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:
def kezl(xlist):
    lenx=len(xlist)
    news=[]
    for i in range(lenx-1):
        news.append(abs(xlist[i+1]-xlist[i]))
    return news

flist=[]

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)
#print(blist)
if swit==1:
    for i in range(n-1):
        if blist[i]==2:
            blist[i]=0
    #print(blist)
    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
        #print(blist)
    print(blist[0])
else:
    for i in range(n-1):
        if blist[i]==2:
            blist[i]=1
    #print(blist)
    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
        #print(blist)
    print(blist[0]*2)