Problem: A **bracket sequence** is a string that is one of the following:    1. An empty string;   2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;   3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /  Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Submission attempts (in order):
from itertools import *
n,*s=open(0).read().split()
u=[[min(accumulate(t,lambda a,b: a+(1 if b=="(" else -1),initial=0)),2*t.count("(")-len(t)] for t in s]
m=0
for c,d in chain(sorted([x for x in u if x[1]>=0])[::-1],sorted([x for x in u if x[1]<0],key=lambda z:z[0]-z[1])):
    if m+c<0:print("No");break
    m+=d
else:print('YNeos'[not m::2])

from sys import exit
from itertools import accumulate,chain
n,*s=open(0).read().split()
t=[2*i.count("(")-len(i) for i in s]
if sum(t)!=0:
    print("No");exit()
st=[[min(accumulate(s_,lambda a,b: a+(1 if b=="(" else -1),initial=0)),t_] for s_,t_ in zip(s,t)]
now=0
for c in chain(sorted([x if x[1]>=0 for x in st])[::-1],sorted([x if x[1]<0 for x in st],lambda z:z[1]-z[0])[::-1]):
    if now+c[0]<0:
        print("No");exit()
    now+=c[1]
print("Yes")

import sys
from functools import reduce
n=int(input())
s=[input() for i in range(n)]
t=[2*(i.count("("))-len(i) for i in s]
if sum(t)!=0:
    print("No")
    sys.exit()
st=[[t[i]] for i in range(n)]

for i in range(n):
    now,mi=0,0
    for j in s[i]:
        if j=="(":
            now+=1
        else:
            now-=1
        mi=min(mi,now)
    st[i].append(mi)

now2=reduce(lambda a,b:a[0]+b[0],filter(lambda x:x[1]>=0,st))
v,w=list(filter(lambda x:x[1]<0 and x[0]>=0,st)),list(filter(lambda x:x[1]<0 and x[0]<0,st))
v.sort(reverse=True,key=lambda z:z[1])
w.sort(key=lambda z:z[0]-z[1],reverse=True)

for vsub in v:
    if now2+vsub[1]<0:
        print("No")
        sys.exit()
    now2+=vsub[0]
for wsub in w:
    if now2+wsub[1]<0:
        print("No")
        sys.exit()
    now2+=wsub[0]
print("Yes")

from itertools import *
n,*s=open(0).read().split()
u=[[min([0,accumulate(t,lambda a,b: a+(1 if b=="(" else -1))]),2*t.count("(")-len(t)] for t in s]
m=0
for c,d in chain(sorted([x for x in u if x[1]>=0])[::-1],sorted([x for x in u if x[1]<0],key=lambda z:z[0]-z[1])):
    if m+c<0:print("No");break
    m+=d
else:print("No" if m else "Yes")

from sys import exit
from itertools import accumulate,chain
n,*s=open(0).read().split()
t=[2*i.count("(")-len(i) for i in s]
if sum(t)!=0:
    print("No");exit()
st=[[min(accumulate(s_,lambda a,b: a+(1 if b=="(" else -1),initial=0)),t_] for s_,t_ in zip(s,t)]
now=0
for c in chain(sorted([x for x in st if x[1]>=0])[::-1],sorted([x for x in st if x[1]<0],lambda z:z[1]-z[0])[::-1]):
    if now+c[0]<0:
        print("No");exit()
    now+=c[1]
print("Yes")

from sys import exit
from itertools import accumulate,chain
n,*s=open(0).read().split()
t=[2*i.count("(")-len(i) for i in s]
if sum(t)!=0:
    print("No");exit()

st=[[min(accumulate(s_,lambda a,b: a+(1 if b=="(" else -1),initial=0)),t_] for s_,t_ in zip(s,t)]

now=0
v=list(filter(lambda x:x[0]>=0,st))
w=list(filter(lambda x:x[0]<0,st))
v.sort()
w.sort()

for c in chain(v[::-1],w[::-1]):
    if now+c[1]<0:
        print("No");exit()
    now+=c[0]
print("Yes")

from itertools import *
n,*s=open(0).read().split()
u=[[min(accumulate(t,lambda a,b: a+(1 if b=="(" else -1),initial=0)),2*t.count("(")-len(t)] for t in s]
m=0
for c,d in chain(sorted([x for x in u if x[1]>=0])[::-1],sorted([x for x in u if x[1]<0],key=lambda z:z[0]-z[1])):
    if m+c<0:print("No");break
    m+=d
else:print('NYoe s'[m::2])

from itertools import *
n,*s=open(0).read().split()
u=[[min(accumulate(chain([0],t),lambda a,b: a+(1 if b=="(" else -1),initial=0)),2*t.count("(")-len(t)] for t in s]
m=0
for c,d in chain(sorted([x for x in u if x[1]>=0])[::-1],sorted([x for x in u if x[1]<0],key=lambda z:z[0]-z[1])):
    if m+c<0:print("No");break
    m+=d
else:print("No" if m else "Yes")

from itertools import *
n,*s=open(0).read().split()
u=[[min(accumulate(t,lambda a,b: a+(1 if b=="(" else -1),initial=0)),2*t.count("(")-len(t)] for t in s]
m=0
for c,d in chain(sorted([x for x in u if x[1]>=0])[::-1],sorted([x for x in u if x[1]<0],key=lambda z:z[1]-z[0])[::-1]):
    if m+c<0:print("No");break;m+=d
else:
    print("No" if m else "Yes")

from sys import exit
from itertools import accumulate
n=int(input())
s=[input() for i in range(n)]
t=[2*(i.count("("))-len(i) for i in s]

st=[[t[i],min(accumulate(s[i],lambda a,b: a+(1 if b=="(" else -1),initial=0))] for i in range(n)]

now2=sum(map(lambda x:x[0],filter(lambda x:x[1]>=0,st)))
v=list(filter(lambda x:x[1]<0 and x[0]>=0,st))
w=list(filter(lambda x:x[1]<0 and x[0]<0,st))
v.sort(reverse=True,key=lambda z:z[1])
w.sort(key=lambda z:z[0]-z[1],reverse=True)

for sub in chain(v,w):
    if now2+sub[1]<0:
        print("No");exit()
    now2+=sub[0]
print("Yes")

from itertools import *
n,*s=open(0).read().split()
u=[[min(accumulate(chain([0],t),lambda a,b: a+(1 if b=="(" else -1))),2*t.count("(")-len(t)] for t in s]
m=0
for c,d in chain(sorted([x for x in u if x[1]>=0])[::-1],sorted([x for x in u if x[1]<0],key=lambda z:z[0]-z[1])):
    if m+c<0:print("No");break
    m+=d
else:print("No" if m else "Yes")

Verdicts: Wrong Answer

Runtime Error

Runtime Error

Runtime Error

Runtime Error

Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Runtime Error

Accepted