[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.util.ArrayList;
2   import java.util.Arrays;
3   import java.util.HashMap;
4   import java.util.List;
5   import java.util.Map;
6   import java.util.Scanner;
7   import java.util.Set;
8   public class Solution {
9   	public static void main(String[] args) {
10  		Scanner sc = new Scanner(System.in);
11  		int t = sc.nextInt();
12  		for (int i = 0; i < t; i++) {
13  			solve(sc, i + 1);
14  		}
15  	}
16  	static Map<Integer, Set<Integer>> all;
17  	static int l;
18  	private static void solve(Scanner sc, int num) {
19  		boolean result = false;
20  		int c = sc.nextInt();
21  		int[] b = new int[c];
22  		int[] r = new int[c];
23  		for (int i = 0; i < c; i++) {
24  			b[i] = sc.nextInt();
25  			r[i] = 1;
26  		}
27  		int[] d = new int[c];
28  		List<String> l = new ArrayList<>();
29  		boolean good = false;
30  		String s = "";
31  		while (true) {
32  			result = true;
33  			for (int i = 0; i < c; i++) {
34  				if (b[i] != r[i]) {
35  					result = false;
36  				}
37  			}
38  			if (result) {
39  				break;
40  			}
41  			int cl = 0;
42  			int last = 0;
43  			int[] z = new int[c];
44  			 good = false;
45  			  s = "";
46  			  int[] rr = new int[c];
47  			for (int i = 0; i < c; i++) {
48  				if (b[i] > 0) {
49  					int want = b[i];
50  					int nexttmp = 0;
51  					for (int j = last; j < c ; j++) {
52  						nexttmp = 0;
53  						if (r[j] == 0) {
54  							s += ".";
55  							continue;
56  						}
57  						want-=r[j];
58  						if (j > i && j > 0&& j  < c-1) {
59  							z[j] = -1;
60  							rr[j-1] += r[j];
61  							good = true;
62  							s += "/";
63  						} else 
64  						if (j < i && j > 0&& j  < c-1) {
65  							z[j] = 1;
66  							rr[j+1]+= r[j];
67  							good = true;
68  							s += "\\";
69  						} else {
70  							s += ".";
71  							rr[j]+=r[j];
72  						}
73  						if (want <= 0) {
74  							last = j+1;
75  							break;
76  						}
77  					}
78  				}
79  			}
80  			r = rr;
81  			l.add(s);
82  			if (!good)
83  			break;
84  		}
85  		if (!result) {
86  			System.out.println("Case #" + num + ": IMPOSSIBLE");
87  		} else {
88  			s = "";
89  			for (int i = 0; i < c ; i++) {
90  				s+=".";
91  			}
92  			l.add(s);
93  			System.out.println("Case #" + num + ": " + l.size());
94  			for (String string : l) {
95  				System.out.println(string);
96  			}
97  		}
98  	}
99  	private static String find(Node root, int h) {
100  		if (h == l) {
101  			return null;
102  		}
103  		if (root.map.size() < all.get(h).size()) {
104  			for (Integer ii : all.get(h)) {
105  				if (root.map.get(ii) == null) {
106  					char rr = (char) ('A' + ii);
107  					return Character.toString(rr);
108  				}
109  			}
110  		} else {
111  			for (Map.Entry<Integer, Node> node : root.map.entrySet()) {
112  				String res = find(node.getValue(), h + 1);
113  				if (res != null) {
114  					char rr = (char) ('A' + node.getKey());
115  					return Character.toString(rr) + res;
116  				}
117  			}
118  		}
119  		return null;
120  	}
121  }
122  class Node {
123  	public Map<Integer, Node> map = new HashMap<>();
124  }
```


**Question**: Does line `31` have control dependence over line `51` in function `solve`? If so, provide a trace.

**Output**:


Ground truth answer: yes