Problem:
Score : 700 points

Problem Statement

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}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Python (3.4.3) (judge verdict: Accepted)

n=int(input())
s=input()
a=[int(s[i])-1 for i in range(n)]

div=[0]*(n+1)
for i in range(1,n+1):
  div[i]+=div[i-1]
  x=i
  while not x&1:
    x>>=1
    div[i]+=1

XOR=0;one=False
for i in range(n):
  one|=a[i]==1
  if div[n-1]<=div[i]+div[n-1-i]:
    XOR^=a[i]
if XOR&1:print(1)
elif one:print(0)
elif XOR&2:print(2)
else:print(0)