[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   public class Main {
4   	private static Scanner sc;
5   	private static Printer pr;
6   	private static void solve() {
7   		int h = sc.nextInt();
8   		int w = sc.nextInt();
9   		int[][] a = new int[h][w];
10  		for (int i = 0; i < h; i++) {
11  			for (int j = 0; j < w; j++) {
12  				a[i][j] = sc.nextInt();
13  			}
14  		}
15  		List<Integer> x = new ArrayList<>();
16  		List<Integer> y = new ArrayList<>();
17  		boolean flag = false;
18  		int prex = 0;
19  		int prey = 0;
20  		boolean odd;
21  		for (int i = 0; i < h; i++) {
22  			if (i % 2 == 1) {
23  				for (int j = w - 1; j >= 0; j--) {
24  					if (a[i][j] % 2 == 1) {
25  						odd = true;
26  					} else {
27  						odd = false;
28  					}
29  					if (odd && flag) {
30  						flag = !flag;
31  						x.add(prex);
32  						y.add(prey);
33  						x.add(j);
34  						y.add(i);
35  						prex = j;
36  						prey = i;
37  					} else if (odd && !flag) {
38  						flag = !flag;
39  						prex = j;
40  						prey = i;
41  					} else if (!odd && flag) {
42  						x.add(prex);
43  						y.add(prey);
44  						x.add(j);
45  						y.add(i);
46  						prex = j;
47  						prey = i;
48  					} else if (!odd && !flag) {
49  					}
50  				}
51  			} else {
52  				for (int j = 0; j < w; j++) {
53  					if (a[i][j] % 2 == 1) {
54  						odd = true;
55  					} else {
56  						odd = false;
57  					}
58  					if (odd && flag) {
59  						flag = !flag;
60  						x.add(prex);
61  						y.add(prey);
62  						x.add(j);
63  						y.add(i);
64  						prex = j;
65  						prey = i;
66  					} else if (odd && !flag) {
67  						flag = !flag;
68  						prex = j;
69  						prey = i;
70  					} else if (!odd && flag) {
71  						x.add(prex);
72  						y.add(prey);
73  						x.add(j);
74  						y.add(i);
75  						prex = j;
76  						prey = i;
77  					} else if (!odd && !flag) {
78  					}
79  				}
80  			}
81  		}
82  		pr.println(x.size() / 2);
83  		for (int i = 0, size = x.size(); i < size / 2 * 2; i++) {
84  			if (i % 2 == 0) {
85  				StringBuilder sb = new StringBuilder();
86  				sb.append(y.get(i) + 1);
87  				sb.append(' ');
88  				sb.append(x.get(i) + 1);
89  				sb.append(' ');
90  				pr.print(sb.toString());
91  			} else {
92  				StringBuilder sb = new StringBuilder();
93  				sb.append(y.get(i) + 1);
94  				sb.append(' ');
95  				sb.append(x.get(i) + 1);
96  				pr.println(sb.toString());
97  			}
98  		}
99  	}
100  	public static void main(String[] args) {
101  		sc = new Scanner(System.in);
102  		pr = new Printer(System.out);
103  		solve();
104  		pr.close();
105  		sc.close();
106  	}
107  	static class Scanner {
108  		BufferedReader br;
109  		Scanner (InputStream in) {
110  			br = new BufferedReader(new InputStreamReader(in));
111  		}
112  		private boolean isPrintable(int ch) {
113  			return ch >= '!' && ch <= '~';
114  		}
115  		private boolean isCRLF(int ch) {
116  			return ch == '\n' || ch == '\r' || ch == -1;
117  		}
118  		private int nextPrintable() {
119  			try {
120  				int ch;
121  				while (!isPrintable(ch = br.read())) {
122  					if (ch == -1) {
123  						throw new NoSuchElementException();
124  					}
125  				}
126  				return ch;
127  			} catch (IOException e) {
128  				throw new NoSuchElementException();
129  			}
130  		}
131  		String next() {
132  			try {
133  				int ch = nextPrintable();
134  				StringBuilder sb = new StringBuilder();
135  				do {
136  					sb.appendCodePoint(ch);
137  				} while (isPrintable(ch = br.read()));
138  				return sb.toString();
139  			} catch (IOException e) {
140  				throw new NoSuchElementException();
141  			}
142  		}
143  		int nextInt() {
144  			try {
145  				boolean negative = false;
146  				int res = 0;
147  				int limit = -Integer.MAX_VALUE;
148  				int radix = 10;
149  				int fc = nextPrintable();
150  				if (fc < '0') {
151  					if (fc == '-') {
152  						negative = true;
153  						limit = Integer.MIN_VALUE;
154  					} else if (fc != '+') {
155  						throw new NumberFormatException();
156  					}
157  					fc = br.read();
158  				}
159  				int multmin = limit / radix;
160  				int ch = fc;
161  				do {
162  					int digit = ch - '0';
163  					if (digit < 0 || digit >= radix) {
164  						throw new NumberFormatException();
165  					}
166  					if (res < multmin) {
167  						throw new NumberFormatException();
168  					}
169  					res *= radix;
170  					if (res < limit + digit) {
171  						throw new NumberFormatException();
172  					}
173  					res -= digit;
174  				} while (isPrintable(ch = br.read()));
175  				return negative ? res : -res;
176  			} catch (IOException e) {
177  				throw new NoSuchElementException();
178  			}
179  		}
180  		long nextLong() {
181  			try {
182  				boolean negative = false;
183  				long res = 0;
184  				long limit = -Long.MAX_VALUE;
185  				int radix = 10;
186  				int fc = nextPrintable();
187  				if (fc < '0') {
188  					if (fc == '-') {
189  						negative = true;
190  						limit = Long.MIN_VALUE;
191  					} else if (fc != '+') {
192  						throw new NumberFormatException();
193  					}
194  					fc = br.read();
195  				}
196  				long multmin = limit / radix;
197  				int ch = fc;
198  				do {
199  					int digit = ch - '0';
200  					if (digit < 0 || digit >= radix) {
201  						throw new NumberFormatException();
202  					}
203  					if (res < multmin) {
204  						throw new NumberFormatException();
205  					}
206  					res *= radix;
207  					if (res < limit + digit) {
208  						throw new NumberFormatException();
209  					}
210  					res -= digit;
211  				} while (isPrintable(ch = br.read()));
212  				return negative ? res : -res;
213  			} catch (IOException e) {
214  				throw new NoSuchElementException();
215  			}
216  		}
217  		float nextFloat() {
218  			return Float.parseFloat(next());
219  		}
220  		double nextDouble() {
221  			return Double.parseDouble(next());
222  		}
223  		String nextLine() {
224  			try {
225  				int ch;
226  				while (isCRLF(ch = br.read())) {
227  					if (ch == -1) {
228  						throw new NoSuchElementException();
229  					}
230  				}
231  				StringBuilder sb = new StringBuilder();
232  				do {
233  					sb.appendCodePoint(ch);
234  				} while (!isCRLF(ch = br.read()));
235  				return sb.toString();
236  			} catch (IOException e) {
237  				throw new NoSuchElementException();
238  			}
239  		}
240  		void close() {
241  			try {
242  				br.close();
243  			} catch (IOException e) {
244  			}
245  		}
246  	}
247  	static class Printer extends PrintWriter {
248  		Printer(OutputStream out) {
249  			super(out);
250  		}
251  	}
252  }
```


**Question**: Does line `52` have control dependence over line `62` in function `solve`? If so, provide a trace.

**Output**:


Ground truth answer: yes