#!/usr/bin/env python3

import math
from typing import List
from heapq import heappush, heappop


class RunningMedian:
    def __init__(self):
        self.lowers, self.highers = [], []

    def add_number(self, number):
        if not self.highers or number > self.highers[0]:
            heappush(self.highers, number)
        else:
            heappush(self.lowers, -number)  # for lowers we need a max heap
        self.rebalance()

    def rebalance(self):
        if len(self.lowers) - len(self.highers) > 1:
            heappush(self.highers, -heappop(self.lowers))
        elif len(self.highers) - len(self.lowers) > 1:
            heappush(self.lowers, -heappop(self.highers))

    def get_median(self):
        if len(self.lowers) == len(self.highers):
            return (-self.lowers[0] + self.highers[0])/2
        elif len(self.lowers) > len(self.highers):
            return -self.lowers[0]
        else:
            return self.highers[0]


def gcd_floats(a: float, b: float) -> float:
    if a < b:
        return gcd_floats(b, a)

    # base case
    if abs(b) < 0.001:
        return a
    return gcd_floats(b, a - math.floor(a / b) * b)


def gcd_float_sequence(lst: List[float]) -> float:
    if len(lst) <= 0:
        raise ValueError("Need at least one number")
    elif len(lst) == 1:
        return lst[0]
    assert len(lst) >= 2
    gcd = gcd_floats(lst[0], lst[1])
    for i in range(2, len(lst)):
        gcd = gcd_floats(gcd, lst[i])
    return gcd


def truncate_float(n: float, decimals: int = 2):
    """Truncate a float to a particular number of decimals."""
    assert decimals > 0 and decimals < 10
    multiplier = 10 ** decimals
    return int(n * multiplier) / multiplier


def is_prime(n: int) -> bool:
    """Returns True if n is prime and False otherwise"""
    if not isinstance(n, int):
        raise TypeError("argument passed to is_prime is not of 'int' type")

    # Corner cases
    if n <= 1:
        return False
    if n <= 3:
        return True

    # This is checked so that we can skip middle five numbers in below
    # loop
    if (n % 2 == 0 or n % 3 == 0):
        return False

    i = 5
    while i * i <= n:
        if (n % i == 0 or n % (i + 2) == 0):
            return False
        i = i + 6
    return True