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.readline
N = int(input())
A = list(input().rstrip())

def two_num(x):
    res = 0
    while x%2==0:
        x //= 2
        res += 1
    return res

C_twos = [0]*N
for i in range(1, N):
    res = C_twos[i-1] + two_num(N-i) - two_num(i)
    C_twos[i] = res

if '2' in A:
    ans = 0
    for i in range(N):
        ans ^= (int(A[i])-1)&1 * (C_twos[i]==0)
    print(ans)
else:
    ans = 0
    for i in range(N):
        ans ^= (int(A[i])-1)//2 * (C_twos[i]==0)
    print(ans*2)