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)

use std::cmp::{max, min};
use std::io::{self, Read};
use std::iter::FromIterator;

#[allow(dead_code)]
struct Source {
    chars: Box<Iterator<Item = char>>,
}

#[allow(dead_code)]
impl Source {
    fn next_chr(&mut self) -> char {
        self.chars
            .by_ref()
            .skip_while(|c| char::is_whitespace(*c))
            .next()
            .expect("eof")
    }

    fn next_str(&mut self) -> String {
        let it = self
            .chars
            .by_ref()
            .skip_while(|c| char::is_whitespace(*c))
            .take_while(|c| !char::is_whitespace(*c));
        let s = String::from_iter(it);
        if s.is_empty() {
            panic!("eof")
        } else {
            s
        }
    }

    fn from_stdin() -> Self {
        let mut data = String::new();
        io::stdin().read_to_string(&mut data).expect("Input error");
        Self::from_str(&data)
    }

    fn from_str(s: &str) -> Self {
        let data = String::from(s);
        let chars = data.chars().collect::<Vec<char>>().into_iter();
        Source {
            chars: Box::new(chars),
        }
    }
}

#[allow(unused_macros)]
macro_rules! input {
    ($src:expr; $($elem:tt)*) => {
        input_inner!($src, $($elem)*)
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($src:expr) => {};
    ($src:expr,) => {};
    ($src:expr, $var:ident : mut $ty:tt $($rest:tt)*) => {
        let mut $var = parse!($src, $ty);
        input_inner!($src $($rest)*)
    };
    ($src:expr, $var:ident : $ty:tt $($rest:tt)*) => {
        let $var = parse!($src, $ty);
        input_inner!($src $($rest)*)
    };
}

#[allow(unused_macros)]
macro_rules! parse {
    ($src:expr, ( $($ty:tt),* )) => {
        ( $(parse!($src,$ty)),* )
    };
    ($src:expr, char) => {
        $src.next_chr()
    };
    ($src:expr, [ $ty:tt; $len:expr ]) => {
        (0..$len).map(|_| parse!($src,$ty)).collect::<Vec<_>>()
    };
    ($src:expr, $ty:tt) => {
        parse_str!($src,$ty)
    };
}

#[allow(unused_macros)]
macro_rules! parse_str {
    ($src:expr, chars) => {
        $src.next_str().chars().collect::<Vec<char>>()
    };
    ($src:expr, $ty:ty) => {
        $src.next_str().parse::<$ty>().expect("Parse error")
    };
}

fn main() {
    let mut src = Source::from_stdin();
    input! { src;
             n: usize, l: mut [usize; n],
    }

    l.sort();

    let s: usize = l.iter().take(n - 1).sum();

    let res = if l[n - 1] < s { "Yes" } else { "No" };

    println!("{}", res)
}