⠀⠀⢠⡇⢀⠆⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠀⡞⠀⠀⠁⠀⠀⢘⣿⣛⢉⡉⠛⢲⣦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠚⠀⣸
⠀⠀⢸⢸⢧⠀⢸⠀⠀⠀⠀⠈⠙⠋⢹⣛⡋⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⡏
⠀⠀⢸⡟⣦⣧⡞⣄⡄⠀⠀⣴⠹⣫⡍⡹⢷⣄⠀⠀⠀⡀⠀⠀⡎⢀⠔⣻⣸⠃
⠀⠀⢸⡞⠸⡙⢻⣺⡀⠀⠀⢽⡗⠋⠇⠙⣿⡏⠀⠀⠀⠁⢠⢮⡾⡟⣞⡜⡇⠀
⠀⠀⠸⢻⢎⣨⢃⢝⣰⡠⠀⠈⣳⡀⠀⢠⣿⡇⢀⠀⢠⣰⡹⡛⠇⠞⠠⠟⠀⠀
⠀⠀⠀⣿⣾⣬⢸⢘⡜⠣⣀⢀⣹⡧⡔⠻⣸⣄⡜⡴⡖⢡⡊⡞⢎⣳⣴⠃⠀⠀
⠀⠀⠀⢿⣿⣇⢼⢺⠱⣨⣸⢴⡽⠋⢥⠀⢹⠉⠱⣰⠡⡿⠇⣶⣹⠹⡟⠀⠀⠀
⠀⠀⠀⠈⠙⡇⡜⢈⣙⠰⠱⢦⠁⢀⠎⠀⢀⣡⡀⣬⠭⢷⣤⡇⢧⠆⠁⠀⠀⠀
⠀⠀⠀⠀⠘⡇⣿⠙⠈⢟⢾⢸⢖⡊⠓⢒⣳⡼⡇⡟⠁⠈⢁⠇⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠇⢸⠀⠀⠈⠘⣸⢸⡁⠠⢾⡜⠀⣇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢼⡝⣿⢠⢀⣞⠀⠀⠸⡚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡀⠀⡘⡴⠁⣻⢤⣌⠀⠾⢟⣦⡄⠑⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣹⣞⡝⠀⢈⢭⠆⠈⣓⡆⣯⡽⣧⠀⢏⡲⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⡦⢰⡏⡇⢖⣓⡟⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⣥⢮⠀⢷⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⢀⡏⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡀⠘⣟⣯⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠠⡇⠀⣿⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠳⡀⠀⣸⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠿⡘⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢱⠸⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠐⡇⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀