Problem: Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.  Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Submission attempts (in order):
def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
number.reversed()
goal=[]
for i in number:
  if i != reversed_num(i)+1:
    goal.append(reversed_num(i)+1)
    number.remove(reversed_num(i)+1)
print(len(set(number)&set(goal)))

def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
count=0
while len(number)>0:
  x=reversed_num(number[-1])+1
  if x in number:
    number.remove(x)
    count+=1
  number.pop()
print(count)


def reversed_num(num):
  num_len=len(bin(num))-2
  f=2*num_len-1
  return num^f

def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
count=0
while len(number)>0:
  if reversed_num(number[-1])+1 in number and number[-1]!=reversed_num(number[-1])+1:
    number.remove(reversed_num(number[-1])+1)
    count+=1
print(count)


def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
number.reverse()
for i in number:
  if i!=reversed_num(i)+1 and reversed_num(i)+1 in number:
    number.remove(reversed_num(i)+1)
    count+=1
print(count)

import bisect

def number(num):
  
  number_len = len(num)-2
  
  f ＝ 2**number_len - 1
  
  return (num^f)+1

line=list(map(int,input().split))

count=0

while len(line)>0:
  
  k=line.pop()
  
  if int(k) != k:
    continue
  x=number(k)
  
  if x>line[-1]:
    continue
  
  if line[bisect.bisect_left(line,x)]==x:
    
    line[bisect.bisect_left(line,x)] += 0.5
    count+=1

print(count)

def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
number.reverse()
goal=[]
for i in number:
  if i != reversed_num(i)+1:
    goal.append(reversed_num(i)+1)
    number.remove(reversed_num(i)+1)
print(len(set(number)&set(goal)))


import bisect

def number(num):
  
  number_len = len(num)-2
  
  f ＝ 2**number_len - 1
  
  return (num^f)+1

n=int(input())
line=list(map(int,input().split))

count=0

while len(line)>0:
  
  k=line.pop()
  
  if int(k) != k:
    continue
  x=number(k)
  
  if x>line[-1]:
    continue
  
  if line[bisect.bisect_left(line,x)]==x:
    
    line[bisect.bisect_left(line,x)] += 0.5
    count+=1

print(count)

def reversed_num(num):
  num_len=len(bin(num))-2
  f=2*num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
goal=[]
for i in number:
  goal.append(reversed_num(i)+1)
print(len(set(number)&set(goal)))

def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
count=0
while len(number)>0:
  q=number[-1]
  x=reversed_num(number[-1])+1
  number.pop()
  if x!=q:
    if x in list:
      number.remove(x)
      count+=1
print(count)


import bisect
def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
count=0
while len(number)>0:
  x=reversed_num(number.pop())+1
  if number[bisect.bisect_left(number,x)] ==x:
    number[bisect.bisect_left(number,x)]=0
    count+=1
print(count)


import bisect
def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
count=0
while len(number)>0:
  x=reversed_num(number.pop())+1
  if number[bisect.bisect_left(number,x)] ==x:
    number.pop(bisect.bisect_left(number,x))
    count+=1
print(count)

import bisect
def reversed_num(num):
  num_len=len(bin(num))-2
  f=2**num_len-1
  return num^f
n=int(input())
number=list(map(int,input().split()))
number.sort()
count=0
while len(number)>0:
  x=reversed_num(number.pop())+1
  if len(number)==0:
    break
  y=bisect.bisect_left(number,x)
  if x>number[-1]:
    y-=1
  if number[y] ==x:
    number[y]+=0.5
    count+=1
print(count)

import bisect

def number(num):
  
  number_len = len(bin(num))-2
  
  f = 2**number_len - 1
  
  return (num^f)+1

n=int(input())
line=list(map(int,input().split()))

line.sort()

count=0

while len(line)>0:
  
  k=line.pop()
  
  if len(line)==0:
    break
  
  if int(k) != k:
    continue
  x=number(k)
  
  if x>line[-1]:
    continue
  
  if line[bisect.bisect_left(line,x)]==x:
    
    line[bisect.bisect_left(line,x)] -= 0.5
    count+=1

print(count)

Verdicts: Runtime Error

Runtime Error

Wrong Answer

Time Limit Exceeded

Runtime Error

Runtime Error

Runtime Error

Runtime Error

Wrong Answer

Runtime Error

Runtime Error

Runtime Error

Runtime Error

Accepted