[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.InputStreamReader;
4   import java.util.Iterator;
5   import java.util.TreeSet;
6   public class Solution {
7   	public static void main(String[] args)throws IOException
8       {
9   		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
10  		int tc = Integer.parseInt(br.readLine()); 
11  		for(int i=0; i<tc; i++) {
12  			int noOfWords = Integer.parseInt(br.readLine()); 
13  			TreeSet<String> set = new TreeSet<String>();
14  			for(int j=0; j<noOfWords; j++) {
15  				String word = br.readLine();
16  				set.add(word);
17  			}
18  			Iterator<String> wrd1 = set.iterator();
19  			Iterator<String> wrd2 = set.iterator();
20  			int c1 = 0;
21  			while(wrd1.hasNext()) {
22  				c1++;
23  				int c2 = 0;
24  				String wordOne = wrd1.next();
25  				int result = 0;
26  				while(wrd2.hasNext()) {
27  					c2++;
28  					if(c1 != c2) {
29  						String wordTwo = wrd2.next();
30  						int max = 0;
31  						String key = "";
32  						for(int l = 0; l< wordTwo.length()-1; l++) {
33  							for(int k = l+2; k<=wordTwo.length(); k++) {
34  								if(wordOne.contains(wordTwo.substring(l, k)) && k-l > max) {
35  									max = k-l;
36  									key = wordTwo.substring(l, k);
37  								}else {
38  									break;
39  								}
40  							}
41  						}
42  					}
43  				}
44  			}
45  		}
46  	}
47  }
48   class Longest_common_substr { 
49      static int printLCSubStr(String X, String Y, int m, int n) {
50          int[][] LCSuff = new int[m + 1][n + 1]; 
51          int len = 0; 
52          int row = 0, col = 0; 
53          for (int i = 0; i <= m; i++) { 
54              for (int j = 0; j <= n; j++) { 
55                  if (i == 0 || j == 0) 
56                      LCSuff[i][j] = 0; 
57                  else if (X.charAt(i - 1) == Y.charAt(j - 1)) { 
58                      LCSuff[i][j] = LCSuff[i - 1][j - 1] + 1; 
59                      if (len < LCSuff[i][j]) { 
60                          len = LCSuff[i][j]; 
61                          row = i; 
62                          col = j; 
63                      } 
64                  } 
65                  else
66                      LCSuff[i][j] = 0; 
67              } 
68          } 
69          if (len == 0) { 
70              return 0; 
71          } 
72          String resultStr = ""; 
73          while (LCSuff[row][col] != 0) { 
74              resultStr = X.charAt(row - 1) + resultStr; 
75              --len; 
76              row--; 
77              col--; 
78          } 
79          return resultStr.length(); 
80      } 
81      public static void main(String args[]) throws IOException 
82      { 
83      	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
84  		int tc = Integer.parseInt(br.readLine()); 
85  		for(int i=1; i<=tc; i++) {
86  			int noOfWords = Integer.parseInt(br.readLine()); 
87  			TreeSet<String> set = new TreeSet<String>();
88  			for(int j=0; j<noOfWords; j++) {
89  				String word = br.readLine();
90  				set.add(word);
91  			}
92  			Iterator<String> wrd1 = set.iterator();
93  			Iterator<String> wrd2 = set.iterator();
94  			int c1 = 0, result = 0;
95  			while(wrd1.hasNext()) {
96  				int max = 0;
97  				String key1 = "";
98  				String key2 = "";
99  				String w1 = wrd1.next();
100  				if(w1.equals(key1)) {
101  					wrd1.remove();
102  					return;
103  				}
104  				while(wrd2.hasNext()) {
105  					String w2 = wrd2.next();
106  					if(w2.equals(key2)) {
107  						wrd2.remove();
108  						return;
109  					}
110  				int count =printLCSubStr(w1,w2,w1.length(),w2.length());
111  				if(count > max) {
112  					key1 = w1;
113  					key2 = w2;
114  					max = count;
115  				}
116  				}
117  				result = result + max;
118  			}
119  			System.out.println("Case #"+i+": "+result);
120  		}
121      } 
122  }
```


**Question**: Does line `21` have control dependence over line `30` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes