[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   from __future__ import division
2   import math
3   import sys
4   def printflush(x):
5       print(x)
6       sys.stdout.flush()
7   def getline():
8       return sys.stdin.readline().split()
9   def getints():
10      return [int(x) for x in getline()]
11  def solvecase():
12      vases = [None] + [[] for i in range(20)]
13      peektime = [0 for i in range(21)]
14      stuffV = None
15      tokens = 0
16      target = 1
17      for d in range(1, 101):
18          (dd,) = getints()
19          assert(d == dd)
20          tokens += 1
21          if d <= 19:
22              V = d
23              P = 100
24          elif d == 100:
25              V = 20
26              P = 100
27          elif stuffV is not None:
28              V = stuffV
29              v = vases[V]
30              sys.stderr.write("TARGET peektime: %s\n" % peektime[target])
31              if peektime[target] <= d - 5:
32                  V = target
33                  P = 0
34                  sys.stderr.write("PEEK TARGET instead\n")
35              elif peektime[V] <= d - 30:
36                  P = 0
37                  sys.stderr.write("PEEK instead\n")
38              else:
39                  P = 1
40                  while True:
41                      if P not in v:
42                          break
43                      P += 1
44          else:
45              V = target
46              P = 0
47          printflush("{} {}".format(V, P))
48          stuffV = None
49          if P == 0:
50              L = getints()
51              L = [x for x in L[1:] if x < 100]
52              vases[V] = L
53              peektime[V] = d
54          elif P != 100:
55              vases[V].append(P)
56              tokens += 1
57          m = min(len(vases[V]) for V in range(1, 21))
58          sys.stderr.write("day = %s; m = %s; target = %s\n" % (d, m, target))
59          sys.stderr.write("sizes: %s\n" % " ".join(str(len(vases[V])) for V in range(1, 21)))
60          if len(vases[target]) == m:
61              m2 = 10000
62              mtime = 0
63              for V in range(1, 21):
64                  if V == target:
65                      continue
66                  if len(vases[V]) < m2 or (len(vases[V]) == m2 and peektime[V] > mtime):
67                      stuffV = V
68                      m2 = len(vases[V])
69                      mtime = peektime[V]
70              sys.stderr.write("STUFFING vase %s\n" % stuffV)
71          else:
72              for target in range(1, 21):
73                  if len(vases[target]) == m:
74                      break
75              sys.stderr.write("NEW target = %s\n" % target)
76  (T,) = getints()
77  for i in range(T):
78      ans = solvecase()
79      sys.stderr.write("*" * 80 + "\n")
```


**Question**: Does line `73` have control dependence over line `43` in function `solvecase`? If so, provide a trace.

**Output**:


Ground truth answer: no