Bob has a lot of mini figurines. He likes to display some of them on a shelf above his computer screen and he likes to regularly change which figurines appear. This ever-changing decoration is really enjoyable. Bob takes care of never adding the same mini figurine more than once. Bob has only $n$ mini figurines and after $n$ days he arrives at the point where each of the $n$ figurines have been added and then removed from the shelf (which is thus empty). Bob has a very good memory. He is able to remember which mini figurines were displayed on each of the past days. So Bob wants to run a little mental exercise to test its memory and computation ability. For this purpose, Bob numbers his figurines with the numbers $0, ..., n - 1$ and selects a sequence of $n$ integers $d_0, ..., d_{n-1}$ all in the range $[0; n]$. Then, Bob computes a sequence $x_0, . . . , x_n$ in the following way: $x_0 = 0$ and $x_{i+1} = (x_i + y_i)~mod~n$ where mod is the modulo operation and $y_i$ is the number of figurines displayed on day $d_i$ that have a number higher or equal to $x_i$. The result of Bob's computation is $x_n$. More formally, if we note $S(i)$ the subset of $\{0, ..., n - 1\}$ corresponding to figurines displayed on the shelf on day $i$, we have: \begin{itemize} \item $S(0)$ is the empty set; \item $S(i)$ is obtained from $S(i - 1)$ by inserting and removing some elements. \end{itemize} Each element $j~(0 \le j < n)$ is inserted and removed exactly once and thus, the last set $S(n)$ is also the empty set. The computation that Bob performs corresponds to the following program: $~~~~~x_0 = 0$ $~~~~~for~i \in [0; n - 1]$ $~~~~~~~~~~x_{i+1} = (x_i + \#\{y \in S(d_i)~such~that~y \ge x_i\})~mod~n$ $~~~~~output~x_n$ Bob asks you to verify his computation. For that he gives you the numbers he used during its computation (the $d_0, ..., d_{n-1})$ as well as the log of which figurines he added or removed every day. Note that a mini figurine added on day $i$ and removed on day $j$ is present on a day $k~(i \le k < j)$. You should tell him the number that you found at the end of the computation. \InputFile The input is composed of $2 \cdot n + 1$ lines. \begin{itemize} \item The first line contains the integer $n~(1 \le n \le 10^5)$. \item Lines $2$ to $n + 1$ describe the figurines added and removed. Line $i + 1$ contains space-separated $+j$ or $-j$, $0 \le j < n$, to indicate that $j$ is added or removed on day $i$. This line may be empty. A line may contain both $+j$ and $-j$, in that order. \item Lines $n + 2$ to $2 \cdot n + 1$ describe the sequence $d_0, ..., d_{n-1}$. Line $n + 2 + i$ contains the integer $d_i~(0 \le d_i \le n)$. \end{itemize} \OutputFile The output should contain a single line with a single integer which is $x_n$. \Examples The output is $2$ since \begin{itemize} \item first, $x = 2$ since $S(1) = \{0, 2\}$ and $\#\{y \in S(1)~such~that~y > 0\} = 2$; \item then, $x = 0$ since $S(2) = \{1, 2\}$ and $\#\{y \in S(2)~such~that~y > 2\} = 1$; \item and finally, $x = 2$ since $S(2) = \{1, 2\}$ and $\#\{y \in S(2)~such~that~y > 0\} = 2$. \end{itemize}