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:
# coding: utf-8
# Your code here!

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
read = sys.stdin.read

#n,*a = [int(i) for i in read().split()]
n = int(input())
a = [int(i) for i in input()]

n -= 1
d = [abs(i-j) for i,j in zip(a,a[1:])]

p2 = [0]
for i in range(1,n+2):
    r = p2[-1]
    while i&1==0:
        r += 1
        i >>= 1
    p2.append(r)    

def choose(n,k):
    if p2[n] > p2[k]+p2[n-k]: return 0
    else: return 1

#print([choose(n,k) for k in range(n+1)])

par = sum(choose(n-1,i)*di for i, di in enumerate(d))%2

if par == 1:
    print(1)
else:
    if 1 in d: print(0)
    else:
        d = [di>>1 for di in d]
        par = sum(choose(n-1,i)*di for i, di in enumerate(d))%2
        
        if par == 0:
            print(0)
        else:
            print(2)