Buggy python submission (verdict: Time Limit Exceeded):
from math import log,floor
N = int(input())
A = list(map(int, input().split()))

# log(10**9 + 10**9)/log(2) = 30.89 < 31
#print(log(2 * 10**9) / log(2))

A.sort(reverse=True)
usedI = [0] * N
cnt = 0

for i in range(N):
  if usedI[i] == 1:
    continue
  #print(i, log(A[i]) / log(2) )
  x = floor(log(A[i]) / log(2)) + 1 #実現可能なべき上
  search_x = 2 ** x - A[i]
  l = i+1
  r = N-1
  while l <= r:
    m = (l+r)//2
    #print(l,r,m)

    if search_x < A[m]:
      l = m if l<m else m+1
    elif search_x > A[m]:
      r = m if m<r else m-1
    else:
      if usedI[m] == 0:
        cnt += 1
        usedI[i] = 1
        usedI[m] = 1
      else:
        isfound = False
        for k in range(m+1,r+1):
          if A[k] != search_x:
              break
          if usedI[k] == 1:
              continue
          isfound = True
          break
        if not isfound:
          for k in range(m-1,l-1,-1):
            if A[k] != search_x:
              break
            if usedI[k] == 1:
              continue
            isfound = True
            break
        if isfound:
          cnt += 1
          usedI[i] = 1
          usedI[k] = 1
      break

print(cnt)

Fixed submission:
from math import log,floor
from collections import Counter
N = int(input())
A = list(map(int, input().split()))

A.sort(reverse=True)
C = Counter(A)

cnt = 0
last_a = -1
for i in range(N):
  a = A[i]
  if last_a == a:
    continue
  last_a = a
  count_a = C[a]
  if count_a <= 0:
    continue
  b = pow(2,floor(log(a)/log(2))+1) - a
  count_b = C[b]
  if count_b <= 0:
    continue
  i += count_a - 1
  x = min(count_a, count_b) if a != b else count_a // 2
  cnt += x
  C[a] -= x
  C[b] -= x
  
print(cnt)

Buggy python submission (verdict: Time Limit Exceeded):
from math import log,floor
N = int(input())
A = list(map(int, input().split()))

# log(10**9 + 10**9)/log(2) = 30.89 < 31
#print(log(2 * 10**9) / log(2))

A.sort(reverse=True)
usedI = [0] * N
cnt = 0

for i in range(N):
  if usedI[i] == 1:
    continue
  #print(i, log(A[i]) / log(2) )
  x = floor(log(A[i]) / log(2)) + 1 #実現可能なべき上
  search_x = 2 ** x - A[i]
  for j in range(N-1,i,-1):
    if search_x == A[j]:
      if usedI[j] == 1:
        continue
      else:
        cnt += 1
        usedI[i] = 1
        usedI[j] = 1
        break
    elif search_x < A[j]:
      break

print(cnt)
    

Fixed submission:
from math import log,floor
from collections import Counter
N = int(input())
A = list(map(int, input().split()))

A.sort(reverse=True)
C = Counter(A)

cnt = 0
last_a = -1
for i in range(N):
  a = A[i]
  if last_a == a:
    continue
  last_a = a
  count_a = C[a]
  if count_a <= 0:
    continue
  b = pow(2,floor(log(a)/log(2))+1) - a
  count_b = C[b]
  if count_b <= 0:
    continue
  i += count_a - 1
  x = min(count_a, count_b) if a != b else count_a // 2
  cnt += x
  C[a] -= x
  C[b] -= x
  
print(cnt)

Buggy python submission (verdict: Time Limit Exceeded):
from math import log,floor
N = int(input())
A = list(map(int, input().split()))

# log(10**9 + 10**9)/log(2) = 30.89 < 31
#print(log(2 * 10**9) / log(2))

A.sort(reverse=True)
usedI = [0] * N
cnt = 0

for i in range(N):
  if usedI[i] == 1:
    continue
  #print(i, log(A[i]) / log(2) )
  x = floor(log(A[i]) / log(2)) + 1 #実現可能なべき上
  search_x = 2 ** x - A[i]
  for j in range(i+1,N):
    if search_x == A[j]:
      if usedI[j] == 1:
        continue
      else:
        cnt += 1
        usedI[i] = 1
        usedI[j] = 1
        break
    elif search_x > A[j]:
      break

print(cnt)
    

Fixed submission:
from math import log,floor
from collections import Counter
N = int(input())
A = list(map(int, input().split()))

A.sort(reverse=True)
C = Counter(A)

cnt = 0
last_a = -1
for i in range(N):
  a = A[i]
  if last_a == a:
    continue
  last_a = a
  count_a = C[a]
  if count_a <= 0:
    continue
  b = pow(2,floor(log(a)/log(2))+1) - a
  count_b = C[b]
  if count_b <= 0:
    continue
  i += count_a - 1
  x = min(count_a, count_b) if a != b else count_a // 2
  cnt += x
  C[a] -= x
  C[b] -= x
  
print(cnt)