[INSTRUCTIONS]

You are a program-analysis assistant. Perform a **static** data-dependence analysis on a given code snippet, treating each branch or loop condition as potentially taking any outcome, without using semantic or symbolic execution to prune paths.


## 1. Data Dependence Definition

   Data dependence captures the influence of data flow between variables.

   We denote each variable instance as `(var,lineNumber)`, meaning the variable `var` defined or updated at `lineNumber`.

   >  **Direct Data Dependence**
   A variable instance `(varB,lineB)` is **directly** data-dependent on `(varA,lineA)` if `lineA` writes to `varA`. Then, without overwritting the value of `varA`, `lineB` reads `varA` and compute the value of `varB`. In other words, the value of `(varB,lineB)` relies on the value produced at `(varA,lineA)`. In addition, changing the execution order of `(varA,lineA)` and `(varB,lineB)` would alter their results.


   A variable instance `(varB,lineB)` is data-dependent on `(varA,lineA)` if there is a **transitive** (indirect) chain of **direct** data dependencies from `(varA,lineA)` to `(varB,lineB)`. This is equivalent to saying that `(varA,lineA)` has data dependence over `(varB,lineB)`, meaning the value written at `(varA,lineA)` can propagate to `(varB,lineB)` through a sequence of read/write operations.


## 2. Output Format
   When asked "Does `(varA,lineA)` have data dependence over `(varB,lineB)`? If so, provide one feasible trace.": 
   - If data dependence exists, respond:
   ```json
   {
   "DataDependence": true,
   "Trace": [
      { "from": ["varA", lineA], "to": ["varX", lineX] },
      ...
      { "from": ["varY", lineY], "to": ["varB", lineB] }
      ]
   }
   ```

   -  If no data dependence exists, respond:
   ```json
   {
   "DataDependence": false
   }
   ```
   
   A **trace** represents a **transitive data flow**, where each item represents a **direct** data dependence edge. The full trace should begin with `(varA,lineA)` and end with `(varB,lineB)`.

   You only need to provide **one** valid chain of data dependence if you conclude a data dependence exists, even if multiple possible chains exist. 


## 3. Intraprocedural Data 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    total = 0
2    value = 1
3    step = value
4    if step > 1:
5        value += 3
6    while total <= 10:
7        total += value
8        difference = total - step
9        step += 1
10   final_result = total * 2
```


#### Example Question 1.1:
Does `(value,2)` have data dependence over `(step,9)`? If so, provide a trace.

**Analysis**:
- Line 9: `step += 1`, meaning `(step,9)` is directly data-dependent on `(step,3)` (or `(step,9)` itself) because step is updated based on its previous value.
- Line 3: `step = value`, meaning `(step,3)` is directly data-dependent on `(value,2)`.
Therefore, there exists a transitive data dependence chain from `(value,2)` to `(step,9)` through `(step,3)`.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["value", 2], "to": ["step", 3] },
    { "from": ["step", 3], "to": ["step", 9] }
  ]
}
```

#### Example Question 1.2 
Does `(value,2)` have data dependence over `(total,7)`? If so, provide a trace.

**Analysis**:
- Line 7: `total += value`, meaning `(total,7)` reads `value` from either `(value,2)` or `(value,5)`.
- Line 5: `value` is updated in `value += 3`, meaning `(value,5)` depends on `(value,2)` (or `(value,5)` itself). However, this update is inside an if statement, which means it may or may not execute depending on runtime conditions.
- Line 2: value is initialized at `(value,2)`.


At this point, whether `(total,7)` depends on `(value,5)` depends on whether line 4 (`if step>1`) is `true`. Since this is a static analysis, all possible paths are considered without analyzing actual reachability. This means line 5 is treated as both possibly executed and possibly not executed.

- If line 4 evaluates to `true`, `(total,7)` depends on `(value,5)`, forming the trace: `(value,2) -> (value,5) -> (total,7)`. 
- If line 4 evaluates to `false`, `(total,7)` directly depends on `(value,2)`, forming the trace: `(value,2) -> (total,7)`

Therefore, the answer is yes.
Only one valid trace is required for the output. 

**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["value", 2], "to": ["value", 5] },
    { "from": ["value", 5], "to": ["total", 7] }
  ]
}

```



#### Example Question 1.3
Does `(step,3)` have data dependence over `(final_result,10)`? If so, provide a trace.  

**Analysis**:
Since there is no direct or transitive data dependence between `(step,3)` and `(final_result,10)`, the answer is No.

**Output**:
```json
{
  "DataDependence": false
}
```

**Analysis**:


### Example 2

```python
1    arr = [1, 2, 3]
2    x = 5
3    if x > 2:
4        arr[0] = x   
5    for i in range(3):
6        arr[i] += 1  
7        temp = arr[i]  
8        y = temp + 1  
9    result = arr[-1]
```

#### Example Question 2.1:
Does `(x,2)` have data dependence over `(arr,6)`? If so, provide a trace.

**Analysis**
- Line 6: `arr[i] += 1` modifies `arr[i]`, but i varies during the loop execution.
   - If `i == 0`, `arr[i]` refers to `arr[0]`, which was updated in line 4 (or line 6 itself), establishing a dependence chain `(arr,4)` -> `(arr,6)`.
   - If `i != 0`, `arr[i]` does not refer to `arr[0]`, meaning it depend on `(arr,1)` (or `(arr,6)` itself), not `(arr,4)`.
   - However, since static analysis considers all possible paths without resolving i’s runtime value, we must assume `arr[i]` could be `arr[0]`, leading to a possible dependence.
- Line 4: `arr[0] = x`, meaning `(arr,4)` depends on `(x,2)`.
- Line 2: `x` is initialized at `(x,2)`.
- Since there is a transitive chain of direct data dependence: `(x,2)->(arr,4)->(arr,6)`, the answer is yes.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["x", 2], "to": ["arr", 4] },
    { "from": ["arr", 4], "to": ["arr", 6] }
  ]
}
```


#### Example Question 2.2:
Does `(i,5)` have data dependence over `(temp,7)`? If so, provide a trace.

**Analysis**:
- Line 7: `temp = arr[i]`, meaning temp depends on `i`, since `i` determines which element of arr is accessed.
- Line 5: `i` is initialized and iterates over the range 0 to 3.
- Since there is a transitive chain of direct data dependence: `(i,5)->(temp,7)`, the answer is yes.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["i", 5], "to": ["temp", 7] }
  ]
}
```

#### Example Question 2.3:
Does `(i,5)` have data dependence over `(result,9)`? If so, provide a trace.

**Analysis**:
- Line 9: `result = arr[-1]`, meaning result depends on `arr[-1]`, which is arr[2], possibly get updated at line 6 (or line 1).
- Line 6: `arr[i] += 1`, meaning `arr[i]` is modified based on the value of `i`.
- Line 5: `i` iterates over 0 to 3.
- Since there is a transitive chain of direct data dependence: `(i,5)->(arr,6)->(result,9)`, the answer is yes.


**Output**:
```json
{
  "DataDependence": true,
  "Trace": [
    { "from": ["i", 5], "to": ["arr", 6] },
    { "from": ["arr", 6], "to": ["result", 9] }
  ]
}
```

---

[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 `(minus,232)` have data dependence over `(n,241)` in function `nextLong`? If so, provide a trace.

**Output**:


Ground truth answer: no