p02736 AtCoder Grand Contest 043 - 123 Triangle
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
```python
N = int(input())
a = input()

def myc(n):
    ret = 0
    while n % 2 == 0:
        ret += 1
        n //= 2
    return ret

def func(c):
    odd = 0
    count = 0
    if a[0] == c:
        count += 1
    if a[-1] == c:
        count += 1
    for i in range(1, N // 2):
        odd += myc(N-i) - myc(i)
        if a[i] == c and odd == 0:
            count += 1
        if a[-i-1] == c and odd == 0:
            count += 1
    if N % 2 == 1:
        if a[N // 2] == c and odd + myc(N // 2 + 1) - myc(N // 2) == 0:
            count += 1
    return count % 2 == 0

if '2' in a:
    if func('2'):
        print(0)
    else:
        print(1)
else:
    if func('3'):
        print(0)
    else:
        print(2)
```