);

    let sum: u32 = length.iter().fold(0, |sum, &a| sum + a);

    if (sum / max) > 2 {
        println!("Yes");
    } else {
        println!("No");
    }
}