[INSTRUCTIONS]

You are a program-analysis assistant. Perform a **static** data-dependence analysis on a given code snippet, treating each branch or loop condition as potentially taking any outcome, without using semantic or symbolic execution to prune paths.


## 1. Data Dependence Definition

   Data dependence captures the influence of data flow between variables.

   We denote each variable instance as `(var,lineNumber)`, meaning the variable `var` defined or updated at `lineNumber`.

   >  **Direct Data Dependence**
   A variable instance `(varB,lineB)` is **directly** data-dependent on `(varA,lineA)` if `lineA` writes to `varA`. Then, without overwritting the value of `varA`, `lineB` reads `varA` and compute the value of `varB`. In other words, the value of `(varB,lineB)` relies on the value produced at `(varA,lineA)`. In addition, changing the execution order of `(varA,lineA)` and `(varB,lineB)` would alter their results.


   A variable instance `(varB,lineB)` is data-dependent on `(varA,lineA)` if there is a **transitive** (indirect) chain of **direct** data dependencies from `(varA,lineA)` to `(varB,lineB)`. This is equivalent to saying that `(varA,lineA)` has data dependence over `(varB,lineB)`, meaning the value written at `(varA,lineA)` can propagate to `(varB,lineB)` through a sequence of read/write operations.


## 2. Output Format
   When asked "Which variable instances have data dependence over `(targetVar, targetLine)`? List all such variables.", respond:
   ```json
   {
    "DataDependenceSources": [
      ["valA", lineA],
      ["valB", lineB],
      ...
    ]
   }
   ```

  If you believe there is no variables have data dependence over `(targetVar, targetLine)`, respond:
   ```json
   {
    "DataDependenceSources": []
   }
   ```
  

## 3. Intraprocedural Data 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    total = 0
2    value = 1
3    step = value
4    if step > 1:
5        value += 3
6    while total <= 10:
7        total += value
8        difference = total - step
9        step += 1
10   final_result = total * 2
```


#### Example Question 1.1:
Which variable instances have data dependence over `(step,9)`? List all such variables.


**Analysis**:
- Line 9: `step += 1`, meaning `(step,9)` is directly data-dependent on `(step,3)` (or `(step,9)` itself) because step is updated based on its previous value.
- Line 3: `step = value`, meaning `(step,3)` is directly data-dependent on `(value,2)`.
Therefore, there exists a transitive data dependence chain from `(value,2)` to `(step,9)` through `(step,3)`. 


**Output**:
```json
   {
    "DataDependenceSources": [
      ["step", 9],
      ["step", 3],
      ["value", 2],
    ]
   }
```





#### Example Question 1.2 
Which variable instances have data dependence over `(total,7)`? List all such variables.


**Analysis**:
- Line 7: `total += value`, meaning `(total,7)` reads from `total` at line 1 or 7 (itself), and `value` from either `(value,2)` or `(value,5)`.
- Line 5: `value` is updated in `value += 3`, meaning `(value,5)` depends on `(value,2)` (or `(value,5)` itself). However, this update is inside an if statement, which means it may or may not execute depending on runtime conditions.
- Line 2: value is initialized at `(value,2)`.


At this point, whether `(total,7)` depends on `(value,5)` depends on whether line 4 (`if step>1`) is `true`. Since this is a static analysis, all possible paths are considered without analyzing actual reachability. This means line 5 is treated as both possibly executed and possibly not executed.

- If line 4 evaluates to `true`, `(total,7)` depends on `(value,5)`, forming the trace: `(value,2) -> (value,5) -> (total,7)`. 
- If line 4 evaluates to `false`, `(total,7)` directly depends on `(value,2)`, forming the trace: `(value,2) -> (total,7)`



**Output**:
```json
   {
    "DataDependenceSources": [
      ["total", 1],
      ["total", 7],
      ["value", 5],
      ["value", 2]
    ]
   }
```



### Example 2

```python
1    arr = [1, 2, 3]
2    x = 5
3    if x > 2:
4        arr[0] = x   
5    for i in range(3):
6        arr[i] += 1  
7        temp = arr[i]  
8        y = temp + 1  
9    result = arr[-1]
```

#### Example Question 2.1:
Which variable instances have data dependence over `(arr,6)`? List all such variables.



**Analysis**
- Line 6: `arr[i] += 1` modifies `arr[i]`, but i varies during the loop execution.
   - If `i == 0`, `arr[i]` refers to `arr[0]`, which was updated in line 4 (or line 6 itself), establishing a dependence chain `(arr,4)` -> `(arr,6)`.
   - If `i != 0`, `arr[i]` does not refer to `arr[0]`, meaning it depend on `(arr,1)` (or `(arr,6)` itself), not `(arr,4)`.
   - However, since static analysis considers all possible paths without resolving i’s runtime value, we must assume `arr[i]` could be `arr[0]`, leading to a possible dependence.
- Line 4: `arr[0] = x`, meaning `(arr,4)` depends on `(x,2)`.
- Line 2: `x` is initialized at `(x,2)`.




**Output**:
```json
   {
    "DataDependenceSources": [
      ["arr", 6],
      ["arr", 4],
      ["arr", 1],
      ["i", 5],
      ["x", 2]
    ]
   }
```


#### Example Question 2.2:
Which variable instances have data dependence over `(temp,7)`? List all such variables.


**Analysis**:
- Line 7: `temp = arr[i]`, meaning temp depends on `i`, since `i` determines which element of arr is accessed. And `arr[i]` can only refer to `(arr,6)` as they have the same index.
- Line 5: `i` is initialized and iterates over the range 0 to 3.


**Output**:
```json
   {
    "DataDependenceSources": [
      ["arr", 6],
      ["i", 5],
    ]
   }
```

#### Example Question 2.3:
Which variable instances have data dependence over `(result,9)`? List all such variables.

**Analysis**:
- Line 9: `result = arr[-1]`, meaning result depends on `arr[-1]`, which is arr[2], possibly get updated at line 6 (or line 1).
  - If it is from line 6: `arr[i] += 1`, `arr[i]` is modified based on the value of `i`. Line 5: `i` iterates over 0 to 3.
  - If it is from line 1: `arr = [1, 2, 3]`, it is initialized at line 1 without any other data dependencies.

**Output**:
```json
   {
    "DataDependenceSources": [
      ["arr", 6],
      ["arr", 1],
      ["i", 5],
    ]
   }
```

---

[YOUR TURN]

Below is **your target snippet**. 

```Java
1   import java.util.Scanner;
2   public class Solution {
3       static Long shootDamage;
4       static Long shootCounter;
5       static Long shield;
6       static String code;
7       static Long damage;
8       static Long movements;
9       static int lastIterableElement;
10      public static String hackTheSystem(String[] softwareToHack) {
11          shootDamage = 1L;
12          shootCounter = 0L;
13          shield = Long.parseLong(softwareToHack[0]);
14          code = softwareToHack[1];
15          damage = 0L;
16          movements = 0L;
17          int sizeScript = code.length() - 1;
18          lastIterableElement = sizeScript;
19          for (int i = 0; i < code.length(); i++) {
20              if (code.charAt(i) == 'S') {
21                  damage += shootDamage;
22                  shootCounter++;
23              }
24              if (code.charAt(i) == 'C') {
25                  shootDamage *= 2;
26              }
27          }
28          if (damage <= shield) {
29              return String.valueOf(movements);
30          }
31          if (shootCounter > shield) {
32              return "IMPOSSIBLE";
33          }
34          for (int i = sizeScript; i >= 0; i--) {
35              for (int j = sizeScript - 1; j >= 0; j--) {
36                  if(code.charAt(j) == 'S' && code.charAt(i) == 'S') {
37                      i--;
38                      continue;
39                  }
40                  if(code.charAt(i) == 'C') {
41                      shootDamage /= 2;
42                      i--;
43                      lastIterableElement--;
44                      continue;
45                  }
46                  if (code.charAt(j) == 'C' && code.charAt(i) == 'S') {
47                      movements++;
48                      damage -= (shootDamage / 2);
49                      char[] c = code.toCharArray();
50                      if (damage <= shield) {
51                          return String.valueOf(movements);
52                      }
53                      char temp = c[j];
54                      c[j] = c[i];
55                      c[i] = temp;
56                      code = String.valueOf(c);
57                      if (i == lastIterableElement) {
58                          shootDamage /= 2;
59                          if(i>0) {
60                              i--;
61                          }
62                      } else {
63                          i++;
64                          j += 2;
65                      }
66                  }
67              }
68          }
69          return String.valueOf(movements);
70      }
71      private static final Scanner scan = new Scanner(System.in);
72      public static void main(String[] args) {
73          int numberOfCases = Integer.parseInt(scan.nextLine());
74          String[][] cases = new String[numberOfCases][2];
75          for (int i = 0; i < numberOfCases; i++) {
76              String[] caseNumber = scan.nextLine().split(" ");
77              cases[i][0] = caseNumber[0];
78              cases[i][1] = caseNumber[1];
79          }
80          for (int i = 0; i < numberOfCases; i++) {
81              System.out.println("Case #" + i + ": " + hackTheSystem(cases[i]));
82          }
83      }
84  }
```


**Question**: Which variable instances have data dependence over `(damage,48)` in function `hackTheSystem`? List all such variables.

**Output**:


Ground truth answer: yes