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 = input()
x = []
x.extend([int(i) for i in a])

# 1,2,3 を0,1,2として考えてもよい(差は変わらないから)
# もし1と0だけだったら簡単そう
# 2は012を210にする効果しかない 1 or 0,2 と考えたら同値
# 1が混ざっている条件で最後の答えが2になることはあり得ない->2を0と考えてよい
if 2 in x:
    flag = True
    x = [1 if i == 2 else 0 for i in x]
else:
    flag = False
    x = [1 if i == 3 else 0 for i in x]
c=0
n=len(x)
n_b=bin(n-1)
if x[0]==1:
    c+=1
for i in range(1,n-1):
    tmp_nck = int((n-1) == (i | (n-1-i)))
    if x[i] == 1:
        c+=tmp_nck
if x[n-1]==1:
    c+=1
if flag:
    print(c%2)
else:
    if c%2 == 1:
        print(2)
    else:
        print(0)