Buggy python submission (verdict: Runtime Error):
from collections import deque, Counter, defaultdict


class Dinic:
    def __init__(self, n):
        self.n = n
        self.links = [[] for _ in range(n)]
        self.depth = None
        self.progress = None

    def add_link(self, _from, to, cap):
        self.links[_from].append([cap, to, len(self.links[to])])
        self.links[to].append([0, _from, len(self.links[_from]) - 1])

    def bfs(self, s):
        depth = [-1] * self.n
        depth[s] = 0
        q = deque([s])
        while q:
            v = q.popleft()
            for cap, to, rev in self.links[v]:
                if cap > 0 and depth[to] < 0:
                    depth[to] = depth[v] + 1
                    q.append(to)
        self.depth = depth

    def dfs(self, v, t, flow):
        if v == t:
            return flow
        links_v = self.links[v]
        for i in range(self.progress[v], len(links_v)):
            self.progress[v] = i
            cap, to, rev = link = links_v[i]
            if cap == 0 or self.depth[v] >= self.depth[to]:
                continue
            d = self.dfs(to, t, min(flow, cap))
            if d == 0:
                continue
            link[0] -= d
            self.links[to][rev][0] += d
            return d
        return 0

    def max_flow(self, s, t):
        flow = 0
        while True:
            self.bfs(s)
            if self.depth[t] < 0:
                return flow
            self.progress = [0] * self.n
            current_flow = self.dfs(s, t, float('inf'))
            while current_flow > 0:
                flow += current_flow
                current_flow = self.dfs(s, t, float('inf'))


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


def solve(count):
    sk = sorted(count.keys())
    rd = {a: i for i, a in enumerate(sk)}
    lc = len(count)
    ma = max(count)

    mf = Dinic(2 * lc + 2)
    s, g = 0, 2 * lc + 1

    for i, a in enumerate(sk):
        cnt = count[a]
        li = i + 1
        k = 2
        b = k - a
        flag = False
        while b <= ma:
            if b > 0 and b in count:
                if a != b or cnt > 1:
                    mf.add_link(li, lc + rd[b] + 1, cnt)
                    flag = True
            k <<= 1
            b = k - a
        if flag:
            mf.add_link(s, li, cnt)
            mf.add_link(lc + li, g, cnt)

    # print(*mf.links, sep='\n')
    return mf.max_flow(s, g) // 2


count_e = defaultdict(lambda: 0)
count_o = defaultdict(lambda: 0)
for a in aaa:
    if a % 2 == 0:
        count_e[a] += 1
    else:
        count_o[a] += 1

print(solve(count_e) + solve(count_o))


Fixed submission:
from collections import defaultdict

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


def solve(count):
    ans = 0
    for a in sorted(count, reverse=True):
        cnt = count[a]
        if cnt <= 0:
            continue
        ma = 1 << (a.bit_length())
        b = ma - a
        if b in count and count[b] > 0:
            if a == b:
                pair = cnt // 2
            else:
                pair = min(cnt, count[b])
                count[b] -= pair
            ans += pair
    return ans


count_e = defaultdict(lambda: 0)
count_o = defaultdict(lambda: 0)
for a in aaa:
    if a % 2 == 0:
        count_e[a] += 1
    else:
        count_o[a] += 1

print(solve(count_e) + solve(count_o))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict

n = int(input())
aaa = list(map(int, input().split()))
rd = defaultdict(set)
ma = 0
for i, a in enumerate(aaa):
    rd[a].add(i)
    ma = max(ma, a)

ma2 = 2
while ma2 <= ma:
    ma2 <<= 1

edges = [None for _ in range(n)]
for a, i_set in rd.items():
    tmp_set = set()
    k = 2
    while k <= ma2:
        if k > a:
            b = k - a
            if b in rd:
                tmp_set.update(rd[b])
        k <<= 1
    for i in i_set:
        ts = tmp_set.copy()
        ts.discard(i)
        edges[i] = ts


def dfs(v, visited):
    for u in edges[v]:
        if u in visited:
            continue
        visited.add(u)
        if matched[u] == -1 or dfs(matched[u], visited):
            matched[u] = v
            return True
    return False


matched = [-1] * n

print(sum(dfs(s, set()) for s in range(n)) // 2)


Fixed submission:
from collections import defaultdict

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


def solve(count):
    ans = 0
    for a in sorted(count, reverse=True):
        cnt = count[a]
        if cnt <= 0:
            continue
        ma = 1 << (a.bit_length())
        b = ma - a
        if b in count and count[b] > 0:
            if a == b:
                pair = cnt // 2
            else:
                pair = min(cnt, count[b])
                count[b] -= pair
            ans += pair
    return ans


count_e = defaultdict(lambda: 0)
count_o = defaultdict(lambda: 0)
for a in aaa:
    if a % 2 == 0:
        count_e[a] += 1
    else:
        count_o[a] += 1

print(solve(count_e) + solve(count_o))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict

n = int(input())
aaa = list(map(int, input().split()))
rd = defaultdict(set)
ma = 0
for i, a in enumerate(aaa):
    rd[a].add(i)
    ma = max(ma, a)

ma2 = 2
while ma2 <= ma:
    ma2 <<= 1

edges = [set() for _ in range(n)]
for i, a in enumerate(aaa):
    k = 2
    while k <= ma2:
        if k > a:
            b = k - a
            if b in rd:
                edges[i].update(j for j in rd[b] if i != j)
        k <<= 1


def dfs(v, visited):
    for u in edges[v]:
        if u in visited:
            continue
        visited.add(u)
        if matched[u] == -1 or dfs(matched[u], visited):
            matched[u] = v
            return True
    return False


matched = [-1] * n

print(sum(dfs(s, set()) for s in range(n)) // 2)


Fixed submission:
from collections import defaultdict

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


def solve(count):
    ans = 0
    for a in sorted(count, reverse=True):
        cnt = count[a]
        if cnt <= 0:
            continue
        ma = 1 << (a.bit_length())
        b = ma - a
        if b in count and count[b] > 0:
            if a == b:
                pair = cnt // 2
            else:
                pair = min(cnt, count[b])
                count[b] -= pair
            ans += pair
    return ans


count_e = defaultdict(lambda: 0)
count_o = defaultdict(lambda: 0)
for a in aaa:
    if a % 2 == 0:
        count_e[a] += 1
    else:
        count_o[a] += 1

print(solve(count_e) + solve(count_o))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict

n = int(input())
aaa = list(map(int, input().split()))
rd = defaultdict(set)
ma = 0
for i, a in enumerate(aaa):
    rd[a].add(i)
    ma = max(ma, a)

ma2 = 2
while ma2 <= ma:
    ma2 <<= 1

edges = [set() for _ in range(n)]
for i, a in enumerate(aaa):
    k = 2
    while k <= ma2:
        if k > a:
            b = k - a
            if b in rd:
                edges[i].update(j for j in rd[b] if i != j)
        k <<= 1


def dfs(v, visited):
    for u in edges[v]:
        if u in visited:
            continue
        visited.add(u)
        if matched[u] == -1 or dfs(matched[u], visited):
            matched[u] = v
            return True
    return False


matched = [-1] * n

print(sum(dfs(s, set()) for s in range(n)) // 2)


Fixed submission:
from collections import defaultdict

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


def solve(count):
    ans = 0
    for a in sorted(count, reverse=True):
        cnt = count[a]
        if cnt <= 0:
            continue
        ma = 1 << (a.bit_length())
        b = ma - a
        if b in count and count[b] > 0:
            if a == b:
                pair = cnt // 2
            else:
                pair = min(cnt, count[b])
                count[b] -= pair
            ans += pair
    return ans


count_e = defaultdict(lambda: 0)
count_o = defaultdict(lambda: 0)
for a in aaa:
    if a % 2 == 0:
        count_e[a] += 1
    else:
        count_o[a] += 1

print(solve(count_e) + solve(count_o))