[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**. 

```Python
1   import sys
2   from datetime import datetime
3   from random import randint
4   from itertools import cycle
5   def debug(x):
6       sys.stderr.write('{} DEBUG: {}\n'.format(datetime.now().time(), x))
7   def read_int():
8       return int(raw_input())
9   def read_float():
10      return float(raw_input())
11  def read_words():
12      return raw_input().split()
13  def read_ints():
14      return map(int, read_words())
15  def read_floats():
16      return map(float, read_words())
17  ALLVALS = set(range(1, 100))
18  OT = {19: 20, 20:19}
19  def solve_test_case():
20      curd = 0
21      while curd < 54:
22          curd = read_int()
23          if curd == -1:
24              sys.exit()
25          if curd > 36:
26              token = 100
27          else:
28              token = randint(1, 99)
29          print '{} {}'.format(1 + (curd % 18), token)
30          sys.stdout.flush()
31      badv = []
32      while curd < 72:
33          curd = read_int()
34          if curd == -1:
35              sys.exit()
36          v = 1 + (curd % 18)
37          print '{} {}'.format(v, 0)
38          sys.stdout.flush()
39          offset = 0
40          if curd <= 63:
41              offset = 1
42          badv.append((len(read_ints()) + offset, v))
43      badv = sorted(badv)
44      while True:
45          i, x = badv[0]
46          curd = read_int()
47          if curd == -1:
48              sys.exit()
49          print '{} {}'.format(x, randint(1, 99))
50          badv[0] = (i+1, x)
51          badv = sorted(badv)
52          sys.stdout.flush()
53          if curd == 95:
54              break
55      lv = rv = None
56      choice = None
57      while curd < 99:
58          curd = read_int()
59          if curd == -1:
60              sys.exit()
61          if not lv:
62              print '{} {}'.format(19, 0)
63              sys.stdout.flush()
64              lv = set(read_ints())
65              continue
66          elif not rv:
67              print '{} {}'.format(20, 0)
68              sys.stdout.flush()
69              rv = set(read_ints())
70              if not choice:
71                  if len(lv) > len(rv):
72                      choice = 19
73                  else:
74                      choice = 20
75              continue
76          print '{} {}'.format(choice, randint(1, 99))
77          sys.stdout.flush()
78      choice = OT[choice]
79      curd = read_int()
80      if curd == -1:
81          sys.exit()
82      print '{} {}'.format(choice, 100)
83      sys.stdout.flush()
84  def main():
85      T = int(raw_input())
86      for tc in xrange(1, T+1):
87          solve_test_case()
88  if __name__ == "__main__":
89      main()
```


**Question**: Which variable instances have data dependence over `(badv,51)` in function `solve_test_case`? List all such variables.

**Output**:


Ground truth answer: yes