Sum of Medians
In one well-known algorithm of finding the k-th order statistics we should divide all elements into groups of five consecutive elements and find the median of each five. A median is called the middle element of a sorted array (it's the third largest element for a group of five). To increase the algorithm's performance speed on a modern video card, you should be able to find a sum of medians in each five of the array.A sum of medians of a sorted k-element set S = {a1, a2, ..., ak}, where a1 < a2 < a3 < ... < ak, will be understood by as The  operator stands for taking the remainder, that is  stands for the remainder of dividing x by y.To organize exercise testing quickly calculating the sum of medians for a changing set was needed.
The first line contains number n (1 ≤ n ≤ 105), the number of operations performed.Then each of n lines contains the description of one of the three operations:   add x — add the element x to the set;  del x — delete the element x from the set;  sum — find the sum of medians of the set. For any add x operation it is true that the element x is not included in the set directly before the operation.For any del x operation it is true that the element x is included in the set directly before the operation.All the numbers in the input are positive integers, not exceeding 109.
For each operation sum print on the single line the sum of medians of the current set. If the set is empty, print 0.Please, do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams (also you may use the %I64d specificator).
import io
import os
import heapq
from collections import Counter, deque
FILE_INPUT_MODE = 0
if FILE_INPUT_MODE >= 0:
    if FILE_INPUT_MODE == 1:
        CURRENT_DIR = os.path.dirname(os.path.abspath(__file__))
        FD = os.open(f'{CURRENT_DIR}\\input.txt', os.O_RDONLY)
    elif FILE_INPUT_MODE == 0:
        FD = 0
    DATA = io.BytesIO(os.read(FD, os.fstat(FD).st_size))
    if FD != 0:
        os.close(FD)

    def input():
        return DATA.readline().decode().rstrip('\r\n')
ALPHA = 0.75

class ScapegoatTree:

    def __init__(self, key=0, deleted=True):
        self.left = None
        self.right = None
        self.siz = 0
        self.sm = [0 for _ in range(5)]
        self.key = key
        self.deleted = deleted
        if not self.deleted:
            self.siz += 1
            self.sm[0] += self.key

    def add(self, x):
        if x == self.key:
            if self.deleted:
                self.deleted = False
                self.__maintain()
                return True
            else:
                return False
        if x < self.key:
            if self.left is None:
                self.left = ScapegoatTree(key=x, deleted=False)
                self.__maintain()
                return True
            elif self.left.add(x):
                self.__maintain()
                if self.left.__unbalanced():
                    self.left = self.__rebuild(self.left)
                return True
        elif self.right is None:
            self.right = ScapegoatTree(key=x, deleted=False)
            self.__maintain()
            return True
        elif self.right.add(x):
            self.__maintain()
            if self.right.__unbalanced():
                self.right = self.__rebuild(self.right)
            return True
        return False

    def discard(self, x):
        if x == self.key:
            if self.deleted:
                return False
            else:
                self.deleted = True
                self.__maintain()
                return True
        flag = True
        if x < self.key:
            if self.left is None:
                flag = False
            else:
                flag = self.left.discard(x)
        elif self.right is None:
            flag = False
        else:
            flag = self.right.discard(x)
        if flag:
            self.__maintain()
        return flag

    def sum(self, i):
        return self.sm[i]

    def __maintain(self):
        for i in range(5):
            self.sm[i] = 0
        cnt = 0
        if self.left is not None:
            cnt += self.left.siz
            for i in range(5):
                self.sm[i] += self.left.sm[i]
        if not self.deleted:
            self.sm[cnt % 5] += self.key
            cnt += 1
        if self.right is not None:
            for i in range(5):
                self.sm[(cnt + i) % 5] += self.right.sm[i]
            cnt += self.right.siz
        self.siz = cnt

    def __unbalanced(self):
        if self is None or self.siz <= 5:
            return False
        if self.left is not None and self.left.siz > self.siz * ALPHA:
            return True
        if self.right is not None and self.right.siz > self.siz * ALPHA:
            return True
        return False

    @classmethod
    def __rebuild(cls, p):
        a = []

        def dfs(q):
            if q is None:
                return
            dfs(q.left)
            if not q.deleted:
                a.append(q)
            dfs(q.right)

        def build(l, r):
            if l > r:
                return None
            mid = (l + r) // 2
            a[mid].left = build(l, mid - 1)
            a[mid].right = build(mid + 1, r)
            a[mid].__maintain()
            return a[mid]
        dfs(p)
        return build(0, len(a) - 1)

def solve():
    n = int(input())
    tree = ScapegoatTree()
    for _ in range(n):
        line = input().strip()
        if line[:3] == 'sum':
            print(tree.sum(2))
        else:
            (opr, x) = [word for word in line.split()]
            x = int(x)
            if opr == 'add':
                tree.add(x)
            else:
                tree.discard(x)

def main():
    solve()
if __name__ == '__main__':
    main()
import io
import os
import heapq
from collections import Counter, deque
FILE_INPUT_MODE = 0
if FILE_INPUT_MODE >= 0:
    if FILE_INPUT_MODE == 1:
        CURRENT_DIR = os.path.dirname(os.path.abspath(__file__))
        FD = os.open(f'{CURRENT_DIR}\\input.txt', os.O_RDONLY)
    elif FILE_INPUT_MODE == 0:
        FD = 0
    DATA = io.BytesIO(os.read(FD, os.fstat(FD).st_size))
    if FD != 0:
        os.close(FD)

    def input():
        return DATA.readline().decode().rstrip('\r\n')
ALPHA = 0.75
BETA = 7

class ScapegoatTree:

    def __init__(self, key=0, deleted=True):
        self.left = None
        self.right = None
        self.siz = 0
        self.sm = [0 for _ in range(5)]
        self.key = key
        self.deleted = deleted
        if not self.deleted:
            self.siz += 1
            self.sm[0] += self.key

    def add(self, x):
        if not self.__add(x):
            return False
        p = self
        while x != p.key:
            if x < p.key:
                if p.left.__unbalanced():
                    p.left = self.__rebuild(p.left)
                    break
                p = p.left
            else:
                if p.right.__unbalanced():
                    p.right = self.__rebuild(p.right)
                    break
                p = p.right
        return True

    def discard(self, x):
        if x == self.key:
            if self.deleted:
                return False
            else:
                self.deleted = True
                self.__maintain()
                return True
        flag = True
        if x < self.key:
            if self.left is None:
                flag = False
            else:
                flag = self.left.discard(x)
        elif self.right is None:
            flag = False
        else:
            flag = self.right.discard(x)
        if flag:
            self.__maintain()
        return flag

    def sum(self, i):
        return self.sm[i]

    def __add(self, x):
        if x == self.key:
            if self.deleted:
                self.deleted = False
                return True
            else:
                return False
        if x < self.key:
            if self.left is None:
                self.left = ScapegoatTree(key=x, deleted=False)
                flag = True
            else:
                flag = self.left.__add(x)
        elif self.right is None:
            self.right = ScapegoatTree(key=x, deleted=False)
            flag = True
        else:
            flag = self.right.__add(x)
        if flag:
            self.__maintain()
        return flag

    def __maintain(self):
        for i in range(5):
            self.sm[i] = 0
        cnt = 0
        if self.left is not None:
            cnt += self.left.siz
            for i in range(5):
                self.sm[i] += self.left.sm[i]
        if not self.deleted:
            self.sm[cnt % 5] += self.key
            cnt += 1
        if self.right is not None:
            for i in range(5):
                self.sm[(cnt + i) % 5] += self.right.sm[i]
            cnt += self.right.siz
        self.siz = cnt

    def __unbalanced(self):
        if self is None or self.siz <= BETA:
            return False
        if self.left is not None and self.left.siz > self.siz * ALPHA:
            return True
        if self.right is not None and self.right.siz > self.siz * ALPHA:
            return True
        return False

    @classmethod
    def __rebuild(cls, p):
        a = []

        def dfs(q):
            if q is None:
                return
            dfs(q.left)
            if not q.deleted:
                a.append(q)
            dfs(q.right)

        def build(l, r):
            if l > r:
                return None
            mid = (l + r) // 2
            a[mid].left = build(l, mid - 1)
            a[mid].right = build(mid + 1, r)
            a[mid].__maintain()
            return a[mid]
        dfs(p)
        return build(0, len(a) - 1)

def solve():
    n = int(input())
    tree = ScapegoatTree()
    for _ in range(n):
        line = input().strip()
        if line[:3] == 'sum':
            print(tree.sum(2))
        else:
            (opr, x) = [word for word in line.split()]
            x = int(x)
            if opr == 'add':
                tree.add(x)
            else:
                tree.discard(x)

def main():
    solve()
if __name__ == '__main__':
    main()
import io
import os
import heapq
from collections import Counter, deque
FILE_INPUT_MODE = 0
if FILE_INPUT_MODE >= 0:
    if FILE_INPUT_MODE == 1:
        CURRENT_DIR = os.path.dirname(os.path.abspath(__file__))
        FD = os.open(f'{CURRENT_DIR}\\input.txt', os.O_RDONLY)
    elif FILE_INPUT_MODE == 0:
        FD = 0
    DATA = io.BytesIO(os.read(FD, os.fstat(FD).st_size))
    if FD != 0:
        os.close(FD)

    def input():
        return DATA.readline().decode().rstrip('\r\n')
ALPHA = 0.75
BETA = 15

class ScapegoatTree:

    def __init__(self, key=0, deleted=True):
        self.left = None
        self.right = None
        self.siz = 0
        self.sm = [0 for _ in range(5)]
        self.key = key
        self.deleted = deleted
        if not self.deleted:
            self.siz += 1
            self.sm[0] += self.key

    def add(self, x):
        if not self.__add(x):
            return False
        p = self
        while x != p.key:
            if x < p.key:
                if p.left.__unbalanced():
                    p.left = self.__rebuild(p.left)
                    break
                p = p.left
            else:
                if p.right.__unbalanced():
                    p.right = self.__rebuild(p.right)
                    break
                p = p.right
        return True

    def discard(self, x):
        if x == self.key:
            if self.deleted:
                return False
            else:
                self.deleted = True
                self.__maintain()
                return True
        flag = True
        if x < self.key:
            if self.left is None:
                flag = False
            else:
                flag = self.left.discard(x)
        elif self.right is None:
            flag = False
        else:
            flag = self.right.discard(x)
        if flag:
            self.__maintain()
        return flag

    def sum(self, i):
        return self.sm[i]

    def __add(self, x):
        if x == self.key:
            if self.deleted:
                self.deleted = False
                return True
            else:
                return False
        if x < self.key:
            if self.left is None:
                self.left = ScapegoatTree(key=x, deleted=False)
                flag = True
            else:
                flag = self.left.__add(x)
        elif self.right is None:
            self.right = ScapegoatTree(key=x, deleted=False)
            flag = True
        else:
            flag = self.right.__add(x)
        if flag:
            self.__maintain()
        return flag

    def __maintain(self):
        for i in range(5):
            self.sm[i] = 0
        cnt = 0
        if self.left is not None:
            cnt += self.left.siz
            for i in range(5):
                self.sm[i] += self.left.sm[i]
        if not self.deleted:
            self.sm[cnt % 5] += self.key
            cnt += 1
        if self.right is not None:
            for i in range(5):
                self.sm[(cnt + i) % 5] += self.right.sm[i]
            cnt += self.right.siz
        self.siz = cnt

    def __unbalanced(self):
        if self is None or self.siz <= BETA:
            return False
        if self.left is not None and self.left.siz > self.siz * ALPHA:
            return True
        if self.right is not None and self.right.siz > self.siz * ALPHA:
            return True
        return False

    @classmethod
    def __rebuild(cls, p):
        a = []

        def dfs(q):
            if q is None:
                return
            dfs(q.left)
            if not q.deleted:
                a.append(q)
            dfs(q.right)

        def build(l, r):
            if l > r:
                return None
            mid = (l + r) // 2
            a[mid].left = build(l, mid - 1)
            a[mid].right = build(mid + 1, r)
            a[mid].__maintain()
            return a[mid]
        dfs(p)
        return build(0, len(a) - 1)

def solve():
    n = int(input())
    tree = ScapegoatTree()
    for _ in range(n):
        line = input().strip()
        if line[:3] == 'sum':
            print(tree.sum(2))
        else:
            (opr, x) = [word for word in line.split()]
            x = int(x)
            if opr == 'add':
                tree.add(x)
            else:
                tree.discard(x)

def main():
    solve()
if __name__ == '__main__':
    main()