⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⠀⠀⠀⣀⣀⣠⠤⠖⢳⠀⣇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⢈⣧⣿⠶⠒⠛⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⣀⣀⠠⠤⣀⡀⠀⠀⠈⠢⡀⠀⠀⢀
⠀⠀⠀⠀⢀⢤⣀⣀⡀⠀⡜⠁⢀⡴⠚⠉⠀⠀⠀⠈⠉⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠖⠉⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⣸⣶⣾⣽
⠀⠀⠀⠀⣸⣾⣷⣶⣿⣿⣦⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⢏⠎⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⣿⣿⣿⣯
⠀⠀⠀⢠⣖⣿⣿⣿⡏⡞⠀⠰⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠘⡀⢻⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⡿⢸⠃⢀⠇⠀⠀⠀⠀⡇⠀⠀⠀⢰⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢃⠘⣿⣿⣿
⠀⠀⠀⠀⣿⣿⡟⢁⣾⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡆⣸⣇⡀⢸⠀⡆⠀⠀⠀⠀⢠⣤⠤⣿⠀⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣆⠹⣟⠿
⠀⠈⠻⠿⠿⠷⡞⠁⣿⠀⢸⠀⠀⠀⢠⢠⡇⠀⢰⡂⡏⢹⠉⢹⡆⢳⠀⠀⠀⠀⠈⡆⢠⠟⡆⣧⠀⠀⢠⣿⠀⠀⠀⠀⠸⢸⢩⢳⢌⣳
⠀⠀⠀⠀⠀⠀⣷⠀⣻⠀⢸⠀⠀⠀⢸⢸⢧⠀⢸⡆⡇⠈⢇⠀⡟⢌⡆⠀⠀⢀⢇⢇⠎⠀⢳⡸⡆⠀⢸⣿⠀⠇⠀⠀⢸⢸⠀⡞⡆⠀
⠀⠀⠀⠀⠀⠀⠸⣄⣿⡀⣼⡞⡀⠀⢸⢸⠈⣄⣘⣷⣷⣒⣚⠦⠱⠀⠻⡀⠀⣜⡜⢛⣻⣯⣭⣿⣾⣦⣼⣿⠀⡆⠀⢀⣎⡎⠀⠜⢞⡄
⣤⠤⠤⣄⣠⠤⠤⡿⣿⣣⣿⣷⡡⠀⠘⡾⣿⠛⢻⡛⠛⠛⢻⠃⠀⠁⠀⠁⣰⠏⠀⠈⢫⠍⠉⠈⡋⠀⢹⡟⢠⠃⢀⡾⠎⡷⡀⠘⡌⠻
⠀⠀⠀⣿⡴⣲⠞⡽⢟⣱⣿⣥⣷⣵⡀⠹⣿⡁⠈⣇⠀⢀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⣀⣀⣠⠃⠀⢡⢃⢎⣤⣛⣓⡾⢽⣵⡀⢘⣦
⠀⠀⠀⣿⠗⢬⡛⡾⠩⠒⠒⠒⠒⠚⠿⢶⡬⠿⠶⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣤⢿⣋⣁⣀⣀⣀⡈⠉⠋⣻⠭⠖
⠀⠀⠀⣾⡀⠀⠈⡰⠀⣀⣀⠤⠤⠤⠄⣈⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⡟⢉⠩⠭⠭⠭⣍⣙⠓⢦⠃⠀⢀
⠀⠀⠀⢸⠿⣷⡦⢧⣠⠴⢞⣛⣛⣛⣛⡓⢷⡀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀⠈⠉⠲⡄⠀⠀⠀⡼⣀⠀⠠⠠⠄⣀⣀⡀⠙⣞⣐⣪⣥
⢄⠀⠀⢸⡀⡀⠉⠋⢻⠉⠉⢀⣀⣀⣀⣈⢹⣷⣤⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣼⠛⠛⠛⠛⠻⠶⣶⢬⣻⠋⠉⠉⠀
⠀⠑⢤⣸⡏⠲⢵⣒⣮⣰⡿⠿⠒⠒⠒⠲⣴⣿⢿⣿⣿⡶⠧⠤⢤⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⣏⣠⣴⣶⣶⣤⢄⡀⡞⣳⣀⠒⢒⣈
⠀⠀⠀⠈⣿⠷⣦⣤⡴⠛⡄⣤⣴⣒⠒⣒⡧⣌⣹⠟⠁⣀⠤⠤⠾⡀⠀⠀⠀⠀⠀⠀⡷⠚⠛⠛⣿⠩⣉⣉⣉⠛⢷⣬⡧⢄⠝⣟⣛⣋
⠀⠀⠀⠀⣿⢿⣱⡒⠃⠀⢉⣻⣶⡖⣢⣟⣹⠊⠀⠀⠈⠀⠀⠀⠰⣇⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢸⣟⡛⠻⣿⣭⣞⣛⣉⣡⠴⣏⣙⣻
⠀⠀⠀⠀⣿⣘⣋⣤⣤⠖⠉⠁⠘⣿⠷⣤⠇⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣤⣤⣄⣿⣯⠀⣀⣤⣴⣶⣿⣔⣾⣿⣿⣿⣿⡅⠀⠀⠀⠀⠈
⡀⠀⠀⠀⣿⠉⠀⡰⠃⠀⠀⠀⡰⠃⣴⠏⠀⠀⠀⠀⠀⢀⠀⠒⠋⣽⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⣿⢀⡜⠁⠀⠀⢀⣶⠇⠀⢹⠀⠀⠀⠀⠀⠐⠁⢀⣤⣾⣿⣿⠟⠛⢿⠟⡛⢿⣿⢛⡛⢛⠛⣿⣿⣿⡿⢛⣉⣀⡀⠀⠀⠀⠀
⠄⠀⠀⠀⡸⠋⠀⠀⠀⢰⣿⣿⡀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣱⣾⠟⣨⢸⣿⢸⣿⢸⣷⢸⡇⢻⣿⣿⢰⣿⡿⢿⣿⣆⠀⠀⠀
⡇⠀⡰⠋⠀⠀⠀⢀⠔⢹⣿⣿⣇⠀⠀⠀⠑⣄⠀⠀⣠⡞⢿⣿⡿⢰⡿⠁⠚⡛⠸⣿⠀⣿⢸⣿⢸⡇⢸⣿⣿⠸⣿⠀⢀⣿⡿⠀⠀⠀
⣇⠎⠀⠀⠀⠀⢀⡎⠀⠈⣿⣿⣿⡄⠀⠀⠀⠈⠳⣶⠋⠀⠀⢻⡇⢸⡇⢠⣿⢿⣦⣿⡇⣿⢸⣿⠸⣿⢸⣿⣿⡄⣿⣷⣿⡿⠁⠀⠀⠀
⣿⡀⠀⠀⠀⣠⡟⠀⠀⠀⢹⣿⣿⣷⡤⠖⠀⠀⠀⢹⡄⠀⠀⠀⢧⢸⣧⠿⠃⣼⡇⣿⣇⠻⢸⣿⡇⣿⠈⠿⠛⠃⣿⡟⠉⠀⠀⠀⠀⠀
⡏⢷⠀⠀⠞⠹⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠈⡇⣀⣀⠀⢸⡌⢿⣦⣴⡿⢁⡘⣿⣿⣿⣿⡇⢹⣷⡿⠿⠃⢸⡇⠀⠀⠀⠀⠀⠀
⣿⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⣯⠉⠀⠀⠘⢿⡆⠉⠋⣵⣿⣷⣦⣭⣥⣬⣥⣦⣭⣴⣾⣿⣦⠁⠀⠀⠀⠀⠀⠀