[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.io.PrintWriter;
4   import java.util.Arrays;
5   import java.util.Collections;
6   import java.util.InputMismatchException;
7   import java.util.NoSuchElementException;
8   import java.util.PriorityQueue;
9   public class Main {
10  	static PrintWriter out;
11  	static InputReader ir;
12  	static void solve() {
13  		int Q = ir.nextInt();
14  		PriorityQueue<Long> f = new PriorityQueue<>(Collections.reverseOrder());
15  		PriorityQueue<Long> l = new PriorityQueue<>();
16  		long fsum = 0, lsum = 0;
17  		long B = 0;
18  		while (Q-- > 0) {
19  			int com = ir.nextInt();
20  			if (com == 1) {
21  				long a = ir.nextLong();
22  				if (f.size() == l.size()) {
23  					if (l.size() == 0) {
24  						f.add(a);
25  						fsum += a;
26  					} else {
27  						long x = l.peek();
28  						if (x < a) {
29  							lsum += a - x;
30  							fsum += x;
31  							l.poll();
32  							l.add(a);
33  							f.add(x);
34  						} else {
35  							fsum += a;
36  							f.add(a);
37  						}
38  					}
39  				} else {
40  					long x = f.peek();
41  					if (x <= a) {
42  						lsum += a;
43  						l.add(a);
44  					} else {
45  						lsum += x;
46  						fsum += a - x;
47  						f.poll();
48  						f.add(a);
49  						l.add(x);
50  					}
51  				}
52  				B += ir.nextLong();
53  			} else {
54  				long x = f.peek();
55  				if (f.size() == l.size()) {
56  					out.println(x + " " + (lsum - fsum + B));
57  				} else {
58  					out.println(x + " " + (lsum - fsum + x + B));
59  				}
60  			}
61  		}
62  	}
63  	public static void main(String[] args) {
64  		ir = new InputReader(System.in);
65  		out = new PrintWriter(System.out);
66  		solve();
67  		out.flush();
68  	}
69  	static class InputReader {
70  		private InputStream in;
71  		private byte[] buffer = new byte[1024];
72  		private int curbuf;
73  		private int lenbuf;
74  		public InputReader(InputStream in) {
75  			this.in = in;
76  			this.curbuf = this.lenbuf = 0;
77  		}
78  		public boolean hasNextByte() {
79  			if (curbuf >= lenbuf) {
80  				curbuf = 0;
81  				try {
82  					lenbuf = in.read(buffer);
83  				} catch (IOException e) {
84  					throw new InputMismatchException();
85  				}
86  				if (lenbuf <= 0)
87  					return false;
88  			}
89  			return true;
90  		}
91  		private int readByte() {
92  			if (hasNextByte())
93  				return buffer[curbuf++];
94  			else
95  				return -1;
96  		}
97  		private boolean isSpaceChar(int c) {
98  			return !(c >= 33 && c <= 126);
99  		}
100  		private void skip() {
101  			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
102  				curbuf++;
103  		}
104  		public boolean hasNext() {
105  			skip();
106  			return hasNextByte();
107  		}
108  		public String next() {
109  			if (!hasNext())
110  				throw new NoSuchElementException();
111  			StringBuilder sb = new StringBuilder();
112  			int b = readByte();
113  			while (!isSpaceChar(b)) {
114  				sb.appendCodePoint(b);
115  				b = readByte();
116  			}
117  			return sb.toString();
118  		}
119  		public int nextInt() {
120  			if (!hasNext())
121  				throw new NoSuchElementException();
122  			int c = readByte();
123  			while (isSpaceChar(c))
124  				c = readByte();
125  			boolean minus = false;
126  			if (c == '-') {
127  				minus = true;
128  				c = readByte();
129  			}
130  			int res = 0;
131  			do {
132  				if (c < '0' || c > '9')
133  					throw new InputMismatchException();
134  				res = res * 10 + c - '0';
135  				c = readByte();
136  			} while (!isSpaceChar(c));
137  			return (minus) ? -res : res;
138  		}
139  		public long nextLong() {
140  			if (!hasNext())
141  				throw new NoSuchElementException();
142  			int c = readByte();
143  			while (isSpaceChar(c))
144  				c = readByte();
145  			boolean minus = false;
146  			if (c == '-') {
147  				minus = true;
148  				c = readByte();
149  			}
150  			long res = 0;
151  			do {
152  				if (c < '0' || c > '9')
153  					throw new InputMismatchException();
154  				res = res * 10 + c - '0';
155  				c = readByte();
156  			} while (!isSpaceChar(c));
157  			return (minus) ? -res : res;
158  		}
159  		public double nextDouble() {
160  			return Double.parseDouble(next());
161  		}
162  		public int[] nextIntArray(int n) {
163  			int[] a = new int[n];
164  			for (int i = 0; i < n; i++)
165  				a[i] = nextInt();
166  			return a;
167  		}
168  		public long[] nextLongArray(int n) {
169  			long[] a = new long[n];
170  			for (int i = 0; i < n; i++)
171  				a[i] = nextLong();
172  			return a;
173  		}
174  		public char[][] nextCharMap(int n, int m) {
175  			char[][] map = new char[n][m];
176  			for (int i = 0; i < n; i++)
177  				map[i] = next().toCharArray();
178  			return map;
179  		}
180  	}
181  	static void tr(Object... o) {
182  		out.println(Arrays.deepToString(o));
183  		out.flush();
184  	}
185  }
```


**Question**: Does line `20` have control dependence over line `21` in function `solve`? If so, provide a trace.

**Output**:


Ground truth answer: yes