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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

typedef struct binaryHeap{
  void *h;
  size_t heapSize;
  size_t maxSize;
  size_t size;
  int (*cmp)(const void *,const void *);
} heap;

heap* newHeap(const size_t size,int (*cmpF)(const void *,const void *)){
  const size_t maxSize=1;
  heap *res=(heap *)malloc(sizeof(heap));
  res->h=malloc(size*(maxSize+1));
  res->heapSize=0;
  res->maxSize=maxSize;
  res->size=size;
  res->cmp=cmpF;
  return res;
}

int isEmpty(const heap *h){
  return h->heapSize==0;
}

void freeHeap(heap *h){
  free(h->h);
  free(h);
  return;
}

void initHeap(heap *h){
  h->heapSize=0;
  return;
}

static inline void heapFunc_swap(void * restrict a,void * restrict b,void * restrict tmp,size_t size){
  memcpy(tmp,a,size);
  memcpy(a,b,size);
  memcpy(b,tmp,size);
  return;
}

void push(heap *q,const void *p){
  if(q->heapSize==q->maxSize){
    q->maxSize*=2;
    q->h=realloc(q->h,q->size*(q->maxSize+1));
  }
  q->heapSize+=1;
  char *h=(char *)(q->h);
  int k=q->heapSize;
  const size_t size=q->size;
  int (*cmp)(const void *,const void *)=q->cmp;
  memcpy(h+k*size,p,size);
  while(k>1){
    size_t parent=k/2;
    if(cmp(h+parent*size,h+k*size)<=0) return;
    heapFunc_swap(h+parent*size,h+k*size,h,size);
    k=parent;
  }
  return;
}

void pop(heap *q,void *res){
  char *h=(char *)(q->h);
  const size_t size=q->size;
  if(res!=NULL) memcpy(res,h+size,size);
  memcpy(h+size,h+size*q->heapSize,size);
  q->heapSize-=1;
  int (*cmp)(const void *,const void *)=q->cmp;
  const size_t n=q->heapSize;
  size_t k=1;
  while(2*k+1<=n){
    size_t next=cmp(h+2*k*size,h+(2*k+1)*size)<=0?2*k:2*k+1;
    if(cmp(h+k*size,h+next*size)<=0) return;
    heapFunc_swap(h+k*size,h+next*size,h,size);
    k=next;
  }
  if(2*k<=n && cmp(h+k*size,h+2*k*size)>0) heapFunc_swap(h+k*size,h+2*k*size,h,size);
  return;
}

void top(const heap *q,void *res){
  memcpy(res,(char *)q->h+q->size,q->size);
  return;
}

typedef long long int int64;

typedef struct edge{
  int a,b;
  int c;
} edge;

typedef struct indexNode{
  int index;
  int val;
} node;

int cmpNode(const void *a,const void *b){
  return ((node *)a)->val-((node *)b)->val;
}

int cmpEdge(const void *a,const void *b){
  return ((edge *)a)->c-((edge *)b)->c;
}

int root(int *u,int x){
  if(u[x]==x) return x;
  return u[x]=root(u,u[x]);
}

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

void unite(int *u,int x,int y){
  x=root(u,x);
  y=root(u,y);
  if(x==y) return;
  u[x]=y;
}

void run(void){
  int n;
  scanf("%d",&n);
  node *x=(node *)calloc(n,sizeof(node));
  node *y=(node *)calloc(n,sizeof(node));
  int i;
  for(i=0;i<n;i++){
    int a,b;
    scanf("%d%d",&a,&b);
    x[i]=(node){i,a};
    y[i]=(node){i,b};
  }
  qsort(x,n,sizeof(node),cmpNode);
  qsort(y,n,sizeof(node),cmpNode);
  heap *h=newHeap(sizeof(edge),cmpEdge);
  for(i=0;i<n-1;i++){
    push(h,&((edge){x[i].index,x[i+1].index,x[i+1].val-x[i].val}));
    push(h,&((edge){y[i].index,y[i+1].index,y[i+1].val-y[i].val}));
  }
  int cnt=0;
  int *u=(int *)calloc(n,sizeof(int));
  for(i=0;i<n;i++) u[i]=i;
  int64 ans=0;
  for(i=0;cnt<n-1;i++){
    edge e;
    pop(h,&e);
    if(same(u,e.a,e.b)) continue;
    unite(u,e.a,e.b);
    ans+=e.c;
    cnt++;
  }
  printf("%lld\n",ans);
}

int main(void){
  run();
  return 0;
}