[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.InputStreamReader;
3   import java.util.*;
4   public class Solution {
5       public static void main(String[] args) {
6           Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
7           solve(in);
8       }
9       public static void solve(Scanner in){
10          int T = in.nextInt();
11          int F = in.nextInt();
12          for (int t = 1; t <= T; ++t) {
13              System.out.println(solveSingle(in));
14              char r = in.next();
15          }
16      }
17      static String solveSingle(Scanner in) {
18          StringBuilder sol = new StringBuilder();
19          List<Character> chars = new ArrayList<>();
20          chars.add('A');
21          chars.add('B');
22          chars.add('C');
23          chars.add('D');
24          chars.add('E');
25          Map<Character, ArrayList<Integer>> occ5 = new HashMap<>();
26          for (char c : chars) {
27              occ5.put(c, new ArrayList<>());
28          }
29          for (int i = 0; i < 119; i++) {
30              int c = i * 5 + 1;
31              System.out.println(c);
32              char n = in.next().charAt(0);
33              List<Integer> curr = occ5.get(n);
34              curr.add(c);
35          }
36          for (Map.Entry<Character, ArrayList<Integer>> e5 : occ5.entrySet()) {
37              if (e5.getValue().size() != 24) {
38                  sol.append(e5.getKey());
39                  chars.remove(e5.getKey());
40                  Map<Character, ArrayList<Integer>> occ4 = new HashMap<>();
41                  for (char c : chars) {
42                      occ4.put(c, new ArrayList<>());
43                  }
44                  for (int i = 0; i < 23; i++) {
45                      int c = i * 5 + 2;
46                      System.out.println(c);
47                      char n = in.next().charAt(0);
48                      List<Integer> curr = occ4.get(n);
49                      curr.add(c);
50                  }
51                  for (Map.Entry<Character, ArrayList<Integer>> e4 : occ4.entrySet()) {
52                      if (e4.getValue().size() != 6) {
53                          sol.append(e4.getKey());
54                          chars.remove(e4.getKey());
55                          Map<Character, ArrayList<Integer>> occ3 = new HashMap<>();
56                          for (char c : chars) {
57                              occ3.put(c, new ArrayList<>());
58                          }
59                          for (int i = 0; i < 5; i++) {
60                              int c = i * 5 + 3;
61                              System.out.println(c);
62                              char n = in.next().charAt(0);
63                              List<Integer> curr = occ3.get(n);
64                              curr.add(c);
65                          }
66                          for (Map.Entry<Character, ArrayList<Integer>> e : occ3.entrySet()) {
67                              if (e.getValue().size() != 2) {
68                                  chars.remove(e.getKey());
69                                  sol.append(e.getKey());
70                                  int askLast = e.getValue().get(0) + 1;
71                                  System.out.println(askLast);
72                                  char n = in.next().charAt(0);
73                                  for (char c : chars) {
74                                      if (c != n) {
75                                          sol.append(c);
76                                          break;
77                                      }
78                                  }
79                                  sol.append(n);
80                              }
81                          }
82                      }
83                  }
84              }
85          }
86          return sol.toString();
87      }
88      public static int toInt(char c) {
89          return c;
90      }
91  }
```


**Question**: Does line `51` have control dependence over line `57` in function `solveSingle`? If so, provide a trace.

**Output**:


Ground truth answer: yes