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
n=int(input())
s=input()
frac=[0]*(n+1)
for i in range(1,n+1):
    k=i
    frac[i]=frac[i-1]
    while k%2==0:
        k//=2
        frac[i]+=1

ans=0
for i in range(n):
    if int(s[i])==2 and frac[n-1]-frac[i]-frac[n-1-i]==0:
        ans^=1

if ans==1: print(1)
elif "2" in s: print(0)
else:
    ans=0
    for i in range(n):
        if int(s[i])==3 and frac[n-1]-frac[i]-frac[n-1-i]==0:
            ans^=1
    print(ans*2)