Buggy python submission (verdict: Time Limit Exceeded):
# atcoder problem solving

# Built?

N = int(input())
d = []
graph = [[] for i in range(N+1)]
for i in range(N):
    x, y = map(int, input().split())
    d.append((i+1, x, y))

edge = []

# x座標に関する辺の設定

d.sort(key=lambda x: x[1])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(px-qx)
    graph[a].append((dis, b))
    graph[b].append((dis, a))
    edge.append((dis, a, b))
    edge.append((dis, b, a))

# y座標に関する辺の設定

d.sort(key=lambda x: x[2])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(py-qy)
    graph[a].append((dis, b))
    graph[b].append((dis, a))
    edge.append((dis, a, b))
    edge.append((dis, b, a))


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

    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())


# 最小全域木
def kruskal():
    res = 0
    G = UnionFind(N)
    edge.sort()
    for cost, p, q, in edge:
        if not G.same(p, q):
            G.union(p, q)
            res += cost
    return res


ans = kruskal()

print(ans)

Fixed submission:
# atcoder problem solving

# Built?
import sys
input=sys.stdin.readline
N = int(input())
d = []

for i in range(N):
    x, y = map(int, input().split())
    d.append((i+1, x, y))

edge = []

# x座標に関する辺の設定

d.sort(key=lambda x: x[1])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(px-qx)

    edge.append((dis, a, b))
    edge.append((dis, b, a))

# y座標に関する辺の設定

d.sort(key=lambda x: x[2])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(py-qy)

    edge.append((dis, a, b))
    edge.append((dis, b, a))


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

    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())

edge.sort()
# 最小全域木（クラスかるほう）
def kruskal():
    res = 0
    G = UnionFind(N)
    for cost, p, q, in edge:
        if not G.same(p, q):
            G.union(p, q)
            res += cost
    return res


ans = kruskal()

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
# atcoder problem solving

# Built?

N = int(input())
d = []
graph = [[] for i in range(N+1)]
for i in range(N):
    x, y = map(int, input().split())
    d.append((i+1, x, y))

edge = []

# x座標に関する辺の設定

d.sort(key=lambda x: x[1])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(px-qx)
    graph[a].append((dis, b))
    graph[b].append((dis, a))
    edge.append((dis, a, b))
    edge.append((dis, b, a))

# y座標に関する辺の設定

d.sort(key=lambda x: x[2])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(py-qy)
    graph[a].append((dis, b))
    graph[b].append((dis, a))
    edge.append((dis, a, b))
    edge.append((dis, b, a))


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

    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())


# 最小全域木（クラスかるほう）
def kruskal():
    res = 0
    G = UnionFind(N)
    edge.sort()
    for cost, p, q, in edge:
        if not G.same(p, q):
            G.union(p, q)
            res += cost
    return res


ans = kruskal()

print(ans)

Fixed submission:
# atcoder problem solving

# Built?
import sys
input=sys.stdin.readline
N = int(input())
d = []

for i in range(N):
    x, y = map(int, input().split())
    d.append((i+1, x, y))

edge = []

# x座標に関する辺の設定

d.sort(key=lambda x: x[1])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(px-qx)

    edge.append((dis, a, b))
    edge.append((dis, b, a))

# y座標に関する辺の設定

d.sort(key=lambda x: x[2])

for i in range(N-1):
    a, px, py = d[i]
    b, qx, qy = d[i+1]
    dis = abs(py-qy)

    edge.append((dis, a, b))
    edge.append((dis, b, a))


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

    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())

edge.sort()
# 最小全域木（クラスかるほう）
def kruskal():
    res = 0
    G = UnionFind(N)
    for cost, p, q, in edge:
        if not G.same(p, q):
            G.union(p, q)
            res += cost
    return res


ans = kruskal()

print(ans)