Buggy python submission (verdict: Time Limit Exceeded):
import math
import bisect


def is_exist_b(search_list, target):
    low = 0
    high = len(search_list)
    if high == 0:
        return False
    index = (low + high) // 2
    while low <= high:
        if target == search_list[index]:
            break
        elif i > search_list[index]:
            low = index + 1
        elif i < search_list[index]:
            high = index - 1
        index = (low + high) // 2
    if target == search_list[index]:
        return True
    else:
        return False


def make_list(base, ceil):
    limit = ceil + base
    max_t = int(math.log2(limit))
    result = []
    for t in range(1, max_t + 2):
        can = 2**t - base
        if 0 < can <= ceil:
            result.append(can)
    return result


n = int(input())

nums = list(map(int, input().split()))
nums = sorted(nums)

combs = []
for i in range(n):
    for num in make_list(nums[i], nums[n - 1]):
        if is_exist_b(nums[i + 1:], num):
            combs.append((nums[i], num))

answer = 0
for i in range(len(combs)):
    existence = []
    for a, b in combs[i:]:
        if not (is_exist_b(existence, a) or is_exist_b(existence, b)):
            bisect.insort_left(existence, a)
            bisect.insort_left(existence, b)
    size = len(existence) // 2
    if size == n // 2:
        answer = size
        break
    if size > answer:
        answer = size

print(answer)


Fixed submission:
from collections import Counter

n = int(input())
nums = sorted(list(map(int, input().split())), reverse=True)

num_map = Counter(nums)

answer = 0
for num in nums:
    pair = (1 << (num.bit_length())) - num

    if num_map[num] > 0 and num_map[pair]:
        if num == pair and num_map[num] > 1:
            answer += 1
            num_map[num] -= 2
        if num > pair:
            answer += 1
            num_map[num] -= 1
            num_map[pair] -= 1

print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
import math


def is_exist_b(search_list, target):
    low = 0
    high = len(search_list)
    if high == 0:
        return False
    index = (low + high) // 2
    while low <= high:
        if target == search_list[index]:
            break
        elif i > search_list[index]:
            low = index + 1
        elif i < search_list[index]:
            high = index - 1
        index = (low + high) // 2
    if target == search_list[index]:
        return True
    else:
        return False


def make_list(base, ceil):
    limit = ceil + base
    max_t = int(math.log2(limit))
    result = []
    for t in range(1, max_t + 1):
        can = 2**t - base
        if 0 < can <= ceil:
            result.append(can)
    return result


n = int(input())

nums = list(map(int, input().split()))
nums = sorted(nums)

combs = []
for i in range(n):
    for num in make_list(nums[i], nums[n - 1]):
        if is_exist_b(nums[i + 1:], num):
            combs.append((nums[i], num))

answer = 0
for i in range(len(combs)):
    existence = []
    for a, b in combs[i:]:
        if not (a in existence or b in existence):
            existence.append(a)
            existence.append(b)
    size = len(existence) // 2
    if size > answer:
        answer = size

print(answer)


Fixed submission:
from collections import Counter

n = int(input())
nums = sorted(list(map(int, input().split())), reverse=True)

num_map = Counter(nums)

answer = 0
for num in nums:
    pair = (1 << (num.bit_length())) - num

    if num_map[num] > 0 and num_map[pair]:
        if num == pair and num_map[num] > 1:
            answer += 1
            num_map[num] -= 2
        if num > pair:
            answer += 1
            num_map[num] -= 1
            num_map[pair] -= 1

print(answer)