├── .gitignore ├── example_data └── mesh │ └── bunny │ ├── data │ ├── README │ └── bun.conf │ └── reconstruction │ ├── README │ └── bun_zipper_res4.ply ├── README.md ├── fps_v0.py ├── load_pcd.py ├── fps_v1.py ├── main_group.py └── main_sample.py /.gitignore: -------------------------------------------------------------------------------- 1 | 2 | __pycache__/ 3 | -------------------------------------------------------------------------------- /example_data/mesh/bunny/data/README: -------------------------------------------------------------------------------- 1 | Range Data 2 | 3 | Stanford Range Repository 4 | Computer Graphics Laboratory 5 | Stanford University 6 | 7 | August 4, 1996 8 | 9 | 10 | These data files were obtained with a Cyberware 3030MS optical 11 | triangulation scanner. They are stored as range images in the "ply" 12 | format. The ".conf" file contains the transformations required to 13 | bring each range image into a single coordinate system. 14 | 15 | For more information, consult the web pages of the Stanford Graphics 16 | Laboratory: 17 | 18 | http://www-graphics.stanford.edu 19 | 20 | -------------------------------------------------------------------------------- /example_data/mesh/bunny/reconstruction/README: -------------------------------------------------------------------------------- 1 | Surface Reconstructions 2 | 3 | Stanford Range Repository 4 | Computer Graphics Laboratory 5 | Stanford University 6 | 7 | August 4, 1996 8 | 9 | 10 | These files are the result of reconstructing a set of range images 11 | using the "zipper" program. The first file is the high resolution 12 | result, while the "_res*" files are decimated versions. Note that 13 | these decimations were performed using a crude algorithm that does not 14 | necessarily preserve mesh topology. While they are not beautiful, 15 | they are suitable for interactive rendering. 16 | 17 | For more information, consult the web pages of the Stanford Graphics 18 | Laboratory: 19 | 20 | http://www-graphics.stanford.edu 21 | 22 | -------------------------------------------------------------------------------- /example_data/mesh/bunny/data/bun.conf: -------------------------------------------------------------------------------- 1 | camera -0.0172 -0.0936 -0.734 -0.0461723 0.970603 -0.235889 0.0124573 2 | bmesh bun000.ply 0 0 0 0 0 0 1 3 | bmesh bun045.ply -0.0520211 -0.000383981 -0.0109223 0.00548449 -0.294635 -0.0038555 0.955586 4 | bmesh bun090.ply 2.20761e-05 -3.34606e-05 -7.20881e-05 0.000335889 -0.708202 0.000602459 0.706009 5 | bmesh bun180.ply 0.000116991 2.47732e-05 -4.6283e-05 -0.00215148 0.999996 -0.0015001 0.000892527 6 | bmesh bun270.ply 0.000130273 1.58623e-05 0.000406764 0.000462632 0.707006 -0.00333301 0.7072 7 | bmesh top2.ply -0.0530127 0.138516 0.0990356 0.908911 -0.0569874 0.154429 0.383126 8 | bmesh top3.ply -0.0277373 0.0583887 -0.0796939 0.0598923 0.670467 0.68082 -0.28874 9 | bmesh bun315.ply -0.00646017 -1.36122e-05 -0.0129064 0.00449209 0.38422 -0.00976512 0.923179 10 | bmesh chin.ply 0.00435102 0.0882863 -0.108853 -0.441019 0.213083 0.00705734 0.871807 11 | bmesh ear_back.ply -0.0829384 0.0353082 0.0711536 0.111743 0.925689 -0.215443 -0.290169 12 | 13 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Farthest Point Sampling (FPS) 2 | This repo is a vanilla implementation of 3D farthest-point-sampling (FPS) algorithm in paper: 3 | >"Eldar, Yuval, Michael Lindenbaum, Moshe Porat, and Yehoshua Y. Zeevi. "The farthest point strategy for progressive image sampling." IEEE Transactions on Image Processing 6, no. 9 (1997): 1305-1315." 4 | 5 | The most important equation is _eq. 2.6_. 6 | 7 | Two demos are avaible in this repo: 8 | 1. `main_sample.py`: demonstrates how the points are sampled in FPS and provides a function to visulise sampling process step by step. 9 | 2. `main_group.py`: A simple point grouping method which groups points using a fix radius sphere over the FPS sampled points. 10 | 11 | 12 | ## Install Dependencies: 13 | ``` 14 | conda install numpy 15 | conda install -c open3d-admin open3d=0.7 16 | ``` 17 | 18 | ## Usage 19 | To simply run the fps **sampling** demo: 20 | ``` 21 | python main_sample.py 22 | ``` 23 | 24 | To simply run the fps **grouping** demo: 25 | ``` 26 | python main_group.py 27 | ``` 28 | 29 | 30 | Other parameters can be set: 31 | 32 | - `--n_samples`: num of samples. 33 | - `--data`: choose an example data to load, available options are "bunny", "circle", "eclipse", or you can set it to a path points to your `ply` file. 34 | - `--manually_step`: **(only in `main_sample`)** step the sampling process manully by pressing "N/n" key. 35 | - `--group_radius`: **(only in `main_group`)** set the grouping radius. 36 | 37 | Example: 38 | ``` 39 | python main_sample.py --data="circle" --n_samples=50 --manually_step=True 40 | python main_group.py --data="circle" --n_samples=50 --group_radius=0.06 41 | ``` 42 | -------------------------------------------------------------------------------- /fps_v0.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | class FPS: 4 | def __init__(self, pcd_xyz, n_samples): 5 | self.n_samples = n_samples 6 | self.pcd_xyz = pcd_xyz 7 | self.n_pts = pcd_xyz.shape[0] 8 | self.dim = pcd_xyz.shape[1] 9 | self.selected_pts = np.zeros(shape=(n_samples, self.dim)) 10 | self.remaining_pts = np.copy(pcd_xyz) 11 | 12 | self.grouping_radius = None 13 | self.labels = None # (n_pts, 1), States which point belong to which cluster. 14 | 15 | # Random pick a start 16 | self.start_idx = np.random.randint(low=0, high=self.n_pts - 1) 17 | self.selected_pts[0] = self.remaining_pts[self.start_idx] 18 | self.n_selected_pts = 1 19 | 20 | def get_selected_pts(self): 21 | return self.selected_pts 22 | 23 | def step(self): 24 | if self.n_selected_pts < self.n_samples: 25 | dist_list = np.zeros((self.remaining_pts.shape[0], 1)) 26 | for pt_idx in range(self.remaining_pts.shape[0]): 27 | dist = self.__distance__(self.remaining_pts[pt_idx], self.selected_pts[:self.n_selected_pts]) 28 | dist_list[pt_idx] = np.min(dist) 29 | 30 | selected_idx = np.argmax(dist_list) 31 | self.selected_pts[self.n_selected_pts] = self.remaining_pts[selected_idx] 32 | self.n_selected_pts += 1 33 | else: 34 | print("Got enough number samples") 35 | 36 | 37 | def fit(self): 38 | for _ in range(1, self.n_samples): 39 | self.step() 40 | return self.get_selected_pts() 41 | 42 | 43 | def group(self, radius): 44 | self.grouping_radius = radius 45 | self.labels = np.zeros((self.n_pts,), dtype=int) 46 | 47 | for i, selected_pt in enumerate(self.selected_pts): 48 | dist = self.__distance__(selected_pt, self.pcd_xyz) 49 | self.labels[dist < self.grouping_radius] = i 50 | 51 | return self.labels 52 | 53 | 54 | @staticmethod 55 | def __distance__(a, b): 56 | return np.linalg.norm(a - b, ord=2, axis=1) 57 | -------------------------------------------------------------------------------- /load_pcd.py: -------------------------------------------------------------------------------- 1 | import open3d as o3d 2 | import numpy as np 3 | import math 4 | 5 | 6 | def __points_on_circle__(radius, num_pts): 7 | pi = math.pi 8 | 9 | # a circle in 2D 10 | result_xy = np.asarray([(math.cos(2 * pi / num_pts * x) * radius, 11 | math.sin(2 * pi / num_pts * x) * radius) for x in range(0, num_pts)]) 12 | 13 | # put it in 3D by adding z = 0 14 | result_xyz = np.append(result_xy, np.zeros((num_pts, 1)), axis=1) 15 | return result_xyz 16 | 17 | 18 | def __points_on_eclipse__(radius, num_pts): 19 | pi = math.pi 20 | eclipse_factor = 2 21 | 22 | # a circle in 2D 23 | result_xy = np.asarray([(math.cos(2 * pi / num_pts * x) * radius, 24 | eclipse_factor * math.sin(2 * pi / num_pts * x) * radius) for x in range(0, num_pts)]) 25 | 26 | # put it in 3D by adding z = 0 27 | result_xyz = np.append(result_xy, np.zeros((num_pts, 1)), axis=1) 28 | return result_xyz 29 | 30 | 31 | 32 | def load_pcd(data="bunny"): 33 | """ 34 | :param data: 35 | Choice: bunny, circle, eclipse, "a_ply_file_path" 36 | :return: 37 | A (N, 3) numpy array contains loaded 3D points 38 | """ 39 | 40 | pcd_xyz = None 41 | if data == "bunny": 42 | pcd = o3d.io.read_point_cloud("./example_data/mesh/bunny/reconstruction/bun_zipper_res2.ply") 43 | pcd_xyz = np.asarray(pcd.points) 44 | elif data == "circle": 45 | pcd_xyz = __points_on_circle__(radius=1, num_pts=1000) 46 | elif data == "eclipse": 47 | pcd_xyz = __points_on_eclipse__(radius=1, num_pts=1000) 48 | else: 49 | # Try to load from specified folder 50 | pcd = o3d.io.read_point_cloud(data) 51 | pcd_xyz = np.asarray(pcd.points) 52 | 53 | return pcd_xyz 54 | 55 | 56 | if __name__ == '__main__': 57 | bunny_xyz = load_pcd("bunny") 58 | print("Bunny data shape: ", bunny_xyz.shape) 59 | 60 | circle_xyz = load_pcd("circle") 61 | print("Cirlce data shape: ", circle_xyz.shape) 62 | 63 | eclipse_xyz = load_pcd("eclipse") 64 | print("Eclipse data shape: ", eclipse_xyz.shape) -------------------------------------------------------------------------------- /fps_v1.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | class FPS: 4 | def __init__(self, pcd_xyz, n_samples): 5 | self.n_samples = n_samples 6 | self.pcd_xyz = pcd_xyz 7 | self.n_pts = pcd_xyz.shape[0] 8 | self.dim = pcd_xyz.shape[1] 9 | self.selected_pts = None 10 | self.selected_pts_expanded = np.zeros(shape=(n_samples, 1, self.dim)) 11 | self.remaining_pts = np.copy(pcd_xyz) 12 | 13 | self.grouping_radius = None 14 | self.dist_pts_to_selected = None # Iteratively updated in step(). Finally re-used in group() 15 | self.labels = None 16 | 17 | # Random pick a start 18 | self.start_idx = np.random.randint(low=0, high=self.n_pts - 1) 19 | self.selected_pts_expanded[0] = self.remaining_pts[self.start_idx] 20 | self.n_selected_pts = 1 21 | 22 | def get_selected_pts(self): 23 | self.selected_pts = np.squeeze(self.selected_pts_expanded, axis=1) 24 | return self.selected_pts 25 | 26 | def step(self): 27 | if self.n_selected_pts < self.n_samples: 28 | self.dist_pts_to_selected = self.__distance__(self.remaining_pts, self.selected_pts_expanded[:self.n_selected_pts]).T 29 | dist_pts_to_selected_min = np.min(self.dist_pts_to_selected, axis=1, keepdims=True) 30 | res_selected_idx = np.argmax(dist_pts_to_selected_min) 31 | self.selected_pts_expanded[self.n_selected_pts] = self.remaining_pts[res_selected_idx] 32 | 33 | self.n_selected_pts += 1 34 | else: 35 | print("Got enough number samples") 36 | 37 | 38 | def fit(self): 39 | for _ in range(1, self.n_samples): 40 | self.step() 41 | return self.get_selected_pts() 42 | 43 | def group(self, radius): 44 | self.grouping_radius = radius # the grouping radius is not actually used 45 | dists = self.dist_pts_to_selected 46 | 47 | # Ignore the "points"-"selected" relations if it's larger than the radius 48 | dists = np.where(dists > radius, dists+1000000*radius, dists) 49 | 50 | # Find the relation with the smallest distance. 51 | # NOTE: the smallest distance may still larger than the radius. 52 | self.labels = np.argmin(dists, axis=1) 53 | return self.labels 54 | 55 | 56 | @staticmethod 57 | def __distance__(a, b): 58 | return np.linalg.norm(a - b, ord=2, axis=2) -------------------------------------------------------------------------------- /main_group.py: -------------------------------------------------------------------------------- 1 | import open3d as o3d 2 | import numpy as np 3 | import argparse 4 | 5 | from load_pcd import load_pcd 6 | # from fps_v0 import FPS # Simple loop 7 | from fps_v1 import FPS # Utilise broadcasting 8 | 9 | 10 | def fps_group_demo(pcd_xyz, num_clusters, colormap, radius): 11 | 12 | fps_v0 = FPS(pcd_xyz, num_clusters) 13 | print("Initialised FPS sampler successfully.") 14 | 15 | fps_v0.fit() 16 | print("FPS sampling finished.") 17 | 18 | labels = fps_v0.group(radius) 19 | print("FPS grouping finished.") 20 | 21 | pcd_obj = o3d.geometry.PointCloud() 22 | pcd_obj.points = o3d.utility.Vector3dVector(pcd_xyz) 23 | 24 | pcd_color = np.zeros_like(pcd_xyz) 25 | for i, l in enumerate(labels): 26 | color = colormap[l] 27 | pcd_color[i] = color 28 | 29 | pcd_obj.colors = o3d.utility.Vector3dVector(pcd_color) 30 | 31 | return pcd_obj 32 | 33 | 34 | if __name__ == '__main__': 35 | 36 | parser = argparse.ArgumentParser() 37 | parser.add_argument("--data", type=str, default="bunny", 38 | help="Load some points data, choices are \"bunny\", \"circle\", \"eclipse\", " 39 | "or \"a_path_to_your_ply_file\".") 40 | parser.add_argument("--n_samples", type=int, default=50, help="Number of samples we would like to draw.") 41 | parser.add_argument("--group_radius", type=float, default=0.05, 42 | help="Radius for grouping. Need to be considered according to the point cloud scale.") 43 | 44 | args = parser.parse_args() 45 | 46 | example_data = args.data 47 | n_samples = args.n_samples 48 | group_radius = args.group_radius 49 | 50 | pcd_xyz = load_pcd(example_data) 51 | print("Loaded ", example_data, "with shape: ", pcd_xyz.shape) 52 | 53 | if n_samples > pcd_xyz.shape[0]: 54 | print("WARNING: required {0:d} samples but the loaded point cloud only has {1:d} points.\n " 55 | "Change the n_sample to {2:d}.".format(n_samples, pcd_xyz.shape[0], pcd_xyz.shape[0])) 56 | print("WARNING: sampling") 57 | n_samples = pcd_xyz.shape[0] 58 | 59 | # Generate some color randomly to mark each cluster. 60 | colormap = np.random.uniform(low=0, high=1, size=(n_samples, 3)) 61 | 62 | print("Running FPS over {0:d} points and getting {1:d} samples.".format(pcd_xyz.shape[0], n_samples)) 63 | fps_pts = fps_group_demo(pcd_xyz, n_samples, colormap, group_radius) 64 | 65 | o3d.visualization.draw_geometries([fps_pts]) 66 | print("Tips: Press `Ctrl` + `+/-` to change point size.") 67 | 68 | -------------------------------------------------------------------------------- /main_sample.py: -------------------------------------------------------------------------------- 1 | import open3d as o3d 2 | import numpy as np 3 | import argparse 4 | 5 | from load_pcd import load_pcd 6 | # from fps_v0 import FPS # Simple loop 7 | from fps_v1 import FPS # Utilise broadcasting 8 | 9 | 10 | if __name__ == '__main__': 11 | 12 | parser = argparse.ArgumentParser() 13 | parser.add_argument("--data", type=str, default="bunny", 14 | help="Load some points data, choices are \"bunny\", \"circle\", \"eclipse\", " 15 | "or \"a_path_to_your_ply_file\".") 16 | parser.add_argument("--n_samples", type=int, default=50, help="Number of samples we would like to draw.") 17 | parser.add_argument("--manually_step", type=bool, default=False, 18 | help="Hit \"N/n\" key to step sampling forward once.") 19 | 20 | args = parser.parse_args() 21 | 22 | example_data = args.data 23 | n_samples = args.n_samples 24 | manually_step = args.manually_step 25 | 26 | pcd_xyz = load_pcd(example_data) 27 | print("Loaded ", example_data, "with shape: ", pcd_xyz.shape) 28 | 29 | if n_samples > pcd_xyz.shape[0]: 30 | print("WARNING: required {0:d} samples but the loaded point cloud only has {1:d} points.\n " 31 | "Change the n_sample to {2:d}.".format(n_samples, pcd_xyz.shape[0], pcd_xyz.shape[0])) 32 | print("WARNING: sampling") 33 | n_samples = pcd_xyz.shape[0] 34 | 35 | fps = FPS(pcd_xyz, n_samples) 36 | print("Initialised FPS sampler successfully.") 37 | print("Running FPS over {0:d} points and geting {1:d} samples.".format(pcd_xyz.shape[0], n_samples)) 38 | 39 | # Init visualisation 40 | pcd_all = o3d.geometry.PointCloud() 41 | pcd_all.points = o3d.utility.Vector3dVector(fps.pcd_xyz) 42 | pcd_all.paint_uniform_color([0, 1, 0]) # original: green 43 | 44 | pcd_selected = o3d.geometry.PointCloud() 45 | 46 | if manually_step is False: 47 | fps.fit() # Get all samples. 48 | print("FPS sampling finished.") 49 | 50 | pcd_selected.points = o3d.utility.Vector3dVector(fps.get_selected_pts()) 51 | pcd_selected.paint_uniform_color([1, 0, 0]) # selected: red 52 | 53 | o3d.visualization.draw_geometries([pcd_all, pcd_selected]) 54 | print("You can step the sampling process by setting \"--manually_step\" to True and press \"N/n\".") 55 | else: 56 | 57 | def fit_step_callback(vis): 58 | fps.step() # Get ONE new sample 59 | 60 | pcd_selected.points = o3d.utility.Vector3dVector(fps.get_selected_pts()) 61 | pcd_selected.paint_uniform_color([1, 0, 0]) # selected: red 62 | vis.update_geometry() 63 | 64 | 65 | key_to_callback = {ord("N"): fit_step_callback} 66 | 67 | # Draw the first sampled points. 68 | pcd_selected.points = o3d.utility.Vector3dVector(fps.get_selected_pts()) 69 | pcd_selected.paint_uniform_color([1, 0, 0]) # selected: red 70 | 71 | # Draw a new sample points every time press "N/n" key. 72 | o3d.visualization.draw_geometries_with_key_callbacks([pcd_all, pcd_selected], key_to_callback) 73 | -------------------------------------------------------------------------------- /example_data/mesh/bunny/reconstruction/bun_zipper_res4.ply: -------------------------------------------------------------------------------- 1 | ply 2 | format ascii 1.0 3 | comment zipper output 4 | element vertex 453 5 | property float x 6 | property float y 7 | property float z 8 | property float confidence 9 | property float intensity 10 | element face 948 11 | property list uchar int vertex_indices 12 | end_header 13 | -0.0312216 0.126304 0.00514924 0.850855 0.5 14 | -0.0446774 0.131204 0.00570479 0.900159 0.5 15 | -0.0683011 0.144828 0.0413688 0.398443 0.5 16 | -0.00600095 0.130398 0.0178986 0.85268 0.5 17 | -0.0173568 0.127613 0.00526885 0.675938 0.5 18 | 0.0330513 0.107034 0.0319543 0.652757 0.5 19 | 0.0400873 0.10521 0.0173419 0.708171 0.5 20 | -0.0301802 0.106322 0.0399745 0.454541 0.437538 21 | 0.0304193 0.118572 0.0188068 0.533079 0.5 22 | -0.0640822 0.159391 -0.0169096 0.404517 0.5 23 | 0.0447046 0.0927877 0.00507585 0.579563 0.425995 24 | -0.0316754 0.170395 -0.00635023 0.365607 0.5 25 | -0.0848523 0.134078 0.0470177 0.499575 0.5 26 | -0.0688547 0.122052 0.0517569 0.564827 0.5 27 | 0.00595475 0.131024 0.0178252 0.748371 0.5 28 | 0.0404629 0.105142 0.00640978 0.680399 0.5 29 | 0.0387342 0.102161 -0.00463112 0.600054 0.5 30 | -0.0914513 0.134136 0.0171026 0.824561 0.5 31 | -0.0818721 0.107166 0.031016 0.690889 0.5 32 | -0.067218 0.156155 0.0178863 0.807492 0.5 33 | -0.0795687 0.152875 0.0299311 0.248168 0.41865 34 | 0.00596007 0.122504 0.0346272 0.555044 0.354559 35 | -0.0516317 0.145001 0.0184804 0.691477 0.5 36 | -0.0779781 0.13255 0.0513494 0.566256 0.5 37 | -0.00590708 0.127934 0.0274623 0.271491 0.462815 38 | -0.0479133 0.129301 0.0269646 0.539149 0.5 39 | -0.082427 0.0928134 -0.00556046 0.710999 0.5 40 | 0.01744 0.127694 0.0185348 0.530957 0.5 41 | -0.0906868 0.120305 0.0066804 0.635593 0.5 42 | -0.0294038 0.17903 -0.00787959 0.269231 0.447035 43 | -0.0797891 0.14376 0.0426994 0.414139 0.5 44 | -0.018288 0.108329 0.0415098 0.482541 0.5 45 | -0.0202326 0.181846 -0.0183274 0.341071 0.440034 46 | -0.0377039 0.167987 -0.0130391 0.396317 0.473039 47 | 0.00582164 0.12806 0.0279016 0.350014 0.41288 48 | -0.0435389 0.130014 0.0175333 0.599596 0.5 49 | 0.0188699 0.119862 0.032409 0.625269 0.5 50 | -0.0440101 0.167035 0.00231898 0.413994 0.469929 51 | -0.089811 0.132401 0.00705743 0.625486 0.5 52 | -0.057352 0.144989 0.0315196 0.696873 0.5 53 | 0.0442622 0.0934526 0.0176417 0.665192 0.5 54 | 0.0412343 0.0921731 0.0285603 0.671611 0.5 55 | -0.0563953 0.154565 0.016878 0.394763 0.437313 56 | -0.0206135 0.159773 -0.00717522 0.136389 0.380194 57 | -0.0729893 0.0656116 0.0181693 0.413051 0.5 58 | -0.0673967 0.155256 0.00581389 0.855717 0.5 59 | -0.0904864 0.118611 0.0412148 0.673877 0.5 60 | 0.0273142 0.117965 0.0286191 0.635485 0.5 61 | 0.041907 0.0916386 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322 1167 | 3 262 163 193 1168 | 3 318 343 352 1169 | 3 299 322 384 1170 | 3 299 393 322 1171 | 3 322 393 384 1172 | 3 137 208 256 1173 | 3 86 197 75 1174 | 3 186 79 336 1175 | 3 222 264 281 1176 | 3 185 361 75 1177 | 3 365 360 366 1178 | 3 386 392 393 1179 | 3 299 386 393 1180 | 3 393 392 384 1181 | 3 392 394 384 1182 | 3 394 398 387 1183 | 3 384 394 387 1184 | 3 404 377 387 1185 | 3 398 404 387 1186 | 3 404 209 377 1187 | 3 209 272 377 1188 | 3 399 400 358 1189 | 3 359 399 358 1190 | 3 101 163 262 1191 | 3 262 193 75 1192 | 3 102 101 375 1193 | 3 204 72 249 1194 | 3 31 148 134 1195 | 3 424 437 427 1196 | 3 359 358 355 1197 | 3 400 402 213 1198 | 3 204 249 185 1199 | 3 351 317 386 1200 | 3 390 351 386 1201 | 3 317 392 386 1202 | 3 392 317 394 1203 | 3 317 395 394 1204 | 3 395 397 398 1205 | 3 394 395 398 1206 | 3 397 405 404 1207 | 3 398 397 404 1208 | 3 199 209 404 1209 | 3 405 199 404 1210 | 3 268 88 239 1211 | 3 75 204 185 1212 | 3 318 352 354 1213 | 3 243 18 227 1214 | 3 397 385 405 1215 | 3 385 199 405 1216 | 3 262 192 194 1217 | 3 101 262 194 1218 | 3 18 131 96 1219 | 3 349 378 199 1220 | 3 385 349 199 1221 | 3 250 158 167 1222 | 3 293 250 167 1223 | 3 379 362 395 1224 | 3 317 379 395 1225 | 3 395 362 397 1226 | 3 362 365 397 1227 | 3 365 401 397 1228 | 3 401 349 385 1229 | 3 397 401 385 1230 | 3 375 194 213 1231 | 3 213 194 113 1232 | 3 375 101 194 1233 | 3 354 352 318 1234 | 3 342 343 318 1235 | 3 375 213 402 1236 | 3 451 261 443 1237 | 3 32 250 293 1238 | 3 258 32 293 1239 | 3 113 194 198 1240 | 3 351 409 368 1241 | 3 355 331 354 1242 | 3 339 340 344 1243 | 3 372 375 363 1244 | 3 339 344 338 1245 | 3 368 321 379 1246 | 3 360 362 379 1247 | 3 360 365 362 1248 | 3 366 365 362 1249 | 3 365 366 362 1250 | 3 406 349 401 1251 | 3 365 406 401 1252 | 3 108 258 52 1253 | 3 258 108 32 1254 | 3 305 349 406 1255 | 3 297 302 301 1256 | 3 52 251 108 1257 | 3 321 360 379 1258 | 3 384 325 314 1259 | 3 373 406 365 1260 | 3 366 373 365 1261 | 3 373 349 406 1262 | 3 349 373 406 1263 | 3 373 124 406 1264 | 3 106 105 323 1265 | 3 439 434 431 1266 | 3 18 243 229 1267 | 3 83 57 260 1268 | 3 447 83 260 1269 | 3 418 425 429 1270 | 3 439 441 434 1271 | 3 441 442 434 1272 | 3 257 106 323 1273 | 3 391 425 418 1274 | 3 435 437 444 1275 | 3 257 323 452 1276 | 3 391 418 294 1277 | 3 296 440 441 1278 | 3 440 296 441 1279 | 3 131 59 138 1280 | 3 294 413 295 1281 | 3 95 30 20 1282 | 3 428 432 434 1283 | 3 422 424 415 1284 | 3 294 420 413 1285 | 3 425 296 429 1286 | 3 414 422 415 1287 | 3 425 121 296 1288 | 3 296 440 431 1289 | 3 452 323 451 1290 | 3 296 83 447 1291 | 3 431 441 439 1292 | 3 445 444 436 1293 | 3 429 296 431 1294 | 3 450 56 106 1295 | 3 301 121 433 1296 | 3 106 257 452 1297 | 3 414 415 411 1298 | 3 390 413 386 1299 | 3 18 229 59 1300 | 3 59 229 46 1301 | 3 386 414 411 1302 | 3 301 433 425 1303 | 3 248 256 196 1304 | 3 411 416 412 1305 | 3 300 391 304 1306 | 3 422 436 424 1307 | 3 46 229 151 1308 | 3 127 121 301 1309 | 3 412 419 356 1310 | 3 295 413 390 1311 | 3 351 390 411 1312 | 3 442 56 125 1313 | 3 409 351 412 1314 | 3 247 243 13 1315 | 3 330 172 155 1316 | 3 451 118 67 1317 | 3 364 44 290 1318 | 3 290 44 166 1319 | 3 166 210 265 1320 | 3 265 210 284 1321 | 3 442 436 434 1322 | 3 229 99 151 1323 | 3 364 449 44 1324 | 3 449 283 44 1325 | 3 418 420 294 1326 | 3 363 449 364 1327 | 3 212 284 210 1328 | 3 44 210 166 1329 | 3 420 428 422 1330 | 3 44 212 210 1331 | 3 247 229 243 1332 | 3 229 247 99 1333 | 3 127 266 178 1334 | 3 56 450 260 1335 | 3 413 420 421 1336 | 3 359 168 363 1337 | 3 363 168 449 1338 | 3 415 424 416 1339 | 3 296 447 260 1340 | 3 212 220 284 1341 | 3 436 437 424 1342 | 3 351 411 412 1343 | 3 440 441 431 1344 | 3 283 212 44 1345 | 3 451 67 261 1346 | 3 168 173 449 1347 | 3 449 173 283 1348 | 3 426 342 318 1349 | 3 381 426 318 1350 | 3 212 348 220 1351 | 3 266 127 301 1352 | 3 426 338 342 1353 | 3 149 283 173 1354 | 3 149 212 283 1355 | 3 438 338 426 1356 | 3 433 121 425 1357 | 3 149 183 212 1358 | 3 414 421 422 1359 | 3 172 170 155 1360 | 3 368 317 351 1361 | 3 350 381 376 1362 | 3 67 259 261 1363 | 3 183 112 212 1364 | 3 212 112 348 1365 | 3 348 112 220 1366 | 3 432 431 434 1367 | 3 448 339 338 1368 | 3 438 448 338 1369 | 3 420 431 432 1370 | 3 112 221 220 1371 | 3 428 420 432 1372 | 3 431 432 434 1373 | 3 417 381 350 1374 | 3 422 428 434 1375 | 3 423 426 381 1376 | 3 417 423 381 1377 | 3 56 260 57 1378 | 3 451 105 118 1379 | 3 296 260 440 1380 | 3 386 413 414 1381 | 3 306 350 316 1382 | 3 448 341 339 1383 | 3 415 416 411 1384 | 3 436 444 437 1385 | 3 259 341 448 1386 | 3 297 425 391 1387 | 3 442 125 445 1388 | 3 450 106 452 1389 | 3 410 350 306 1390 | 3 341 259 223 1391 | 3 355 417 350 1392 | 3 410 355 350 1393 | 3 259 64 223 1394 | 3 410 356 350 1395 | 3 356 410 350 1396 | 3 356 355 410 1397 | 3 355 419 417 1398 | 3 247 13 99 1399 | 3 195 112 183 1400 | 3 180 112 195 1401 | 3 419 355 356 1402 | 3 301 425 297 1403 | 3 390 386 411 1404 | 3 446 259 448 1405 | 3 446 261 259 1406 | 3 434 436 422 1407 | 3 421 420 422 1408 | 3 409 410 306 1409 | 3 368 409 306 1410 | 3 412 356 410 1411 | 3 409 412 410 1412 | 3 442 445 436 1413 | 3 435 423 430 1414 | --------------------------------------------------------------------------------