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: Wrong Answer)

#include<bits/stdc++.h>

using namespace std;

int main(){
    int n;
    scanf("%d",&n);
    getchar();
    string s;
    char c,prev;
    while(c=getchar()){
        if(c==prev){
            continue;
        }
        if(c=='\n'){
            break;
        }else{
            s+=c;
            prev=c;
        }
    }
    int a=-1;
    while(s.size()>1){
        string temp="";
        for(int i=0;i<s.size()-1;++i){
            int t=abs(s[i]-s[i+1]);
            if(t==a){
                continue;
            }else{
                temp+=to_string(t);
                a=t;
            }

        }
        s=temp;
    }
    if(s.size()==0){
        cout<<"0";
    }else{
        cout<<s;
    }






return 0;
}