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)

#![allow(unused_variables)]
#![allow(unused_imports)]
#![allow(dead_code)]
use std::io;
use std::str::FromStr;
use std::iter::FromIterator;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::mem::{replace, swap};


// abcde
fn read_string() -> String {
    let mut line = String::new();
    io::stdin().read_line(&mut line).unwrap();
    line
}

// -3.2
fn read_as_primitive<T: FromStr>() -> T {
    let s = read_string();
    s.trim().parse().ok().expect("failed to parse input")
}

// 1 -3 0 999
fn read_as_collection<U: FromStr, T: FromIterator<U>>() -> T {
    let s = read_string();
    s.trim().split_whitespace().map(|s| s.parse().ok().expect("failed to parse")).collect()
}

// #.#.###..
fn read_as_chars<T: FromIterator<char>>() -> T {
    let s = read_string();
    s.trim().chars().collect()
}

// 1 abc
fn read_as_pair<T: FromStr, U: FromStr>() -> (T, U) {
    let s = read_string();
    let elems: Vec<_> = s.trim().split_whitespace().collect();    
    (
        elems[0].parse().ok().expect("failed to parse"), 
        elems[1].parse().ok().expect("failed to parse"),
    )
}

// 1.5 -2 abc
fn read_as_triple<T: FromStr, U: FromStr, V: FromStr>() -> (T, U, V) {
    let s = read_string();
    let elems: Vec<_> = s.trim().split_whitespace().collect();
    (
        elems[0].parse().ok().expect("failed to parse"), 
        elems[1].parse().ok().expect("failed to parse"),
        elems[2].parse().ok().expect("failed to parse"),
    )
}

fn main() {

    let n: usize = read_as_primitive();
    let mut xs: Vec<i64> = read_as_collection();
    xs.sort();
    let ans = if xs[n - 1] < xs[0..n-1].iter().sum() {"Yes"} else {"No"};
    println!("{}", ans);
}