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_1$$a_2$$\ldots$$a_N$

Output

Print $x_{N,1}$.

4
1231

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 $1$.

10
2311312312

0