Buggy python submission (verdict: Time Limit Exceeded):
from operator import itemgetter
from collections import defaultdict


class UnionFindTree():
    def __init__(self):
        self.__parent_of = defaultdict(lambda: None)
        self.__rank_of = defaultdict(lambda: 0)
        self.__size = defaultdict(lambda: 1)

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree()
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
from operator import itemgetter


class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adjx = [None] * (N-1)
    adjy = [None] * (N-1)
    for i in range(N-1):
        adjx[i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adjy[i] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adjx.sort(key=itemgetter(0))
    adjy.sort(key=itemgetter(0))
    adjx += [(float("inf"), 0, 0)]
    adjy += [(float("inf"), 0, 0)]
    uft = UnionFindTree(range(N))
    ans = 0
    xi = 0
    yi = 0
    while xi < len(adjx)-1 or yi < len(adjy)-1:
        if adjx[xi][0] <= adjy[yi][0]:
            cost, a, b = adjx[xi]
            xi += 1
        else:
            cost, a, b = adjy[yi]
            yi += 1
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
from operator import itemgetter


class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(range(N))
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = []
    Y = []
    for i in range(N):
        x, y = map(int, input().split())
        X += [(x, i)]
        Y += [(y, i)]
    X.sort()
    Y.sort()
    adj = []
    for i in range(N-1):
        adj += [(X[i+1][0] - X[i][0], X[i][1], X[i+1][1])]
        adj += [(Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])]
    adj.sort()
    uft = UnionFindTree(range(N))
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = []
    Y = []
    for i in range(N):
        x, y = map(int, input().split())
        X += [(x, i)]
        Y += [(y, i)]
    X.sort()
    Y.sort()
    adjx = []
    adjy = []
    for i in range(N-1):
        adjx += [(X[i+1][0] - X[i][0], X[i][1], X[i+1][1])]
        adjy += [(Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])]
    adjx.sort()
    adjy.sort()
    adjx += [(float("inf"), 0, 0)]
    adjy += [(float("inf"), 0, 0)]
    uft = UnionFindTree(range(N))
    ans = 0
    xi = 0
    yi = 0
    while xi < len(adjx)-1 or yi < len(adjy)-1:
        if adjx[xi][0] <= adjy[yi][0]:
            cost, a, b = adjx[xi]
            xi += 1
        else:
            cost, a, b = adjy[yi]
            yi += 1
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort()
    Y.sort()
    adj = [None] * (2*N-2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=lambda x: x[0])
    uft = UnionFindTree(range(N))
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort()
    Y.sort()
    adj = []
    for i in range(N-1):
        adj += [(X[i+1][0] - X[i][0], X[i][1], X[i+1][1])]
        adj += [(Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])]
    adj.sort(key=lambda x: x[0])
    uft = UnionFindTree(range(N))
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFindTree():
    def __init__(self, values=[]):
        self.__parent_of = {}
        self.__rank_of = {}
        self.__size = {}
        for value in values:
            self.add(value)

    def add(self, value):
        if value in self.__parent_of:
            raise RuntimeError("Dupulicated Value Added")
        self.__parent_of[value] = None
        self.__rank_of[value] = 0
        self.__size[value] = 1

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort()
    Y.sort()
    adj = []
    for i in range(N-1):
        adj.append((X[i+1][0] - X[i][0], X[i][1], X[i+1][1]))
        adj.append((Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1]))
    adj.sort(key=lambda x: x[0])
    uft = UnionFindTree(range(N))
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from operator import itemgetter


class UnionFindTree():
    def __init__(self, N):
        self.__parent_of = [None] * N
        self.__rank_of = [0] * N
        self.__size = [1] * N

    def __root(self, value):
        if self.__parent_of[value] is None:
            return value
        else:
            self.__parent_of[value] = self.__root(self.__parent_of[value])
            return self.__parent_of[value]

    def unite(self, a, b):
        r1 = self.__root(a)
        r2 = self.__root(b)
        if r1 != r2:
            if self.__rank_of[r1] < self.__rank_of[r2]:
                self.__parent_of[r1] = r2
                self.__size[r2] += self.__size[r1]
            else:
                self.__parent_of[r2] = r1
                self.__size[r1] += self.__size[r2]
                if self.__rank_of[r1] == self.__rank_of[r2]:
                    self.__rank_of[r1] += 1

    def is_same(self, a, b):
        return self.__root(a) == self.__root(b)

    def size(self, a):
        return self.__size[self.__root(a)]

    def groups(self):
        groups = {}
        for k in self.__parent_of.keys():
            r = self.__root(k)
            if r not in groups:
                groups[r] = []
            groups[r].append(k)
        return [groups[x] for x in groups]


def main():
    N = int(input())
    X = [None] * N
    Y = [None] * N
    for i in range(N):
        x, y = map(int, input().split())
        X[i] = (x, i)
        Y[i] = (y, i)
    X.sort(key=itemgetter(0))
    Y.sort(key=itemgetter(0))
    adj = [None] * (2*N - 2)
    for i in range(N-1):
        adj[2*i] = (X[i+1][0] - X[i][0], X[i][1], X[i+1][1])
        adj[2*i+1] = (Y[i+1][0] - Y[i][0], Y[i][1], Y[i+1][1])
    adj.sort(key=itemgetter(0))
    uft = UnionFindTree(N)
    ans = 0
    for pair in adj:
        cost, a, b = pair
        if not uft.is_same(a, b):
            uft.unite(a, b)
            ans += cost
        if uft.size(a) == N:
            break
    print(ans)


if __name__ == "__main__":
    main()