[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   import java.math.*;
4   public class Main {
5       InputStream is;
6       PrintWriter out;
7       String INPUT = "";
8       static int mod = 1_000_000_007;
9       long inf = Long.MAX_VALUE/2;
10      void solve(){
11          int n = ni();
12          int[] a = new int[n];
13          for(int i = 0; i < n; i++){
14              a[i] = ni();
15          }
16          boolean[] seen = new boolean[n];
17          ArrayList<Integer> ans = new ArrayList<>();
18          int t = 1;
19          int l = 0;
20          int r = n-1;
21          while(true){
22              outer:
23              for(int i = n-1; i >= 0; i--){
24                  if(seen[i]) continue;
25                  if(i<l){
26                      out.println(-1);
27                      return;
28                  }
29                  if(a[i]==t){
30                      seen[i] = true;
31                      ans.add(a[i]);
32                      boolean flag = true;
33                      for(int j = i+1; j < n; j++){
34                          if(!seen[j]){
35                              flag = false;
36                          }
37                      }
38                      if(flag){
39                          break;
40                      }
41                      else{
42                          t++;
43                          i = n;
44                          continue;
45                      }
46                  }
47              }
48              if(!seen[n-1]){
49                  out.println(-1);
50                  return;
51              }
52              boolean flag = true;
53              for(int i = n-1; i >= 0; i--){
54                  if(!seen[i]){
55                      t = a[i+1];
56                      flag = false;
57                      r = i;
58                      for(int j = i; j >= 0; j--){
59                          if(seen[j]) break;
60                          l = j;
61                      }
62                      break;
63                  }
64              }
65              if(flag) break;
66          }
67          for(int i : ans){
68              out.println(i);
69          }
70      }
71      void run() throws Exception
72      {
73          is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
74          out = new PrintWriter(System.out);
75          long s = System.currentTimeMillis();
76          solve();
77          out.flush();
78          if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
79      }
80      public static void main(String[] args) throws Exception { new Main().run(); }
81      private byte[] inbuf = new byte[1024];
82      private int lenbuf = 0, ptrbuf = 0;
83      private int readByte()
84      {
85          if(lenbuf == -1)throw new InputMismatchException();
86          if(ptrbuf >= lenbuf){
87              ptrbuf = 0;
88              try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
89              if(lenbuf <= 0)return -1;
90          }
91          return inbuf[ptrbuf++];
92      }
93      private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
94      private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
95      private double nd() { return Double.parseDouble(ns()); }
96      private char nc() { return (char)skip(); }
97      private String ns()
98      {
99          int b = skip();
100          StringBuilder sb = new StringBuilder();
101          while(!(isSpaceChar(b) && b != ' ')){
102              sb.appendCodePoint(b);
103              b = readByte();
104          }
105          return sb.toString();
106      }
107      private char[] ns(int n)
108      {
109          char[] buf = new char[n];
110          int b = skip(), p = 0;
111          while(p < n && !(isSpaceChar(b))){
112              buf[p++] = (char)b;
113              b = readByte();
114          }
115          return n == p ? buf : Arrays.copyOf(buf, p);
116      }
117      private char[][] nm(int n, int m)
118      {
119          char[][] map = new char[n][];
120          for(int i = 0;i < n;i++)map[i] = ns(m);
121          return map;
122      }
123      private int[] na(int n)
124      {
125          int[] a = new int[n];
126          for(int i = 0;i < n;i++)a[i] = ni();
127          return a;
128      }
129      private int ni()
130      {
131          int num = 0, b;
132          boolean minus = false;
133          while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
134          if(b == '-'){
135              minus = true;
136              b = readByte();
137          }
138          while(true){
139              if(b >= '0' && b <= '9'){
140                  num = num * 10 + (b - '0');
141              }else{
142                  return minus ? -num : num;
143              }
144              b = readByte();
145          }
146      }
147      private long nl()
148      {
149          long num = 0;
150          int b;
151          boolean minus = false;
152          while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
153          if(b == '-'){
154              minus = true;
155              b = readByte();
156          }
157          while(true){
158              if(b >= '0' && b <= '9'){
159                  num = num * 10 + (b - '0');
160              }else{
161                  return minus ? -num : num;
162              }
163              b = readByte();
164          }
165      }
166      private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
167  }
```


**Question**: Does line `21` have control dependence over line `55` in function `solve`? If so, provide a trace.

**Output**:


Ground truth answer: yes