⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠱⡝⢦⣀⡤⠖⢋⡽⠁⠀
⠀⠀⠀⢀⣾⠟⠛⠦⣄⣦⠀⠀⠀⠀⠀⡀⠀⢛⢦⡀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⣠⠜⠊⠁⢀⡴⠋⠀⠀⠀
⠀⠀⣤⣣⠏⠀⠀⠀⠀⡟⠳⡀⠰⡀⠀⠘⢦⠀⠺⣿⣦⣄⠙⠢⡀⠹⣄⠀⠠⡀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢣⠀⢀⠀⠀⠀⠀⠹⣳⣀⡤⠚⠉⠀⣀⡠⢠⠚⢦⡀⠀⠀⠀
⠠⠟⠋⡝⠀⠀⠀⢰⢠⠃⠀⠘⢦⡹⣶⣄⠀⠑⢄⡙⢿⡟⠳⢦⡈⠢⡘⣦⠀⠹⣦⠀⠀⠀⢧⠀⠀⠀⡀⠀⠱⡀⢂⠀⢀⣠⠔⢋⡡⣔⠖⣉⡀⠀⡰⠉⢧⠀⢣⠀⠀⠀
⠀⠀⢀⠃⠀⠀⠀⢸⢸⠀⠀⠀⠀⠉⠻⣟⠓⢤⣀⠙⠠⣹⣶⠒⠉⠒⠼⣾⣧⠀⢻⣧⡀⠀⠘⡇⠀⠀⠱⡀⠀⠘⣿⠖⢉⣠⡖⢉⠎⠑⢒⣖⣽⠼⣷⡀⠸⠂⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⠟⠓⠚⠿⣿⣄⣀⡀⣬⣿⣿⢶⡏⣵⠐⠒⢿⠀⠀⠀⢱⠀⠀⡘⣶⣷⡾⠛⠁⠀⢀⠜⣡⡇⠀⢸⣸⢀⠀⠀⠀⠀⠀
⠀⢀⣜⣀⠀⠀⣇⣼⠘⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣀⢤⣒⣯⡷⠋⠁⢈⣿⣬⣷⠈⠀⠀⠀⣇⠀⠀⠈⣆⠀⢰⠻⣫⠃⠀⢀⡴⠁⡔⠑⣔⠄⢸⢻⡏⠀⠀⠀⠀⠀
⣠⡾⢿⠁⠀⡀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠉⣀⢤⣐⣮⠓⠊⣁⡀⠤⣤⣐⣠⡞⠁⣩⣹⡀⢠⠀⠀⢹⡆⠀⠀⣯⡄⢸⣬⠁⡠⣲⠋⣠⠊⠀⠀⠈⢪⢿⠀⠇⠀⠀⠀⠀⠀
⠀⠀⡏⣼⠀⡇⢸⣿⠀⠀⢀⣀⢤⣐⠮⠕⠊⠁⣀⢥⣒⣭⣖⣿⣽⣾⣿⣛⣻⠟⣿⡿⣧⠘⡀⠀⢸⡇⢀⣧⡇⣷⢸⡿⠋⠚⢁⡔⠁⠀⢀⠀⠀⡸⠻⣧⠀⠀⠀⠀⠀⠀
⠀⣸⣵⡇⠀⢹⠈⣟⢉⣝⡵⢎⠉⠀⠀⠀⠀⠈⠀⠐⢿⠟⢹⣿⣋⣩⣴⡟⢘⠴⠚⠃⢸⢀⣇⣵⢸⠇⣦⡿⢹⣹⣿⠃⣀⣴⠏⠀⠀⢰⡎⠀⡘⠀⠀⢹⢧⠀⠀⠀⠀⠀
⣠⠟⠁⡇⠀⠀⢆⡹⣫⣞⡩⠭⠵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢓⡤⠚⠁⠀⠀⠀⣸⠞⡿⣟⡾⣆⢹⠃⠈⣿⣥⣾⢿⠃⠀⠀⠀⡟⣣⢰⠁⠀⠀⠀⢏⣇⠀⠀⠀⠀
⠉⠀⠀⣇⣤⢀⣼⡟⡉⢣⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠋⠸⢁⣿⠃⠘⣮⣄⠀⠃⣿⡇⠈⠀⠀⠀⢰⢨⠿⣶⠀⠀⠀⠀⠈⡞⡇⠀⠀⠀
⠀⣀⣀⣸⣿⣿⢿⣿⢿⣾⢿⡈⢿⣹⠧⠤⣀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠈⠈⠀⠀⢹⠳⠆⠀⠀⡌⠀⡏⠀⠈⠓⠂⠀⠀⠀⠸⣷⠀⠀⠀
⠀⠈⡹⡻⢿⡿⣧⡹⣦⣿⣅⡅⢁⡞⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⣤⣿⡀⠀⣷⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀
⠀⡜⡑⠁⠀⠈⠉⠛⠾⣟⣿⣹⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠘⢟⣷⡀⢹⣧⡀⢣⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀
⠀⡔⠀⠀⠀⠀⠀⠀⠀⠈⣾⢻⡆⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠀⠙⠻⣿⣷⡼⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠰⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠏⢸⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡔⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢸⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⢾⠏⠈⠳⣄⠀⠀⠀⣀⠴⣾⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⣠⢼⡹⠃⣀⠤⠐⠊⢓⡲⡿⠁⠀⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣀⣀⣼⣱⠋⣠⠋⠀⠀⢠⠖⠉⢰⠁⠀⢠⢻⣾⣿⠦⠤⣤⣤⡶⡺⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⠀⠿⣽⣴⠁⠀⠀⢠⡏⠀⠀⡟⠀⠀⢻⢼⡿⣋⠭⠔⠩⢭⣿⣱⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⠘⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⡼⠃⠀⠀⢠⡟⠀⠀⢠⡇⠀⠀⢸⣸⠀⣀⠈⣉⠉⠁⠀⢧⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠙⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⣦⡜⠀⠀⠀⢠⡟⠀⠀⠀⢮⠇⠀⠀⢸⣷⣾⡶⠶⣌⠙⣄⠀⢸⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢠⠇⡷⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣼⠀⠀⠀⠀⡟⠀⠀⠀⠀⠼⠀⠀⠀⢸⣿⡏⠉⣿⣹⡆⢸⡄⠈⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣾⣼⣇⠹⣦⡀⠀
⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠐⠁⠀⠀⠀⠀⡆⠀⠀⢀⣿⣿⣧⣠⣿⢣⡇⢸⠃⠀⣧⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠿⣿⠀⠱⡉⠢
⠀⠀⠀⠀⢠⠋⠀⢀⠄⠀⠀⠀⠀⠀⢹⠀⠀⠰⣆⠀⠀⠀⠘⠄⠀⠀⠨⢿⣿⠳⣶⠒⢋⡴⠋⠀⠀⢸⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠎⠀⣿⡇⠀⠀⠀
⠀⠀⠀⢠⠃⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠘⣷⣤⣄⣀⣀⣀⣀⣤⡼⢇⢯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡠⠋⠀⠴⠋⠀⠀⠀⠀⠀