[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**. 

```C
1   #include <stdio.h>
2   int moves[50000];
3   char in_str[100000];
4   void job();
5   int main(){
6     int t;
7     scanf("%d", &t);
8     for(int i=1; i<=t; i++){
9       printf("Case #%d: ", i);
10      job();
11      printf("\n");
12    }
13    return 0;
14  }
15  void job(){
16    char ggg = 'E' ^ 'S';
17    int n;
18    int goodp=-1;
19    int movesp=0;
20    char cur = 'E';
21    scanf("%d%s", &n, in_str);
22    n = n*2 - 2;
23    moves[0]=0;
24    for(int i=0; i<n; i++) {
25      if(in_str[i] != cur){
26        cur = cur ^ ggg;
27        moves[movesp+1] = 1;
28        movesp += 1;
29      }
30      else{
31        moves[movesp]++;
32        if( ((moves[0]) && (i%2)) || (!(moves[0]) && !(i%2)))
33          goodp=movesp;
34      }
35    }
36    int parity = movesp;
37    if(moves[0] != 0)
38      parity++;
39    if(parity % 2 == 0){
40      int En=0;
41      for(int i=0; i<=movesp; i+=2)
42        En+=moves[i];
43      if(moves[0] == 0){
44        for(int i=0; i<En; i++)
45          printf("E");
46        for(int i=0; i<n-En; i++)
47          printf("S");
48      }
49      else{
50        for(int i=0; i<n-En; i++)
51          printf("S");
52        for(int i=0; i<En; i++)
53          printf("E");
54      }
55    }
56    else{
57      int s1=0,s2=0,e1=0,e2=0;
58      for(int i=0; i<goodp; i+=2)
59        e1+=moves[i];
60      for(int i=1; i<goodp; i+=2)
61        s1+=moves[i];
62      for(int i= 2*((goodp+1)/2); i<=movesp; i+=2)
63        e2+=moves[i];
64      for(int i=2*(goodp/2)+1; i<=movesp; i+=2)
65        s2+=moves[i];
66      if(moves[0] == 0){
67        for(int i=-1; i<e1; i++)
68          printf("E");
69        for(int i=0; i<s1+s2; i++)
70          printf("S");
71        for(int i=1; i<e2; i++)
72          printf("E");
73      }
74      else{
75        for(int i=-1; i<s1; i++)
76          printf("S");
77        for(int i=0; i<e1+e2; i++)
78          printf("E");
79        for(int i=1; i<s2; i++)
80          printf("S");
81      }
82    }
83  }
```


**Question**: Does line `39` have control dependence over line `65` in function `job`? If so, provide a trace.

**Output**:


Ground truth answer: yes