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:
#!/usr/bin/env python3
import sys

def solve(N: int, a: str):
    a = [int(a[i])-1 for i in range(N)]
    zeroone = [a[i]%2 for i in range(N)]

    SUM = 0
    comb = [0]*N
    comb[0] = 1

    for i in range(1, N):
        comb[i] = 1 if (N-1)&i == i else 0

    for i in range(N):
        SUM += zeroone[i]*comb[i]
    SUM %= 2

    if SUM == 1:
        print(1)
        return
    
    if 1 in a:
        print(0)
        return
    
    ## 0か2
    zerotwo = [a[i]//2 for i in range(N)]

    SUM = 0
    for i in range(N):
        SUM += zerotwo[i]*comb[i]
    SUM %= 2

    if SUM == 1:
        print(2)
        return
    
    print(0)
    return


def main():
    N = int(input())  # type: int
    a = input() 
    solve(N, a)

if __name__ == '__main__':
    main()