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)

/*------------------------------------------------------------------*/
/*------------------------- begin template -------------------------*/
/*------------------------------------------------------------------*/

// ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
// diff: using Parser
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

use std::io;
use std::io::BufRead;
use std::str;

// ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
// ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
// diff: using std::io::BufRead::fill_buf()
pub struct Parser<R> {
    pub reader: R,
    buf: Vec<u8>,
    pos: usize,
}

impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}

impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
    pub fn fast_i64(&mut self) -> i64 {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            if begin == self.buf.len() {
                self.update_buf();
                continue;
            }
            let mut res = 0;
            let (is_positive, mut end) = match self.buf[begin] {
                b'+' => (true, begin + 1),
                b'-' => (false, begin + 1),
                _ => (true, begin),
            };
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return if is_positive { res } else { -res };
            } else {
                self.update_buf();
            }
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;
use std::collections::BinaryHeap;
struct UnionFindNode {
    parent: usize,
    num: usize,
}

impl UnionFindNode {
    fn new(parent: usize) -> UnionFindNode {
        UnionFindNode {
            parent: parent,
            num: 1,
        }
    }
}

pub struct UnionFind(Vec<UnionFindNode>);

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let mut xs = vec![];
        for i in 0..n {
            xs.push(UnionFindNode::new(i));
        }
        UnionFind(xs)
    }
    pub fn root(&mut self, i: usize) -> usize {
        let parent = self.0[i].parent;
        if parent == i {
            i
        } else {
            let res = self.root(parent);
            self.0[i].parent = res;
            res
        }
    }
    pub fn unite(&mut self, i: usize, k: usize) {
        let i = self.root(i);
        let k = self.root(k);
        if i == k {
            return;
        }
        let (i, k) = if self.0[i].num < self.0[k].num {
            (i, k)
        } else {
            (k, i)
        };
        self.0[i].parent = k;
        self.0[k].num += self.0[i].num;
    }
    pub fn is_same_set(&mut self, i: usize, k: usize) -> bool {
        self.root(i) == self.root(k)
    }
    pub fn num(&mut self, i: usize) -> usize {
        let i = self.root(i);
        self.0[i].num
    }
}

fn main() {
    input! {
        new_stdin_parser = parser,
    }
    let res = solve(&mut parser);
    print!("{}", res);
}

/*------------------------------------------------------------------*/
/*-------------------------- end template --------------------------*/
/*------------------------------------------------------------------*/

use std::fmt::Write;
fn solve<R: BufRead>(parser: &mut Parser<R>) -> String {
    let mut buf = String::new();
    input! {
        parser = parser,
        n: usize,
        ps: [(i64,i64); n],
    }
    let mut heap = BinaryHeap::new();
    // x
    let mut ps2: Vec<(i64, i64, usize)> = ps
        .iter()
        .enumerate()
        .map(|(i, &(x, y))| (x, y, i))
        .collect();
    ps2.sort();
    for k in 1..n {
        let (x1, y1, i1) = ps2[k - 1];
        let (x2, y2, i2) = ps2[k];
        let d = min((x1 - x2).abs(), (y1 - y2).abs());
        heap.push((-d, i1, i2));
    }
    // y
    let mut ps2: Vec<(i64, i64, usize)> = ps
        .iter()
        .enumerate()
        .map(|(i, &(x, y))| (y, x, i))
        .collect();
    ps2.sort();
    for k in 1..n {
        let (y1, x1, i1) = ps2[k - 1];
        let (y2, x2, i2) = ps2[k];
        let d = min((x1 - x2).abs(), (y1 - y2).abs());
        heap.push((-d, i1, i2));
    }
    let mut uf = UnionFind::new(n);
    let mut res = 0;
    while uf.num(0) != n {
        let (d, i1, i2) = heap.pop().unwrap();
        let d = -d;
        if !uf.is_same_set(i1, i2) {
            res += d;
            uf.unite(i1, i2);
        }
    }
    writeln!(buf, "{}", res);
    buf
}