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())
a = list(map(int, input()))
a = [e - 1 for e in a]


def cnt_div2(x):
    ret = 0
    while x % 2 == 0 and x != 0:
        x //= 2
        ret += 1

    return ret


now = 0
cnt = [0]
for i in range(1, n):
    now += cnt_div2(n - i)
    now -= cnt_div2(i)
    cnt.append(now)

div2 = [e == 0 for e in cnt]


def f(li):
    ret = 0
    for e1, e2 in zip(li, div2):
        e1 %= 2
        ret ^= e1 * e2

    return ret


if f(a):
    ans = 1

elif 1 in a:
    ans = 0

else:
    a = [e // 2 for e in a]
    if f(a):
        ans = 2
    else:
        ans = 0

print(ans)