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:
def Lucas(n, k):
    if n&k == k:
        return 1
    else:
        return 0

n = int(input())
a = list(map(int, list(input())))
odd = 0
cnt = 0
for i in range(n):
    a[i] -= 1
    if a[i] == 1:
        odd += Lucas(n-1, i)
        cnt = 1
if odd % 2 == 1:
    print(1)
else:
    if cnt == 1:
        print(0)
    else:
        for i in range(n):
            a[i] //= 2
            if a[i] == 1:
                odd += Lucas(n-1, i)
        print(odd%2 * 2)