[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.OutputStream;
2   import java.io.IOException;
3   import java.io.InputStream;
4   import java.io.PrintWriter;
5   import java.util.InputMismatchException;
6   import java.io.IOException;
7   import java.io.InputStream;
8   public class Main {
9       public static void main(String[] args) {
10          InputStream inputStream = System.in;
11          OutputStream outputStream = System.out;
12          FastScanner in = new FastScanner(inputStream);
13          PrintWriter out = new PrintWriter(outputStream);
14          FStringsOfEternity solver = new FStringsOfEternity();
15          solver.solve(1, in, out);
16          out.close();
17      }
18      static class FStringsOfEternity {
19          public void solve(int testNumber, FastScanner br, PrintWriter pw) {
20              String in1 = br.nextString();
21              String in2 = br.nextString();
22              char[] t = in1.toCharArray();
23              char[] s = in2.toCharArray();
24              if (t.length > s.length) {
25                  int orig = 0;
26                  boolean poss = true;
27                  for (int i = 0; i < t.length - s.length; i += s.length) {
28                      if (!in1.substring(i, i + s.length).equals(in2)) {
29                          poss = false;
30                      } else {
31                          orig++;
32                      }
33                  }
34                  if (poss) {
35                      pw.println(-1);
36                      pw.close();
37                  }
38                  int ans = 0;
39                  for (int i = 0; i < t.length - s.length; i += s.length) {
40                      if (in1.substring(i, i + s.length).equals(in2)) {
41                          ans++;
42                      } else {
43                          break;
44                      }
45                  }
46                  for (int i = t.length - s.length; i >= 0; i -= s.length) {
47                      if (in1.substring(i, i + s.length).equals(in2)) {
48                          ans++;
49                      } else {
50                          break;
51                      }
52                  }
53                  pw.println(Math.max(orig, ans));
54                  pw.close();
55              } else if (s.length == t.length) {
56                  if (s.equals(t)) {
57                      pw.println(-1);
58                  } else {
59                      pw.println(0);
60                  }
61              } else {
62                  int orig = 0;
63                  boolean poss = true;
64                  for (int i = 0; i < s.length - t.length; i += s.length) {
65                      if (!in2.substring(i, i + t.length).equals(in1)) {
66                          poss = false;
67                      }
68                  }
69                  if (poss) {
70                      pw.println(-1);
71                      pw.close();
72                  }
73                  int ans = 0;
74                  for (int i = 0; i < s.length - t.length; i += t.length) {
75                      if (in2.substring(i, i + t.length).equals(in1)) {
76                          ans++;
77                      } else {
78                          break;
79                      }
80                  }
81                  for (int i = s.length - t.length; i >= 0; i -= t.length) {
82                      if (in2.substring(i, i + t.length).equals(in1)) {
83                          ans++;
84                      } else {
85                          break;
86                      }
87                  }
88                  pw.println(Math.max(orig, ans));
89                  pw.close();
90              }
91          }
92      }
93      static class FastScanner {
94          private InputStream stream;
95          private byte[] buf = new byte[1024];
96          private int curChar;
97          private int numChars;
98          private FastScanner.SpaceCharFilter filter;
99          public FastScanner(InputStream stream) {
100              this.stream = stream;
101          }
102          public int read() {
103              if (numChars == -1) {
104                  throw new InputMismatchException();
105              }
106              if (curChar >= numChars) {
107                  curChar = 0;
108                  try {
109                      numChars = stream.read(buf);
110                  } catch (IOException e) {
111                      throw new InputMismatchException();
112                  }
113                  if (numChars <= 0) {
114                      return -1;
115                  }
116              }
117              return buf[curChar++];
118          }
119          public String nextString() {
120              int c = read();
121              while (isSpaceChar(c)) {
122                  c = read();
123              }
124              StringBuilder res = new StringBuilder();
125              do {
126                  if (Character.isValidCodePoint(c)) {
127                      res.appendCodePoint(c);
128                  }
129                  c = read();
130              } while (!isSpaceChar(c));
131              return res.toString();
132          }
133          public boolean isSpaceChar(int c) {
134              if (filter != null) {
135                  return filter.isSpaceChar(c);
136              }
137              return isWhitespace(c);
138          }
139          public static boolean isWhitespace(int c) {
140              return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
141          }
142          public interface SpaceCharFilter {
143              public boolean isSpaceChar(int ch);
144          }
145      }
146  }
```


**Question**: Does line `55` have control dependence over line `75` in function `solve`? If so, provide a trace.

**Output**:


Ground truth answer: yes