Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = list(map(lambda x: int(x)-1, input()))

f = 1 in a
if f:
    a = [int(i==1) for i in a]
else:
    a = [int(i==2) for i in a]

tmp = 1
ans = 0
for i in range(n):
    ans += tmp*a[i]
    tmp = tmp*(n-i-1)//(i+1)

ans %= 2
if not f:
    ans *= 2

print(ans)

Fixed submission:
n = int(input())
a = list(map(lambda x: int(x)-1, input()))

cnt = [0]
for i in range(1,n+1):
    x = 0
    while i%2==0:
        x += 1
        i //=2
    cnt.append(cnt[-1]+x)

def comb(k):
    left = cnt[n-1]
    right = cnt[k]+cnt[n-1-k]
    return left-right == 0

f = 1 in a
if f:
    a = [int(i==1) for i in a]
else:
    a = [int(i==2) for i in a]

ans = 0
for i in range(n):
    if comb(i):
        ans += a[i]

ans %= 2
if not f:
    ans *= 2

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
class Binary_Indexed_Tree():
    def __init__(self, n):
        self.n = n
        self.data = [0]*(n+1)

    def add(self, i, x):
        i += 1
        while i <= self.n:
            self.data[i] += x
            i += i & -i

    def get(self, i):
        return self.sum_range(i, i)

    def sum(self, i):
        i += 1
        ret = 0
        while i:
            ret += self.data[i]
            i &= i-1
        return ret

    def sum_range(self, l, r):
        return self.sum(r)-self.sum(l-1)

    def lower_bound(self, w):
        if w<=0:
            return 0
        i = 0
        k = 1<<(self.n.bit_length())
        while k:
            if i+k <= self.n and self.data[i+k] < w:
                w -= self.data[i+k]
                i += k
            k >>= 1
        return i

n = int(input())
a = list(map(lambda x: int(x)-1, input()))

if 1 in a:
    BIT = Binary_Indexed_Tree(n+1)
    for i, ai in enumerate(a):
        if ai == 1:
            BIT.add(i, 1)
        while True:
            s = BIT.sum(i)
            if s == 0:
                break
            i = BIT.lower_bound(s)
            s = BIT.sum(i)
            if s > 1:
                j = BIT.lower_bound(s-1)
                for k in range(j+1, i):
                    BIT.add(k,1)
                BIT.add(j, -1)
                i = j
            else:
                for k in range(i):
                    BIT.add(k,1)
                break
    ans = BIT.get(0)
else:
    BIT = Binary_Indexed_Tree(n+1)
    a = [int(i==2) for i in a]
    for i, ai in enumerate(a):
        if ai == 1:
            BIT.add(i, 1)
        while True:
            s = BIT.sum(i)
            if s == 0:
                break
            i = BIT.lower_bound(s)
            s = BIT.sum(i)
            if s > 1:
                j = BIT.lower_bound(s-1)
                for k in range(j+1, i):
                    BIT.add(k,1)
                BIT.add(j, -1)
                i = j
            else:
                for k in range(i):
                    BIT.add(k,1)
                break
    ans = 2*BIT.get(0)

print(ans)

Fixed submission:
n = int(input())
a = list(map(lambda x: int(x)-1, input()))

cnt = [0]
for i in range(1,n+1):
    x = 0
    while i%2==0:
        x += 1
        i //=2
    cnt.append(cnt[-1]+x)

def comb(k):
    left = cnt[n-1]
    right = cnt[k]+cnt[n-1-k]
    return left-right == 0

f = 1 in a
if f:
    a = [int(i==1) for i in a]
else:
    a = [int(i==2) for i in a]

ans = 0
for i in range(n):
    if comb(i):
        ans += a[i]

ans %= 2
if not f:
    ans *= 2

print(ans)