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 fn read1<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
    let s = read1::<String>();
    s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
}

pub struct UnionFind {
    pub par: Vec<usize>,
    pub rank: Vec<usize>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let par = (0..n).collect::<Vec<usize>>();
        let rank = vec![0; n];
        UnionFind { par: par, rank: rank }
    }

    pub fn root(&mut self, x: usize) -> usize {
        let cand = self.par[x];
        if cand == x {
            return x;
        } else {
            let ret = self.root(cand);
            self.par[x] = ret;
            return ret;
        }
    }

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

    pub fn unite(&mut self, x: usize, y: usize) {
        let root_x = self.root(x);
        let root_y = self.root(y);
        if root_x == root_y { return; }

        if self.rank[root_x] < self.rank[root_y] {
            self.par[root_x] = self.par[root_y];
        } else {
            self.par[root_y] = self.par[root_x];
            if self.rank[root_y] == self.rank[root_x] {
                self.rank[root_x] += 1;
            }
        }
    }
}

fn main() {
    let n = read1::<usize>();
    let mut xy = (0..n).map(|i| {
        let temp = readn::<usize>(" ");
        (temp[0], temp[1], i)
    }).collect::<Vec<(usize, usize, usize)>>();
    let mut yx = xy.iter().map(|&t| (t.1, t.0, t.2)).collect::<Vec<(usize, usize, usize)>>();

    xy.sort();
    yx.sort();

    let mut edge = Vec::with_capacity((n - 1) * 2);
    for i in 0..(n-1) {
        let xy0 = xy[i];
        let xy1 = xy[i+1];
        edge.push((xy0.2, xy1.2, xy1.0 - xy0.0));
        let yx0 = yx[i];
        let yx1 = yx[i+1];
        edge.push((yx0.2, yx1.2, yx1.0 - yx0.0));
    }
    edge.sort_by(|a, b| (a.2).cmp(&(b.2)));

    let mut uf = UnionFind::new(n);
    let mut ans = 0;
    for &e in edge.iter() {
        let a = e.0;
        let b = e.1;
        let c = e.2;
        if !uf.same(a, b) {
            uf.unite(a, b);
            ans += c;
        }
    }

    println!("{}", ans);
}