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(lambda x:int(x)-1,list(input())))
memo=[-1]*(n+1)
def log(x):
    if memo[x]!=-1:return memo[x]
    ret=0
    xx=x
    while x and x%2==0:
        x//=2
        ret+=1
    memo[xx]=ret
    return ret

def slv(n,a):
    v=a[0]
    if all(v==x for x in a):return 0
    # 答えの偶奇を求める
    chk=0
    tmppl=0
    tmpmi=0
    for i in range(n):
        x=a[i]%2
        if tmppl>tmpmi:
            pass
        else:
            chk+=a[i]
            chk%=2
        tmppl+=log(n-i-1)
        tmpmi+=log(i+1)
    if chk:return 1
    if 1 in a:return 0
    a=[x//2 for x in a]
    return slv(n,a)*2
print(slv(n,a))