[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.IOException;
2   import java.io.InputStream;
3   import java.util.Arrays;
4   import java.util.NoSuchElementException;
5   import java.util.Random;
6   import java.util.Scanner;
7   class UnionFind{
8   	int Parent[];
9   	UnionFind(int n){
10  		Parent=new int[n];
11  		Arrays.fill(Parent, -1);
12  	}
13  	int root(int A) {
14  		if(Parent[A]<0)return A;
15  		return Parent[A]=root(Parent[A]);
16  	}
17  	int size(int A) {
18  		return -Parent[root(A)];
19  	}
20  	boolean connect(int A,int B) {
21  		A=root(A);
22  		B=root(B);
23  		if(A==B) return false;
24  		if(size(A)<size(B)) {int C=0;C=B;B=A;A=C;}
25  		Parent[A]+=Parent[B];
26  		Parent[B]=A;
27  		return true;
28  	}
29  }
30  public class Main {
31  	static FastScanner scan=new FastScanner();
32  	static Scanner scanner=new Scanner(System.in);
33  	static Random rand=new Random();
34  	static long mod=1000000007;
35  	static double eps=0.0000000001;
36  	static int big=Integer.MAX_VALUE;
37  	static long modlcm(long a,long b) {return a*b*modint(gcd(a,b),mod);}
38  	static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
39  	static long lcm (long a, long b) {return a*b/gcd(a,b);}
40  	static int max(int a,int b) {return a>b?a:b;}
41  	static int min(int a,int b) {return a<b?a:b;}
42  	static long lmax(long a,long b) {return Math.max(a, b);}
43  	static long lmin(long a,long b) {return Math.min(a, b);}
44  	static long factorial(int i) {return i==1?1:i*factorial(i-1);}
45  	public static void main(String[] args) throws IOException {
46  		String str=scan.next();
47  		boolean b=false;
48  		for(int i=0;i<str.length();i++) {
49  			if(str.charAt(i)=='C')b=true;
50  			if(b&&str.charAt(i)=='F') {
51  				System.out.println("Yes");
52  				return;
53  			}
54  		}
55  		System.out.println("No");
56  	}
57  	static int lower_bound(int a[],int key) {
58  		int right=a.length;
59  		int left=0;
60  		while(right-left>1) {
61  			int mid=(right+left)/2;
62  			if(a[mid]<key) {
63  				left=mid;
64  			}
65  			else {
66  				right=mid;
67  			}
68  		}
69  		return left;
70  	}
71  	static int upper_bound(int a[],int key) {
72  		int right=a.length;
73  		int left=0;
74  		while(right-left>1) {
75  			int mid=(right+left)/2;
76  			if(a[mid]<=key) {
77  				left=mid;
78  			}
79  			else {
80  				right=mid;
81  			}
82  		}
83  		return left;
84  	}
85  	static boolean isPrime (long n) {
86  		if (n==2) return true;
87  		if (n<2 || n%2==0) return false;
88  		double d = Math.sqrt(n);
89  		for (int i=3; i<=d; i+=2)if(n%i==0){return false;}
90  		return true;
91  	}
92  	static int upper_division(int a,int b) {
93  		if(a%b==0) {
94  			return a/b;
95  		}
96  		else {
97  			return a/b+1;
98  		}
99  	}
100  	static long lupper_division(long a,long b) {
101  		if(a%b==0) {
102  			return a/b;
103  		}
104  		else {
105  			return a/b+1;
106  		}
107  	}
108  	static int[] setArray(int a) {
109  		int b[]=new int[a];
110  		for(int i=0;i<a;i++) {
111  			b[i]=scan.nextInt();
112  		}
113  		return b;
114  	}
115  	static long[] lsetArray(int a) {
116  		long b[]=new long[a];
117  		for(int i=0;i<a;i++) {
118  			b[i]=scan.nextLong();
119  		}
120  		return b;
121  	}
122  	static String reverce(String str) {
123  		String strr="";
124  		for(int i=str.length()-1;i>=0;i--) {
125  			strr+=str.charAt(i);
126  		}
127  		return strr;
128  	}
129  	public static void printArray(int[] que) {
130  		for(int i=0;i<que.length-1;i++) {
131  			System.out.print(que[i]+" ");
132  		}
133  		System.out.println(que[que.length-1]);
134  	}
135  	public static int[][] doublesort(int[][]a) {
136  		Arrays.sort(a,(x,y)->Integer.compare(x[0],y[0]));
137  		return a;
138  	}
139  	public static long[][] ldoublesort(long[][]a) {
140  		Arrays.sort(a,(x,y)->Long.compare(x[0],y[0]));
141  		return a;
142  	}
143  	static long modpow(long x,long n,long mo) {
144  		long sum=1;
145  		while(n>0) {
146  			if((n&1)==1) {
147  				sum=sum*x%mo;
148  			}
149  			x=x*x%mo;
150  			n>>=1;
151  		}
152  		return sum;
153  	}
154  	public static char[] revch(char ch[]) {
155  		char ret[]=new char[ch.length];
156  		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
157  			ret[j]=ch[i];
158  		}
159  		return ret;
160  	}
161  	public static int[] revint(int ch[]) {
162  		int ret[]=new int[ch.length];
163  		for(int i=ch.length-1,j=0;i>=0;i--,j++) {
164  			ret[j]=ch[i];
165  		}
166  		return ret;
167  	}
168  	public static void warshall_floyd(int v[][],int n) {
169  		for(int k=0;k<n;k++)
170  			for(int i=0;i<n;i++)
171  				for(int j=0;j<n;j++)
172  					v[i][j]=min(v[i][j],v[i][k]+v[k][j]);
173  	}
174  	public static long modint(long a,long m) {
175  		long b=m,u=1,v=0;
176  		while(b!=0) {
177  			long t=a/b;
178  			a-=t*b;
179  			long x=a;
180  			a=b;
181  			b=x;
182  			u-=t*v;
183  			x=u;
184  			u=v;
185  			v=x;
186  		}
187  		u%=m;
188  		if(u<0)u+=m;
189  		return u;
190  	}
191  }
192  class FastScanner {
193  	private final InputStream in = System.in;
194  	private final byte[] buffer = new byte[1024];
195  	private int ptr = 0;
196  	private int buflen = 0;
197  	private boolean hasNextByte() {
198  		if (ptr < buflen) {
199  			return true;
200  		}else{
201  			ptr = 0;
202  			try {
203  				buflen = in.read(buffer);
204  			} catch (IOException e) {
205  				e.printStackTrace();
206  			}
207  			if (buflen <= 0) {
208  				return false;
209  			}
210  		}
211  		return true;
212  	}
213  	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
214  	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
215  	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
216  	public String next() {
217  		if (!hasNext()) throw new NoSuchElementException();
218  		StringBuilder sb = new StringBuilder();
219  		int b = readByte();
220  		while(isPrintableChar(b)) {
221  			sb.appendCodePoint(b);
222  			b = readByte();
223  		}
224  		return sb.toString();
225  	}
226  	public long nextLong() {
227  		if (!hasNext()) throw new NoSuchElementException();
228  		long n = 0;
229  		boolean minus = false;
230  		int b = readByte();
231  		if (b == '-') {
232  			minus = true;
233  			b = readByte();
234  		}
235  		if (b < '0' || '9' < b) {
236  			throw new NumberFormatException();
237  		}
238  		while(true){
239  			if ('0' <= b && b <= '9') {
240  				n *= 10;
241  				n += b - '0';
242  			}else if(b == -1 || !isPrintableChar(b)){
243  				return minus ? -n : n;
244  			}else{
245  				throw new NumberFormatException();
246  			}
247  			b = readByte();
248  		}
249  	}
250  	public int nextInt() {
251  		long nl = nextLong();
252  		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
253  		return (int) nl;
254  	}
255  	public double nextDouble() { return Double.parseDouble(next());}
256  	public char nextchar() {
257  		try { return (char)System.in.read(); } catch(Exception e) {
258  			throw new RuntimeException(e);
259  		}
260  	}
261  }
```


**Question**: Does line `235` have control dependence over line `241` in function `nextLong`? If so, provide a trace.

**Output**:


Ground truth answer: yes