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 = input()

fac2 = [0] * (n+1)
i = 2
while(i <= n ):
    for j in range(i,n+1,i):
        fac2[j] += 1
    i *= 2

for i in range(1,n+1):
    fac2[i] += fac2[i-1]

def calc(x):
    len_x = len(x)
    res = 0
    for i,xi in enumerate(x):
        if(fac2[len_x-1] - fac2[len_x-1-i] - fac2[i] > 0):
            continue
        res = res ^ xi
    return res

if(a.count('2')==0):
    x = []
    for ai in a:
        x.append(int(ai)//2)
    res = calc(x)
    if(res==0):
        print(0)
    else:
        print(2)
else:
    x = []
    for ai in a:
        x.append( (int(ai)-1) % 2)
    res = calc(x)
    print(res)