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: Accepted)

#include <iostream>
#include <sstream>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <memory>
#include <complex>
#include <numeric>
#include <cstdio>
#include <iomanip>
#include <random>

#define REP(i,m,n) for(int i=int(m);i<int(n);i++)
#define RREP(i,m,n) for(int i=int(n)-1;i>=int(m);--i)
#define EACH(i,c) for (auto &(i): c)
#define all(c) begin(c),end(c)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort(begin(c),end(c))
#define pb emplace_back
#define MP make_pair
#define SZ(a) int((a).size())
//#define int long long

#ifdef LOCAL
#define DEBUG(s) cout << (s) << endl
#define dump(x)  cerr << #x << " = " << (x) << endl
#define BR cout << endl;
#else
#define DEBUG(s) do{}while(0)
#define dump(x) do{}while(0)
#define BR 
#endif
using namespace std;

using UI = unsigned int;
using UL = unsigned long;
using LL = long long;
using ULL = unsigned long long;
using VI = vector<int>;
using VVI = vector<VI>;
using VLL = vector<LL>;
using VVLL = vector<VLL>;
using VS = vector<string>;
using PII = pair<int,int>;
using VP = vector<PII>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

constexpr int MOD = 2;

long long power(long long x, long long n, long long mod = MOD) {
    if (n == 0) return 1;
    if (n % 2 == 0) return power(x * x % mod, n/2, mod);
    else return x * power(x, n-1, mod) % mod;
}

void solve() {
    int n;
    string s;
    cin >> n >> s;
    VI a(n);
    REP(i,0,n) a[i] = s[i] - '0';
    VI b(n-1);
    REP(i,0,n-1) b[i] = abs(a[i] - a[i+1]);
    bool is02 = true;
    REP(i,0,n-1) if (b[i] == 1) {
        is02 = false;
        break;
    }
    int ans = 0;
    if (is02) {
        bool odd = false;
        REP(i,0,n-1) {
            if (b[i] != 2) continue;
            if (((n-2) & i) != i) continue;
            odd = !odd;
        }
        if (odd) ans = 2;
    } else {
        bool odd = false;
        REP(i,0,n-1) {
            if (b[i] != 1) continue;
            if (((n-2) & i) != i) continue;
            odd = !odd;
        }
        if (odd) ans = 1;
    }
    cout << ans << endl;
    //REP(i,0,n-1) dump(b[i]);
}

signed main() {
    solve();
    
    return 0;
}