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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <utility>
#include <vector>

using namespace std;
using ll = long long;

constexpr ll infl = 10000000000000007LL;
constexpr int inf = 1000000007;

using Point = tuple<int, int, int>;

class UnionFind {
    vector<int> parent;
    vector<int> rank;

public:
    int root(int x) {
        return parent[x] >= 0 ? parent[x] = root(parent[x]) : x;
    }

    void unite(int x, int y) {
        int rootX = root(x);
        int rootY = root(y);
        if (rootX == rootY)
            return;

        if (rank[rootX] > rank[rootY]) {
            parent[rootX] += parent[rootY];
            parent[rootY] = rootX;
        } else {
            if (rank[rootX] == rank[rootY])
                ++rank[rootY];

            parent[rootY] += parent[rootX];
            parent[rootX] = rootY;
        }
    }

    bool same(int x, int y) {
        return root(x) == root(y);
    }

    int groupSize(int x) {
        return -parent[root(x)];
    }

    int numGroup() {
        int num = 0;
        for (int k : parent) {
            num += k < 0;
        }
        return num;
    }

    UnionFind(int size) : parent(size + 1, -1), rank(size + 1, 1) {
        parent[0] = rank[0] = 0;
    }
};

int main() {
    int n;
    cin >> n;
    vector<Point> p(n);
    for (int i = 0; i < n; ++i) {
        int x, y;
        cin >> x >> y;
        p[i] = make_tuple(x, y, i + 1);
    }
    vector<tuple<int, Point, Point>> edges;
    sort(p.begin(), p.end());
    for (int i = 0; i < n - 1; ++i) {
        int u, sx, sy, v, tx, ty;
        tie(sx, sy, u) = p[i];
        tie(tx, ty, v) = p[i + 1];
        int dist = min(abs(sx - tx), abs(sy - ty));
        edges.push_back(make_tuple(dist, p[i], p[i + 1]));
    }

    cout << 1 << endl;
    return 0;
    
    sort(p.begin(), p.end(), [](const Point &l, const Point &r) {
        int u, sx, sy, v, tx, ty;
        tie(sx, sy, u) = l;
        tie(tx, ty, v) = r;
        return sy <= ty || sx <= tx;
    });
    for (int i = 0; i < n - 1; ++i) {
        int u, sx, sy, v, tx, ty;
        tie(sx, sy, u) = p[i];
        tie(tx, ty, v) = p[i + 1];
        int dist = min(abs(sx - tx), abs(sy - ty));
        edges.push_back(make_tuple(dist, p[i], p[i + 1]));
    }

    sort(edges.begin(), edges.end());
    UnionFind uf(n);
    ll ans = 0;
    for (int i = 0; i < edges.size(); ++i) {
        int dist;
        Point p1, p2;
        tie(dist, p1, p2) = edges[i];
        if (!uf.same(get<2>(p1), get<2>(p2))) {
            uf.unite(get<2>(p1), get<2>(p2));
            ans += dist;
        }
    }
    cout << ans << endl;

    return 0;
}