import copy
begining = [False,False,False,False,False,None,True,True,True,True,True]
#False = black True = white
its = [0]
def swap(layout, step):
    layoutCopy = copy.deepcopy(layout)
    layoutCopy[(step[0]+step[1])], layoutCopy[step[1]] = layoutCopy[step[1]], layoutCopy[(step[0]+step[1])]
    return layoutCopy
def isSolved(layout):
    for i in range(len(layout)):
        if(layout[i] == False):
            return (i >= (len(layout)/2))
def recurse(layout, its, steps = []):
    if isSolved(layout):
        its[0] += 1
        print(layout,list(x[0] for x in steps))
        return
    step = None
    for i in range(len(layout)):
        if(layout[i] == None):
            if(i >= 1): #If the empty space could have something to the left
                if(layout[i - 1] == False):
                    step = [-1,i]
                    recurse(swap(layout,step), its, (steps+[step]))
                if(i > 1): #If the empty space could have something 2 to the left
                    if(layout[i - 2] == False):
                        step = [-2,i]
                        recurse(swap(layout,step), its, (steps+[step]))
            if(i < (len(layout)-1)): #If the empty space could have something to the right
                if(layout[i + 1] == True):
                    step = [1,i]
                    recurse(swap(layout,step), its, (steps+[step]))
                if(i < (len(layout)-2)): #If the empty space could have something to the right
                    if(layout[i + 2] == True):
                        step = [2,i]
                        recurse(swap(layout,step), its, (steps+[step]))
    its[0] += 1
    #return None
recurse(begining,its,[])
print(its[0])

# Input for row and column
R = int(input())
C = int(input())

# Using list comprehension for input
matrix = [[int(input()) for x in range (C)] for y in range(R)]

""" Binary Search Algorithm 
----------------------------------------
"""
#iterative implementation of binary search in Python
def binary_search(a_list, item):
    """Performs iterative binary search to find the position of an integer in a given, sorted, list.
    a_list -- sorted list of integers
    item -- integer you are searching for the position of
    """
    first = 0
    last = len(a_list) - 1
    while first <= last:
        i = (first + last) / 2
        if a_list[i] == item:
            return ' found at position '.format(item=item, i=i)
        elif a_list[i] > item:
            last = i - 1
        elif a_list[i] < item:
            first = i + 1
        else:
            return ' not found in the list'.format(item=item)
#recursive implementation of binary search in Python
def binary_search_recursive(a_list, item):
    """Performs recursive binary search of an integer in a given, sorted, list.
    a_list -- sorted list of integers
    item -- integer you are searching for the position of
    """
    first = 0
    last = len(a_list) - 1
    if len(a_list) == 0:
        return ' was not found in the list'.format(item=item)
    else:
        i = (first + last) // 2
        if item == a_list[i]:
            return ' found'.format(item=item)
        else:
            if a_list[i] < item:
                return binary_search_recursive(a_list[i+1:], item)
            else:
                return binary_search_recursive(a_list[:i], item)

# question3.py
from itertools import product
V='∀'
E='∃'

def tt(f,n) :
  xss=product((0,1),repeat=n)
  print('function:',f.__name__)
  for xs in xss : print(*xs,':',int(f(*xs)))
  print('')

# this is the logic for part A (p\/q\/r) /\ (p\/q\/~r) /\ (p\/~q\/r) /\ (p\/~q\/~r) /\ (~p\/q\/r) /\ (~p\/q\/~r) /\ (~p\/~q\/r) /\ (~p\/~q\/~r)

def parta(p,q,r) :
  
  a=(p or q or r) and (p or q or not r) and (p or not q or r)and (p or not q or  not r)
  b=(not p or q or r ) and (not p or q or not r) and (not p or not q or r) and (not p or not q or not r)
  c= a and b
  return c

def partb(p,q,r) :
  a=(p or q and r) and (p or not q or not r) and (p or not q or not  r)and (p or q or  not r)
  b=(not p or q or r ) and (not p or q or not r) and (not p or not q or r) and (not p or not q or not r)
  c= a and b
  return c

print("part A:")
tt(parta,3)

print("part B:")
tt(partb,3)

def clamp_number(num, a, b):
  return max(min(num, max(a, b)), min(a, b))
  
clamp_number(2, 3, 5) # 3
clamp_number(1, -1, -5) # -1

from collections import defaultdict

def collect_dictionary(obj):
  inv_obj = defaultdict(list)
  for key, value in obj.items():
    inv_obj[value].append(key)
  return dict(inv_obj)
  
ages = {
  'Peter': 10,
  'Isabel': 10,
  'Anna': 9,
}
collect_dictionary(ages) # { 10: ['Peter', 'Isabel'], 9: ['Anna'] }