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, input()))

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

def comb(k):
    left = cnt[n-1]
    right = cnt[k]+cnt[n-1-k]
    return left-right == 0

f = 1 in a
if f:
    a = [int(i==1) for i in a]
else:
    a = [int(i==2) for i in a]

ans = 0
for i in range(n):
    if comb(i):
        ans += a[i]

ans %= 2
if not f:
    ans *= 2

print(ans)