⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣽⡹⣿⣭⣿⣿⣿⡿⡀⡀⣰⠫⣜⣣⡟⢡⠘⠂⡀⡀⡈⡀⡀⢸⣿⣟⡾⣷⢈⠦⡑⡬⣘⠡⢇⡿⢎⠱⠌⣆⢣⣿⣟⡷⣯⣿⣿⡷⣟⣯⣿⣿⣷⣻⡽⣿⣯⣟⣷⣻⣿⡾⣽⣳⣯⣷⢯⣟⡿⣾⡽⣿⣧
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣧⢟⣼⣳⢿⣻⣿⠇⡀⡀⠸⣱⠞⡡⠎⢂⠉⡀⡀⠠⡀⡀⡀⢼⣿⣯⣟⣿⠐⡪⠴⡑⠤⣋⠞⣡⢊⠱⢊⠴⢨⣷⡿⣽⣟⣾⣿⣿⢯⣟⣾⣿⣷⢯⣿⣽⣿⡾⣽⢯⣿⡿⣽⣻⣷⡿⣯⢿⣽⣳⡿⣽⣿⡆
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⢣⣟⡾⣽⣻⣿⡏⡀⡀⡀⡀⠁⢨⠑⡀⠠⡀⡀⢀⠁⡀⡀⡀⢺⣿⣷⣻⢾⡅⡃⠞⣈⠱⡌⠲⡐⠬⣁⢋⡔⢣⣿⣻⢷⣯⣟⣿⣿⢯⣟⣾⣿⣿⣻⢾⣽⣿⡽⣯⣟⣿⣿⣽⣻⣽⣿⣯⢿⣞⡷⣟⣯⣷⣿
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣾⡹⣮⣟⡷⣿⡟⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⠄⡀⡀⡀⡀⢸⣿⢷⣻⢿⡆⢹⠐⡀⠁⠆⠑⣈⠒⡄⢢⠘⠆⣿⣯⢿⡾⣽⣿⣿⡿⣽⣞⣿⣿⡽⣟⣾⣿⣟⣷⣻⢾⣿⢾⣽⣿⣿⣽⣻⣞⣿⡽⣿⣻⣿⡄
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⢵⣻⢷⣯⢿⣽⠁⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⢀⡀⡀⡀⡀⡀⢸⣯⣟⣯⡿⣇⠣⡀⡀⢈⡀⡀⠄⡃⢌⠂⢍⠊⣿⣽⢯⣟⡷⣿⣿⣿⡽⣾⣻⣿⣿⢯⣿⣿⡾⣽⢯⣟⣿⣟⣾⣿⣿⣞⣷⣻⢾⣽⣿⡿⣿⡇
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⢏⣾⣻⣟⡾⣯⠇⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⠄⡀⡀⡀⡀⡀⠈⠷⠿⠳⠟⢛⠄⠁⡀⠄⡀⡀⡀⠈⠔⣈⠂⢍⢺⣯⡿⣽⣻⣽⣿⣿⡽⣷⣻⣿⣿⣻⢾⣿⢿⡽⣯⢿⣽⣾⣻⣯⣷⢿⡾⣽⣯⢿⣾⣿⣿⣧
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡼⣫⢞⣷⡿⣽⡟⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠌⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⠈⠄⢺⡿⣽⢯⣷⣻⣿⣿⡿⣽⣳⣿⣿⣯⢿⣿⣯⢿⣽⣻⢾⣿⣽⣿⣟⣯⣟⡷⣯⣿⡿⣷⣿⢿
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⠷⣭⣻⢷⣻⢷⡇⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢈⠐⣿⣯⣟⣷⣻⣿⣿⣿⡽⣷⣻⣿⣿⣻⣿⣽⣻⢾⣽⣻⣯⣿⣿⣟⣾⣽⣻⢷⣿⢿⣿⣻⣿⠆
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣾⡹⢶⢯⣿⣿⣟⡇⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⢽⣾⡽⣾⣳⣿⣿⣿⡽⣷⣻⣿⣿⣽⣿⣳⣟⣯⡷⣿⣿⢿⣿⣞⡷⣯⣟⡿⣾⣿⣟⣿⡿⡇
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣠⢞⣯⣝⢯⣟⣾⡿⣿⣇⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⠌⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡜⣷⡿⣽⣳⢿⣿⣿⡿⣽⡷⣿⣿⣯⣿⢷⣯⢷⡿⣽⣿⣿⡿⣞⣿⣳⣯⢿⣿⣽⡿⣯⣿⣗
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⠴⣹⢞⣿⡼⣛⡾⣽⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠰⢹⣿⣯⣟⡿⣿⣿⣿⢯⣿⣽⣿⣿⣯⣿⣞⣯⣟⣿⣽⣾⡿⣯⢷⣟⣾⢯⣿⣾⢿⣿⣽⣏
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⠴⣉⢮⡱⣯⣿⢾⣽⣻⣽⣻⣾⣿⣷⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡌⢿⣿⣿⣽⣿⣿⣿⣿⣳⣯⣿⣿⣽⣾⡽⣞⡿⣾⣟⣿⡿⣽⣻⢾⡽⣯⣷⡿⣿⣯⣿⡷
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡰⢃⡜⢤⢣⡻⣵⣿⣟⣾⣳⢯⣷⣟⣿⣿⣿⣦⡀⡀⡀⡀⡀⡀⡀⡁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠘⡌⢿⣿⣿⣟⣿⣿⣿⣯⣷⣿⣿⣿⣳⢿⣻⣽⣿⣻⣿⢿⡽⣯⣟⣿⣳⣯⢿⣟⣷⡿⣿
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡰⢊⡐⢦⣘⢣⡳⣝⣷⣻⣿⢾⣽⣻⢾⡽⣿⣾⣿⣿⣿⣷⡦⣌⡐⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⡀⡀⠘⡌⢿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣽⣻⣽⢾⣿⣽⣿⢯⣟⣷⣻⣞⡷⣯⣟⡿⣯⣿⢿⡀
⡀⡀⡀⡀⡀⡀⡀⡠⠊⠔⢢⡘⠦⣜⢣⡝⣞⡾⣽⣿⣟⡾⣽⢯⣿⣻⣿⣷⣿⣿⣿⣷⡹⢿⣲⣤⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⠈⠤⢁⠂⡀⡀⠑⢬⠹⣿⣷⣿⣿⣿⣿⣿⣿⣯⣷⢿⣽⣻⣯⣿⣿⢯⣟⡾⣷⢯⣟⣷⢯⣿⣻⣽⣿⡇
⡀⡀⡀⡀⡀⠠⠈⢄⠱⡘⢢⡙⡼⣌⢷⡹⣎⡿⣷⣻⣿⡽⣯⣟⣷⡿⣯⣿⣿⣿⣾⣿⣯⢹⣷⢻⣿⡷⣄⡀⡀⡀⡀⠐⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⠂⠅⡒⠠⡀⠑⠌⡻⢿⣿⣿⣿⣿⣿⣿⣽⡿⣾⣿⣽⣿⡿⣯⢿⡽⣯⢿⡽⣾⣻⢷⣻⣽⡾⡇
⡀⡀⡀⠠⠌⠠⢁⠊⡔⣡⢃⡞⣱⢎⡷⣹⢧⣟⡿⣽⣿⣟⣷⣻⢾⣽⣿⣻⣽⣿⣿⣿⣿⡣⢿⣧⢿⣿⣿⣿⣦⣀⡀⠌⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠂⡀⡀⠈⠊⠝⢿⣿⣿⣿⣯⣷⣿⢿⣾⣟⣿⡿⣽⣯⢿⡽⣯⣟⣷⣻⢯⣟⣷⢿⣿
⡀⢀⠔⠁⠄⠣⢌⢒⡱⢢⡝⡼⣡⢟⡼⣏⡾⣽⣻⢿⣿⣟⡾⣽⣻⣞⣷⣿⣿⣿⣿⣿⣿⣏⢯⣿⢞⣿⣯⣟⡿⣿⣶⣤⡀⡀⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠐⠢⠤⣀⡀⡀⡀⡀⠉⠿⣿⣿⣿⣾⣿⣟⣿⣿⣟⡷⣯⣟⣿⣳⣟⣾⣽⣻⣽⢾⣟⣾⡄
⡠⠃⡀⢊⠌⡱⢌⢆⠧⡳⣜⡱⣏⢾⡱⣯⡽⣯⣟⣿⣯⡿⣽⣳⣟⣾⣽⣾⣟⣿⣿⣿⣿⣿⢎⣿⣯⡿⣽⢿⣿⣵⢯⣟⣿⣶⣦⣄⣀⡀⡀⡀⡀⡀⡀⡀⡀⣀⠠⡀⠐⡀⠂⡀⡀⠁⠁⠒⠐⢢⣐⣌⣥⣣⣶⣦⢶⢼⣿⣷⣿⣟⣿⣿⣿⢯⣟⣷⣻⣞⣷⣻⣞⡷⣯⣟⡿⣾⢯⣇
⢀⠰⢀⠣⡘⠴⣉⢎⡞⣱⢎⡷⣹⢎⣷⡳⣿⣽⣾⢿⣽⣟⣷⣻⣞⡷⣯⣿⣾⣿⣿⣿⣿⣿⢎⣿⡶⣿⣯⣟⣞⣿⣿⣾⣳⣟⣿⣿⡿⣿⢿⣶⣶⣾⣶⣿⡿⣝⡿⣛⣟⣻⣳⢟⣻⣛⣟⣻⡟⣯⠿⣽⢯⣷⣻⣞⠯⡜⣿⣿⣯⣿⣿⣿⣟⣯⢿⣞⣷⣻⢾⣳⣯⣟⡷⣯⢿⡽⣟⢾
