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;

//g++ -g -o yourexe yourfile.cpp
//./yourexe < yourinput.in > youroutput.out

#define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

#define M 998244353

#define ll long long
#define ld long double
#define vi vector<ll>
#define pi pair<ll, ll>
#define vii vector<pi>
#define vvi vector<vi>
#define pb push_back
#define endl "\n"

#define REP(i, s, e) for (ll i = s; i < e; i++)
#define RREP(i, s, e) for (ll i = s; i > e; i--)

#define all(v) v.begin(), v.end()
#define part(v, s, e) v.begin() + s, v.begin() + e
#define print(v) for (auto i: v) cout << i << " ";

ll solve(string s, ll n) {
    ll ans = 2;
    if (s[0] == '3') {
        REP(i, 1, n) {
            if (s[i] != '1') {
                ans = 1;
                break;
            }
        }
        if (ans == 2)
            return 2;
    }
    ans = 2;
    if (s[n-1] == '3') {
        REP(i, 0, n-1) {
            if (s[i] != '1') {
                ans = 1;
                break;
            }
        }
        if (ans == 2)
            return 2;
    }
    return 2;
}

int main() {
    fast;
    ll n;
    cin >> n;
    string s;
    cin >> s;
    cout << 3 << endl;
}