#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<ll, ll> P;
typedef vector<ll> VI;
typedef vector<VI> VVI;
const ll MOD = 1000000007;
const ll INF = 4611686018427387903;
#define REP(i, n) for (int i = 0; i < n; i++)
#define ALL(v) v.begin(), v.end()

int main(){
	int n; cin >> n;
	string s; cin >> s;
	VI a(n); bool f=0;
	REP(i,n){
		a[i]=s[i]-'0';
		if(a[i]==2)
			f=1;
	}
	ll ans=0;
	if(f){
		REP(i,n){
			if(a[i]==2)
				ans+=(i==(i&n-1));
			ans%=2;
		}
		cout << ans << endl;
	}
	else{
		REP(i,n){
			if(a[i]==3)
				ans+=(i==(i&n-1));
			ans%=2;
		}
		cout << ans*2 << endl;
	}
	return 0;
}
### Prompt

Your challenge is to write a cpp solution to the following problem:

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}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<ll, ll> P;
typedef vector<ll> VI;
typedef vector<VI> VVI;
const ll MOD = 1000000007;
const ll INF = 4611686018427387903;
#define REP(i, n) for (int i = 0; i < n; i++)
#define ALL(v) v.begin(), v.end()

int main(){
	int n; cin >> n;
	string s; cin >> s;
	VI a(n); bool f=0;
	REP(i,n){
		a[i]=s[i]-'0';
		if(a[i]==2)
			f=1;
	}
	ll ans=0;
	if(f){
		REP(i,n){
			if(a[i]==2)
				ans+=(i==(i&n-1));
			ans%=2;
		}
		cout << ans << endl;
	}
	else{
		REP(i,n){
			if(a[i]==3)
				ans+=(i==(i&n-1));
			ans%=2;
		}
		cout << ans*2 << endl;
	}
	return 0;
}
```