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;
    static const double pi = 3.141592653589793;
 typedef pair<int64_t,int64_t> P;
#define rep(i, n) for (int i = 0; i < (n); i++)
 #define all(v) (v).begin(),(v).end()
 using ll = long long;
using Graph = vector<vector<int>>;
const int MAX = 510000;
const int MOD = 1000000007;
 const int NINE=1000000000;
 
 
int main(){
ll N;
  cin>>N;
  string a;
  cin>>a;
  vector<ll>op(3);
  op[0]=a[0]-'0';
 op[1]=a[1]-'0';
  op[2]=a[2]-'0';
  for(ll i=3;i<N;i++){
op[0]=abs(op[0]-op[1])+1;
    op[1]=abs(op[2]-op[1])+1;
  op[2]=abs(op[2]-a[i]+'0')+1;
  
  }
  
  ll k=abs(op[2]-op[1]);
  ll s=abs(op[1]-op[0]);
  cout<<abs(k-s);
  
  

}