⢐⡽⣪⢗⡽⣪⢗⡽⣪⢗⡽⣪⢷⢝⡮⣗⢽⢮⡳⡯⣺⢵⡫⣞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⣗⢽⡺⣕⡯⣺⢕⡯⣺⢪⡺⣪⡳⣝⢾⠕⠀ ⠀⠀⠀⠀⠀⠀⠀⢜⡮⡳⣝⢮⡳⡝⡮⡳⣝⢮⡳⡽⣕⢯⡺⣕⢯⡺⣝⢮⣳⡫⣗⢽⡺⣝⢮⣳⢽⡪⣗⢯⣺⢵⡫⣞⡽⣺⢕⣯⡺⡵⡝⣎⢧⡫⡮⡺⣕⢯⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⣳⢝⣝⢮⢳⡹⡜⣕⢯⡺⣕⢯⣫⡺⣕⢯⡺⣕⢯⡺⣕⢗⣝⢮⡳⣝⢮⡳⡳⣝⢮⣳⢝⡮⣳⡫⣗⢽⡺⣝⢮⡺⣕⢽⡸⣪⡺⡪⡯⡺⣝⠀⠀ ⠀⠀⠀⠀⠀⠀⠨⣪⡳⡵⡹⡜⣜⠮⡮⡳⣝⢮⢳⢕⣝⢮⢳⢝⢮⡳⣝⢮⡳⣕⢯⡺⣕⢯⡺⣝⢮⡳⡳⣝⢮⣳⢽⡺⡳⣝⢮⡳⡝⣎⢧⢫⠮⣎⢯⡺⡹⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡪⡞⡎⡮⡺⡸⣝⢮⡫⡞⡮⡳⡹⣜⢮⢳⢝⢵⡹⣜⢮⡺⣪⡳⡝⣎⢗⣝⢎⣗⢽⣹⡪⡯⡮⣳⢝⡽⣪⢗⣝⢮⢪⢮⢳⢝⣎⢧⡫⡳⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⣪⢺⡸⡜⣜⢮⡫⡮⡳⣝⣝⢎⢯⣚⢮⡪⡳⣝⢵⢹⡪⣇⢯⡺⣜⢝⡎⣗⣕⢯⡪⡧⣳⡹⣪⠯⡮⣳⢝⢮⡳⣱⢳⡹⡜⣕⢧⢳⢕⡝⣎⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⢮⡪⡮⢮⡳⡳⣝⢮⡻⣪⢮⣫⡺⡸⡜⣎⢏⢮⢎⢧⡳⡕⡧⡳⡕⣇⢏⡎⣎⢮⢪⡳⣕⢝⢮⡫⣞⢵⢝⢵⢝⡜⣎⢮⢺⢪⡳⣹⢪⡺⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⣎⢗⣝⢮⡳⣝⢞⢮⣳⢽⣺⢵⡳⣹⢕⢽⡸⡕⣝⢎⢧⡳⡝⣎⢯⡺⡪⣇⢏⢮⢪⢎⢎⢎⢗⠵⣝⢜⣎⢯⢪⢇⡏⡮⡪⣣⡳⣝⢼⢱⠕⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⢮⣳⢵⣳⣝⣮⣯⡿⣾⣻⣽⡳⣝⢮⢯⣗⢵⡹⣜⢭⣣⡳⣝⢮⡣⡯⡺⣪⡫⣎⢧⢳⢹⡸⡪⡝⣜⢕⢎⡎⡧⡣⡳⡱⡝⡼⣸⢪⢎⠧⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣯⣿⣽⣾⣻⣾⣯⢿⢯⢗⣗⣝⢮⡳⣝⢾⣻⣞⡮⣣⢧⡳⣕⢗⣝⢎⢯⣪⡺⡜⡮⡳⣣⢳⢕⢝⡜⡜⡕⡕⣕⢝⢜⣕⢝⢮⢎⢗⡕⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣯⣷⣻⢽⣺⡺⣝⢽⢕⢧⡳⡳⣝⢮⡳⣕⢿⢽⣯⡷⣯⣞⣗⣷⢯⣷⣳⣽⣺⣝⢮⡳⣝⢎⢧⢣⢫⢪⢪⢪⡪⡳⣜⢵⢝⡎⡗⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⣗⣝⢮⣺⡪⣏⢯⡳⣝⢞⢮⡳⣝⢮⡳⣝⢞⣟⡯⣿⣯⣿⣻⣽⡿⣾⣻⡾⣯⣟⡮⣫⢮⢣⡣⡣⡣⡣⣳⢹⢜⢮⡣⠇⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢯⡺⣪⢗⣗⢽⡪⣏⣗⢵⢳⡳⣝⢮⡳⡵⣝⢞⢮⢯⡻⡽⣟⡿⣟⣿⣻⣾⣻⢮⡳⡕⡕⡕⡕⣝⢼⢕⢯⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢪⢷⣽⣳⣻⣺⣪⡳⡳⣝⢮⣳⢝⣞⢮⢯⡳⣝⡮⡯⡮⣫⢯⡻⡽⡷⣿⡽⡮⡳⡱⡱⡹⣜⢵⡫⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⣓⣿⣻⣷⣷⣝⣝⢮⢯⣺⢝⡮⣯⡳⣯⣳⢽⣺⢝⡮⣳⢽⡹⡽⡵⣻⢽⡪⡎⡮⣺⣪⣗⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⢲⣽⣿⣫⢷⣗⢵⡫⣗⡽⣳⢯⡷⡿⡿⣾⣿⣾⣯⡯⣞⡵⣫⢞⡽⣺⢝⢎⢎⢮⣪⣞⣗⢵⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡪⡺⣟⣿⣟⣿⣗⢽⡺⣕⡯⣯⡯⡫⡪⣿⣽⢿⣻⣿⡿⣷⣫⢷⢝⡾⣕⢯⢪⡪⣗⣗⢷⢽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢕⡯⡿⡽⣾⢽⡳⡣⣗⢯⡳⣽⣳⡏⡎⣞⣿⣾⣝⣽⣯⣟⢟⣯⢯⢳⢝⢞⢜⢜⣞⣗⣗⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢳⢝⡽⡽⡝⡝⡮⣹⡪⣗⣟⢮⢷⡯⡪⡺⡯⣟⣿⣻⣟⢎⣗⢟⢜⢕⢍⢎⢎⢗⠗⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣣⢗⢵⡹⡜⣞⢮⣻⡺⣪⢿⢽⣽⡻⣮⢯⣟⣾⡳⣗⡟⡮⣓⢕⢕⢅⠇⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣪⢫⡪⡪⣞⢮⢗⡷⣝⢮⢯⣳⡳⡯⣗⣟⣞⡮⡯⡳⡝⣎⢎⢎⢆⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡪⡪⡎⡯⡮⣫⡳⣝⢮⢯⡳⡵⣝⢮⡳⣕⣗⢽⡪⣯⡺⣪⢞⢎⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⢹⡸⣕⢝⢎⢮⢺⢸⢕⣗⢽⢝⡮⣳⡫⣗⡵⣫⢯⡺⡮⡳⡝⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⡎⡮⡪⡪⡪⢪⠪⡪⡪⣎⢮⡳⣝⣗⢽⡺⡮⣳⢯⡺⣝⢵⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⢜⢜⢜⢜⢌⢒⢜⢰⢱⢱⢹⢸⢜⡾⣕⡯⣗⢯⢯⡺⡵⣝⢜⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⢎⢎⢎⢪⠢⣑⠱⡰⣑⢕⡵⣝⢮⡻⣪⢗⣟⢮⢯⡳⣝⢮⢪⢎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⣞⡜⡜⡔⡕⡜⣜⢼⡸⡕⡕⡕⡕⡝⣎⢯⣺⢽⢕⢯⡪⡎⡮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡪⢯⢮⣳⣝⣮⣣⣣⢣⡣⡣⡣⡣⡣⡳⣕⢯⢏⢧⡣⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣕⣷⣗⣷⣳⡳⣳⢹⡸⡹⡱⡧⣣⡳⣫⢏⡇⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡺⣞⢿⢾⡳⡯⡳⢯⢺⠮⡳⡹⡺⡪⡗⡗⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀