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 math
n=int(input())
alist=input()
blist=[]
swit=0
for i in range(n-1):
    now=abs(int(alist[i+1])-int(alist[i]))
    if now==1:
        swit=1
    blist.append(now)
if swit==1:
    for i in range(n-1):
        if blist[i]==2:
            blist[i]=0
else:
    for i in range(n-1):
        if blist[i]==2:
            blist[i]=1
dekai=100
while len(blist)>1:
    clist=[]
    dekai=math.floor(math.log(len(blist),2))
    katamari=2**dekai
    kosu=len(blist)-katamari+1
    nanko=0
    for i in range(katamari):
        if blist[i]==1:
            nanko+=1
    clist.append(nanko%2)
    for i in range(kosu-1):
        nanko+=blist[katamari+i]-blist[i]
        clist.append(nanko%2)
    blist=clist

if swit==1:
    print(blist[0])
else:
    print(blist[0]*2)