[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.*;
2   import java.util.*;
3   public class Main {
4       static int N;
5       static int[] t;
6       static int[] v;
7       static int[] maxv;
8       public static void main(String[] args) throws IOException {
9           int totalt = 0;
10          MyScanner sc = new MyScanner(System.in);
11          int n = sc.nextInt();
12          t = new int[n];
13          v = new int[n];
14          for (int i = 0; i < n; i++) {
15              t[i] = sc.nextInt();
16              totalt += t[i];
17          }
18          for (int i = 0; i < n; i++) {
19              v[i] = sc.nextInt();
20          }
21          maxv = new int[totalt + 1];
22          int[] ctr = new int[totalt + 1];
23          Arrays.fill(maxv, -1);
24          maxv[0] = 0;
25          maxv[totalt] = 0;
26          int tidx = n - 1;
27          int mov = 0;
28          for (int i = totalt - 1; i > 0; i--) {
29              mov++;
30              maxv[i] = Math.min(maxv[i + 1] + 1, v[tidx]);
31              ctr[i] = v[tidx];
32              if (mov == t[tidx]){
33                  mov = 0;
34                  tidx--;
35              }
36          }
37          long size = 0;
38          long btt = 0;
39          int prevHei = 0;
40          int ttt = 0;
41          int curHei = 0;
42          int prepre = 0;
43          int perform = 0; 
44          for (int i = 1; i < totalt + 1; i++) {
45              int mv = maxv[i];
46              switch (perform){
47                  case 0:
48                      if (mv >= curHei + 1){
49                          curHei++;
50                          ttt++;
51                      } else {
52                          size += (curHei + prevHei) * ttt;
53                          prevHei = curHei;
54                          ttt = 0;
55                          if (mv == curHei){
56                              if (maxv[i + 1] == curHei - 1 && ctr[i + 1] > curHei){
57                                  btt += 1;
58                              }
59                              perform = 1;
60                          } else {
61                              perform = 2;
62                          }
63                          prepre = 0;
64                          i--;
65                      }
66                      break;
67                  case 1:
68                      if (mv == curHei){
69                          ttt++;
70                      } else {
71                          size += curHei * ttt * 2;
72                          ttt = 0;
73                          prevHei = curHei;
74                          if (mv > curHei){
75                              perform = 0;
76                              size += curHei * 2;
77                              i++;
78                          } else {
79                              perform = 2;
80                              if (prepre == 0){
81                              }
82                          }
83                          i--;
84                      }
85                      break;
86                  case 2:
87                      if (mv == curHei - 1){
88                          curHei--;
89                          ttt++;
90                      } else {
91                          size += (prevHei + curHei) * ttt;
92                          prevHei = curHei;
93                          ttt = 0;
94                          if (mv == curHei){
95                              perform = 1;
96                          } else {
97                              perform = 0;
98                          }
99                          i--;
100                      }
101                      prepre = 2;
102                      break;
103              }
104          }
105          size += (prevHei + curHei) * ttt;
106          System.out.println((size+0.0)/ 2 + (btt+0.0)/4);
107      }
108      static class MyScanner {
109          StringTokenizer st;
110          BufferedReader br;
111          public MyScanner(InputStream s){  br = new BufferedReader(new InputStreamReader(s));}
112          public MyScanner(FileReader s) throws FileNotFoundException {br = new BufferedReader(s);}
113          public String next() throws IOException
114          {
115              while (st == null || !st.hasMoreTokens())
116                  st = new StringTokenizer(br.readLine());
117              return st.nextToken();
118          }
119          public int nextInt() throws IOException {return Integer.parseInt(next());}
120          public long nextLong() throws IOException {return Long.parseLong(next());}
121          public String nextLine() throws IOException {return br.readLine();}
122          public double nextDouble() throws IOException { return Double.parseDouble(next()); }
123          public boolean ready() throws IOException {return br.ready();}
124      }
125  }
```


**Question**: Does line `55` have control dependence over line `59` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes