------
## 最终结论
To solve the problem of identifying the exact shape of the zombie lair, which is a strictly convex polygon on a lattice, we need to follow these steps:

1. **Read Input**: We'll read multiple test cases where each test case consists of a grid size `N` and an `N x N` grid of contamination levels.

2. **Parse Contamination Levels**: For each cell in the grid, we'll determine which corners are inside or on the border of the lair based on its contamination level.

3. **Identify Polygon Vertices**: Using the parsed contamination levels, identify potential vertices of the polygon by checking specific conditions that indicate a vertex.

4. **Order Vertices Clockwise**: Once we have all potential vertices, order them in a clockwise manner starting from the lexicographically smallest vertex.

5. **Output Results**: For each test case, output the number of vertices and their coordinates in clockwise order.

Here's how you can implement this solution in Python:

```python
import sys
import math

def read_input():
    test_cases = []
    for line in sys.stdin:
        line = line.strip()
        if line == '0':
            break
        N = int(line)
        grid = [sys.stdin.readline().strip() for _ in range(N)]
        test_cases.append((N, grid))
    return test_cases

def parse_contamination_levels(test_cases):
    contamination_levels = []
    
    for N, grid in test_cases:
        levels = [[0] * (N + 1) for _ in range(N + 1)]
        
        for y in range(N):
            for x in range(N):
                contamination_level = int(grid[y][x])
                
                # Increment the count of corners inside or on the border of the lair
                if contamination_level > 0:
                    if contamination_level >= 1:
                        levels[x + 1][y + 1] += 1  # Top-left corner
                    if contamination_level >= 2:
                        levels[x + 2][y + 1] += 1  # Top-right corner
                    if contamination_level >= 3:
                        levels[x + 2][y + 2] += 1  # Bottom-right corner
                    if contamination_level >= 4:
                        levels[x + 1][y + 2] += 1  # Bottom-left corner
        
        contamination_levels.append(levels)
    
    return contamination_levels

def identify_polygon_vertices(contamination_levels):
    polygons = []

    for levels in contamination_levels:
        N = len(levels) - 1
        vertices = []
        
        for y in range(1, N):
            for x in range(1, N):
                # Check if this point is a vertex of the polygon
                if (levels[x][y] == 4 and 
                    levels[x + 1][y] > 0 and 
                    levels[x][y + 1] > 0 and 
                    levels[x + 1][y + 1] > 0):
                    vertices.append((x, y))
        
        polygons.append(vertices)
    
    return polygons

def order_vertices_clockwise(vertices):
    # Find the centroid of the polygon
    cx = sum(x for x, y in vertices) / len(vertices)
    cy = sum(y for x, y in vertices) / len(vertices)

    # Sort the vertices based on angle with respect to centroid
    def angle_from_centroid(vertex):
        return math.atan2(vertex[1] - cy, vertex[0] - cx)

    vertices.sort(key=angle_from_centroid)

    return vertices

def get_polygon_vertices(contamination_levels):
    all_polygons = identify_polygon_vertices(contamination_levels)
    
    ordered_polygons = []
    
    for vertices in all_polygons:
        if not vertices:
            ordered_polygons.append([])
            continue
        
        start_vertex = min(vertices)
        
        ordered_vertices = order_vertices_clockwise(vertices)
        
        while ordered_vertices[0] != start_vertex:
            ordered_vertices.append(ordered_vertices.pop(0))
        
        ordered_polygons.append(ordered_vertices)
    
    return ordered_polygons

def output_results(polygon_vertices):
    results = []
    for vertices in polygon_vertices:
        V = len(vertices)
        results.append(str(V))
        for x, y in vertices:
            results.append(f"{x} {y}")
    print("\n".join(results))

if __name__ == "__main__":
    test_cases = read_input()
    contamination_levels = parse_contamination_levels(test_cases)
    polygon_vertices = get_polygon_vertices(contamination_levels)
    output_results(polygon_vertices)
```

This code will correctly read input data from standard input (`sys.stdin`), process each test case to determine the shape of the zombie lair as a convex polygon, and then output the number of vertices along with their coordinates.