Three-dimensional Turtle Super Computer

### 题目描述 有一个 $n\times m \times k$ 的立方体，分成 $1\times 1 \times 1$ 的不同的小方格。 小方格的状态由 $0$ 或 $1$ 表示，$1$ 表示该点为一个有效点，$0$ 表示该点为一个非有效点。 定义每一个点周围的 $6$ 个与该点有两维坐标相等且不同维度坐标绝对差为 $1$ 的点直接相连。 任意两个不同的有效点 $x_1$ 与 $x_2$ 如果存在**有且仅有**一个与两点直接相连且不同的点 $x_3$ 使得两点间接相连，则称 $x_3$ 具有关键性。 ### 输入格式 第一行输入该立方体的 $x,y,z(1\le n,m,k \le 100)$。 接下来有 $z$ 个 $x\times y$ 的矩阵，表示每一层小方格的状态。 ### 输出格式 第一行输出一个整数，表示具有关键性的小方格的个数。

A super computer has been built in the Turtle Academy of Sciences. The computer consists of $ n·m·k $ CPUs. The architecture was the paralellepiped of size $ n×m×k $ , split into $ 1×1×1 $ cells, each cell contains exactly one CPU. Thus, each CPU can be simultaneously identified as a group of three numbers from the layer number from $ 1 $ to $ n $ , the line number from $ 1 $ to $ m $ and the column number from $ 1 $ to $ k $ . In the process of the Super Computer's work the CPUs can send each other messages by the famous turtle scheme: CPU $ (x,y,z) $ can send messages to CPUs $ (x+1,y,z) $ , $ (x,y+1,z) $ and $ (x,y,z+1) $ (of course, if they exist), there is no feedback, that is, CPUs $ (x+1,y,z) $ , $ (x,y+1,z) $ and $ (x,y,z+1) $ cannot send messages to CPU $ (x,y,z) $ . Over time some CPUs broke down and stopped working. Such CPUs cannot send messages, receive messages or serve as intermediates in transmitting messages. We will say that CPU $ (a,b,c) $ controls CPU $ (d,e,f) $ , if there is a chain of CPUs $ (x_{i},y_{i},z_{i}) $ , such that $ (x_{1}=a,y_{1}=b,z_{1}=c) $ , $ (x_{p}=d,y_{p}=e,z_{p}=f) $ (here and below $ p $ is the length of the chain) and the CPU in the chain with number $ i $ ( $ i<p $ ) can send messages to CPU $ i+1 $ . Turtles are quite concerned about the denial-proofness of the system of communication between the remaining CPUs. For that they want to know the number of critical CPUs. A CPU $ (x,y,z) $ is critical, if turning it off will disrupt some control, that is, if there are two distinctive from $ (x,y,z) $ CPUs: $ (a,b,c) $ and $ (d,e,f) $ , such that $ (a,b,c) $ controls $ (d,e,f) $ before $ (x,y,z) $ is turned off and stopped controlling it after the turning off.

The first line contains three integers $ n $ , $ m $ and $ k $ ( $ 1<=n,m,k<=100 $ ) — the dimensions of the Super Computer. Then $ n $ blocks follow, describing the current state of the processes. The blocks correspond to the layers of the Super Computer in the order from $ 1 $ to $ n $ . Each block consists of $ m $ lines, $ k $ characters in each — the description of a layer in the format of an $ m×k $ table. Thus, the state of the CPU $ (x,y,z) $ is corresponded to the $ z $ -th character of the $ y $ -th line of the block number $ x $ . Character "1" corresponds to a working CPU and character "0" corresponds to a malfunctioning one. The blocks are separated by exactly one empty line.

Print a single integer — the number of critical CPUs, that is, such that turning only this CPU off will disrupt some control.

2 2 3
000
000

111
111

2

3 3 3
111
111
111

111
111
111

111
111
111

19

1 1 10
0101010101

0

In the first sample the whole first layer of CPUs is malfunctional. In the second layer when CPU $ (2,1,2) $ turns off, it disrupts the control by CPU $ (2,1,3) $ over CPU $ (2,1,1) $ , and when CPU $ (2,2,2) $ is turned off, it disrupts the control over CPU $ (2,2,3) $ by CPU $ (2,2,1) $ . In the second sample all processors except for the corner ones are critical. In the third sample there is not a single processor controlling another processor, so the answer is $ 0 $ .