⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋

⠀⣞⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋

⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋

⠀⣞⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋

⠀⣞⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋

⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋