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;
typedef long long ll;
typedef vector<ll> vl;
typedef pair<ll,ll> pll;
typedef double db;
#define INF 1e8
#define EPS 1e-9
#define ALL(x) x.begin() , x.end()
#define ALLR(x) x.rbegin() , x.rend()
#define UNIQUE(c) (c).resize(unique(ALL(c)) - (c).begin())
#define PI acos(-1.0) 

int main()
{
  int n;
  string s;
  cin>>n>>s;
  vl c,d;
  for(int i=0;i<n;i++)
  {
    c.push_back((s[i]-'0'));

  }
  if(c.size()!=1)
  {
    for(int i=0;i<c.size()-1;i++)
    {
      d.push_back(abs(c[i]-c[i+1]));
      if(d[i]==2)d[i]=0;

    }
    c.clear();
    c.assign(ALL(d));
    d.clear();
  }
  while(c.size()!=1)
  {
    int maxlog = 31 - __builtin_clz(c.size());
    ll des = 1<<maxlog;
    for(int i=0;i<c.size()-des+1;i++)
    {
      d.push_back(c[i]^c[i+des-1]);
    }
    c.clear();
    c.assign(ALL(d));
    d.clear();
  }
  cout<<c[0]<<"\n";
}