[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**. 

```C
1   #include <stdio.h>
2   #include <math.h>
3   #include <string.h>
4   #include <stdlib.h>
5   typedef struct
6   {
7   	int x;
8   	int y;
9   } par;
10  double get_double();
11  int get_int();
12  int max(int, int);
13  int min(int, int);
14  int main()
15  {
16  	int i, j, k;
17  	int t = get_int();
18  	for (i = 0; i < t; i++)
19  	{
20  		int n = get_int();
21  		int w[n];
22  		int c[n][n];
23  		memset(c, 0, sizeof(c));
24  		for (j = 0; j < n; j++)
25  		{
26  			w[j] = get_int();
27  		}
28  		c[0][0] = w[0];
29  		for (j = 1; j < n; j++)
30  		{
31  			c[0][j] = min(w[j], c[0][j - 1]);
32  		}
33  		for (j = 1; j < n; j++)
34  		{
35  			if (c[j - 1][j - 1] == -1)
36  			{
37  				c[j][j] = -1;
38  			}
39  			else
40  			{
41  				if (c[j - 1][j - 1] > w[j]*6)
42  				{
43  					c[j][j] = -1;
44  				}
45  				else
46  				{
47  					c[j][j] = c[j - 1][j - 1] + w[j];
48  				}
49  			}
50  		}
51  		for (j = 1; j < n; j++)
52  		{
53  			for (k = j + 1; k < n; k++)
54  			{
55  				if (c[j - 1][k - 1] == -1 && c[j][k - 1] == -1)
56  				{
57  					c[j][k] = -1;
58  				}
59  				else if (c[j - 1][k - 1] == -1)
60  				{
61  					if (c[j][k - 1] > w[k]*6)
62  					{
63  						c[j][k] == -1;
64  					}
65  					else
66  					{
67  						c[j][k] = c[j][k - 1] + w[k];
68  					}
69  				}
70  				else if(c[j][k - 1] == -1)
71  				{
72  					if (c[j - 1][k - 1] > w[k]*6)
73  					{
74  						c[j][k] == -1;
75  					}
76  					else
77  					{
78  						c[j][k] = c[j - 1][k - 1] + w[k];
79  					}
80  				}
81  				else
82  				{
83  					int tmp = min(c[j - 1][k - 1], c[j][k - 1]);
84  					if (tmp > w[k]*6)
85  					{
86  						c[j][k] = -1;
87  					}
88  					else
89  					{
90  						c[j][k] = tmp + w[k];
91  					}
92  				}
93  			}
94  		}
95  		for (j = 0; j < n; j++)
96  		{
97  			if (c[j][n - 1] == -1)
98  			{
99  				break;
100  			}
101  		}
102  		printf("Case #%d: %d\n", i + 1, j);
103  	}
104  }
105  int max(int a, int b)
106  {
107  	if (a > b)
108  	{
109  		return a;
110  	}
111  	return b;
112  }
113  int min(int a, int b)
114  {
115  	if (a < b)
116  	{
117  		return a;
118  	}
119  	return b;
120  }
121  double get_double()
122  {
123  	double ret = 0;
124  	char c     = getchar();
125  	int sgn;
126  	while (1)
127  	{
128  		if (c == EOF)
129  		{
130  			return EOF;
131  		}
132  		if (c >= '0' && c <= '9')
133  		{
134  			sgn = 1;
135  			break;
136  		}
137  		if (c == '-')
138  		{
139  			c = getchar();
140  			if (c < '0' || c > '9')
141  			{
142  				continue;
143  			}
144  			sgn = -1;
145  			break;
146  		}
147  		c = getchar();
148  	}
149  	while (1)
150  	{
151  		ret = ret*10 + c - '0';
152  		c = getchar();
153  		if (c == '.')
154  		{
155  			double pos = 0.1;
156  			c = getchar();
157  			while (c >= '0' && c <= '9')
158  			{
159  				ret += pos*(c - '0');
160  				pos /= 10;
161  				c = getchar();
162  			}
163  			return sgn*ret;
164  		}
165  		else if (c < '0' || c > '9')
166  		{
167  			return sgn*ret;
168  		}
169  	}
170  }
171  int get_int()
172  {
173  	int ret = 0;
174  	char c  = getchar();
175  	int sgn;
176  	while (1)
177  	{
178  		if (c == EOF)
179  		{
180  			return EOF;
181  		}
182  		if (c >= '0' && c <= '9')
183  		{
184  			sgn = 1;
185  			break;
186  		}
187  		if (c == '-')
188  		{
189  			c = getchar();
190  			if (c < '0' || c > '9')
191  			{
192  				continue;
193  			}
194  			sgn = -1;
195  			break;
196  		}
197  		c = getchar();
198  	}
199  	while (1)
200  	{
201  		ret = (ret << 3) + (ret << 1) + c - '0';
202  		c = getchar();
203  		if (c < '0' || c > '9')
204  		{
205  			return sgn*ret;
206  		}
207  	}
208  }
```


**Question**: Does line `126` have control dependence over line `151` in function `get_double`? If so, provide a trace.

**Output**:


Ground truth answer: no