[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.OutputStream;
2   import java.io.IOException;
3   import java.io.InputStream;
4   import java.io.PrintWriter;
5   import java.util.InputMismatchException;
6   import java.io.IOException;
7   import java.io.InputStream;
8   public class Main {
9       public static void main(String[] args) {
10          InputStream inputStream = System.in;
11          OutputStream outputStream = System.out;
12          FastScanner in = new FastScanner(inputStream);
13          PrintWriter out = new PrintWriter(outputStream);
14          FStringsOfEternity solver = new FStringsOfEternity();
15          solver.solve(1, in, out);
16          out.close();
17      }
18      static class FStringsOfEternity {
19          public void solve(int testNumber, FastScanner br, PrintWriter pw) {
20              String in1 = br.nextString();
21              String in2 = br.nextString();
22              char[] t = in1.toCharArray();
23              char[] s = in2.toCharArray();
24              if (t.length > s.length) {
25                  int orig = 0;
26                  boolean poss = true;
27                  for (int i = 0; i < t.length - s.length; i += s.length) {
28                      if (!in1.substring(i, i + s.length).equals(in2)) {
29                          poss = false;
30                      } else {
31                          orig++;
32                      }
33                  }
34                  if (poss) {
35                      pw.println(-1);
36                      pw.close();
37                  }
38                  int ans = 0;
39                  for (int i = 0; i < t.length - s.length; i += s.length) {
40                      if (in1.substring(i, i + s.length).equals(in2)) {
41                          ans++;
42                      } else {
43                          break;
44                      }
45                  }
46                  for (int i = t.length - s.length; i >= 0; i -= s.length) {
47                      if (in1.substring(i, i + s.length).equals(in2)) {
48                          ans++;
49                      } else {
50                          break;
51                      }
52                  }
53                  pw.println(Math.max(orig, ans));
54                  pw.close();
55              } else if (s.length == t.length) {
56                  if (s.equals(t)) {
57                      pw.println(-1);
58                  } else {
59                      pw.println(0);
60                  }
61              } else {
62                  int orig = 0;
63                  boolean poss = true;
64                  for (int i = 0; i < s.length - t.length; i += s.length) {
65                      if (!in2.substring(i, i + t.length).equals(in1)) {
66                          poss = false;
67                      }
68                  }
69                  if (poss) {
70                      pw.println(-1);
71                      pw.close();
72                  }
73                  int ans = 0;
74                  for (int i = 0; i < s.length - t.length; i += t.length) {
75                      if (in2.substring(i, i + t.length).equals(in1)) {
76                          ans++;
77                      } else {
78                          break;
79                      }
80                  }
81                  for (int i = s.length - t.length; i >= 0; i -= t.length) {
82                      if (in2.substring(i, i + t.length).equals(in1)) {
83                          ans++;
84                      } else {
85                          break;
86                      }
87                  }
88                  pw.println(Math.max(orig, ans));
89                  pw.close();
90              }
91          }
92      }
93      static class FastScanner {
94          private InputStream stream;
95          private byte[] buf = new byte[1024];
96          private int curChar;
97          private int numChars;
98          private FastScanner.SpaceCharFilter filter;
99          public FastScanner(InputStream stream) {
100              this.stream = stream;
101          }
102          public int read() {
103              if (numChars == -1) {
104                  throw new InputMismatchException();
105              }
106              if (curChar >= numChars) {
107                  curChar = 0;
108                  try {
109                      numChars = stream.read(buf);
110                  } catch (IOException e) {
111                      throw new InputMismatchException();
112                  }
113                  if (numChars <= 0) {
114                      return -1;
115                  }
116              }
117              return buf[curChar++];
118          }
119          public String nextString() {
120              int c = read();
121              while (isSpaceChar(c)) {
122                  c = read();
123              }
124              StringBuilder res = new StringBuilder();
125              do {
126                  if (Character.isValidCodePoint(c)) {
127                      res.appendCodePoint(c);
128                  }
129                  c = read();
130              } while (!isSpaceChar(c));
131              return res.toString();
132          }
133          public boolean isSpaceChar(int c) {
134              if (filter != null) {
135                  return filter.isSpaceChar(c);
136              }
137              return isWhitespace(c);
138          }
139          public static boolean isWhitespace(int c) {
140              return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
141          }
142          public interface SpaceCharFilter {
143              public boolean isSpaceChar(int ch);
144          }
145      }
146  }
```


**Question**: Does `(in1,20)` have data dependence over `(i,81)` in function `solve`? If so, provide a trace.

**Output**:


Ground truth answer: yes