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<bits/stdc++.h>
#define lowbit(i) ((i)&(-i))
#define lson(i) ((i)<<1)
#define rson(i) ((i)<<1|1)
#define ft first
#define se second
#define MAXN 100007
using namespace std;

typedef long long ll;typedef unsigned long long ul;
typedef pair<int,int> pii;typedef pair<ll,ll> pll;
typedef vector<string> vss;
typedef vector<int> vii;typedef vector<pii> vpi;
typedef queue<int> qii;typedef queue<pii> qpi;

const int inf=2e9+7;

struct edge{
	ll x,y,val;
	edge(int _x,int _y,int _val){x=_x,y=_y,val=_val;}
};

vector<edge> v;

struct node{
	int x,y,num;
}dot1[MAXN],dot2[MAXN];

bool cmp1(node x,node y){
	return x.x<y.x;
}

bool cmp2(node x,node y){
	return x.y<y.y;
}

bool comp(edge x,edge y){
	return x.val<y.val;
}

int n,fa[MAXN];
ll res;

int find(int x){
	if(fa[x]==x) return x;
	return fa[x]=find(fa[x]);
}

void merge(int x,int y){
	int fx=find(x),fy=find(y);
	if(fx!=fy)
		fa[x]=y;
}

int main()
{
// 	freopen("","r",stdin);
// 	freopen("","w",stdout);
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d%d",&dot1[i].x,&dot1[i].y);
		dot2[i].x=dot1[i].x;dot2[i].y=dot1[i].y;
		dot2[i].num=dot1[i].num=i;
	}
	
	//建边(删除无用边) 
	sort(dot1+1,dot1+n+1,cmp1);
	sort(dot2+1,dot2+n+1,cmp2);
	/*
	for(int i=1;i<=n;i++){
		printf("num %d:(%d,%d)\n",i,dot1[i].x,dot1[i].y);
	}
	*/
	for(int i=2;i<=n;i++){
		v.push_back( edge(dot1[i-1].num,dot1[i].num,dot1[i].x-dot1[i-1].x) );
		v.push_back( edge(dot2[i-1].num,dot2[i].num,dot2[i].y-dot2[i-1].y) );
	}
	sort(v.begin(),v.end(),comp);
	
	//初始化 
	for(int i=1;i<=n;i++)
		fa[i]=i;
/*
	for(int i=0;i<v.size();i++){
		printf("(%d,%d) dis=%d\n",v[i].x,v[i].y,v[i].val);
	}
	*/
	//Kruscal
	for(int i=0;i<v.size();i++){
		if(find(v[i].x)!=find(v[i].y)){
			merge(v[i].x,v[i].y);
			res+=v[i].val;
		}
	}
	printf("%lld\n",res);
	return 0;
}