Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


n = int(input())
graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append([x,y,i])
    graphy.append([x,y,i])
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = []

def S(G):
    for k in range(n-1):
        i,j = G[k][2], G[k+1][2]
        x0,y0,x1,y1 = G[k][0],G[k][1],G[k+1][0],G[k+1][1]
        m = min(abs(x0-x1),abs(y0-y1))
        graph.append([m,i,j])


S(graphx)
S(graphy)

graph.sort()
#print(graph)

ans = 0
uf = UnionFind(n)
for l in graph:
    if not uf.same(l[1],l[2]):
        ans += l[0]
        uf.union(l[1],l[2])
    if uf.group_count() == 1:
        print(ans)
        quit()

Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


n = int(input())
graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append((x,y,i))
    graphy.append((x,y,i))
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = []


for k in range(n-1):
    i,j = graphx[k][2], graphx[k+1][2]
    x0,x1 = graphx[k][0],graphx[k+1][0]
    m = abs(x0-x1)
    graph.append((m,i,j))

for k in range(n-1):
    i,j = graphy[k][2], graphy[k+1][2]
    y0,y1 = graphy[k][1],graphy[k+1][1]
    m = abs(y0-y1)
    graph.append((m,i,j))


graph.sort()
#print(graph)

ans = 0
uf = UnionFind(n)
for c,i,j in graph:
    if not uf.same(i,j):
        ans += c
        uf.union(i,j)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


n = int(input())
graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append([x,y,i])
    graphy.append([x,y,i])
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = []

def S(G):
    for k in range(n-1):
        i,j = G[k][2], G[k+1][2]
        x0,y0,x1,y1 = G[k][0],G[k][1],G[k+1][0],G[k+1][1]
        m = min(abs(x0-x1),abs(y0-y1))
        graph.append([m,i,j])


S(graphx)
S(graphy)

graph.sort()
#print(graph)

ans = 0
uf = UnionFind(n)
for l in graph:
    if not uf.same(l[1],l[2]):
        ans += l[0]
        uf.union(l[1],l[2])
print(ans)

Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


n = int(input())
graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append((x,y,i))
    graphy.append((x,y,i))
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = []


for k in range(n-1):
    i,j = graphx[k][2], graphx[k+1][2]
    x0,x1 = graphx[k][0],graphx[k+1][0]
    m = abs(x0-x1)
    graph.append((m,i,j))

for k in range(n-1):
    i,j = graphy[k][2], graphy[k+1][2]
    y0,y1 = graphy[k][1],graphy[k+1][1]
    m = abs(y0-y1)
    graph.append((m,i,j))


graph.sort()
#print(graph)

ans = 0
uf = UnionFind(n)
for c,i,j in graph:
    if not uf.same(i,j):
        ans += c
        uf.union(i,j)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import heapq
n = int(input())

def prim_heap():
    used = [False]*n
    edgelist = []
    for e in graph[0]:
        heapq.heappush(edgelist,e)
    used[0] = True
    ans = 0
    while edgelist:
        minedge = heapq.heappop(edgelist)
        v = minedge[1]
        if used[minedge[1]]:
            continue
        used[v] = True
        for e in graph[v]:
            if not used[e[1]]:
                heapq.heappush(edgelist,e)
        ans += minedge[0]
    return ans

graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append([x,y,i])
    graphy.append([x,y,i])
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = [[] for _ in range(n)]


def S(G):
    for k in range(n-1):
        i,j = G[k][2], G[k+1][2]
        x0,y0,x1,y1 = G[k][0],G[k][1],G[k+1][0],G[k+1][1]
        m = min(abs(x0-x1),abs(y0-y1))
        graph[i].append([m,j])
        graph[j].append([m,i])
S(graphx)
S(graphy)

print(prim_heap())

Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


n = int(input())
graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append((x,y,i))
    graphy.append((x,y,i))
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = []


for k in range(n-1):
    i,j = graphx[k][2], graphx[k+1][2]
    x0,x1 = graphx[k][0],graphx[k+1][0]
    m = abs(x0-x1)
    graph.append((m,i,j))

for k in range(n-1):
    i,j = graphy[k][2], graphy[k+1][2]
    y0,y1 = graphy[k][1],graphy[k+1][1]
    m = abs(y0-y1)
    graph.append((m,i,j))


graph.sort()
#print(graph)

ans = 0
uf = UnionFind(n)
for c,i,j in graph:
    if not uf.same(i,j):
        ans += c
        uf.union(i,j)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import heapq
n = int(input())

def prim_heap():
    used = [False]*n
    edgelist = []
    for e in graph[0]:
        heapq.heappush(edgelist,e)
    used[0] = True
    ans = 0
    while edgelist:
        minedge = heapq.heappop(edgelist)
        v = minedge[1]
        if used[minedge[1]]:
            continue
        used[v] = True
        for e in graph[v]:
            if not used[e[1]]:
                heapq.heappush(edgelist,e)
        ans += minedge[0]
    return ans

graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append([x,y,i])
    graphy.append([x,y,i])
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = [[] for _ in range(n)]


def S(G):
    for k in range(n-1):
        i,j = G[k][2], G[k+1][2]
        x0,y0,x1,y1 = G[k][0],G[k][1],G[k+1][0],G[k+1][1]
        m = min(abs(x0-x1),abs(y0-y1))
        graph[i].append([m,j])
        graph[j].append([m,i])
S(graphx)
S(graphy)

print(prim_heap())

Fixed submission:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


n = int(input())
graphx = []
graphy = []

for i in range(n):
    x,y = map(int,input().split())
    graphx.append((x,y,i))
    graphy.append((x,y,i))
graphx = sorted(graphx, key=lambda x:x[0])
graphy = sorted(graphy, key=lambda x:x[1])
graph = []


for k in range(n-1):
    i,j = graphx[k][2], graphx[k+1][2]
    x0,x1 = graphx[k][0],graphx[k+1][0]
    m = abs(x0-x1)
    graph.append((m,i,j))

for k in range(n-1):
    i,j = graphy[k][2], graphy[k+1][2]
    y0,y1 = graphy[k][1],graphy[k+1][1]
    m = abs(y0-y1)
    graph.append((m,i,j))


graph.sort()
#print(graph)

ans = 0
uf = UnionFind(n)
for c,i,j in graph:
    if not uf.same(i,j):
        ans += c
        uf.union(i,j)
print(ans)