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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#define lld long long
#define N 2000005
lld power(lld a,lld b,lld c){
  lld ans=1;
  while(b){
    if(b&1){
      ans=ans*a%c;
    }
    a=a*a%c;
    b=b/2;
  }
  return ans;
}
int main() {
	int n; cin>>n;
	string s; cin>>s;
	vector<int> v;
	for(int i=0;i<n;++i){
		int x=s[i]-'0';
		v.push_back(x);
	}
	while(1){
		int k=v.size();
		if(k==1)break;
		vector<int> g;
		int l=1;
		int ind=0;
		for(;l<k;++l)
		{
			int pp=0;
			while(l<k&&v[l]==v[l-1])pp++,l++;
			if(pp>=1)g.push_back(0);
			if(l<k)g.push_back(abs(v[l]-v[ind]));
			ind=l;
		}
		v.clear();
		for(auto x: g){v.push_back(x);}
			//cout<<endl;
	}
cout<<v[0];
}