Problem:
Score : 500 points

Problem Statement

There are N towns on a plane. The i-th town is located at the coordinates (x_i,y_i). There may be more than one town at the same coordinates.

You can build a road between two towns at coordinates (a,b) and (c,d) for a cost of min(|a-c|,|b-d|) yen (the currency of Japan). It is not possible to build other types of roads.

Your objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?

Constraints

2 ≤ N ≤ 10^5

0 ≤ x_i,y_i ≤ 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.

Sample Input 1

3
1 5
3 9
7 8

Sample Output 1

3

Build a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.

Sample Input 2

6
8 3
4 9
12 19
18 1
13 5
7 6

Sample Output 2

8

Solution in Rust (1.15.1) (judge verdict: Accepted)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//                                                     _        _ _ _____  ___
//                               _ __ ___   __ _ _ __ | |_ __ _/ / |___ / / _ \
//                              | '_ ` _ \ / _` | '_ \| __/ _` | | | |_ \| | | |
//                              | | | | | | (_| | | | | || (_| | | |___) | |_| |
//                              |_| |_| |_|\__,_|_| |_|\__\__,_|_|_|____/ \___/

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

mod union_find {

///素集合データ構造
pub struct UnionFind {
    v: Vec<usize>,
}

impl UnionFind {
    ///要素数nの素集合データ構造を構築する。
    pub fn new(n: usize) -> UnionFind {
        let mut v = Vec::new();
        for i in 0..n {
            v.push(i);
        }
        UnionFind { v: v }
    }

    ///親を探索する。
    pub fn find(&mut self, a: usize) -> usize {
        if a == self.v[a] {
            return a;
        }

        let buf = self.v[a];
        let parent = self.find(buf);
        self.v[a] = parent;
        parent
    }

    ///親が同じか判定する。
    pub fn same(&mut self, a: usize, b: usize) -> bool {
        self.find(a) == self.find(b)
    }

    ///結合する。
    pub fn union(&mut self, a: usize, b: usize) {
        let parent_a = self.find(a);
        let parent_b = self.find(b);
        self.v[parent_a] = parent_b;
    }
}
}

use input::*;
use union_find::*;

fn kruskal(e: &Vec<(usize, usize, usize)>, n: usize) -> usize {
    let mut uf = UnionFind::new(n);
    let mut res = 0;
    for i in e {
        let &(cost, from, to) = i;
        if uf.same(from, to) {
            continue;
        }

        res += cost;
        uf.union(from, to);
    }

    res
}
fn main() {
    let n: usize;
    input!(n);

    let mut v = vec![];
    let mut ex = vec![];

    for i in 0..n {
        let (a, b): (usize, usize);
        input!(a, b);
        v.push((a, b, i));
    }

    v.sort_by(|q, w| q.0.cmp(&w.0));

    for i in 1..n {
        ex.push((v[i].0 - v[i - 1].0, v[i].2, v[i - 1].2));
    }

    v.sort_by(|q, w| q.1.cmp(&w.1));
    for i in 1..n {
        ex.push((v[i].1 - v[i - 1].1, v[i].2, v[i - 1].2));
    }

    ex.sort();

    p(kruskal(&ex, n));
}