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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define Maxn 1000007
using namespace std;
int n;
int a[Maxn],p[Maxn];
bool calc(int x,int y)
{
    return ((p[x]-p[y]-p[x-y])==0);
}
int main()
{
    scanf("%d",&n);
    bool flag=false;
    for (int i=1;i<=n;i++)
    {
        char ch=getchar();
        while (ch<'1'||ch>'3') ch=getchar();
        a[i]=ch-'0'-1;
        if (a[i]==1) flag=true;
    }
    for (int i=1;i<=n;i++)
        if (i%2==1) p[i]=0; else p[i]=p[i/2]+1;
    for (int i=1;i<=n;i++)
        p[i]+=p[i-1];
    if (flag)
    {
        int ans=0;
        for (int i=1;i<=n;i++)
            if (calc(n-1,i-1)) ans^=(a[i]%2);
        printf("%d\n",ans);
    } else
    {
        int ans=0;
        for (int i=1;i<=n;i++)
            if (calc(n-1,i-1)) ans^=(a[i]/2);
        printf("%d\n",2*ans);
    }
    return 0;
}