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:
#!/usr/bin/env python3

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
a = input()
a = list(map(lambda x:int(x)-1, list(a)))
b = [0 if i % 2 == 0 else i for i in a]
cnt = 0
for i in range(n):
    if b[i] % 2:
        if (n-1) & i == i:
            cnt += 1
if cnt % 2:
    print(1)
else:
    if 1 in b:
        print(0)
    else:
        c = [i // 2 if i % 2 == 0 else i for i in a]
        cnt = 0
        for i in range(n):
            if c[i] % 2:
                if (n-1) & i == i:
                    cnt += 1
        if cnt % 2:
            print(2)
        else:
            print(0)