import math
 
def calculate_stability(p1, p2, p3):
    """Calculates the stability of a triumvirate."""
    distances = [
        math.dist(p1, p2),
        math.dist(p1, p3),
        math.dist(p2, p3)
    ]
    return max(distances) - min(distances)
 
def find_optimal_triumvirates(points):
    """Finds the optimal arrangement of triumvirates."""
    n = len(points)
    # Calculate all pairwise distances.
    distances = [[0 for _ in range(n)] for _ in range(n)]
    for i in range(n):
        for j in range(i + 1, n):
            distances[i][j] = distances[j][i] = math.dist(points[i], points[j])
 
    # Sort points by increasing x-coordinate for initial grouping.
    points.sort(key=lambda x: x[0])
 
    # Initialize groups.
    groups = [[i] for i in range(n)]
 
    # Greedy algorithm to form groups.
    for i in range(n // 3):
        # Find the closest point to the first point in the current group.
        min_dist = float('inf')
        closest_index = None
        for j in range(n):
            if j in groups[i] or distances[groups[i][0]][j] == 0:
                continue
            if distances[groups[i][0]][j] < min_dist:
                min_dist = distances[groups[i][0]][j]
                closest_index = j
        # Add the closest point to the group.
        groups[i].append(closest_index)
        # Find the closest point to the second point in the current group.
        min_dist = float('inf')
        closest_index = None
        for j in range(n):
            if j in groups[i] or distances[groups[i][1]][j] == 0:
                continue
            if distances[groups[i][1]][j] < min_dist:
                min_dist = distances[groups[i][1]][j]
                closest_

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