Our dear Nathan, when a little child, used to like chess a lot, but this was a long time ago. One of these days he was challenged by @luisgust to a chess match and, as he is a guy that likes hard challenges, he accepted it. The problem is that Nathan keeps forgetting the rules of the game, so he asked you to help him determine if a given opponent's piece can be captured in one move.
Chess, in MaratonIME, is represented as a matrix of characters. Instead of playing with black and white pieces, they play with uppercase and lowercase letters. Nathan has chosen to play with the lowercase letters.
Besides that, as usual, the positions on the matrix are given in the following coordinates system: Each position is a pair with a character between _a_ and _h_ (inclusive), representing the column, and an integer between _1_ and _8_ (inclusive), representing the row. For exemple, the position _d2_ refers to the fourth column (from left to right) and second row (from bottom to top), and the position _f6_ refers to the sixth column and sixth row. Lowercase letters start on the bottom of the grid, on lines _1_ and _2_.
Here position A is adjacent position B if A shares a vertex with B, that is, if the distance between their rows is at most one and the distance between their columns is at most one. For example, the position _c4_ is adjacent to 8 positions: _b3_, _b4_, _b5_, _c3_, _c5_, _d3_, _d4_ and _d5_.
They decided to play a simplified version of chess. To help you, they gave you the following manual on how to play it:
Given a matrix representing a chess board and an opponent's piece, your program needs to determine whether you can capture it with one of your pieces. It is guaranteed that each player has at most two bishops, two rooks, two knights, eight pawns, one king and one queen.
The input begins with 8 lines with 8 characters each, representing the chess board. The first line contains the characters on the positions _a8_, _b8_, ... , _h8_. The second line contains the characters on positions _a7_, _b7_, ... , _h7_, and so on. After that follows a line containing the position of the opponent's piece you wish to capture.
Print a single line containing the word _Sim_ if it is possible to capture the piece or _Nao_ otherwise.
## Input
The input begins with 8 lines with 8 characters each, representing the chess board. The first line contains the characters on the positions _a8_, _b8_, ... , _h8_. The second line contains the characters on positions _a7_, _b7_, ... , _h7_, and so on. After that follows a line containing the position of the opponent's piece you wish to capture.
## Output
Print a single line containing the word _Sim_ if it is possible to capture the piece or _Nao_ otherwise.
[samples]
**Definitions**
Let $ N, Q \in \mathbb{Z}^+ $ denote the number of tables and number of events, respectively.
Let $ C = (c_1, c_2, \dots, c_N) \in \mathbb{Z}^N $ be the sequence of table capacities, where $ c_i $ is the number of chairs at table $ i $, with $ 1 \leq i \leq N $ and $ 1 \leq c_i \leq 10^5 $.
Let $ S \subseteq \{1, 2, \dots, N\} $ be the set of currently available (empty) tables. Initially, $ S = \{1, 2, \dots, N\} $.
**Constraints**
1. $ 1 \leq N, Q \leq 10^5 $
2. For each event:
- If `in X`: $ 1 \leq X \leq 10^5 $
- If `out T`: $ 1 \leq T \leq N $, and table $ T $ was occupied prior to this event.
**Objective**
For each `in X` event:
Find the smallest-indexed table $ i \in S $ such that $ c_i \geq X $.
If no such $ i $ exists, output $ -1 $.
If such an $ i $ exists, assign the group to table $ i $, remove $ i $ from $ S $, and output $ i $.
For each `out T` event:
Add table $ T $ back to $ S $.
**Output**
For each `in X` event, output the assigned table number or $ -1 $.