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:
import sys
#input = sys.stdin.buffer.readline

def main():
    N = int(input())
    a = input()
    nl = []
    
    for num in a:
        num = int(num)
        nl.append(num-1)

    if 1 in nl:
        cnt = 0
        for i,num in enumerate(nl):
            cnt += num*(N-1 == i|((N-1)-i))
        print(cnt%2)
    else:
        for i in range(N):
            nl[i] //= 2
        cnt = 0
        for i,num in enumerate(nl):
            cnt += num*(N-1 == i|((N-1)-i))
        print((cnt%2)*2)

if __name__ == "__main__":
    main()