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:
N = int(input())
a = list(map(int, list(input())))
t = [0 for i in range(N+1)]
i = 2
while i < N:
	for j in range(i, N+1, i):
		t[j] += 1
	i *= 2
sum_t = [0]
for i in range(1, N+1):
	sum_t.append(sum_t[-1] + t[i])

x = [max(a[i], a[i+1]) - min(a[i], a[i+1]) for i in range(N-1)]


def isCombOdd(n,k):
	bunshi = sum_t[n] - sum_t[n-k]
	bunbo = sum_t[k]
	return bunshi == bunbo

f1 = False
for n in x:
	if n == 1:
		f1 = True
		break
if f1:
	x = [n if n != 2 else 0 for n in x]

candidate = 1 if f1 else 2
ans = 0
for i in range(N-1):
	if x[i] > 0 and isCombOdd(N-2, i):
		ans = 1 - ans

print(0 if ans == 0 else candidate)