⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡟⠀⢸⡀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣠⠞⢡⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢰⡇⠀⠀⣇⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⣰⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⢚⣿⠞⠁⠀⢸⡄⠀⢸⠀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⣾⣇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⢀⣀⠤⠔⠛⠁⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⣰⠇⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠏⠀⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⣇⠀⠀⠀⢮⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⣤⣤⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⡴⠋⠀⠀⣼⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠾⠯⠶⢻⠂⠀⠀⠈⠉⠻⠦⣄⣀⠀⠀⠀⠀⡴⢋⣴⠆⠀⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠳⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣀⠀⣀⡞⠀⠀⢀⣀⣀⣀⠀⠀⠉⠉⠛⣲⡾⠟⢹⠃⠀⠀⠀⣿⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠹⡦⠤⠤⠿⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠉⠁⠀⡤⠚⠋⠉⠀⠙⠻⣦⠀⣠⠞⠃⠀⠀⡿⠀⠀⠀⢸⠏⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠚⠁⠀⠀⠀⢠⡇⢀⣠⣄⡼⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠤⠖⠒⠚⣩⣽⡿⠀⠀⠀⢀⣠⡾⠓⢉⣟⡾⠃⢀⡼⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⠮⣷⣄⠀⠀⠀⠈⠙⠆⠀⠿⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠈⠀⢀⣴⠟⢋⣠⣶⣋⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡑⢄⠀⠀⠀⠀⠀⠀⠀⢰⠂⣠⣶⠟⠋⠀⠀⠀⠀⣀⣀⡀⠀⠀⠋⠉⠀⠉⠁⠀⠀⣠⡾⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⡻⣮⣧⠀⠀⠀⠀⠀⠀⣿⣾⣋⣀⣤⣴⣶⠿⠿⠟⠛⠛⠃⠀⠀⠷⢤⣄⣀⣀⣤⣞⣡⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠭⠿⠶⠒⠒⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⣿⣿⠦⠖⠒⠒⠒⠶⣿⣿⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠉⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣤⡴⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠈⠳⣄⣀⡀⢀⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⢠⣶⢿⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢉⣁⣀⣀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠁⠀⠀⠀⠀⢀⣀⣠⣴⠾⡟⠁⠀⠒⢻⡟⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣀⣤⡶⢿⠛⠛⠛⠛⠛⠛⢻⠁⠙⠲⠇⠀⠀⠴⢯⡤⠻⢶⣤⣄⣀⣈⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣥⡀⠀⠀⠀⠀⠸⡞⠛⠒⠂⠀⠀⠀⢯⣻⠶⣶⠶⠟⠋⠁⠀⠘⡆⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠈⠙⢮⡉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢶⡶⠟⠲⠤⡄⠀⠀⠀⠈⠁⠀⠈⣆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈⠁⢀⣠⣤⠤⠶⠶⠦⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⣀⣴⣞⣉⣀⣀⣀⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡤⢤⣤⣤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠈⠀⠀⣠⠼⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⠛⠋⠉⠉⠀⠀⠈⠉⠛⠓⠶⠦⢤⣤⣀⣀⣀⣀⠀⠀⣀⣠⣴⣶⣾⠋⠁⢀⣀⣀⣀⡀⢠⣴⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⠽⠗⢲⣤⣶⠶⠚⠛⠳⢶⣦⣄⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⡶⠟⠛⠉⠉⠙⠛⢶⣅⠉⠙⠓⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⠈⠙⠛⠻⠟⠛⢫⣵⠾⢋⠏⠀⠀⠀⠀⠀⠀⢠⡏⠙⣷⠀⢠⡾⠋
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⢀⣴⠟⠁⢀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠸⣿⠋⠀
⠀⠸⣿⡛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠈⢻⣧⣀⡾⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣿⣇
⣄⣀⠘⢷⡄⠀⠙⠳⣄⠀⠀⠀⠀⢀⡴⢻⡇⣠⠞⠋⠉⠉⠛⢯⡝⠀⠀⠀⠀⠀⠀⠙⡿⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣿⠸⣧
⠉⠙⠓⢾⣷⡀⠀⠀⠘⢷⠀⢀⡴⠋⢀⣼⡷⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢀⣿⠀⠹⣧
⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡾⠋⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣯⣤⣄⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⣼⠋⠀⠀⢹⣧⠀⠀⠀