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 = [int(x)-1 for x in input()]

am = [a[i] % 2 for i in range(n)]

tmp = 0
ans = am[0] % 2

for i in range(1, n):
    ind = 0
    k = (n-i) & -(n-i)
    while k > 1:
        k = k // 2
        ind += 1
    kk = i & -i
    while kk > 1:
        kk = kk // 2
        ind -= 1
    tmp += ind
    if tmp == 0:
        ans += am[i]
        ans %= 2

if ans == 1:
    print(1)
    exit()

# あとは0か2かの判定！


if 1 in a:
    print(0)
else:
    b = [1 if a[i] == 2 else 0 for i in range(n)]
    tmp = 0
    ans = b[0] % 2
    for i in range(1, n):
        ind = 0
        k = (n-i) & -(n-i)
        while k > 1:
            k = k // 2
            ind += 1
        kk = i & -i
        while kk > 1:
            kk = kk // 2
            ind -= 1
        tmp += ind
        if tmp == 0:
            ans += b[i]
            ans %= 2
    if ans == 1:
        print(2)
    else:
        print(0)