Buggy python submission (verdict: Runtime Error):
import math
from collections import defaultdict

def main():
    _ = int(input())
    nums = list(map(int, input().split()))
    n = len(nums)
    nums.sort()
    used = [False] * n

    nums_cnt = defaultdict(int)
    for num in nums:
        nums_cnt[num] += 1

    cnt = 0
    #print(num_bin_digits)

    for cur in reversed(range(n)):
        if used[cur]:
            continue
        num = nums[cur]
        power_of_2 = 1 << math.ceil(math.log2(num))

        pair = power_of_2 - num

        if nums_cnt[pair] != 0:
            nums_cnt[pair] -= 1
            used[pair] = True
            cnt += 1


        '''
        idx = bisect.bisect_left(nums, pair)
        if idx >= cur or nums[idx] != pair:
            #print('continue',pair, idx)
            continue

        while used[idx]:
            idx += 1

        if nums[idx] == pair:
            used[idx] = True
            cnt += 1

        #print(idx, num, power_of_2, pair)
        #print(cnt, nums, used)
        '''

    print(cnt)

    return

main()

Fixed submission:
import math
from collections import defaultdict

def main():
    _ = int(input())
    nums = list(map(int, input().split()))
    n = len(nums)
    nums.sort()

    nums_cnt = defaultdict(int)
    for num in nums:
        nums_cnt[num] += 1

    cnt = 0
    #print(num_bin_digits)

    for cur in reversed(range(n)):
        num = nums[cur]
        if nums_cnt[num] <= 0:
            continue

        power_of_2 = 1 << math.ceil(math.log2(num))

        pair = power_of_2 - num


        if pair != 0 and nums_cnt[pair] > 0:
            nums_cnt[pair] -= 1
            nums_cnt[num] -= 1
            cnt += 1
        elif pair == 0 and nums_cnt[num] >= 2:
            nums_cnt[num] -= 2
            cnt += 1


        '''
        idx = bisect.bisect_left(nums, pair)
        if idx >= cur or nums[idx] != pair:
            #print('continue',pair, idx)
            continue

        while used[idx]:
            idx += 1

        if nums[idx] == pair:
            used[idx] = True
            cnt += 1

        #print(idx, num, power_of_2, pair)
        #print(cnt, nums, used)
        '''

        #print(nums_cnt)

    print(cnt)

    return

main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    _ = int(input())
    nums = list(map(int, input().split()))
    n = len(nums)
    nums.sort()

    #print(n)
    #print(nums)

    num_bin_digits = [1 << len("{:b}".format(x)) for x in nums]
    cnt = 0
    #print(num_bin_digits)

    for cur in reversed(range(n)):
        num = nums[cur]
        if not num:
            continue
        power_of_2 = num_bin_digits[cur]
        pair = power_of_2 - num
        idx = -1
        if pair in nums[:cur]:
            idx = nums.index(pair)

        if idx != -1:
            nums[idx] = False
            cnt += 1

        #print(idx, num, power_of_2, pair)
        #print(cnt, nums)

    print(cnt)

    return

main()

Fixed submission:
import math
from collections import defaultdict

def main():
    _ = int(input())
    nums = list(map(int, input().split()))
    n = len(nums)
    nums.sort()

    nums_cnt = defaultdict(int)
    for num in nums:
        nums_cnt[num] += 1

    cnt = 0
    #print(num_bin_digits)

    for cur in reversed(range(n)):
        num = nums[cur]
        if nums_cnt[num] <= 0:
            continue

        power_of_2 = 1 << math.ceil(math.log2(num))

        pair = power_of_2 - num


        if pair != 0 and nums_cnt[pair] > 0:
            nums_cnt[pair] -= 1
            nums_cnt[num] -= 1
            cnt += 1
        elif pair == 0 and nums_cnt[num] >= 2:
            nums_cnt[num] -= 2
            cnt += 1


        '''
        idx = bisect.bisect_left(nums, pair)
        if idx >= cur or nums[idx] != pair:
            #print('continue',pair, idx)
            continue

        while used[idx]:
            idx += 1

        if nums[idx] == pair:
            used[idx] = True
            cnt += 1

        #print(idx, num, power_of_2, pair)
        #print(cnt, nums, used)
        '''

        #print(nums_cnt)

    print(cnt)

    return

main()

Buggy python submission (verdict: Runtime Error):
def main():
    n = int(input())
    nums = list(map(int, input().split()))
    nums.sort()
    used = [False] * n

    num_bin_digits = [1 << len(f"{x:b}") for x in nums]
    cnt = 0

    for cur in reversed(range(n)):
        if used[cur]:
            continue

        num = nums[cur]
        power_of_2 = num_bin_digits[cur]
        pair = power_of_2 - num
        idx = -1
        if pair in nums[:cur]:
            idx = nums.index(pair)

        if idx != -1 and not used[idx]:
            used[idx] = True
            cnt += 1

    print(cnt)
    return

main()

Fixed submission:
import math
from collections import defaultdict

def main():
    _ = int(input())
    nums = list(map(int, input().split()))
    n = len(nums)
    nums.sort()

    nums_cnt = defaultdict(int)
    for num in nums:
        nums_cnt[num] += 1

    cnt = 0
    #print(num_bin_digits)

    for cur in reversed(range(n)):
        num = nums[cur]
        if nums_cnt[num] <= 0:
            continue

        power_of_2 = 1 << math.ceil(math.log2(num))

        pair = power_of_2 - num


        if pair != 0 and nums_cnt[pair] > 0:
            nums_cnt[pair] -= 1
            nums_cnt[num] -= 1
            cnt += 1
        elif pair == 0 and nums_cnt[num] >= 2:
            nums_cnt[num] -= 2
            cnt += 1


        '''
        idx = bisect.bisect_left(nums, pair)
        if idx >= cur or nums[idx] != pair:
            #print('continue',pair, idx)
            continue

        while used[idx]:
            idx += 1

        if nums[idx] == pair:
            used[idx] = True
            cnt += 1

        #print(idx, num, power_of_2, pair)
        #print(cnt, nums, used)
        '''

        #print(nums_cnt)

    print(cnt)

    return

main()