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>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
using namespace std;
const int RANDOM1 = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {
    int operator()(int x) const { return hash<int>{}(x ^ RANDOM1); }
};
#define ll long long
#define mod 1000000007
#define pb push_back
#define mp make_pair
#define deb(x) cout<<#x<<" : "<<x<<"\n";
#define debug(x,y) cout<<#x<<" : "<<x<<"\t"<<#y<<" : "<<y<<"\n";
#define ff first
#define ss second
#define ub upper_bound
#define lb lower_bound
#define all(a) (a).begin(),(a).end()
#define bs binary_search
#define sz size()
#define vi vector<int>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define ld long double
#define clr fflush(stdout);
//#define clr cout.flush();
#define N 100001
#define fpr(i,a,b) for(int i=a;i<b;i++)
#define fdr(i,a,b) for(int i=a;i>b;i--)
#define repp(i,a,b,d) for(int i=a;i<b;i+=d)
#define repd(i,a,b,d) for(int i=a;i>b;i-=d)
#define LLMIN LLONG_MIN
#define LLMAX LLONG_MAX
#define AKASH_PATEL ios_base::sync_with_stdio(false);
#define SVNIT_SURAT cin.tie(NULL);cout.tie(NULL);
#define mset(x,a) memset(x,a,sizeof(x));
#define nl cout<<'\n';
#define print(c) cout<<c<<'\n';
#define setp(n) cout << fixed << setprecision(n)
#define take_arr(a,n) fpr(i,0,n) cin>>a[i];
#define print_arr(a,n) for(int i=0;i<n;i++) {cout<<a[i]<<" ";} cout<<'\n';
#define take_mat(mat,n,m) fpr(i,0,n) fpr(j,0,m) cin>>mat[i][j];
#define set_mat(mat,n,m,k) fpr(i,0,n) fpr(j,0,m) mat[i][j]=k;
#define print_mat(dist,n,m) for(int i=0;i<n;i++){for(int j=0;j<m;j++){cout<<dist[i][j]<<" ";}cout<<'\n';}
template< class T > bool inside(T a, T b, T c) { return a<=b && b<=c; }
int main()
{
    AKASH_PATEL;
    SVNIT_SURAT;
    int n;
    cin>>n;
    string s;
    cin>>s;
    ll a[n];
    fpr(i,0,n)
    {
        a[i]=s[i]-'0';
    }
    ll sum=0;
    //sort(a,a+n);
    fdr(i,n-1,-1)
    {
        sum+=(a[i]*i)-a[i]*(n-i-1);
    }
    print(((sum%3)+3)%3)
    return 0;
}