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)

pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $ t : ty , $ words_count : expr , |$ words : ident | $ read_words : expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize {
                $words_count
            }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize {
        1
    }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse \"{}\" as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize {
        1
    }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
macro_rules ! impl_readable_for_ints { ( $ ( $ t : ty ) * ) => { $ ( impl Readable for $ t { type Output = Self ; fn words_count ( ) -> usize { 1 } fn read_words ( words : & [ & str ] ) -> Result <$ t , String > { use std :: str :: FromStr ; <$ t >:: from_str ( words [ 0 ] ) . map_err ( | _ | { format ! ( "cannot parse \"{}\" as {}" , words [ 0 ] , stringify ! ( $ t ) ) } ) } } ) * } ; }
impl_readable_for_ints ! ( i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64 ) ;
macro_rules ! define_one_origin_int_types { ( $ new_t : ident $ int_t : ty ) => { # [ doc = " Converts 1-origin integer into 0-origin when read from stdin." ] # [ doc = "" ] # [ doc = " # Example" ] # [ doc = "" ] # [ doc = " ```no_run" ] # [ doc = " # #[macro_use] extern crate atcoder_snippets;" ] # [ doc = " # use atcoder_snippets::read::*;" ] # [ doc = " // Stdin: \"1\"" ] # [ doc = " read!(a = usize_);" ] # [ doc = " assert_eq!(a, 0);" ] # [ doc = " ```" ] # [ allow ( non_camel_case_types ) ] pub struct $ new_t ( ) ; impl Readable for $ new_t { type Output = $ int_t ; fn words_count ( ) -> usize { 1 } fn read_words ( words : & [ & str ] ) -> Result < Self :: Output , String > { <$ int_t >:: read_words ( words ) . map ( | n | n - 1 ) } } } ; ( $ new_t : ident $ int_t : ty ; $ ( $ inner_new_t : ident $ inner_int_t : ty ) ;* ) => { define_one_origin_int_types ! ( $ new_t $ int_t ) ; define_one_origin_int_types ! ( $ ( $ inner_new_t $ inner_int_t ) ;* ) ; } ; }
define_one_origin_int_types ! ( u8_ u8 ; u16_ u16 ; u32_ u32 ; u64_ u64 ; usize_ usize ) ;
macro_rules ! impl_readable_for_tuples { ( $ t : ident $ var : ident ) => ( ) ; ( $ t : ident $ var : ident ; $ ( $ inner_t : ident $ inner_var : ident ) ;* ) => { impl_readable_for_tuples ! ( $ ( $ inner_t $ inner_var ) ;* ) ; impl <$ t : Readable , $ ( $ inner_t : Readable ) ,*> Readable for ( $ t , $ ( $ inner_t ) ,* ) { type Output = ( <$ t >:: Output , $ ( <$ inner_t >:: Output ) ,* ) ; fn words_count ( ) -> usize { let mut n = <$ t >:: words_count ( ) ; $ ( n += <$ inner_t >:: words_count ( ) ; ) * n } # [ allow ( unused_assignments ) ] fn read_words ( words : & [ & str ] ) -> Result < Self :: Output , String > { let mut start = 0 ; let $ var = <$ t >:: read_words ( & words [ start .. start +<$ t >:: words_count ( ) ] ) ?; start += <$ t >:: words_count ( ) ; $ ( let $ inner_var = <$ inner_t >:: read_words ( & words [ start .. start +<$ inner_t >:: words_count ( ) ] ) ?; start += <$ inner_t >:: words_count ( ) ; ) * Ok ( ( $ var , $ ( $ inner_var ) ,* ) ) } } } ; }
impl_readable_for_tuples ! ( T4 x4 ; T3 x3 ; T2 x2 ; T1 x1 ) ;
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!(
                "line \"{}\" has {} words, expected {}",
                line,
                words.len(),
                T::words_count()
            ));
        }
        T::read_words(&words)
    }
}
impl<T: Readable> ReadableFromLine for Vec<T> {
    type Output = Vec<T::Output>;
    fn read_line(line: &str) -> Result<Self::Output, String> {
        let n = T::words_count();
        let words = split_into_words(line);
        if words.len() % n != 0 {
            return Err(format!(
                "line \"{}\" has {} words, expected multiple of {}",
                line,
                words.len(),
                n
            ));
        }
        let mut result = Vec::new();
        for chunk in words.chunks(n) {
            match T::read_words(chunk) {
                Ok(v) => result.push(v),
                Err(msg) => {
                    let flagment_msg = if n == 1 {
                        format!("word {}", result.len())
                    } else {
                        let l = result.len();
                        format!("words {}-{}", n * l + 1, (n + 1) * l)
                    };
                    return Err(format!("{} of line \"{}\": {}", flagment_msg, line, msg));
                }
            }
        }
        Ok(result)
    }
}
impl<T: Readable, U: Readable> ReadableFromLine for (T, Vec<U>) {
    type Output = (T::Output, <Vec<U> as ReadableFromLine>::Output);
    fn read_line(line: &str) -> Result<Self::Output, String> {
        let n = T::words_count();
        #[allow(deprecated)]
        let trimmed = line.trim_right_matches('\n');
        let words_and_rest: Vec<&str> = trimmed.splitn(n + 1, ' ').collect();
        if words_and_rest.len() < n {
            return Err(format!(
                "line \"{}\" has {} words, expected at least {}",
                line,
                words_and_rest.len(),
                n
            ));
        }
        let words = &words_and_rest[..n];
        let empty_str = "";
        let rest = words_and_rest.get(n).unwrap_or(&empty_str);
        Ok((T::read_words(words)?, Vec::<U>::read_line(rest)?))
    }
}
macro_rules ! impl_readable_from_line_for_tuples_with_vec { ( $ t : ident $ var : ident ) => ( ) ; ( $ t : ident $ var : ident ; $ ( $ inner_t : ident $ inner_var : ident ) ;+ ) => { impl_readable_from_line_for_tuples_with_vec ! ( $ ( $ inner_t $ inner_var ) ;+ ) ; impl <$ t : Readable , $ ( $ inner_t : Readable ) ,+ , U : Readable > ReadableFromLine for ( $ t , $ ( $ inner_t ) ,+ , Vec < U > ) { type Output = ( $ t :: Output , $ ( $ inner_t :: Output ) ,+ , Vec < U :: Output > ) ; fn read_line ( line : & str ) -> Result < Self :: Output , String > { let mut n = $ t :: words_count ( ) ; $ ( n += $ inner_t :: words_count ( ) ; ) + # [ allow ( deprecated ) ] let trimmed = line . trim_right_matches ( '\n' ) ; let words_and_rest : Vec <& str > = trimmed . splitn ( n + 1 , ' ' ) . collect ( ) ; if words_and_rest . len ( ) < n { return Err ( format ! ( "line \"{}\" has {} words, expected at least {}" , line , words_and_rest . len ( ) , n ) ) ; } let words = & words_and_rest [ .. n ] ; let empty_str = "" ; let rest = words_and_rest . get ( n ) . unwrap_or ( & empty_str ) ; let ( $ var , $ ( $ inner_var ) ,* ) = < ( $ t , $ ( $ inner_t ) ,+ ) >:: read_words ( words ) ?; Ok ( ( $ var , $ ( $ inner_var ) ,* , Vec ::< U >:: read_line ( rest ) ? ) ) } } } ; }
impl_readable_from_line_for_tuples_with_vec ! ( T4 t4 ; T3 t3 ; T2 t2 ; T1 t1 ) ;
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules ! read { ( ) => { let mut line = String :: new ( ) ; std :: io :: stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; } ; ( $ pat : pat = $ t : ty ) => { let $ pat = read ::<$ t > ( ) ; } ; ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { read ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ) ; } ; }
#[macro_export]
macro_rules ! readls { ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { $ ( read ! ( $ pat = $ t ) ; ) * } ; }
pub fn readx<T: ReadableFromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin
        .lock()
        .lines()
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::read_line(&line).unwrap()
        }).collect();
    result
}
#[macro_export]
macro_rules ! readx_loop { ( |$ pat : pat = $ t : ty | $ body : expr ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; for line in stdin . lock ( ) . lines ( ) { let line = line . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: read_line ( & line ) . unwrap ( ) ; $ body } } ; ( |$ ( $ pat : pat = $ t : ty ) ,*| $ body : expr ) => { readx_loop ! ( | ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) | $ body ) ; } ; }
pub fn readn<T: ReadableFromLine>(n: usize) -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result: Vec<T::Output> = stdin
        .lock()
        .lines()
        .take(n)
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::read_line(&line).unwrap()
        }).collect();
    if result.len() < n {
        panic!(
            "expected reading {} lines, but only {} lines are read",
            n,
            result.len()
        );
    }
    result
}
#[macro_export]
macro_rules ! readn_loop { ( $ n : expr , |$ pat : pat = $ t : ty | $ body : expr ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; { let mut lock = stdin . lock ( ) ; for _ in 0 ..$ n { let mut line = String :: new ( ) ; lock . read_line ( & mut line ) . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: read_line ( & line ) . unwrap ( ) ; $ body } } } ; ( $ n : expr , |$ ( $ pat : pat = $ t : ty ) ,*| $ body : expr ) => { readn_loop ! ( $ n , | ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) | $ body ) ; } ; }
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

pub struct HashUnionFindSets<T: Eq + std::hash::Hash + std::fmt::Debug> {
    items: std::collections::HashMap<T, UnionFindNode<T>>,
}
#[derive(Clone)]
enum UnionFindNodeInner<T: Eq + std::hash::Hash> {
    Root { len: usize },
    Child { parent: UnionFindNode<T> },
}
#[derive(Clone)]
struct UnionFindNode<T: Eq + std::hash::Hash>(
    std::rc::Rc<std::cell::RefCell<UnionFindNodeInner<T>>>,
    T,
);
impl<T: Eq + std::hash::Hash + Clone> UnionFindNode<T> {
    fn new(item: T) -> UnionFindNode<T> {
        UnionFindNode(
            std::rc::Rc::new(std::cell::RefCell::new(UnionFindNodeInner::Root { len: 1 })),
            item,
        )
    }
}
impl<T: Eq + std::hash::Hash> std::cmp::PartialEq for UnionFindNode<T> {
    fn eq(&self, other: &UnionFindNode<T>) -> bool {
        self.1 == other.1
    }
}
impl<T: Eq + std::hash::Hash> std::cmp::Eq for UnionFindNode<T> {}
impl<T: Eq + std::hash::Hash> std::hash::Hash for UnionFindNode<T> {
    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
        self.1.hash(state);
    }
}
impl<T: Eq + std::hash::Hash + std::fmt::Debug + Clone> HashUnionFindSets<T> {
    pub fn new() -> HashUnionFindSets<T> {
        HashUnionFindSets {
            items: std::collections::HashMap::new(),
        }
    }
    fn error_msg(items: &[&T]) -> String {
        assert!(items.len() == 1 || items.len() == 2);
        if items.len() == 1 {
            format!("no set contains {:?}", items[0])
        } else {
            format!(
                "no set contains {:?} and no set contains {:?}",
                items[0], items[1]
            )
        }
    }
    pub fn add(&mut self, item: T) -> bool {
        if self.items.contains_key(&item) {
            false
        } else {
            self.items.insert(item.clone(), UnionFindNode::new(item));
            true
        }
    }
    pub fn items_len(&self) -> usize {
        self.items.len()
    }
    fn find(&self, item: &T) -> Option<(UnionFindNode<T>, usize)> {
        fn go<T: Eq + std::hash::Hash + Clone>(
            node: UnionFindNode<T>,
        ) -> (UnionFindNode<T>, usize) {
            let inner = node.0.as_ref().clone().into_inner();
            match inner {
                UnionFindNodeInner::Root { len } => (node, len),
                UnionFindNodeInner::Child { parent } => {
                    let (root, len) = go(parent);
                    let mut borrowed = node.0.borrow_mut();
                    *borrowed = UnionFindNodeInner::Child {
                        parent: root.clone(),
                    };
                    (root, len)
                }
            }
        }
        self.items.get(item).cloned().map(go)
    }
    pub fn len_of(&self, item: &T) -> Result<usize, String> {
        self.find(item)
            .map(|(_, len)| len)
            .ok_or_else(|| HashUnionFindSets::error_msg(&[item]))
    }
    pub fn set_eq(&self, item1: &T, item2: &T) -> Result<bool, String> {
        match (self.find(item1), self.find(item2)) {
            (Some((root1, _)), Some((root2, _))) => Ok(root1 == root2),
            (Some(_), None) => Err(HashUnionFindSets::error_msg(&[item2])),
            (None, Some(_)) => Err(HashUnionFindSets::error_msg(&[item1])),
            (None, None) => Err(HashUnionFindSets::error_msg(&[item1, item2])),
        }
    }
    pub fn unite(&mut self, item1: &T, item2: &T) -> Result<bool, String> {
        match (self.find(item1), self.find(item2)) {
            (Some((root1, len1)), Some((root2, len2))) => {
                if root1 == root2 {
                    Ok(false)
                } else {
                    let (mut root, mut child, root_node) = if len1 < len2 {
                        (root2.0.borrow_mut(), root1.0.borrow_mut(), &root2)
                    } else {
                        (root1.0.borrow_mut(), root2.0.borrow_mut(), &root1)
                    };
                    *root = UnionFindNodeInner::Root { len: len1 + len2 };
                    *child = UnionFindNodeInner::Child {
                        parent: root_node.clone(),
                    };
                    Ok(true)
                }
            }
            (Some(_), None) => Err(HashUnionFindSets::error_msg(&[item2])),
            (None, Some(_)) => Err(HashUnionFindSets::error_msg(&[item1])),
            (None, None) => Err(HashUnionFindSets::error_msg(&[item1, item2])),
        }
    }
}
impl<T: Eq + std::hash::Hash + std::fmt::Debug + Clone> std::fmt::Debug for HashUnionFindSets<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        use std::collections::{HashMap, HashSet};
        let mut root_to_set = HashMap::new();
        for item in self.items.keys() {
            let root = self.find(item);
            let set = root_to_set.entry(root).or_insert(HashSet::new());
            set.insert(item);
        }
        let sets: Vec<HashSet<&T>> = root_to_set.into_iter().map(|(_, v)| v).collect();
        if sets.len() == 0 {
            write!(f, "{{}}")
        } else {
            write!(f, "{{{:?}", sets[0])?;
            for set in &sets[1..] {
                write!(f, ", {:?}", set)?;
            }
            write!(f, "}}")
        }
    }
}
impl<T: Eq + std::hash::Hash + std::fmt::Debug + Clone> std::iter::FromIterator<T>
    for HashUnionFindSets<T>
{
    fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> HashUnionFindSets<T> {
        HashUnionFindSets {
            items: iter
                .into_iter()
                .map(|x| (x.clone(), UnionFindNode::new(x)))
                .collect(),
        }
    }
}

#[derive(Clone)]
pub struct StepBy<I> {
    iter: I,
    step: usize,
    first_take: bool,
}
impl<I: Iterator> Iterator for StepBy<I> {
    type Item = I::Item;
    fn next(&mut self) -> Option<Self::Item> {
        if self.first_take {
            self.first_take = false;
            self.iter.next()
        } else {
            self.iter.nth(self.step)
        }
    }
}
#[derive(Clone)]
pub struct LScan<I: Iterator, S: Clone, F: FnMut(&S, I::Item) -> S> {
    iter: I,
    state: Option<S>,
    f: F,
}
impl<I: Iterator, S: Clone, F> Iterator for LScan<I, S, F>
where
    F: FnMut(&S, I::Item) -> S,
{
    type Item = S;
    fn next(&mut self) -> Option<S> {
        if self.state.is_none() {
            return None;
        }
        let state_inner = self.state.take().unwrap();
        if let Some(item) = self.iter.next() {
            self.state = Some((self.f)(&state_inner, item));
        }
        Some(state_inner)
    }
}
pub struct Flatten<I: Iterator>
where
    I::Item: IntoIterator,
{
    outer_iter: I,
    inner_iter: Option<<<I as Iterator>::Item as IntoIterator>::IntoIter>,
}
impl<I, J> Iterator for Flatten<I>
where
    I: Iterator<Item = J>,
    J: IntoIterator,
{
    type Item = <<J as IntoIterator>::IntoIter as Iterator>::Item;
    fn next(&mut self) -> Option<J::Item> {
        loop {
            if let Some(inner_iter) = self.inner_iter.as_mut() {
                if let item @ Some(_) = inner_iter.next() {
                    return item;
                }
            }
            match self.outer_iter.next() {
                None => return None,
                Some(inner) => self.inner_iter = Some(inner.into_iter()),
            }
        }
    }
}
pub struct GroupBy<K: Eq, I: Iterator, F: FnMut(&I::Item) -> K> {
    cur: Option<(I::Item, K)>,
    iter: I,
    key_fn: F,
}
impl<K: Eq, I: Iterator, F: FnMut(&I::Item) -> K> Iterator for GroupBy<K, I, F> {
    type Item = (K, Vec<I::Item>);
    fn next(&mut self) -> Option<(K, Vec<I::Item>)> {
        let cur = self.cur.take();
        cur.map(|(item, key)| {
            let mut group = vec![item];
            loop {
                let next = self.iter.next();
                match next {
                    Some(next_item) => {
                        let next_key = (self.key_fn)(&next_item);
                        if key == next_key {
                            group.push(next_item);
                        } else {
                            self.cur = Some((next_item, next_key));
                            break;
                        }
                    }
                    None => {
                        self.cur = None;
                        break;
                    }
                }
            }
            (key, group)
        })
    }
}
pub trait IteratorExt: Iterator {
    fn step_by_(self, step: usize) -> StepBy<Self>
    where
        Self: Sized,
    {
        assert_ne!(step, 0);
        StepBy {
            iter: self,
            step: step - 1,
            first_take: true,
        }
    }
    fn for_each<F: FnMut(Self::Item)>(self, mut f: F)
    where
        Self: Sized,
    {
        for item in self {
            f(item);
        }
    }
    fn lscan<S: Clone, F>(self, state: S, f: F) -> LScan<Self, S, F>
    where
        Self: Sized,
        F: FnMut(&S, Self::Item) -> S,
    {
        LScan {
            iter: self,
            state: Some(state),
            f: f,
        }
    }
    fn get_unique(mut self) -> Option<Self::Item>
    where
        Self: Sized,
        Self::Item: Eq,
    {
        let first_opt = self.next();
        first_opt.and_then(|first| {
            if self.all(|item| item == first) {
                Some(first)
            } else {
                None
            }
        })
    }
    fn flatten(mut self) -> Flatten<Self>
    where
        Self: Sized,
        Self::Item: IntoIterator,
    {
        let inner_opt = self.next();
        Flatten {
            outer_iter: self,
            inner_iter: inner_opt.map(|inner| inner.into_iter()),
        }
    }
    fn group_by<K: Eq, F: FnMut(&Self::Item) -> K>(mut self, mut f: F) -> GroupBy<K, Self, F>
    where
        Self: Sized,
    {
        let next = self.next();
        GroupBy {
            cur: next.map(|item| {
                let key = f(&item);
                (item, key)
            }),
            iter: self,
            key_fn: f,
        }
    }
    fn join(mut self, sep: &str) -> String
    where
        Self: Sized,
        Self::Item: std::fmt::Display,
    {
        let mut result = String::new();
        if let Some(first) = self.next() {
            result.push_str(&format!("{}", first));
        }
        for s in self {
            result.push_str(&format!("{}{}", sep, s));
        }
        result
    }
    fn cat(self) -> String
    where
        Self: Sized,
        Self::Item: std::fmt::Display,
    {
        self.join("")
    }
}
impl<I: Iterator> IteratorExt for I {}
pub struct Unfold<T, F>
where
    F: FnMut(&T) -> Option<T>,
{
    state: Option<T>,
    f: F,
}
impl<T, F> Iterator for Unfold<T, F>
where
    F: FnMut(&T) -> Option<T>,
{
    type Item = T;
    fn next(&mut self) -> Option<T> {
        if self.state.is_none() {
            return None;
        }
        let state_inner = self.state.take().unwrap();
        self.state = (self.f)(&state_inner);
        Some(state_inner)
    }
}
pub fn unfold<T, F>(init: T, f: F) -> Unfold<T, F>
where
    F: FnMut(&T) -> Option<T>,
{
    Unfold {
        state: Some(init),
        f: f,
    }
}
pub struct Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    state: T,
    f: F,
}
impl<T, F> Iterator for Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    type Item = T;
    fn next(&mut self) -> Option<T> {
        use std::mem::swap;
        let mut state = (self.f)(&self.state);
        swap(&mut state, &mut self.state);
        Some(state)
    }
}
pub fn iterate<T, F>(init: T, f: F) -> Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    Iterate { state: init, f: f }
}

fn main() {
    read!(n = usize);
    let mut ps: Vec<(usize, (u64, u64))> =
        readx::<(u64, u64)>().into_iter().enumerate().collect();
    let mut edges = Vec::new();

    ps.sort_by_key(|&(_i, (x, _y))| x);
    ps.windows(2).for_each(|pair| {
        edges.push((pair[0].0, pair[1].0, (pair[1].1).0 - (pair[0].1).0));
    });
    ps.sort_by_key(|&(_i, (_x, y))| y);
    ps.windows(2).for_each(|pair| {
        edges.push((pair[0].0, pair[1].0, (pair[1].1).1 - (pair[0].1).1));
    });
    edges.sort_by_key(|&(_, _, cost)| cost);

    let mut ans = 0;
    let mut connectivity: HashUnionFindSets<usize> = (0..n).collect();
    for (v1, v2, cost) in edges {
        if !connectivity.set_eq(&v1, &v2).unwrap() {
            connectivity.unite(&v1, &v2).unwrap();
            ans += cost;
        }
    }
    println!("{}", ans);
}