Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())

def find(x, U, r):
  p = []
  while not x == U[x]:
    p.append(x)
    x = U[x]
  for x_ in p:
    U[x_] == x
  return x
  
def merge(x, y, U, r):
  x = find(x, U, r)
  y = find(y, U, r)
  
  if x == y:
    return False
  #print(x,y, U)
  if r[x] < r[y]:
    x, y = y, x
  U[y] = x
  r[x] = max(r[y]+1, r[x])
  #print(x,y, U)
  return True
  
U = [i for i in range(N)]
r = [0 for _ in range(N)]

B = []
C = []
for i in range(N):
  u, v = map(int, input().split())
  B.append((u, v, i))
  C.append((v, u, i))
B.sort()
C.sort()


#辺の作成
R = []
for i in range(1,N):
  c = B[i][0] - B[i-1][0]
  p1 = B[i][2]
  p2 = B[i-1][2]
  R.append((c, p1, p2))
  R.append((c, p2, p1))
  
  c = C[i][0] - C[i-1][0]
  p1 = C[i][2]
  p2 = C[i-1][2]
  R.append((c, p1, p2))
  R.append((c, p2, p1))
R.sort()

#Union Find:
U = [i for i in range(N)]
r = [0 for _ in range(N)]
#print(U)  
ans = 0
for road in R:
  c = road[0]
  x = road[1]
  y = road[2]
  if merge(x, y, U, r):
    #print(U)  
    ans += c
#print(U)    
print(ans)

Fixed submission:
N = int(input())

def find(x, U, r):
  p = []
  while not x == U[x]:
    p.append(x)
    x = U[x]
  for x_ in p:
    U[x_] == x
  return x
  
def merge(x, y, U, r):
  x = find(x, U, r)
  y = find(y, U, r)
  
  if x == y:
    return False
  #print(x,y, U)
  if r[x] < r[y]:
    x, y = y, x
  U[y] = x
  r[x] = max(r[y]+1, r[x])
  #print(x,y, U)
  return True
  
U = [i for i in range(N)]
r = [0 for _ in range(N)]

B = []
C = []
for i in range(N):
  u, v = map(int, input().split())
  B.append((u, v, i))
  C.append((v, u, i))
B.sort()
C.sort()

#辺の作成
R = []
for i in range(1,N):
  c = B[i][0] - B[i-1][0]
  p1 = B[i][2]
  p2 = B[i-1][2]
  R.append((c, p1, p2))
  
  c = C[i][0] - C[i-1][0]
  p1 = C[i][2]
  p2 = C[i-1][2]
  R.append((c, p1, p2))
R.sort()

#Union Find:
U = [i for i in range(N)]
r = [0 for _ in range(N)]
#print(U)  
ans = 0
for road in R:
  c = road[0]
  x = road[1]
  y = road[2]
  if merge(x, y, U, r):
    #print(U)  
    ans += c
#print(U)    
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())

def find(x, U, r):
  p = []
  while not x == U[x]:
    p.append(x)
    x = U[x]
  for x_ in p:
    U[x_] == x
  return x
  
def merge(x, y, U, r):
  x = find(x, U, r)
  y = find(y, U, r)
  
  if x == y:
    return False
  #print(x,y, U)
  if r[x] < r[y]:
    x, y = y, x
  U[y] = x
  r[x] = max(r[y]+1, r[x])
  #print(x,y, U)
  return True
  
U = [i for i in range(N)]
r = [0 for _ in range(N)]

A = [(tuple(map(int, input().split())), j) for j in range(N)]
B = sorted(A)
C = sorted(A, key=lambda t: ((t[0][1],t[0][0]),t[1]))

#辺の作成
R = []
for i in range(1,N):
  c = B[i][0][0] - B[i-1][0][0]
  p1 = B[i][1]
  p2 = B[i-1][1]
  R.append((c, p1, p2))
  R.append((c, p2, p1))
  
  c = C[i][0][1] - C[i-1][0][1]
  p1 = C[i][1]
  p2 = C[i-1][1]
  R.append((c, p1, p2))
  R.append((c, p2, p1))
R.sort()

#Union Find:
U = [i for i in range(N)]
r = [0 for _ in range(N)]
#print(U)  
ans = 0
for road in R:
  c = road[0]
  x = road[1]
  y = road[2]
  if merge(x, y, U, r):
    #print(U)  
    ans += c
#print(U)    
print(ans)

Fixed submission:
N = int(input())

def find(x, U, r):
  p = []
  while not x == U[x]:
    p.append(x)
    x = U[x]
  for x_ in p:
    U[x_] == x
  return x
  
def merge(x, y, U, r):
  x = find(x, U, r)
  y = find(y, U, r)
  
  if x == y:
    return False
  #print(x,y, U)
  if r[x] < r[y]:
    x, y = y, x
  U[y] = x
  r[x] = max(r[y]+1, r[x])
  #print(x,y, U)
  return True
  
U = [i for i in range(N)]
r = [0 for _ in range(N)]

B = []
C = []
for i in range(N):
  u, v = map(int, input().split())
  B.append((u, v, i))
  C.append((v, u, i))
B.sort()
C.sort()

#辺の作成
R = []
for i in range(1,N):
  c = B[i][0] - B[i-1][0]
  p1 = B[i][2]
  p2 = B[i-1][2]
  R.append((c, p1, p2))
  
  c = C[i][0] - C[i-1][0]
  p1 = C[i][2]
  p2 = C[i-1][2]
  R.append((c, p1, p2))
R.sort()

#Union Find:
U = [i for i in range(N)]
r = [0 for _ in range(N)]
#print(U)  
ans = 0
for road in R:
  c = road[0]
  x = road[1]
  y = road[2]
  if merge(x, y, U, r):
    #print(U)  
    ans += c
#print(U)    
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())

def find(x, U, r):
  while not x == U[x]:
    x = U[x]
  return x
  
def merge(x, y, U, r):
  x = find(x, U, r)
  y = find(y, U, r)
  
  if x == y:
    return False
  #print(x,y, U)
  if r[x] < r[y]:
    x, y = y, x
  U[y] = x
  r[x] = max(r[y]+1, r[x])
  #print(x,y, U)
  return True
  
U = [i for i in range(N)]
r = [0 for _ in range(N)]

A = [(tuple(map(int, input().split())), j) for j in range(N)]
B = sorted(A)
C = sorted(A, key=lambda t: ((t[0][1],t[0][0]),t[1]))

#辺の作成
R = []
for i in range(1,N):
  c = B[i][0][0] - B[i-1][0][0]
  p1 = B[i][1]
  p2 = B[i-1][1]
  R.append((c, p1, p2))
  R.append((c, p2, p1))
  
  c = C[i][0][1] - C[i-1][0][1]
  p1 = C[i][1]
  p2 = C[i-1][1]
  R.append((c, p1, p2))
  R.append((c, p2, p1))
R.sort()

#Union Find:
U = [i for i in range(N)]
r = [0 for _ in range(N)]
#print(U)  
ans = 0
for road in R:
  c = road[0]
  x = road[1]
  y = road[2]
  if merge(x, y, U, r):
    #print(U)  
    ans += c
#print(U)    
print(ans)

Fixed submission:
N = int(input())

def find(x, U, r):
  p = []
  while not x == U[x]:
    p.append(x)
    x = U[x]
  for x_ in p:
    U[x_] == x
  return x
  
def merge(x, y, U, r):
  x = find(x, U, r)
  y = find(y, U, r)
  
  if x == y:
    return False
  #print(x,y, U)
  if r[x] < r[y]:
    x, y = y, x
  U[y] = x
  r[x] = max(r[y]+1, r[x])
  #print(x,y, U)
  return True
  
U = [i for i in range(N)]
r = [0 for _ in range(N)]

B = []
C = []
for i in range(N):
  u, v = map(int, input().split())
  B.append((u, v, i))
  C.append((v, u, i))
B.sort()
C.sort()

#辺の作成
R = []
for i in range(1,N):
  c = B[i][0] - B[i-1][0]
  p1 = B[i][2]
  p2 = B[i-1][2]
  R.append((c, p1, p2))
  
  c = C[i][0] - C[i-1][0]
  p1 = C[i][2]
  p2 = C[i-1][2]
  R.append((c, p1, p2))
R.sort()

#Union Find:
U = [i for i in range(N)]
r = [0 for _ in range(N)]
#print(U)  
ans = 0
for road in R:
  c = road[0]
  x = road[1]
  y = road[2]
  if merge(x, y, U, r):
    #print(U)  
    ans += c
#print(U)    
print(ans)