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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define fi first
#define se second
typedef pair<ll,ll> P;
using VP = vector<P>; using VVP = vector<VP>;
using VI = vector<ll>; using VVI = vector<VI>; using VVVI = vector<VVI>;
const int inf=1e9+7;
const ll INF=1LL<<61;
const ll mod=1e9+7;

template<class T>
inline bool chmax(T &a, T b) {
  if(a < b) {
    a = b;
    return true;
  }
  return false;
}

template<class T>
inline bool chmin(T &a, T b) {
  if(a > b) {
    a = b;
    return true;
  }
  return false;
}

int po[1010101];

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int i,j;
  for(i=1;i<1010101;i++){
    int p=i;
    int cnt=0;
    while(p%2==0){
      cnt++;
      p=p/2;
    }
    po[i]=cnt;
  }
  int n;
  cin>>n;
  string a;
  cin>>a;
  VI v(n);
  for(i=0;i<n;i++) v[i]=a[i]-'1';
  bool fl=1;
  for(i=0;i<n;i++){
    if(v[i]==1) fl=0;
  }
  if(fl){
    for(i=0;i<n;i++) v[i]=v[i]/2;
  }
  int tw=0;
  int ans=0;
  if(v[0]==1) ans=1;
  for(i=1;i<n;i++){
    tw+=po[n-i];
    tw-=po[i];
    if(v[i]==1&&tw==0) ans=1-ans;
  }
  if(fl) ans*=2;
  cout<<ans<<endl;

}