[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.util.ArrayList;
6   import java.util.List;
7   import java.util.StringTokenizer;
8   public class Main {
9       public static void main(final String[] args) {
10          final FastScanner scanner = new FastScanner(System.in);
11          final int n = scanner.nextInt();
12          int a = scanner.nextInt();
13          int b = scanner.nextInt();
14          int c = scanner.nextInt();
15          final List<String> answer = new ArrayList<>();
16          for (int i = 0; i < n; i++) {
17              final String s = scanner.next();
18              switch (s) {
19                  case "AB": {
20                      if (a == 0 && b == 0) {
21                          System.out.println("No");
22                          return;
23                      }
24                      if (a < b) {
25                          answer.add("A");
26                          a++;
27                          b--;
28                      } else {
29                          answer.add("B");
30                          a--;
31                          b++;
32                      }
33                      break;
34                  }
35                  case "BC": {
36                      if (b == 0 && c == 0) {
37                          System.out.println("No");
38                          return;
39                      }
40                      if (b < c) {
41                          answer.add("B");
42                          b++;
43                          c--;
44                      } else {
45                          answer.add("C");
46                          b--;
47                          c++;
48                      }
49                      break;
50                  }
51                  default: {
52                      if (a == 0 && c == 0) {
53                          System.out.println("No");
54                          return;
55                      }
56                      if (a < c) {
57                          answer.add("A");
58                          a++;
59                          c--;
60                      } else {
61                          answer.add("C");
62                          a--;
63                          c++;
64                      }
65                  }
66              }
67          }
68          System.out.println("Yes");
69          answer.forEach(System.out::println);
70      }
71      private static class FastScanner {
72          private final BufferedReader reader;
73          private StringTokenizer tokenizer;
74          FastScanner(final InputStream in) {
75              reader = new BufferedReader(new InputStreamReader(in));
76          }
77          String next() {
78              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
79                  try {
80                      tokenizer = new StringTokenizer(reader.readLine());
81                  } catch (final IOException e) {
82                      throw new RuntimeException(e);
83                  }
84              }
85              return tokenizer.nextToken();
86          }
87          int nextInt() {
88              return Integer.parseInt(next());
89          }
90          long nextLong() {
91              return Long.parseLong(next());
92          }
93          double nextDouble() {
94              return Double.parseDouble(next());
95          }
96          String nextLine() {
97              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
98                  try {
99                      return reader.readLine();
100                  } catch (final IOException e) {
101                      throw new RuntimeException(e);
102                  }
103              }
104              return tokenizer.nextToken("\n");
105          }
106      }
107  }
```


**Question**: Does line `35` have control dependence over line `63` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes