Buggy python submission (verdict: Runtime Error):
def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in As:
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 

if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))

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

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    while len(C):
        d = max(C.keys())
        n = (2 ** d.bit_length()) - d
        if d != n:
            dc = C[d]
            dn = C[n] if n in C else 1
            mn = min(dc, dn)
            C[d] -= mn
            if n in C:
                C[n] -= mn
                ans += mn
        else:
            if C[d] >= 2:
                ans += C[d]//2
                C[d] -= 2 * C[d]//2
            elif C[d] >= 1:
                C[d] -= 1

        if C[d] == 0:
            del C[d]
        if n in C and C[n] == 0:
            del C[n]
    return ans


if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))

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

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    while len(C):
        d = max(C.keys())
        n = (2 ** d.bit_length()) - d
        if d != n:
            dc = C[d]
            dn = C[n] if n in C else 1
            mn = min(dc, dn)
            C[d] -= mn
            if n in C:
                C[n] -= mn
                ans += mn
        else:
            if C[d] >= 2:
                ans += C[d]//2
                C[d] -= 2 * C[d]//2
            elif C[d] >= 1:
                C[d] -= 1

        if C[d] == 0:
            del C[d]
        if n in C and C[n] == 0:
            del C[n]
    return ans


if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))

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

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    while len(C):
        d = max(C.keys())
        C[d] -= 1
        if C[d] == 0:
            del C[d]

        n = (2 ** d.bit_length()) - d
        if n in C:
            C[n] -= 1
            ans += 1
            if C[n] == 0:
                del C[n]
    return ans


if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))

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

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    while len(C):
        d = max(C.keys())
        C[d] -= 1
        if C[d] == 0:
            del C[d]

        n = (2 ** d.bit_length()) - d
        if n in C:
            C[n] -= 1
            ans += 1
            if C[n] == 0:
                del C[n]
    return ans


if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
from itertools import combinations

def solve(N, As):
    data = {}
    for i, a in enumerate(As):
        data.setdefault(a, []).append(i)
    d_pairs = []
    counters = Counter()
    keys = list(sorted(data.keys()))
    for v in combinations(keys, 2):
        if bin(v[0] + v[1]).count("1") == 1:
            d_pairs.append((v[0], v[1]))
            counters.update([v[0]] * len(data[v[0]]))
            counters.update([v[1]] * len(data[v[1]]))
    for v in keys:
        if bin(v * 2).count("1") == 1:
            d_pairs.append((v, v))
            counters.update([v] * len(data[v]))
    cost = []
    for p in d_pairs:
        if p[0] != p[1]:
            c1 = counters[p[0]] if bin(p[0]).count("1") != 1 else 10 ** 10
            c2 = counters[p[1]] if bin(p[1]).count("1") != 1 else 10 ** 10
            cost.append((c1 + c2, p[0], p[1]))
        else:
            cost.append((10 ** 10 * 2 + 1, p[0], p[1]))
    ans = 0
    cost.sort()
    for cost_pair in sorted(cost):
        if cost_pair[1] != cost_pair[2]:
            while len(data[cost_pair[1]]) > 0 and len(data[cost_pair[2]]) > 0:
                ans += 1
                data[cost_pair[1]].pop()
                data[cost_pair[2]].pop()
        else:
            while len(data[cost_pair[1]]) > 1:
                ans += 1
                data[cost_pair[1]].pop()
                data[cost_pair[2]].pop()
    return ans

if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))

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

def slow_solve(N, As):
    As.sort()
    pairs = []
    counter = Counter()
    for i, a in enumerate(As):
        for j, aa in enumerate(As[i + 1:]):
            if bin(a + aa).count("1") == 1:
                pairs.append((i, j + i + 1))
                counter.update([i, j + i + 1])
    cost = []
    for p in pairs:
        cost.append((counter[p[0]] + counter[p[1]], p[0], p[1]))

    used = set()
    ans = 0
    for cost_pair in sorted(cost):
        if cost_pair[1] not in used and cost_pair[2] not in used:
            ans += 1
            used.add(cost_pair[1])
            used.add(cost_pair[2])
    return ans


if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(slow_solve(N, As))


Fixed submission:
from collections import Counter

def ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))