[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**. 

```Python
1   import random
2   def main():
3   	T=eval(input())
4   	for i in range (T):
5   		N=eval(input())
6   		s=input()
7   		print("Case #"+str(i+1)+":", end=' ')
8   		ownWay(s,N)
9   def ownWay(s,n):
10  	maze=[]
11  	for i in range (n):
12  		maze.append([])
13  		for j in range (n):
14  			maze[i].append([])
15  			for k in range (2):
16  				if k==0:
17  					maze[i][j].append(i)
18  				else:
19  					maze[i][j].append(j)
20  	l=list(s)
21  	c_l=[]    
22  	for i in range (1):
23  		c_l.append([])
24  		for j in range(2*n-1):
25  			c_l[i].append([])
26  			for k in range (2):
27  				c_l[i][j].append(0)
28  	x=0
29  	y=0
30  	c_l[0][0][0]=maze[x][y][0]
31  	c_l[0][0][1]=maze[x][y][1]
32  	for i in range(2*n-2):
33  		if l[i]=='S':
34  			y=y+1
35  			c_l[0][i+1][1]=maze[x][y][1]
36  			c_l[0][i+1][0]=maze[x][y][0]
37  		if l[i]=='E':
38  			x=x+1
39  			c_l[0][i+1][0]=maze[x][y][0]
40  			c_l[0][i+1][1]=maze[x][y][1]       
41  	check=True
42  	random.shuffle(l)
43  	c_l1=[]
44  	for i in range (1):
45  		c_l1.append([])
46  		for j in range(2*n-1):
47  			c_l1[i].append([])
48  			for k in range (2):
49  				c_l1[i][j].append(0)
50  	x1=0
51  	y1=0
52  	c_l1[0][0][0]=maze[x1][y1][0]
53  	c_l1[0][0][1]=maze[x1][y1][1]
54  	for i in range(2*n-2):
55  		if l[i]=='S':
56  			y1=y1+1
57  			c_l1[0][i+1][1]=maze[x1][y1][1]
58  			c_l1[0][i+1][0]=maze[x1][y1][0]
59  		if l[i]=='E':
60  			x1=x1+1
61  			c_l1[0][i+1][0]=maze[x1][y1][0]
62  			c_l1[0][i+1][1]=maze[x1][y1][1]
63  	while check:
64  		check=False
65  		for i in range(2*n-2):
66  			if (c_l[0][i][0]==c_l1[0][i][0]) and (c_l[0][i][1]==c_l1[0][i][1]) and (c_l[0][i+1][0]==c_l1[0][i+1][0]) \
67  				and (c_l[0][i+1][1]==c_l1[0][i+1][1]):
68  				check=True
69  		if check:
70  			random.shuffle(l)
71  			c_l1=[]
72  			for i in range (1):
73  				c_l1.append([])
74  				for j in range(2*n-1):
75  					c_l1[i].append([])
76  					for k in range (2):
77  						c_l1[i][j].append(0)
78  			x1=0
79  			y1=0
80  			c_l1[0][0][0]=maze[x1][y1][0]
81  			c_l1[0][0][1]=maze[x1][y1][1]
82  			for i in range(2*n-2):
83  				if l[i]=='S':
84  					y1=y1+1
85  					c_l1[0][i+1][1]=maze[x1][y1][1]
86  					c_l1[0][i+1][0]=maze[x1][y1][0]
87  				if l[i]=='E':
88  					x1=x1+1
89  					c_l1[0][i+1][0]=maze[x1][y1][0]
90  					c_l1[0][i+1][1]=maze[x1][y1][1]
91  	print(''.join(l))
92  main()
```


**Question**: Does line `16` have control dependence over line `15` in function `ownWay`? If so, provide a trace.

**Output**:


Ground truth answer: no