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 Python (3.4.3) (judge verdict: Accepted)

'''
https://atcoder.jp/contests/abc065/tasks/arc076_b
最小全域木を考える際にある頂点について他の頂点への最小コストを
考えて繋げていくのは間違い(全域木になる保証がない)
考えたいのはあくまでも全辺のコスト

今回はxとyでそれぞれソートして隣り合う2点のコストのみを考えれば良い
'''
def main():
    import sys
    input = sys.stdin.readline
    sys.setrecursionlimit(10000000)
    from collections import Counter, deque
    #from collections import defaultdict
    from itertools import combinations, permutations, accumulate
    #from itertools import product
    from bisect import bisect_left,bisect_right
    import heapq
    from math import floor, ceil
    #from operator import itemgetter

    #inf = 10**17
    #mod = 1000000007

    N = int(input())
    xy = []
    for i in range(N):
        x,y = map(int, input().split())
        xy.append([x, y, i])
    x_sort = sorted(xy, key=lambda x: x[0])
    y_sort = sorted(xy, key=lambda x: x[1])

    #[cost, 頂点1, 頂点2]
    cost = []
    for i in range(N-1):
        cost.append([abs(x_sort[i][0]-x_sort[i+1][0]), x_sort[i][2], x_sort[i+1][2]])
        cost.append([abs(y_sort[i][1]-y_sort[i+1][1]), y_sort[i][2], y_sort[i+1][2]])
    cost = sorted(cost, key=lambda x: x[0])

    def find(x):
        if par[x] < 0:
            return x
        else:
            par[x] = find(par[x])
            return par[x]
    
    def unite(x,y):
        x = find(x)
        y = find(y)
        if x == y:
            return False
        else:
            if par[x] > par[y]:
                x,y = y,x
            par[x] += par[y]
            par[y] = x
            return True
    
    def same(x,y):
        return find(x) == find(y)

    par = [-1]*N

    res = 0
    for c, v1, v2 in cost:
        if not same(v1, v2):
            unite(v1, v2)
            res += c
    print(res)


if __name__ == '__main__':
    main()