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)

#![allow(unused_imports, unused_variables, dead_code, non_snake_case, unused_macros)]
use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

fn getline() -> String{
    let mut res = String::new();
    std::io::stdin().read_line(&mut res).ok();
    res
}

macro_rules! readl {
    ($t: ty) => {
        {
            let s = getline();
            s.trim().parse::<$t>().unwrap()
        }
    };
    ($( $t: ty),+ ) => {
        {
            let s = getline();
            let mut iter = s.trim().split(' ');
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*) 
        }
    };
}

macro_rules! readlvec {
    ($t: ty) => {
        {
            let s = getline();
            let iter = s.trim().split(' ');
            iter.map(|x| x.parse().unwrap()).collect::<Vec<$t>>()
        }
    }
}

macro_rules! mvec {
    ($v: expr, $s: expr) => {
        vec![$v; $s]
    };
    ($v: expr, $s: expr, $($t: expr),*) => {
        vec![mvec!($v, $($t),*); $s]
    };
}

macro_rules! debug {
    ($x: expr) => {
        println!("{}: {:?}", stringify!($x), $x)
    }
}

fn printiter<'a, T>(v: &'a T)
where
    &'a T: std::iter::IntoIterator, 
    <&'a T as std::iter::IntoIterator>::Item: std::fmt::Display {
    for (i,e) in v.into_iter().enumerate() {
        if i != 0 {
            print!(" ");
        }
        print!("{}", e);
    }
    println!("");
}

struct ContestPrinter {
    s: String,
}

impl ContestPrinter {
    fn new() -> ContestPrinter {
        ContestPrinter {
        s: String::new(),
        }
    }

    fn print<T>(&mut self, x: T)
        where T: std::fmt::Display {
        self.s.push_str(format!("{}", x).as_str());
    }

    fn println<T>(&mut self, x: T)
        where T: std::fmt::Display {
        self.s.push_str(format!("{}\n", x).as_str());
    }
}

impl std::ops::Drop for ContestPrinter {
    fn drop(&mut self) {
        print!("{}", self.s);
    }
}

// euclidの互除法
fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 { a }
    else { gcd(b, a % b) }
}
// ab = lcm(a, b)gcd(a, b)
fn lcm(a: i64, b: i64) -> i64 {
    let g = gcd(a, b);
    (a / g) * b
}
// 約数列挙 昇順ではない
fn divisors(n: i64) -> Vec<i64> {
    let mut ret = Vec::new();
    if n == 1 { ret.push(1); return ret; }
    let mut i = 1;
    loop {
        if (n % i) == 0 {
            ret.push(i);
            if (i != 1) & ((i*i) != n) {
                ret.push(n / i);
            }
        }
        i += 1; if n < (i*i) { break; }
    }
    ret.push(n);
    ret
}

fn is_max_i64(num: i64) -> bool { if num == i64::max_value() { true } else { false } }

// 2部グラフ判定かどうか，片方の色の数，もう片方の色の数
fn is_bipartite(graph: &Vec<Vec<usize>>) -> (bool, usize, usize) {
    let size = graph.len();
    let mut color: Vec<i32> = vec![0; size];
    fn dfs(g: &Vec<Vec<usize>>, color: &mut Vec<i32>, v: usize, c: i32) -> bool {
        color[v] = c;
        for i in 0..g[v].len() {
            let nb = g[v][i];
            let nbc = color[nb];
            if nbc == c { return false; }
            if nbc == 0 { if !dfs(g, color, nb, -c) { return false; } }
        }
        return true;
    }
    for i in 0..size {
        if color[i] == 0 { if !dfs(graph, &mut color, i, 1) { return (false, 0, 0); } }
    }
    
    let (mut c1, mut c2) = (0, 0);
    for c in color { match c {
        1 => c1 += 1,
        _ => c2 += 1,
    } }
    (true, c1, c2)
}

#[derive(Debug)]
struct UnionFind {
    parent: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFind {
    fn new(size: usize) -> UnionFind {
        UnionFind{ parent: (0..size).collect(), rank: vec![0; size] }
    }

    fn find_root(&mut self, index: usize) -> usize {
        let p = self.parent[index];
        if p == index {
            return index;
        } else {
            self.parent[index] = self.find_root(p);
            return self.parent[index];
        }
    }

    // xとyの属する木を併合
    fn unite(&mut self, x: usize, y: usize) {
        let x = self.find_root(x);
        let y = self.find_root(y);
        if x != y {
            if self.rank[x] < self.rank[y] {
                self.parent[x] = y;
            } else {
                self.parent[y] = x;
                if self.rank[x] == self.rank[y] { self.rank[x] += 1; }
            }
        }
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find_root(x) == self.find_root(y)
    }
}

// 無向グラフで使える！　最小全域木
struct MinimumSpanningTree {
    pub node_num: usize,
    pub edges: Vec<(i64, usize, usize)>, // cost, node_idx, node_idx
}

impl MinimumSpanningTree {
    fn new(size: usize) -> MinimumSpanningTree {
        MinimumSpanningTree{ node_num: size, edges: Vec::new() }
    }

    // O(|E|log|V|)
    fn calc(&mut self) -> i64 {
        self.edges.sort();
        let mut uf = UnionFind::new(self.node_num);
        let mut sum = 0;
        for i in 0..self.edges.len() {
            let (cost, u, v) = self.edges[i];
            if uf.same(u, v) { continue; }
            uf.unite(u, v);
            sum += cost;
        }
        sum
    }
}

fn main() {
    let mut pr = ContestPrinter::new();
    
    let N = readl!(usize);
    let mut psx: Vec<(i64, i64, usize)> = Vec::new();
    let mut psy: Vec<(i64, i64, usize)> = Vec::new();

    for i in 0..N {
        let (x, y) = readl!(i64, i64);
        psx.push((x, y, i));
        psy.push((y, x, i));
    }

    psx.sort();
    psy.sort();

    let mut mst = MinimumSpanningTree::new(N);
    let mut before = psx[0];
    for i in 1..N {
        let cost = min((psx[i].0 - before.0).abs(), (psx[i].1 - before.1).abs());
        mst.edges.push((cost, before.2, psx[i].2));
        before = psx[i];
    }
    let mut before = psy[0];
    for i in 1..N {
        let cost = min((psy[i].0 - before.0).abs(), (psy[i].1 - before.1).abs());
        mst.edges.push((cost, before.2, psy[i].2));
        before = psy[i];
    }

    pr.println(mst.calc());
}