[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.util.*;
2   import java.util.regex.*;
3   import static java.lang.Math.*;
4   import static java.lang.System.out;
5   public class Main {
6   	final Scanner sc=new Scanner(System.in);
7   	final int[] vx={0,1,0,-1}, vy={-1,0,1,0};
8   	static class Point{
9   		int x, y;
10  		Point(int x, int y){	this.x=x;	this.y=y;}
11  		Point(){	this.x=0; this.y=0;}
12  		@Override public String toString(){	return "("+this.x+","+this.y+")";}
13  		static boolean ok(int x,int y,int X,int Y,int min){
14  			return (min<=x&&x<X && min<=y&&y<Y)?true:false;
15  		}
16  		static boolean ok(int x,int y,int X,int Y){	return ok(x,y,X,Y,0);}
17  	}
18  	public static void main(String[] args) {
19  		new Main().AOJ0144();
20  	}
21  	void AOJ0145(){
22  		while(sc.hasNext()){
23  			int N=sc.nextInt(),ans=Integer.MAX_VALUE;
24  			C0145[] c=new C0145[N];
25  			for(int i=0; i<N; i++)	c[i]=new C0145(sc.nextInt(),sc.nextInt());
26  			out.println(ans);
27  		}
28  	}
29  	class C0145{
30  		int upper,down;
31  		C0145(int u,int d){	this.upper=u;	this.down=d;	}
32  	}
33  	void AOJ0147(){
34  		LinkedList<Integer> queue=new LinkedList<Integer>();
35  		int MAX=120;
36  		while(sc.hasNext()){
37  			int temp=sc.nextInt();
38  			MAX=max(MAX,temp);
39  			queue.add(temp);
40  		}
41  		int[] num=new int[MAX],time=new int[MAX],seat=new int[17];
42  		Arrays.fill(seat, -1);
43  		for(int i=0; i<MAX; i++){
44  			num[i]=(i%5==1?5:2);
45  			time[i]=(17*(i%2)+3*(i%3)+19);
46  		}
47  		int j=0,min=0;
48  		while(!queue.isEmpty()){
49  			seat=exit(seat,min,time);
50  			int temp=find(seat,num[j]);
51  			if(temp>=0 && min>=j*5){
52  				int q=queue.getFirst();
53  				if(j==q){
54  					out.println(max(0,min-j*5));
55  					queue.removeFirst();
56  				}
57  				for(int i=temp; i<temp+num[j]; i++)	seat[i]=j;
58  				j++;
59  			}else{
60  				min++;
61  			}
62  		}
63  	}
64  	int find(int[] seat,int n){
65  		for(int i=0; i<17-n; i++){
66  			boolean flag=true;
67  			for(int j=0; j<n; j++){
68  				if(seat[i+j]!=-1){
69  					flag=false;
70  					break;
71  				}
72  			}
73  			if(flag)	return i;
74  		}
75  		return -1;
76  	}
77  	int[] exit(int[] seat,int min,int[] time){
78  		for(int i=0; i<17; i++){
79  			if(seat[i]<0)	continue;
80  			int idx=seat[i],emin=idx*5+time[seat[i]];
81  			if(min>=emin)	seat[i]=-1;
82  		}
83  		return seat;
84  	}
85  	void disp(int[] seat,int min){
86  		out.print(min+"m : ");
87  		for(int i=0; i<17; i++)	out.print(seat[i]+" ");
88  		out.println();
89  	}
90  	void AOJ0144(){
91  		while(sc.hasNext()){
92  			int N=sc.nextInt();
93  			boolean[][] R=new boolean[N+1][N+1];
94  			for(int i=1; i<=N; i++){
95  				int r=sc.nextInt(),k=sc.nextInt();
96  				for(int j=0; j<k; j++)	
97  					R[r][sc.nextInt()]=true;
98  			}
99  			int P=sc.nextInt();
100  			for(int i=0; i<P; i++){
101  				int s=sc.nextInt(),d=sc.nextInt(),v=sc.nextInt(),ans=-1;
102  				PriorityQueue<C0144> open=new PriorityQueue<C0144>();
103  				open.add(new C0144(s,v,1));
104  				C0144[] close=new C0144[N+1];
105  				while(!open.isEmpty()){
106  					C0144 now=open.poll();
107  					if(--now.ttl==0)	continue;
108  					for(int j=1; j<=N; j++){
109  						if(R[now.now][j]){
110  							if(close[j]==null){
111  								if(j==d){
112  									ans=(ans<0?now.c+1:min(ans,now.c+1));
113  									continue;
114  								}
115  								open.add(new C0144(j,now.ttl,now.c+1));
116  								close[j]=new C0144(j,now.ttl,now.c+1);
117  							}else{
118  								if(now.c+1<close[j].c || now.ttl>close[j].ttl){
119  									if(j==d){
120  										ans=(ans<0?now.c+1:min(ans,now.c+1));
121  										continue;
122  									}
123  									open.add(new C0144(j,now.ttl,now.c+1));
124  									close[j]=new C0144(j,now.ttl,now.c+1);
125  								}
126  							}
127  						}
128  					}
129  				}
130  				out.println((ans<0?"NA":ans));
131  			}
132  		}
133  	}
134  	class C0144 implements Comparable<C0144>{
135  		int now,ttl,c;
136  		C0144(int now,int ttl,int c){
137  			this.now=now;	this.ttl=ttl;	this.c=c;
138  		}
139  		@Override public int compareTo(C0144 o) {
140  			if(this.c<o.c)	return -1;
141  			if(this.c>o.c)	return 1;
142  			return 0;
143  		}
144  	}
145  }
```


**Question**: Does line `110` have control dependence over line `115` in function `AOJ0144`? If so, provide a trace.

**Output**:


Ground truth answer: yes