[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 sys import stdout
2   from bisect import bisect_left as binl
3   from copy import copy, deepcopy
4   mod = 1
5   def intin():
6       input_tuple = input().split()
7       if len(input_tuple) <= 1:
8           return int(input_tuple[0])
9       return tuple(map(int, input_tuple))
10  def intina():
11      return [int(i) for i in input().split()]
12  def intinl(count):
13      return [intin() for _ in range(count)]
14  def modadd(x, y):
15      global mod
16      return (x + y) % mod
17  def modmlt(x, y):
18      global mod
19      return (x * y) % mod
20  def lcm(x, y):
21      while y != 0:
22          z = x % y
23          x = y
24          y = z
25      return x
26  def combination(x, y):
27      assert(x >= y)
28      if y > x // 2:
29          y = x - y
30      ret = 1
31      for i in range(0, y):
32          j = x - i
33          i = i + 1
34          ret = ret * j
35          ret = ret // i
36      return ret
37  def get_divisors(x):
38      retlist = []
39      for i in range(1, int(x**0.5) + 3):
40          if x % i == 0:
41              retlist.append(i)
42              retlist.append(x // i)
43      return retlist
44  def get_factors(x):
45      retlist = []
46      for i in range(2, int(x**0.5) + 3):
47          while x % i == 0:
48              retlist.append(i)
49              x = x // i
50      retlist.append(x)
51      return retlist
52  def make_linklist(xylist):
53      linklist = {}
54      for a, b in xylist:
55          linklist.setdefault(a, [])
56          linklist.setdefault(b, [])
57          linklist[a].append(b)
58          linklist[b].append(a)
59      return linklist
60  def calc_longest_distance(linklist, v=1):
61      distance_list = {}
62      distance_count = 0
63      distance = 0
64      vlist_previous = []
65      vlist = [v]
66      nodecount = len(linklist)
67      while distance_count < nodecount:
68          vlist_next = []
69          for v in vlist:
70              distance_list[v] = distance
71              distance_count += 1
72              vlist_next.extend(linklist[v])
73          distance += 1
74          vlist_to_del = vlist_previous
75          vlist_previous = vlist
76          vlist = list(set(vlist_next) - set(vlist_to_del))
77      max_distance = -1
78      max_v = None
79      for v, distance in distance_list.items():
80          if distance > max_distance:
81              max_distance = distance
82              max_v = v
83      return (max_distance, max_v)
84  def calc_tree_diameter(linklist, v=1):
85      _, u = calc_longest_distance(linklist, v)
86      distance, _ = calc_longest_distance(linklist, u)
87      return distance
88  def main():
89      a, b = intin()
90      if a % 2 == 1 and b % 2 == 1:
91          print('Yes')
92      else:
93          print('No')
94  if __name__ == '__main__':
95      main()
```


**Question**: Does line `67` have control dependence over line `75` in function `calc_longest_distance`? If so, provide a trace.

**Output**:


Ground truth answer: yes