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: Accepted)

fn polygon() -> Result<&'static str, &'static str> {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input)
        .map_err(|_| "input error")?;
    let n: u32 = input.trim_right().parse()
        .map_err(|_| "parse error")?;

    let mut input = String::new();
    std::io::stdin().read_line(&mut input)
        .map_err(|_| "input error")?;
    let l: Vec<u32> = input.trim_right()
        .split_whitespace()
        .filter_map(|s| s.parse::<u32>().ok())
        .collect();

    let max = l.iter().max().ok_or("input empty")?;
    let sum = l.iter().sum();

    if max * 2 < sum {
        Ok("Yes")
    }
    else {
        Ok("No")
    }
}

fn main() {
    println!("{}", polygon().unwrap());
}