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
import random
input = sys.stdin.readline


def solve(n, s):
    sub = [int(s[i])-1 for i in range(n)]
    
    table = [0]*(n+1)
    p = 2
    for i in range(len(bin(n))-1):
        for j in range(p, n+1, p):
            table[j] += 1
        p *= 2
    
    for i in range(n):
        table[i+1] += table[i]
    
    ans = 0
    for i in range(n):
        if sub[i]%2:
            judge = table[n-1]-table[n-1-i]-table[i]
            if not judge:
                ans += 1
    
    
    if ans%2:
        res = 1
    else:
        if 1 in sub:
            res = 0
        else:
            res = 0
            for i in range(n):
                if sub[i]:
                    judge = table[n-1]-table[n-1-i]-table[i]
                    if not judge:
                        res += 1
            return res%2*2
    
    return res
    
    
def main():
    n = int(input())
    s = input()
    
    ans = solve(n, s)
    print(ans)
    
    
if __name__ == "__main__":
    main()