⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⣴⠋⠁⠀⠙⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⣷⣄⣀⡀⠈⠉⠳⣄⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠈⠁⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⢀⣠⢞⡽⠋⠀⠀⠀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⢸⡁⠀⠀⠀⠈⠙⠛⠓⠚⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡘⠷⣤⣤⠴⠖⠶⢦⣄⡀⠀⠀⠀⠀⠸⣿⣟⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⠶⣦⣀⣀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠈⠛⢷⡈⢻⡽⣆⠀⠀⣤⣄⣀⠀⠀⠉⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⣧⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⡇⣸⠟⠙⢷⣄⠀⣿⢹⣿⣄⣀⠀⠰⣿⢶⣞⠛⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⣠⡴⠿⢧⣄⣠⣀⣹⠼⠛⣿⣿⢿⠉⠻⡶⠽⡾⠙⠳⣄⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⣴⠋⠀⠀⠀⠀⠙⢿⣍⠛⠓⠶⢦⣬⣓⠋⠳⠞⠁⠀⠀⠘⣧⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⠄⠀⠈⠙⠛⢷⡄⠀⠀⠀⠀⠘⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⣾⠛⠻⢦⣽⠈⠙⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⣽⠳⣤⡀⠀⠘⠛⠁⠀⠀⠀⣸⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⣤⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⣰⢞⣿⡀⠀⢠⣟⣩⣥⡶⠈⢙⣶⣦⠴⠶⠛⠛⠛⠛⠷⣄⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢠⡏⠈⢹⣇⣤⠙⠋⠙⡷⠿⠟⠋⠁⠀⢀⣀⣄⣄⡀⠀⠳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⣍⠛⠛⢯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠶⠛⠁⠀⠀⠀⠘⠚⢶⡶⠶⠶⠶⠶⠶⠞⣋⣉⡈⠙⠻⠶⣤⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠺⠦⢤⡀⠀⠙⠿⠦⠶⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠉⠓⠿⠽⣛⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀⢀⣤⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⣦⠀⠙⢦⡀⠀⠀⠀⣰⠇⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠉⠙⣛⡿⠃⢀⣤⣾⡿⠃⣠⣾⣿⠀⠀⠀⠀⣼⣧⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢰⣦⣌⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠤⣤⡞⠁⣠⣴⣿⣿⣋⣴⣿⡟⢹⣷⠀⠀⢀⣾⡏⠻⣷⡀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠹⣿⡿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⣴⡿⢻⡿⣿⣿⠟⠹⣿⣷⣿⣻⠀⢠⣾⠝⢿⣄⠹⣧⠀⢸⡏⠹⣷⣄⠀⠀⠀⠀⢹⣿⣿⣿⡻⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡵⠟⠁⠀⠀⢰⠏⠁⠀⢸⣿⡟⠁⢹⣠⡿⠁⠀⠀⠻⣧⣿⢷⣸⡃⠀⠈⢻⣷⣄⠀⠀⠀⣿⡿⠈⠃⠘⠻⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢼⡟⠉⠀⠀⠀⠀⠙⣿⠈⢿⠆⠀⠀⠀⠀⠸⣿⣷⡀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⡰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀