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:
n = int(input())
al = list(input())

al = [int(a) - 1 for a in al]
flag = False
if 1 not in al:
    flag = True
    al = [a // 2 for a in al]
else:
    al = [a if a != 2 else 0 for a in al]

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

def comb(a,b):
    if countl[a] - countl[a-b] - countl[b] > 0:
        return 0
    else:
        return 1

ans = 0
for idx, a in enumerate(al):
    if a == 1:
        ans += comb(n-1, idx)


if ans % 2 == 0:
    print(0)
else:
    if flag:
        print(2)
    else:
        print(1)