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:
f2=[0]*10**6
p2=2
while p2<10**6:
    for i in range(p2,10**6,p2):
        f2[i]+=1
    p2*=2
for i in range(1,10**6):
    f2[i]+=f2[i-1]

n=int(input())
s=input()

p = '2' if '2' in s else '3'

ans=0
for i,c in enumerate(s):
    if c==p:
        ans += 0 if f2[n-1]-f2[i]-f2[n-1-i] else 1
print(int(p)-1 if ans%2==1 else 0)