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;
const int N=1e6+5;

int n,sum;
string s;
int a[N];
int po[N],head[N],tail[N];
bool ok[N];

bool func()
{
	for(int i=1;i<=n;i++)
		if(a[i]==2) return 0;
	int cnt=0;
	for(int i=1;i<n;i++)
		if(a[i]+a[i+1]==4) cnt++;
	int mx=0,nx=0;
	for(int i=1;i<n;i++)
		if(a[i]==3) nx++;
		else mx=max(mx,nx),nx=0;
	nx=0;
	for(int i=1;i<n;i++)
		if(a[i]==1) nx++;
		else mx=max(mx,nx),nx=0;
	if(mx>=n/2+1) return 1;
	return cnt&1;
}

int main()
{
	cin>>n>>s;
	for(int i=1;i<=n;i++)
		a[i]=s[i-1]-'0';
	if(func()) return cout<<"2\n",0;
	for(int i=1;i<=n;i++)
	{
		int x=i;
		while(x%2==0)
			x/=2,po[i]++;
	}
	for(int i=1;i<=n;i++)
		head[i]=head[i-1]+po[i];
	for(int i=1;i<=n;i++)
		tail[i]=tail[i-1]+po[n-i];
	for(int i=1;i<=n;i++)
		ok[i]=(tail[i-1]==head[i-1]);
	for(int i=1;i<=n;i++)
		if(ok[i]) sum+=a[i];
	if(sum&1) cout<<"1\n";
	else cout<<"0\n";
	
	//for(int i=1;i<=n;i++)
	//	cout<<po[i]<<' ';
	//cout<<'\n';
	//for(int i=1;i<=n;i++)
	//	cout<<head[i]<<' ';
	//cout<<'\n';
	//for(int i=1;i<=n;i++)
	//	cout<<tail[i]<<' ';
	
	return 0;
}