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 $x_{N,1}$.