[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.DataInputStream;
2   import java.io.FileInputStream;
3   import java.io.IOException;
4   import java.io.InputStreamReader;
5   import java.util.Arrays;
6   import java.util.LinkedList;
7   import java.util.List;
8   import java.util.Scanner;
9   import java.util.StringTokenizer;
10  public class Solution {
11  	int[] array;
12      int[] tempMergArr;
13      int length;
14  	public static void main(String[] args) {
15  		Scanner reader = new Scanner(System.in);  
16  		int numberOfTests= reader.nextInt();
17  		int a=0;
18  		int b=0;
19  		for(int m=0; m< numberOfTests;m++) { 
20  			int n  = reader.nextInt();
21  			if(n%2==1) {
22  				a=n/2 +1;
23  				b=n/2;
24  			}
25  			else {
26  				a=n/2;
27  				b=n/2;
28  			}
29  			int[] oddArray = new int[a];
30  			int[] evenArray = new int[a];
31  			int c=0;
32  			int d=0;
33  			for(int i=0;i<n;i++) {
34  				if(i%2==0) {
35  					oddArray[c]=reader.nextInt();
36  					c++;
37  				}
38  				else {
39  					evenArray[d]=reader.nextInt();
40  					d++;
41  				}
42  			}
43  			evenArray[evenArray.length-1]=Integer.MAX_VALUE;
44  			Solution mms = new Solution();
45  	        mms.sort(oddArray);
46  	        mms.sort(evenArray);
47  	        int x=0;
48  	        for(int h=0;h<oddArray.length;h++) { 
49  	        	try {
50  	        		if(oddArray[h]<=evenArray[h]) {
51  	        			if(h==oddArray.length-1) {
52  	        				break;
53  	        			}
54  	        			if(evenArray[h]<=oddArray[h+1]) {
55  	        			}
56  	        			else {
57  	        				System.out.println("Case #"+(m+1)+": "+(2*h+1));
58  	        				x++;
59  	        				break;
60  	        			}
61  	        		}
62  	        		else {
63  	        			System.out.println("Case #"+(m+1)+": "+2*h);
64  	        			x++;
65  	        			break;
66  	        		}
67  	        	}
68  	        	finally {
69  	        	}
70  	        }
71  	        if(x==0) {
72  	        	System.out.println("Case #"+(m+1)+": OK");
73  	        }
74  		}
75  		reader.close();
76  	}
77  	public void sort(int inputArr[]) {
78          this.array = inputArr;
79          this.length = inputArr.length;
80          this.tempMergArr = new int[length];
81          doMergeSort(0, length - 1);
82      }
83      private void doMergeSort(int lowerIndex, int higherIndex) {
84          if (lowerIndex < higherIndex) {
85              int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
86              doMergeSort(lowerIndex, middle);
87              doMergeSort(middle + 1, higherIndex);
88              mergeParts(lowerIndex, middle, higherIndex);
89          }
90      }
91      private void mergeParts(int lowerIndex, int middle, int higherIndex) {
92  		for (int i = lowerIndex; i <= higherIndex; i++) {
93              tempMergArr[i] = array[i];
94          }
95          int i = lowerIndex;
96          int j = middle + 1;
97          int k = lowerIndex;
98          while (i <= middle && j <= higherIndex) {
99              if (tempMergArr[i] <= tempMergArr[j]) {
100                  array[k] = tempMergArr[i];
101                  i++;
102              } else {
103                  array[k] = tempMergArr[j];
104                  j++;
105              }
106              k++;
107          }
108          while (i <= middle) {
109              array[k] = tempMergArr[i];
110              k++;
111              i++;
112          }
113      }
114  }
```


**Question**: Does line `54` have control dependence over line `58` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes