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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N = int(input())
a = list(map(int, list(input())))
x = [max(a[i], a[i+1]) - min(a[i], a[i+1]) for i in range(N-1)]
f0,f1,f2 = False, False, False
for n in x:
	if n == 0:
		f0 = True
	elif n == 1:
		f1 = True
	else:
		f2 = True
	if f0 and f1 and f2:
		break
candidate = 1 if f1 else 2
if f1:
	x = [0 if x[i] == 2 else x[i] for i in range(N-1)]
else:
	x = [1 if x[i] == 2 else x[i] for i in range(N-1)]
current = x[-1]
g = 1
bef = x[0]
for i in range(1, N-1):
	if bef == x[i]:
		continue
	else:
		bef = x[i]
		g += 1

print(0 if g == 0 or (g+N) % 2 == 1 else candidate)