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
import random
input = sys.stdin.readline

n = int(input())
s = input().rstrip()
a = [int(ch) for ch in s]
# a = [random.randrange(0,3) for _ in range(12)]

def naive(a):
    c = a[:]
    while len(c) > 1:
        b = []
        for c1, c2 in zip(c, c[1:]):
            b.append(abs(c1 - c2))
        c = b[:]
    return c[0]

def solve(a):
    c = a[:]
    while len(c) > 1:
        b = []
        if len(c) % 2 == 0:
            for c1, c2 in zip(c[::2], c[1::2]):
                b.append(abs(c1 - c2))
        else:
            for c1, c2 in zip(c, c[1:]):
                b.append(abs(c1 - c2))
        c = b[:]
    return c[0]

b = []
for a1, a2 in zip(a, a[1:]):
    b.append(abs(a1 - a2))
if 1 not in b:
    tmp = []
    for item in b:
        if item == 2:
            tmp.append(1)
        else:
            tmp.append(0)
    ret = solve(tmp)
    if ret == 1:
        print(2)
    else:
        print(0)
else:
    tmp = []
    for item in b:
        if item == 2:
            tmp.append(0)
        else:
            tmp.append(item)
    ret = solve(tmp)
    print(ret)