Problem: Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3. Let x_{i,j} defined as follows:

* x_{1,j} := a_j \quad (1 \leq j \leq N)
* x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)



Find x_{N,1}.

Constraints

* 2 \leq N \leq 10^6
* a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:


N
a_1a_2\ldotsa_N


Output

Print x_{N,1}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

Solution (in PYTHON3):

Solution:
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, gcd, sqrt
from operator import mul
from functools import reduce
from operator import mul
from pprint import pprint
from copy import deepcopy



sys.setrecursionlimit(2147483647)
INF = 10 ** 20
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 2


n = I()
s = S()
l = len(s)
L = []
one_cnt = 0
for i in range(l - 1):
    ret = abs(int(s[i]) - int(s[i + 1]))
    L += [ret]
    if ret == 1:
        one_cnt += 1

m = 0
for j in range(l - 1):
    m += int(l - 2 & j == j) * L[j]
    m %= 2

if m % 2:
    print(1)
    exit()
else:
    if one_cnt:
        print(0)
    else:
        L = [k // 2 for k in L]
        ret2 = 0
        for jj in range(l - 1):
            ret2 += int(l - 2 & jj == jj) * L[jj]
            ret2 %= 2
        if ret2:
            print(2)
        else:
            print(0)