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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <stack>
#include <set>
#include <queue>
#include <iomanip>
#include <math.h>
#include <fstream>

using namespace std;

// long long mod = 998244353;
long long mod = 1000000007;
vector<long long> fact(1000001);
vector<long long> invFact(1000001);

vector<int> setSize(100000, 1);

long long gcd(long long a, long long b)
{
    if (b == 0)
    {
        return a;
    }
    return gcd(b, a % b);
}

long long binpow(long long x, long long k)
{
    if (k == 0)
    {
        return 1LL;
    }
    long long temp = binpow(x, k / 2);
    if (k % 2 == 1)
    {
        return (((temp * temp) % mod) * x) % mod;
    }
    else
    {
        return (temp * temp) % mod;
    }
}

long long modular_inverse(long long x)
{
    return binpow(x, mod - 2);
}

long long binomial(long long n, long long k)
{
    long long rez = 1;
    for (long long i = n - k + 1; i <= n; i++)
    {
        rez *= i;
        rez %= mod;
    }
    long long temp = 1;
    for (long long i = 1; i <= k; i++)
    {
        temp *= i;
        temp %= mod;
    }
    rez *= modular_inverse(temp);
    rez %= mod;
    return rez;
}

int fi(int a, vector<int> &p)
{
    if (p[a] != p[p[a]])
    {
        p[a] = fi(p[a], p);
    }
    return p[a];
}

void uni(int a, int b, vector<int> &p)
{
    int x = fi(a, p), y = fi(b, p);
    if (x != y)
    {
        p[x] = y;
        setSize[y] += setSize[x];
    }
}

long long euclidianDistanceSquared(pair<int, int> a, pair<int, int> b)
{
    return (a.first - b.first) * (a.first - b.first) + (a.second - b.second) * (a.second - b.second);
}

double euclidianDistanceSquared(pair<double, double> a, pair<double, double> b)
{
    return (a.first - b.first) * (a.first - b.first) + (a.second - b.second) * (a.second - b.second);
}

double euclidianDistance(pair<double, double> a, pair<double, double> b)
{
    return sqrt(euclidianDistanceSquared(a, b));
}

bool circleIntersections(pair<double, double> pos1, double r1, pair<double, double> pos2, double r2, pair<double, double> &int1, pair<double, double> &int2)
{
    double d = euclidianDistance(pos1, pos2);
    if (r1 + r2 < d || d < fabs(r1 - r2))
    {
        return false;
    }
    double a = (r1 * r1 - r2 * r2 + d * d) / (2 * d);
    double h = sqrt(r1 * r1 - a * a);
    pair<double, double> pos3 = { pos1.first + a * (pos2.first - pos1.first) / d, pos1.second + a * (pos2.second - pos1.second) / d };
    int1.first = pos3.first + h * (pos2.second - pos1.second) / d;
    int1.second = pos3.second - h * (pos2.first - pos1.first) / d;
    int2.first = pos3.first - h * (pos2.second - pos1.second) / d;
    int2.second = pos3.second + h * (pos2.first - pos1.first) / d;
    return true;
}

class SegmentTree
{
public:
    class Node
    {
    public:
        vector<int> value;
        Node *l, *r;
        int left, right;

        Node(int x, int y)
        {
            value = vector<int>(26, 0);
            l = nullptr;
            r = nullptr;
            left = x;
            right = y;
        }

        void update(int p, char c)
        {
            if (left > p || p > right)
            {
                return;
            }
            if (left == p && p == right)
            {
                for (int i = 0; i < 26; i++)
                {
                    value[i] = 0;
                }
                value[c - 'a'] = 1;
                return;
            }
            if (l == nullptr)
            {
                int mid = (left + right) / 2;
                l = new Node(left, mid);
                r = new Node(mid + 1, right);
            }
            l->update(p, c);
            r->update(p, c);
            for (int i = 0; i < 26; i++)
            {
                value[i] = l->value[i] + r->value[i];
            }
        }

        int query(int x, int y)
        {
            if (left > y || x > right)
            {
                return 0;
            }
            if (x <= left  && right <= y)
            {
                int rez = 0;
                for (int i = 0; i < 26; i++)
                {
                    if (value[i] != 0)
                    {
                        rez |= (1 << i);
                    }
                }
                return rez;
            }
            if (l == nullptr)
            {
                return 0;
            }
            return l->query(x, y) | r->query(x, y);
        }
    };

    Node *root;
    SegmentTree(int n)
    {
        root = new Node(0, n - 1);
    }

    void update(int p, char c)
    {
        root->update(p, c);
    }

    int query(int x, int y)
    {
        return root->query(x, y);
    }
};

int main()
{
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(12);
    
    
    int n;
    cin >> n;
    vector<int> v(n);
    for (int i = 0; i < n; i++)
    {
        char c;
        cin >> c;
        v[i] = (c - '0');
    }
    vector<int> x(n - 1);
    for (int i = 1; i < n; i++)
    {
        x[i - 1] = abs(v[i] - v[i - 1]);
    }
    int res = 0;
    for (int i = 0; i < x.size(); i++)
    {
        res += x[i];
    }
    res %= 3;
    cout << res << '\n';
    


    return 0;
}