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def qsort(nums):
    qsort_impl(nums, 0, len(nums)-1)
    return nums

def qsort_impl(nums, start, end):
    if start >= end: return
    pivot = partition(nums, start, end)
    qsort_impl(nums, start, pivot-1)
    qsort_impl(nums, pivot+1, end)

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class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None
        
def front_travel(root):
    if not root: return
    s = [root]
    while s:

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def reversePairs_using_merge_sort(nums):
    n = len(nums)
    buffer = [None] * n

    # 最本质的方法其实应该想到使用merge_sort，因为天然的思考过程可以考虑到分为两个部分
    # reversePairs的个数等于左边reverse的和右边reverse的，然后加上合并过程中reverse的
    # 这和merge_sort的过程不谋而和。实现的过程中，控制左边变量i的移动，每次找到一个i
    # 不停的移动p指针找到符合要求节点的上限，使用j指针找到比i节点小的节点上限，合并和
    # 计算reverse pair过程重叠，非常nice的solution
    def merge_sort_impl(l, r):

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# copyed from http://code.activestate.com/recipes/522995-priority-dict-a-priority-queue-with-updatable-prio/
from heapq import heapify, heappush, heappop

class priority_dict(dict):
    """Dictionary that can be used as a priority queue.

    Keys of the dictionary are items to be put into the queue, and values
    are their respective priorities. All dictionary methods work as expected.
    The advantage over a standard heapq-based priority queue is
    that priorities of items can be efficiently updated (amortized O(1))

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# logging_example.py

import logging

# Create a custom logger
logger = logging.getLogger(__name__)

# Create handlers
c_handler = logging.StreamHandler()
f_handler = logging.FileHandler('file.log')

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"""
Add copy to clipboard from IPython!
To install, just copy it to your profile/startup directory, typically:

    ~/.ipython/profile_default/startup/

Example usage:

    %clip hello world
    # will store "hello world"

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from functools import wraps

def memoize(function):
    memo = {}
    @wraps(function)
    def wrapper(*args):
        try:
            return memo[args]
        except KeyError:
            rv = function(*args)

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from pandas_datareader import data
goog = data.DataReader('GOOG', start='2014', end='2020', data_source='yahoo')
goog.columns = goog.columns.str.lower()
goog = goog.asfreq('D', method='bfill')

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def f(x, y):
    return np.sin(x) ** 10 + np.cos(10+x*y) + np.cos(x)
  
x = np.linspace(0, 5, 50)
y = np.linspace(0, 5, 50)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)

# draw contour
contour = plt.contour(X, Y, Z, 3, colors='black')

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from sklearn.datasets import load_digits
digits = load_digits()

# split data
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(digits.data, digits.target, shuffle=True)

# use Gaussian Naive Bayes
from sklearn.naive_bayes import GaussianNB
model = GaussianNB()