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

Solution (in CPP):

Solution:
#include <cstdio>

#define Int register int

const int MAXN = 1e6;
int n;
char s[MAXN + 5];

inline void Work () {
	scanf ( "%d %s", &n, s + 1 );
	for ( Int i = 1; i <= n; ++ i ) s[i] ^= '1';
	bool ex1 = false;
	for ( Int i = 1; i <= n && ! ex1; ex1 |= s[i ++] & 1 );
	for ( Int i = 1; i <= n; ++ i ) {
		if ( ex1 ) s[i] &= 1;
		else s[i] >>= 1;
	}
	int Cnt = 0;
	for ( Int i = 1; i <= n; ++ i ) ( Cnt += s[i] * ( n - 1 == ( ( i - 1 ) | ( n - i ) ) ) ) &= 1;
	printf ( "%d\n", Cnt << ( ex1 ^ 1 ) );
}

int main () {
	Work ();
	return 0;
}