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
from itertools import product
readline = sys.stdin.readline

N = int(readline())
A = list(map(int, readline().strip()))
A1 = [a%2 for a in A]
for i in range(31, -1, -1):
    if (1<<i) & len(A1):
        k = 1<<i
        B = []
        B.append(sum(A1[:k])%2)
        for j in range(k, len(A1)):
            B.append((B[-1] + A1[j] - A1[j-k])%2)
        A1 = B[:]
    if (1<<i) & len(A1):
        k = 1<<i
        B = []
        B.append(sum(A1[:k])%2)
        for j in range(k, len(A1)):
            B.append((B[-1] + A1[j] - A1[j-k])%2)
        A1 = B[:]
pari = A1[0]
if pari == 1:
    ans = 1
else:
    if 2 in A:
        ans = 0
    else:
        A2 = [abs(a2-a1)//2 for a1, a2 in zip(A, A[1:])]
        N2 = len(A2)
        for i in range(31, -1, -1):
            if (1<<i) & len(A2):
                k = 1<<i
                B = []
                B.append(sum(A2[:k])%2)
                for j in range(k, len(A2)):
                    B.append((B[-1] + A2[j] - A2[j-k])%2)
                A2 = B[:]
            if (1<<i) & len(A2):
                k = 1<<i
                B = []
                B.append(sum(A2[:k])%2)
                for j in range(k, len(A2)):
                    B.append((B[-1] + A2[j] - A2[j-k])%2)
                A2 = B[:]
        
        if A2[0] == 0:
            ans = 0
        else:
            ans = 2

print(ans)