[INSTRUCTIONS]

You are a program-analysis assistant. Your task is to statically analyze the control dependence of a given code snippet. 

## 1. Control Dependence Definition
  Control dependence captures the influence of control-flow decisions on the execution of statements.

  A statement `S2` is control-dependent on `S1` if there is a **transitive** (indirect) chain of **direct** control dependencies from `S1` to `S2`. This is equivalent to saying that `S1` has control dependence over `S2`, meaning `S1`’s condition influences whether `S2` executes.


  **Direct Control Dependence**:
  A statement `S2` is **directly** control-dependent on a statement `S1` if:
  
  1.	`S1` is a conditional control statement (e.g., an `if`, `while`, `for`, `switch`, etc.).
  
  2.	`S1` directly determines whether `S2` executes. That is, `S1` has multiple successor branches, 

  - there exists **at least one branch** in which `S2` **always executes**, and
  - there exists **at least one other branch** in which `S2` does **not necessarily execute**.

    “Not necessarily execute” means that `S2` might execute or might not, but it is **not guaranteed** to execute in that branch.

  `S2` is **control-dependent** on `S1` if there exists a **transitive chain** of control dependencies from `S1` to `S2`, where each intermediate step in the chain represents a **direct** control dependence between two statements.



## 2. Output Format
When asked, “Does line `S1` have control dependence over line `S2`? If so, provide a trace.” You should respond in JSON format as follows:

- If there is a control dependence:

```json
{
  "ControlDependence": true,
  "Trace": [S1, ..., S2]
}
```

- If there is no control dependence:
```json
{
  "ControlDependence": false
}
```

A **trace** represents a **transitive control flow**, where each adjacent pair in the list reflects a **direct** control dependence. The trace must starts with `S1` and ends with `S2`.


    

## 3. Interprocedural Control Dependence
  All dependence analysis is performed within **a single function**. We do not track dependencies across function boundaries. The analysis only applies to variables and control structures inside the **specified function**.


## 4. Example Code Snippet

### Example 1

```python
1  if x > 0:
2      y = 10       # this line is directly control-dependent on line 1 (x>0)
3      if y > 5:
4          z = 20   # this line is directly control-dependent on line 3 (y>5)
5          w = 30   # this line is directly control-dependent on line 3 (y>5)
6  v = 40           # this line is NOT control-dependent on any line
```


**Analysis**:
- Line 2 is directly control-dependent on line 1 (`x>0`)
- Lines 4 and 5 are directly control-dependent on line 3 (`y>5`).
- Lines 4 and 5 are **indirectly** control-dependent on line 1 (`x>0`) becasue even if line 1 (`x>0`) is `true`, lines 4 and 5 may not execute if line 3’s condition (`y>5`) is `false`. However, since control dependence is transitive, lines 4 and 5 are **indirectly** control-dependent on line 1. 
- Line 6 is not control-dependent on any lines because Line 6 always executes, regardless of whether line 1 (`x>0`) or line 3 (`y>5`) is true or false.



#### Example Question 1.1: 
Does line `1` have control dependence over line `5`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": true,
  "Trace": [1, 3, 5]
}
```

#### Example Question 1.2:
Does line `3` have control dependence over line `6`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": false
}
```


### Example 2

```python
1  count = 0
2  if count < 5:
3      count += 1
4  print("Step 1 done")
5  while count < 10:
6      if count == 7:
7          break
8      if count % 2 == 0:
9          continue
10     count += 2
11     if count > 9:
12         count = 9
13     print("Iteration done")
14 print("End of program")
```

#### Example Question 2.1: 
Does line `5` have control dependence over line `13`? If so, provide a trace.

**Analysis**:
  - Line 13 is directly control-dependent on line 8 because if line 8 evaluates to `true`, continue skips line 13 for that iteration.
  - Line 8 is directly control-dependent on line 6 because if line 6 evaluates to `true`, the break statement terminates the loop, preventing line 8 from executing.
  - Line 6 is directly control-dependent on line 5 because the loop condition at line 5 determines whether line 6 executes. If line 5 evaluates to `false`, execution skips the loop entirely.


Since control dependence is transitive, line 5 indirectly controls line 13 through lines 6 and 8. The trace is `5->6->8->13`.

**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [5, 6, 8, 13]
}
```

#### Example Question 2.2: 
Does line `8` have control dependence over line `10`? If so, provide a trace.


**Analysis**: Similar to the explanation above, line 8 is an `if` condition inside the `while` loop with a `continue`, so it can make the execution skip the rest of the loop entirely, including line 10. Therefore, line 10 directly control-dependent on 8.



**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [8, 10]
}
```

#### Example Question 2.3: 
Does line `5` have control dependence over line `14`? If so, provide a trace.

**Analysis**: Line 5 doesn't affect whether line 14 is reached. Line 14 is outside the while loop (lines 5 -- 13) and will be executed regardless of the condition. 

**Output**:
```json
{
  "ControlDependence": false
}
```


#### Example Question 2.4: 
Does line `2` have control dependence over line `12`? If so, provide a trace.

**Analysis**: Line 2 doesn't affect whether line 12 is reached. The condition in line 2 only controls whether line 3 is executed. Line 12 is in while loop (line 5 -- 13) and will or will not be executed regardless of the condition in line 2. 

**Output**:
```json
{
  "ControlDependence": false
}
```

---

[YOUR TURN]

Below is **your target snippet**. 

```Java
1   import java.io.BufferedReader;
2   import java.io.IOException;
3   import java.io.InputStream;
4   import java.io.InputStreamReader;
5   import java.io.PrintWriter;
6   import java.io.StringReader;
7   import java.util.ArrayList;
8   import java.util.StringTokenizer;
9   import java.util.Scanner;
10  public class Main  implements Runnable { 
11      public static void main(String[] args) {
12          new Thread(null, new Main(), "", 16 * 1024 * 1024).start(); 
13      }
14      public void run() {
15      	Scanner sc = new Scanner(System.in);
16  		int h = Integer.parseInt(sc.next());
17  		int w = Integer.parseInt(sc.next());
18  		char a[][] = new char[h][w];
19  		int atmp[] = new int[h];
20  		int max= 0;
21  		int blackar[][] = new int[h*w][2];
22  		int p=0;
23  		for (int i = 0; i < h; i++)
24  		{
25  				a[i]= sc.next().toCharArray();
26  				for (char j = 0; j < w; j++)
27  				{
28  					if(a[i][j]=='#')
29  					{
30  						blackar[p][0]=i;
31  						blackar[p][1]=j;
32  						p++;
33  					}
34  				}
35  		}
36  		int maxp = p;
37      	int p2=p;
38  		p=0;
39  	    while(p<h*w)
40  	    {
41  		    int hap = 0;
42  			for (; p<maxp;p++)
43  			{
44  				int i = blackar[p][0];
45  				int j = blackar[p][1];
46  					if(i-1>=0)
47  					{
48  						if (a[i-1][j] == '.')
49  						{
50  							a[i-1][j] = '#';
51  							blackar[p2][0]=i-1;
52  							blackar[p2][1]=j;
53  							p2++;
54  						}
55  					}
56  					if(j-1>=0)
57  					{
58  						if (a[i][j-1] == '.')
59  						{
60  							a[i][j-1] = '#';
61  							blackar[p2][0]=i;
62  							blackar[p2][1]=j-1;
63  							p2++;
64  						}
65  					}
66  					if(i+1<h)
67  					{
68  						if (a[i+1][j] == '.')
69  						{
70  							a[i+1][j] = '#';
71  							blackar[p2][0]=i+1;
72  							blackar[p2][1]=j;
73  							p2++;
74  						}
75  					}
76  					if(j+1<w)
77  					{
78  						if (a[i][j+1] == '.')
79  						{
80  							a[i][j+1] = '#';
81  							blackar[p2][0]=i;
82  							blackar[p2][1]=j+1;
83  							p2++;
84  						}
85  					}
86  		    }
87  			maxp=p2;
88  			max++;
89  		}
90  	    max= max-1;
91  		int ans = max;
92  		PrintWriter out = new PrintWriter(System.out);
93  		out.println(ans);
94  		out.flush();
95  	}
96      static class FastScanner {
97          private BufferedReader reader = null;
98          private StringTokenizer tokenizer = null;
99          public FastScanner(String in) {
100          	StringReader sr = new StringReader(in);
101              reader = new BufferedReader(new BufferedReader(sr));
102              tokenizer = null;
103          }
104          public FastScanner(InputStream in) {
105              reader = new BufferedReader(new InputStreamReader(in));
106              tokenizer = null;
107          }
108          public String next() {
109              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
110                  try {
111                      tokenizer = new StringTokenizer(reader.readLine());
112                  } catch (IOException e) {
113                      throw new RuntimeException(e);
114                  }
115              }
116              return tokenizer.nextToken();
117          }
118          public String nextLine() {
119              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
120                  try {
121                      return reader.readLine();
122                  } catch (IOException e) {
123                      throw new RuntimeException(e);
124                  }
125              }
126              return tokenizer.nextToken("\n");
127          }
128          public long nextLong() {
129              return Long.parseLong(next());
130          }
131          public long nextInt() {
132              return Integer.parseInt(next());
133          }
134      }
135  }
```


**Question**: Does line `39` have control dependence over line `87` in function `run`? If so, provide a trace.

**Output**:


Ground truth answer: yes