Buggy python submission (verdict: Time Limit Exceeded):
import collections
N=int(input())
x=list(map(int,input().split()))
c=collections.Counter(x)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
x.sort()
for i in range(len(x))[::-1]:
    for j in range(len(t)):
        if t[j]-x[i] in c.keys():
            if t[j] < x[i]:
                break
            if t[j]-x[i] == x[i]:
                if c[x[i]] >= 2:
                    c[x[i]] -= 2
                    count +=1
            else:
                if c[t[j]-x[i]]>0 and c[x[i]]>0:
                    c[t[j]-x[i]] -= 1
                    c[x[i]] -= 1
                    count+=1
print(count)

Fixed submission:
import collections
N=int(input())
x=list(map(int,input().split()))
c=collections.Counter(x)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
start=0
x.sort()
for i in range(len(x))[::-1]:
    for j in range(start,len(t)):
        if t[j] > 2*x[i]:
            start = j
        if t[j] < x[i]:
            break
        if t[j]-x[i] in c.keys():
            if t[j]-x[i] == x[i]:
                if c[x[i]] >= 2:
                    c[x[i]] -= 2
                    count +=1
            else:
                if c[t[j]-x[i]]>0 and c[x[i]]>0:
                    c[t[j]-x[i]] -= 1
                    c[x[i]] -= 1
                    count+=1
print(count)

Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
x=list(map(int,input().split()))
x.sort(reverse=True)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
start=0
for i in range(len(x)):
    if x[i] != 0:
        #print("X=",x[i])
        for j in range(start,len(t)):
            #print(j)
            if t[j] > 2*x[i]:
                start=j
            if t[j] < x[i]:
                break
            if t[j]-x[i] in x[i+1:]:
                if t[j]-x[i] != 0:
                    x[i+1+x[i+1:].index(t[j]-x[i])] = 0
                    x[i]=0
                    count+=1
                    break
#print(x)
print(count)

Fixed submission:
import collections
N=int(input())
x=list(map(int,input().split()))
c=collections.Counter(x)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
start=0
x.sort()
for i in range(len(x))[::-1]:
    for j in range(start,len(t)):
        if t[j] > 2*x[i]:
            start = j
        if t[j] < x[i]:
            break
        if t[j]-x[i] in c.keys():
            if t[j]-x[i] == x[i]:
                if c[x[i]] >= 2:
                    c[x[i]] -= 2
                    count +=1
            else:
                if c[t[j]-x[i]]>0 and c[x[i]]>0:
                    c[t[j]-x[i]] -= 1
                    c[x[i]] -= 1
                    count+=1
print(count)

Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
x=list(map(int,input().split()))
x.sort(reverse=True)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
start=0
for i in range(len(x)):
    if x[i] != 0:
        #print("X=",x[i])
        for j in range(start,len(t)):
            #print(j)
            if t[j] > 2*x[i]:
                start=j
            if t[j] < x[i]:
                break
            if t[j]-x[i] in x[i:]:
                if t[j]-x[i] != 0 and x.index(t[j]-x[i]) != i:
                    x[x.index(t[j]-x[i])] = 0
                    x[i]=0
                    count+=1
                    break
            j+=1
print(count)

Fixed submission:
import collections
N=int(input())
x=list(map(int,input().split()))
c=collections.Counter(x)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
start=0
x.sort()
for i in range(len(x))[::-1]:
    for j in range(start,len(t)):
        if t[j] > 2*x[i]:
            start = j
        if t[j] < x[i]:
            break
        if t[j]-x[i] in c.keys():
            if t[j]-x[i] == x[i]:
                if c[x[i]] >= 2:
                    c[x[i]] -= 2
                    count +=1
            else:
                if c[t[j]-x[i]]>0 and c[x[i]]>0:
                    c[t[j]-x[i]] -= 1
                    c[x[i]] -= 1
                    count+=1
print(count)

Buggy python submission (verdict: Time Limit Exceeded):
N=int(input())
x=list(map(int,input().split()))
x.sort(reverse=True)
t=[2**i for i in range(len(str(bin(max(x)))[2:])+1)[::-1]]
count=0
for i in range(len(x)):
    if x[i] != 0:
        j=0
        while t[j] > x[i] and j < len(t):
            if t[j]-x[i] in x:
                if t[j]-x[i] != 0 and x.index(t[j]-x[i]) != i:
                    x[x.index(t[j]-x[i])] = 0
                    x[i]=0
                    count+=1
                    break
            j+=1
print(x.count(0)//2)

Fixed submission:
import collections
N=int(input())
x=list(map(int,input().split()))
c=collections.Counter(x)
t=[2**i for i in range(len(str(bin(max(x)*2))[2:])+1)[::-1]]
count=0
start=0
x.sort()
for i in range(len(x))[::-1]:
    for j in range(start,len(t)):
        if t[j] > 2*x[i]:
            start = j
        if t[j] < x[i]:
            break
        if t[j]-x[i] in c.keys():
            if t[j]-x[i] == x[i]:
                if c[x[i]] >= 2:
                    c[x[i]] -= 2
                    count +=1
            else:
                if c[t[j]-x[i]]>0 and c[x[i]]>0:
                    c[t[j]-x[i]] -= 1
                    c[x[i]] -= 1
                    count+=1
print(count)