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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define ll long long
#define MAXN 1000005
using namespace std;
ll n,a[MAXN],ch[3],ansch[2],cnt,ans;
char x;
bool bl1;
ll cnt2(ll i){
    ll ret=0;
    while(i%2==0){
        ret++;
        i/=2;
    }
    return ret;
}
int main(){
    cin>>n;
    for (int i=0; i<n; i++){
        cin>>x;
        a[i]=x-'1';
        if (a[i]==1) bl1=1;
    }
    if (bl1){
        ch[0]=ch[2]=0;
        ch[1]=1;
        ansch[0]=0;
        ansch[1]=1;
    }
    else{
        ch[0]=0;
        ch[2]=1;
        ansch[0]=0;
        ansch[1]=2;
    }
    if (ch[a[0]]==1) ans=1;
    for (int i=1; i<n; i++){
        cnt+=cnt2(n-i)-cnt2(i);
        if (cnt==0 && ch[a[i]]==1) ans=1-ans;
        // cout<<cnt<<endl;
    }
    cout<<ansch[ans]<<endl;
}