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)

#pragma GCC optimize("Ofast")
#include<vector>
#include<queue>
#include<iostream>
#include<fstream>
#include<string>
#include<cassert>
#include<algorithm>
#include<random>
#include<map>
#include<set>
#include <bitset>
#include<ctime>

using namespace std;

int mod = 998244353;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef long double ld;
typedef vector<int>vi;
typedef vector<ll>vl;
typedef vector<char>vc;
typedef vector<string>vs;
typedef vector<vector<int>>vii;
typedef vector<vector<char>>vvc;
typedef vector<vector<ll>>vll;
typedef vector< pair<ll, ll>>vpll;
typedef vector< pair<ld, ld>>vpld;
typedef vector< pair<int, int>>vpi;
typedef pair<ld, ld>pld;
#define mp make_pair
#define pb push_back

int add(int a, int b)
{
	int c = a + b;
	if (c >= mod)
	{
		c -= mod;
	}
	return c;
}
int dif(int a, int b)
{
	int c = a - b;
	if (c < 0)
	{
		c += mod;
	}
	return c;
}
int mlt(int a, int b)
{
	ll c = a * 1LL * b;
	return c % mod;
}
int ibit(int n, int i)
{
	return ((n >> i) & 1);
}
void outp(vii &ou)
{
	for (int i = 0; i < ou.size(); i++)
	{
		for (int j = 0; j < ou[i].size(); j++)
		{
			cout << ou[i][j] << ' ';
		}
		cout << '\n';
	}
}
int bp(int x, int y)
{
	if (y == 0)
	{
		return 1;
	}
	int a = 0;
	if (!(y % 2))
	{
		a = bp(x, y / 2);
	}
	return (y % 2) ? mlt(bp(x, y - 1), x) : mlt(a, a);
}
int obr(int x)
{
	return bp(x, mod - 2);
}
const int maxn = 200007;
int fact[1000007], ofact[1000007];
vii del(maxn), alldivs(maxn);
vi maxpr(maxn);
vi mu(maxn), sqf(maxn, 1);
void prec()
{
	fact[0] = 1;
	ofact[0] = 1;
	for (int i = 1; i < maxn; i++)
	{
		fact[i] = mlt(fact[i - 1], i);
	}
	//cerr << "sdsds" << endl;
	ofact[maxn - 1] = obr(fact[maxn - 1]);
	for (int i = maxn - 2; i > 0; i--)
	{
		ofact[i] = mlt(ofact[i + 1], i + 1);
	}
}
int c(int a, int b)
{
	return ((a <= b) && (a >= 0)) ? mlt(fact[b], mlt(ofact[a], ofact[b - a])) : 0;
}
ll gcd(ll x, ll y)
{
	//cerr << x << y << endl;
	if (x == 0)return y;
	return(x > y) ? gcd(y, x) : gcd(y%x, x);
}
int solve(vector<int>coefs, int n)
{
	int suum = 0;
	for (int i = 0; i < n; i++)
	{
		int s1 = i, s2 = n - 1 - i;
		if ((s1^s2) == n - 1)
		{
		//	cerr << s1 << ' ' << s2 <<' '<<(s1^s2)<< endl;
			suum ^= coefs[i];
		}
	}
	return suum;
}
int main()
{
	int n, count = 0;
	cin >> n;
	vector<int>v(n);
	for (int i = 0; i < n; i++)
	{
		char x;
		cin >> x;
		v[i]=x-'0';
		v[i]--;
		if (v[i] == 1)count++;
	}
	//cerr << "Here" << endl;
	if (count == 0)
	{
		for (int i = 0; i < n; i++)v[i] / 2;
		cout << 2 * (solve(v, n));
	}
	else
	{
		for (int i = 0; i < n; i++)v[i] %= 2;
		cout << solve(v, n);
	}
	cin >> n;
}