Christmas pudding Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠳⠤⣄⠀⠀⠀⠀⣀⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢄⠘⡦⠰⢤⣴⡥⠀⠠⠀⢑⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠳⠔⠒⡿⠒⢧⣀⡟⠓⠴⠲⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⠀⠀⠀⢈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⡀⠀⢀⡴⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⢀⠏⠱⠀⣸⠀⠐⠧⠋⡇⢰⠛⠀⡎⢣⠀⠀⡀⠀⠀⣶⡸⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀⣸⣇⡞⠀⡆⠀⡇⠀⠀⠀⠀⠃⠸⠀⠉⠀⠰⡀⢸⢹⡀⠀⡇⣇⢧⣈⡉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⡴⠊⠁⢸⠀⢠⠁⢰⠃⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠳⠞⠈⡇⠀⡇⢻⠋⠀⠉⠲⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⡴⠋⠀⠀⠀⢸⠀⢸⣀⡞⠀⠀⠀⠀⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⢻⣀⡇⢸⡄⠀⠀⠀⠀⠳⡄⠈⢣
⠀⠀⠀⠀⠀⡘⠀⠀⡜⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡀⠀⢇
⠀⠀⠀⠀⠀⢇⠀⠀⢇⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠁⠀⠀⠀⠀⠀⢠⠃⠀⢸
⠀⠀⠀⠀⠀⠘⡜⠆⠈⢆⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣠⣤⠴⠖⠋⠁⠀⠀⠀⡀⠀⠀⣠⠎⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢁⡠⠞⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⡀⠀⠉⠉⠒⠒⠲⠶⠤⠤⠤⠤⠤⠶⠶⠒⠒⠚⠉⠉⠀⠀⢀⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠦⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠉⠁




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢈⡆⠀⡤⠴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⠚⠤⣞⣦⣜⣱⢲⣋⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠓⠚⠲⠶⠻⣿⠗⠛⠱⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⡤⠒⢲⡀⠀⡴⠁⠀⠀⠙⡆⢰⠃⠀⠙⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⠀⠀⠈⠧⠴⠃⠀⠀⠀⠀⠑⠜⠁⠀⠀⠘⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠒⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠑⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡃⠀⠀⠑⠒⠤⢤⣒⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠒⠁⡀⠠⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠀⠊⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠟⠙⠛⠛⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠳⠶⠖⠋⠻⠦⣤⣤⠀⢀⣤⠞⢃⣤⠀⠀⣀⣀⢠⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⣰⣏⣤⠤⠞⣉⠉⠛⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠦⣄⠀⠐⠛⠛⠲⢿⣶⠋⠙⣧⣴⣖⡛⠉⠓⠲⠖⠚⠉⠹⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠳⣄⣀⣤⣴⡏⠉⡿⠛⢻⡯⣭⡉⠛⠒⠀⠀⠀⠀⠀⢀⡽⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠐⠋⠁⠀⠀⠛⠚⠳⠤⠞⠁⠀⠙⢦⡀⣠⣤⢤⣤⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢷⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣠⣄⠀⠀⢠⡞⣷⠀⠀⣴⢦⠀⠀⡞⢦⠀⠀⠀⣾⢧⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡼⠁⡇⠀⠀⡾⠀⢸⣄⣰⠇⠘⣇⠀⣿⠘⣇⠀⠀⣿⠸⣇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠟⠄⢸⡇⠀⢠⠇⠀⠀⠈⠀⢀⠀⠘⢦⡟⠀⢹⡄⠀⣿⠀⠙⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠸⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠏⠀⠐⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠛⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠒⠒⠶⠶⠶⠶⠷⠒⠒⠛⠛⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⢙⣆⣐⡛⢏⣿⣦⣴⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠉⢳⣶⠿⢟⣿⣿⡈⢿⣭⡭⣟⣻⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⣤⣤⣾⡿⣱⣾⣿⣿⣿⣷⣶⣶⢌⣿⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠿⠿⣿⣿⣿⡗⣽⣾⣿⣿⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⢮⣿⣳⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣀⣀⣀⣴⠆⠀⠀⠀⣴⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠹⡄
⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⢠⣿⣆⣀⣀⣴⣷⣤⣴⣾⣧⡀⠀⠀⠈⢷⡇
⠀⠀⠀⠀⠀⠀⠳⣴⣾⣿⣿⣟⣿⣿⡁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣭⣿⣿⣿⣟⣿⣿⣷⣾⣧
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁



⣿⣿⠟⠿⠛⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠁⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣹⣁⣚⣃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢀⡙⡛⣿⠿⢻⣿⣺⡟⢫⣬⡝⣿⣬⣟⠿⣈⢻⠳⡴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣈⠅⣟⠃⣾⢏⣥⣺⣿⡞⠋⡴⢧⡘⢡⡰⡶⣽⣭⣌⠛⢤⠖⢫⠈⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣾⣥⣍⣠⣭⡥⣭⣃⣼⣯⣥⣴⣤⣤⣷⣶⣷⣶⣶⣶⣶⣿⣿⣿⠙⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣽⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢏⣽⣿⣿⡟⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⢿⣿⣿⣙⢿⣇⡣⣿⣿⣿⣿⣿⣬⡝⣿⣿⣿⠉⣥⡸⣥⣾⣿⡿⣗⣩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣼⣿⣿⡻⣿⢠⢽⡇⣿⣼⣿⡏⣭⣿⣿⣿⣟⠺⣧⡼⡗⣿⣿⣟⣿⢁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣷⣾⣾⣿⠈⢧⠔⢰⣾⣿⣿⣿⠷⠬⢻⣿⣿⣧⡀⡌⣖⢋⢹⣿⣿⢞⡊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⡤⠴⢀⢻⣿⣿⣿⣶⣟⢿⣿⣿⣿⡇⢠⣬⠅⢺⣿⣿⡿⠑⡇
⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣾⣙⢶⣸⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣯⢘⣿⣾⣿⣇⣿⢟⡇⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣻⣿⣿⣿⣿⣿⣸⣶⣶⣾⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣸⣾⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⢀⠰⡌⠀⢴⡶⢶⣿⣻⣿⣿⣿⣿⣯⣿⣭⣯⣿⣿⣿⣿⡷⢘⣹⣿⣿⣿⡯⣽⢿⡿⣿⣿⣿⢿⡿⠥⠋⠀⠀⠈⢂⡞⠇
⠀⠀⠀⠀⠙⠒⠂⠠⠍⣘⠉⠙⠛⠛⠻⠿⣷⣯⣝⣈⣿⣿⣿⣿⣓⣙⣛⣿⣿⣟⣛⣏⣭⣓⣋⣋⣋⣁⣀⠀⣀⠒⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢄⠐⡂⣬⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠤⢤⣬⣤⠤⢤⡶⢶⣶⣄⠴⣶⣶⣶⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠆⠤⠤⠜⠯⠍⠉⠛⠋⠉⠉⠉⠁⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠿⢶⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣸⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⢿⣤⣀⠀⠀⠀⠀⣼⠿⠛⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠉⢻⡷⠟⢷⣴⣿⣀⣀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣦⣄⢸⣧⣀⣠⣿⠉⠉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⠛⠛⠙⠳⣼⡟⠉⢻⣶⣶⠟⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⣤⣼⠏⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⡾⠋⢸⡇⠀⠀⣠⣴⠶⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⡿⠁⠀⢸⡇⢀⣾⠋⢀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⠀⢀⡿⠀⣾⠇⠀⠸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣾⠏⠀⠀⣾⠁⢸⡟⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⡄⠀⠀⠀⣾⠛⠻⣧⠀⠀⠀⣴⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⣸⠃⠀⣼⡇⠀⠀⠀⠀⠀⠆⠀⠈⠉⢻⣇⠀⠀⠀⣿⠀⠀⢻⡄⠀⠀⣿⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⡀⠀⢀⡏⠀⠀⣿⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣿⡇⠀⢸⡇⠀⠀⣿⠀⠀⢿⣧
⠀⠀⠀⠀⢀⣤⣶⢿⣿⡇⢠⡇⠀⣸⠁⠀⢰⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⣿⡇⠀⠀⢿⡄⠀⣿⡄⠷⢸⣿⣶⣤⡀
⠀⠀⣠⣾⠟⠉⠀⢸⣿⠁⠀⠀⠀⢿⣦⣤⡾⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠁⠀⣿⠁⠀⡀⠈⣿⠀⢹⣧⠀⢸⣿⠂⠈⠻⣶⡄
⠀⢰⣿⡏⠀⠀⠀⢸⣿⣆⠀⠀⡆⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧⠀⢿⡆⠀⣧⠀⠸⣇⠀⢻⣷⣿⡿⠀⠀⠀⠘⣿⡆
⠀⢹⣿⡆⠀⠀⠀⠈⠻⣿⣷⣦⣤⣀⣀⠀⠀⣰⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⢠⡀⠀⣿⡀⠈⣿⡀⠀⣀⣀⣿⣾⣿⡿⠛⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣿⣿⣾⣿⡿⠿⠿⢻⡿⠛⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠈⠛⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠿⣿⣦⣄⠀⠀⠀⠀⢿⣧⣀⡀⢀⣠⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣃⣀⣀⣤⣤⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣚⡛⠛⠛⢛⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⡿⠻⣧⣄⣀⡀⢀⣄⣠⣾⠟⢿⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⠀⣀⡈⠉⢙⣿⣿⡉⠉⢁⣀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⡀⠙⠻⣶⡟⠋⠙⢻⣶⠟⠋⢀⣀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣹⣿⣆⣀⣿⣆⠀⠀⣸⣿⣀⣴⣿⣏⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠙⠉⠉⠛⠿⠿⠛⠉⠙⠋⠉⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢀⣴⡶⠶⣶⣄⠀⠀⠀⠀⠀⠀⣤⣶⠶⢶⣤⡀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢀⣠⡿⠋⠀⠀⠀⠙⣷⣄⠀⠀⣠⣾⠋⠀⠀⠀⠙⢿⣄⡀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣿⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⣁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣄⠀⠀⠀⢀⡴⠋⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠹⣦⣀⠀⣀⡼⢻⡆⠀⠀⠀⠀⠀⢀⣼⠃⠀⠈⠛⠛⠛⠋⠀⠀⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠈⠙⠛⠋⠀⠈⠳⣄⣠⣄⣀⣤⣾⡁⠀⠀⣀⣠⣤⡴⠶⠶⠛⠂⠀⠀⠀⢉⣿⠆
⠀⠀⠀⠀⠀⠀⣤⣶⠟⠛⠁⠀⠀⠀⢠⣤⡶⠶⠶⠶⠶⢤⣤⣀⣿⠁⠉⣿⠁⢀⣿⣾⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⢻⡟⠉⢻⡏⠁⠈⠹⣦⣠⡶⠛⠓⠲⢦⣄⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢀⣴⠾⠛⠛⠛⢦⡀⢀⡾⠁⠀⠀⠙⠒⠛⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⠻⣾⡇⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⣦⡾⠁⠀⠀⠀⠀⠀⢻⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⣿⠻⣦⣀⣀⣀⣤⡾⢻⣆⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⣦⡀⠀⠀⠀⠀⣠⡿⢹⡇
⠀⠀⠀⣿⠀⠀⠉⠉⠉⠀⠀⠀⠙⢦⣀⣀⣀⣀⣤⠞⠁⠙⣦⡀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠙⣦⣀⠀⠀⠀⢀⣀⡴⠟⠁⠀⠈⠙⠓⠶⠖⠛⠉⠀⢸⡇
⠀⠀⠀⣿⠀⠀⢀⡴⠶⣦⡀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠙⠷⠦⣤⡤⠶⠛⠁⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⡇
⠀⠀⠀⢿⡆⠀⠸⣇⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠻⡽⠇⠀⣿⠁
⠀⠀⠀⠸⣇⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⢻⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⣠⣤⣀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⢿⡀⢾⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣴⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⣧⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠈⠳⢶⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⢄⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠑⠒⠊⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢟⡒⠂⠀⠀⠀⣀⢀⠀⠀⠈⠢⠤⠄⡶⠂⠀⠀⠀⠀⠀⣴⠀⠀⠀⡠⠋⢇⠀⠀⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠈⠱⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⠜⠙⣄⢀⠔⠁⡄⠈⠉⢉⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠐⡀⠀⠀⠀⣯⠤⠤⣀⠀⢀⠎⠀⠀⠈⠁⠀⠠⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠷⢄⣀⠀⠀⢠⠞⠒⢲⣰⠁⠀⠀⠈⢣⡯⠔⠦⣀⠄⠀⠁⠀⢀⡈⠴⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣑⠾⢄⣀⡴⠛⢆⣀⢀⣠⠞⢇⡀⣀⠧⡀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠈⠳⡦⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⡠⠔⠉⠀⠀⠈⠦⣀⣀⠔⠉⠀⠀⠘⢆⠀⢀⠤⠤⡀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⣉⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠁⠀⠀⠈⠑⠒⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠈⠉⠀⠀⠀⣠⡀⠀⠘⠃⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣤⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠙⠀⠀⢀⣀⠈⠋⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⠀⡇
⠀⠀⠀⠀⠀⠐⡟⠛⠓⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⢰⡄
⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠸⡦⣄⣀⡀⢀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠖⠒⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⢀⡄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢠⡀⠀⠈⠳⠤⣤⡄⠀⠀⣀⡤⠞⠀⡰⠋⠀⠀⢀⣸⡦
⠀⠀⠀⠀⠀⠀⠀⠰⠧⠤⠤⣄⡀⠈⠲⣄⠀⠀⢸⠒⠒⠒⢻⠀⢠⠞⠁⠀⠀⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡄⠀⠈⠑⢤⡘⡶⠲⢤⢏⡴⢃⡠⠤⠤⠼⠃⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠸⠗⠒⠓⠲⢤⣹⠷⢤⠞⠛⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠜⠣⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡄
⠀⠀⠀⠀⠀⡞⢳⡀⠀⢀⡴⡆⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⡸⠈⠉⠁⡇
⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠀⠙⠦⣤⣤⡤⠔⠋⠀⠙⣄⠀⠀⠀⠀⢀⠞⠀⠑⠦⣄⣀⡠⠔⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠒⠒⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣴⣷⡞⢋⣉⣉⡙⢳⣾⣦⣴⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⡟⢠⣿⣿⣿⣿⡄⢻⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠙⠿⠷⠈⠿⣿⣿⠿⠁⠾⠿⠋⣉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⣴⣶⣤⣴⣤⣤⣦⣤⣶⣦⣴⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡿⠟⣡⣾⡇⢸⣿⣿⣿⣿⠏⣠⣄⠹⣿⣿⣿⣿⡇⢸⣷⣌⠻⢿⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣴⣾⣿⣿⣷⠘⣿⣿⡿⠃⣴⣿⣿⣦⠘⢿⣿⣿⠃⣾⣿⣿⣷⣦⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠛⢿⣿⣿⣿⣧⣬⣡⣤⣾⣿⣿⣿⣿⣷⣤⣍⣥⣴⣿⣿⣿⣿⣿⣿⠟⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣹⣿⣿⣿⣿⣦⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⣸⣿⣟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣛⢛⣻⣻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣇⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣏⣀⣈⣿⣟⣿⠏⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣌⡙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢋⣡⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣦⣤⣬⣉⣉⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣋⣉⣉⣉⣥⣤⣴⣶⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⠄⠔⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠶⣚⠀⠀⠀⠀⢀⢠⠀⠀⠳⠤⠤⡴⠂⠀⠀⠀⠀⣠⠀⠀⠀⡔⠹⡀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠈⠱⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡴⠋⢄⣠⠎⢀⠀⠉⢩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠜⠀⠀⠀⠐⣀⠀⠀⡸⠄⠠⢄⠀⡜⠀⠀⠀⠀⠀⠐⠀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣀⣔⠉⠉⣶⡁⠀⠀⠀⣿⠊⠉⢦⠀⠀⠀⡠⠔⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠒⠚⠀⠑⠲⠐⠊⠈⠲⠰⠋⠢⣄⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⣀⠔⠊⠀⠈⠳⣄⣀⠴⠋⠀⠈⠣⡀⢀⠤⢤⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢉⣁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⡄⠀⠈⠁⠀⠀⠈⠑⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⡄⠀⠀⠀⢠⡄⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠃⠀⠀⠀⠰⠀⠀⠰⠆⠀⠀⠀⣄⠀⠀⠀⠀⠖⠀⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⡤⠴⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠉⠀⠀⣀⣀⣀⣀⣀⣀⣉⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⠋⠁⠘⠛⠙⠟⠋⠉⠉⠉⠙⠛⢉⣭⣿⣷⣶⠦⢄⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⡏⠉⠉⠀⢀⣀⣀⣠⡀⢠⣤⣄⠰⢶⣇⡀⠈⠛⠉⠉⠁⠀⢾⣿⠷⠦⣄⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀
⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠘⠿⣿⡿⠛⠛⣿⣷⣶⣿⣿⠷⣿⡏⠛⠂⠀⢰⣶⣶⡟⠒⣄⠀⠀⢸⣷⣄⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⢀⣾⠋⠉⠀⠀⢀⣀⣾⣆⠀⠀⠀⠐⡾⠿⠟⠁⠀⣡⣤⣿⠇⠀⣻⣶⠿⡷⠀⣶⣾⠏⢀⣀⡀⠈⢿⣷⡀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⢀⡾⠛⣀⡀⠀⠶⠏⠘⠃⣉⣀⣴⣤⣾⡇⠀⣤⡀⠀⠉⠉⠁⠀⠀⠉⠁⠀⠰⠾⠟⠀⣴⠞⢟⠁⠀⣈⢻⣷⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⢸⣦⣄⠈⣩⣶⠶⠂⠀⣾⣉⣍⣵⣾⣿⣧⠀⢼⣿⣤⣶⣤⣴⠇⠀⠐⢶⣀⠘⠷⠶⢿⣷⣿⢧⣄⠀⠛⠛⢿⡇⠀⠀⠀⠀⢹⣿⣿⣧
⢠⣿⣿⡿⠀⠀⠀⡠⠠⣀⣸⡿⠃⠀⢻⣿⣂⣀⣤⠉⢿⣿⣿⣿⣿⣿⣷⣾⢻⣥⣤⠭⠴⠀⠀⠀⠺⢟⣳⣶⠀⠘⠃⠘⠀⠀⠀⠀⠀⢰⣧⠀⢀⠤⡀⠀⢿⣿⣿
⢸⣿⣿⡇⠀⠀⠀⠁⠀⢸⢨⣀⠀⠀⢠⣼⡋⠁⣀⣠⣾⣿⣿⣿⣿⣿⣿⠋⠘⠟⠲⠃⠀⠀⠀⠀⠀⢠⣿⠉⠁⠀⣶⡾⠶⠀⠀⢰⣶⣿⣿⠱⠋⠀⠸⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⢰⠀⠀⠀⠸⣿⣟⠀⠈⣭⣿⣿⣍⣉⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠨⡇⠸⡆⣠⣦⠀⠰⠶⢿⣾⡟⠃⢈⣴⣿⡏⠀⠀⠀⢨⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⢄⣠⠘⠣⢿⣿⣤⣄⠸⠿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⢰⡿⢀⣛⣿⣋⡀⠀⣶⡿⠯⠀⠐⢿⣿⣿⠗⢧⠀⢀⠜⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⣿⠉⠛⠻⠿⠇⠈⠁⢴⣦⣤⣾⣿⠇⠀⠀⠉⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠈⠉⠁⠀⠶⣶⣆⣀⣀⣀⣸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟
⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿
⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠏⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⢰⡀⠀⢀⠀⠁⠀⠀⠀⠀⠀⢀⣀⡈⡃⠰⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⢏⠀⠀⠀⠀⠀⠈⠀⠰⢆⠞⣿⣿⣿⠿⠋⣡⣶⣾⠁⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠿⠋⣀⡴⣾⣿⡿⢈⣀⢤⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠺⣿⣿⣾⡿⠓⠉⢠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣯⠀⣴⡿⠛⠅⠐⡧⠀⠘
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠁⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⢋⠄⠀⠀⠀⣢
⠈⠙⠋⠙⠛⠋⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⡀⣤⣶⢟⡵⣾⣿⠋⢰⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠅⠀⢀⣠⣴⣿⣬⣷⣿⡿⠏⠈⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣛⠀⣘⣾⣿⣿⣫⣼⣿⠟⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡛⠁⢠⣴⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣧⡾⠿⠿⠿⠟⠉⠁⠀⠀⢀⡄⣺⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣴⣿⠟⡏⠁⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⡄⠈⠿⠀⠸⠛⢿⠿⡿⠋⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠢⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡿⣆⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠲⣦⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡇⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇⢸⡇⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇⢸⡇⠀⣾⠁⠀⢹⣤⣀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇⢸⡇⠈⠉⠳⡆⠀⠈⢉⣉⡽⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⠀⠀⢸⡇⢸⡇⠀⠀⠀⠻⣤⣀⣀⣤⠿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡏⠹⣆⠀⢸⡇⢸⡇⠀⠀⠀⠀⠤⠿⠅⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡟⠀⠀⠹⣆⢸⡇⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠀⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇

⠀⠀⠀⠀⠀⢀⠀⠀⠔⠂⢸⣆⠀⠠⡁⠀⠪⠁⠈⠏⠁⠈⠑⠢⠀⠀⠀⠀⠈
⠀⠀⠀⠄⠀⠀⠀⠀⢀⠠⠾⠿⡆⡘⢁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠣⠀⣄⠘⢿⠿⢶⣄⠀⠀⠠⠄⢠⣤⣤⣄⡀⠀⡀⠀⢀
⠀⣠⣤⣤⣤⡀⡀⣴⠁⠀⠀⠀⠈⠀⠀⠃⠀⢠⡀⢠⣾⡁⠀⠰⠶⡅⠈⠀⠀⡈⢀⡀⡀⠑⠀⡔⠉⠀⠀⠙⠁⠀⠅⠀⠀⠄⠀⣠⡆
⣿⣯⣽⣿⣿⣿⠟⣁⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠌⢳⠀⠀⠀⠀⠄⠤⢞⣻⣟⣁⣀⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠠⠋⠧⠄
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⣠⠴⠒⠈⠁⠀⠀⢨⢨⠂⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠈⢠⡔⠊⠀⠀⡄⠀⠀⠀⠀⢰⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⠻⠃⠀⣠⣶⠋⠀⠀⢠⡎⠀⠀⠀⠀⠀⠻⢾⠟⠺⠃⠀⠀⠀⠀⠀⠐⢄⠑⢄
⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣴⢿⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⢳⡀
⡝⣪⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠒⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⢳
⢃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢸⣨⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣩⠷⠞
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣴⣀⠀⠀⠀⠀⢸⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣏⢻⣿⣿⠧⣀⠀⠀⠘⠀⢀⡀⠀⢀⡀⠀⣀⣄⡀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⢿⣏⣰⠋⠡⡄⠁⣴⣿⠁⠸⠿⡏⢸⣟⣍⣹⣦⡀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⢸⣿⣷⠀⠀⠀⢸⠘⠃⠀⠀⠐⠁⠀⠁⠈⠙⠿⣿⣷⣄
⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⡾⠿⠛⠉⠉⠉⠙⠻⢭⣉⡉⠀⠀⠀⣀⡴⢋⣀⠀⣀⠀⠀⢺⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⠉⠓⠠⠄
⣿⣿⣷⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠿⠟⠛⠛⠉⠉⠁⠈⠀⠁⠀⠀⠐⠒⠲⠶⢷⣶⣶⣤⣤
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣠⣤⣴⡖⣀⣤⡄⠄⠀⠐⢶⣴⣦⡤⠤⣤⠄⢩⣽⡇
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠄⠀⢀⠀⠀⠀⠙⠻⣇⣹⣦⣄⣒⡐⣾⣫⣍⣱⣿⣓⣦⠤⠀⣀⡉⠉⠀⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⡶⠛⠛⠻⣄⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⣿⣿⡇⠀⠀⠀⠀⣠⠞⠁⣸⠇⠀⠀⠀⠈⠳⣄
⣿⣿⠇⠀⠀⣴⠟⠁⠀⢰⣇⠤⢐⣦⢽⢟⣛⣫⣴⠶⡄
⣿⣿⣤⡤⠾⠇⠀⠀⡾⣿⠟⢭⣭⠷⡞⠋⠋⠀⣀⣠⡄
⣿⣿⠋⠀⠀⠀⠀⠀⡇⣸⠀⠀⡇⢀⡥⠵⠗⠈⣯⠀⡇
⣿⣿⠀⠀⠀⠀⠀⠀⡇⡏⠈⠉⡏⠀⠔⢂⣡⠤⡟⠉⡇
⣿⣿⠀⠀⠀⠀⠀⠀⡗⠷⠥⢴⠖⠚⡏⢉⡇⠀⣇⡤⡇
⣿⡟⠀⠀⠀⠀⠀⢸⡏⣇⡒⢸⣀⢸⡧⢤⡏⠉⡇⠀⡇
⣿⡇⠀⠀⠀⠀⠀⠸⡇⡏⠉⢹⠍⢸⠃⢈⣇⣠⡷⠚⠃
⣿⠁⠀⠀⠀⠀⠀⢸⡦⡧⠤⣼⠧⢾⠓⢹⡇⠀⣇⣠
⣿⠀⠀⠀⠀⠀⠀⢸⠁⡇⠄⣸⠘⣸⣀⠼⠖⠊⠉
⣏⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⢶⣒⡒⠶⣤⡴⠒⠒⠒⢦⡤⠖⠒⢒⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⣠⠤⠴⠶⠤⣬⣙⣢⡱⡄⢀⣰⡋⢀⣴⣋⣭⣤⠤⠤⣤⣉⡛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣠⠖⠉⠀⠀⣠⠖⠉⠁⠀⠉⢹⠟⠉⠀⠉⠛⢏⠀⠀⠈⠙⠦⣄⠀⠉⠳⢌⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠳⡌⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⣆⠘⣆
⠀⠀⠀⠀⠀⢠⠏⠀⡴⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢧⠈⢧
⠀⠀⠀⠀⢀⡏⠀⡼⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⢧⠈⢣⡀
⠀⠀⠀⠀⡞⠀⡼⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢧⠈⢧
⠀⠀⠀⡼⠀⡼⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⢧⠈⢧
⠀⠀⠰⡇⣸⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⢧⢸⠆
⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠘⣏
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠙⠲⠶⠶⠶⠶⠒⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠲⠖⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⢀⣀⣀⡤⠼⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠦⣄⣀⣀⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠓⠶⠦⠤⠤⠴⠖⠚⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠁⠉⠀⠉⠁⠉⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡀
⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒
⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁
⠀⠀⠀⠈⡆⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠤⠔⠊⠁
⠀⠀⠀⠀⠱⡀⢈⣦⣠⠀⠀⠀⠀⠀⢦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉
⠀⠀⠀⠀⠀⠘⢿⡉⠛⠾⣄⣠⣀⣀⣾⣧⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⢀⠀⠀⠈⣿⣂⡶⢎⣿⠁⠀⣧⣿⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢀⣰⢧⣄⣘⡥⠃⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉
⠀⠀⠀⠈⠀⢒⣾⠟⢿⣿⣿⣏⡖⢈⣿⣷⡿⠁⣦⣤⢴⡶⠃⠀⠀⠀⠀⠀⠀⠐⢄⠈⠻⡗⣄⣽⡿⠃⠀⠀⠀⠀⠀⢃⣠⠜⠁
⠀⠀⠀⠀⠂⠀⠀⠀⢲⣶⣾⣿⣧⡆⡿⠋⠀⠀⣴⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢲⣿⣿⠟⢅⠀⢀⣠⣴⡿⣶⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⡭⢋⢄⣼⠀⢀⠤⠐⠈⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣱⡽⠡⠒⣈⣿⠿⡻⢋⣋⣍⣙⠋⠙⠛⡛⠋⠉⠙⠟⠉⣿
⠀⠀⠀⠀⡄⠀⠀⠀⠈⢉⣒⡋⡄⠊⠀⡀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢽⡷⢴⣿⠛⠋⡀⣀⣤⡼⠏⣽⢲⣴⠆⠀⣀⣢⠀⢀⢀⡇
⠀⠀⠀⠀⢲⣤⣴⣓⣋⢁⣰⣀⣀⢠⣀⣤⡀⣄⡠⣀⡀⣿⣿⡃⠀⠀⠀⠀⠀⠀⢸⠐⢀⠰⠾⡿⠿⠏⣿⣷⣶⣬⡿⠋⢀⡰⠺⠟⣿⠆⠀⢸⡟
⠀⠀⠀⠀⢸⡗⣟⣿⠟⠝⠉⡯⠩⠋⢹⡏⢹⠁⠯⠀⢣⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠈⣴⠰⠆⠐⢐⡩⠀⣼⣿⣟⣋⠲⠀⣉⠣⣤⣠⣀⡀⣿⠁
⠀⠀⠀⠀⠸⡇⣧⡾⣴⢟⣾⢳⢶⠰⢾⠷⢎⠴⢆⠶⠆⣿⣯⡇⠀⠀⠀⠀⠀⠀⢸⠾⢟⣠⣬⣄⡴⠀⣸⣿⡿⣸⠏⠴⠘⡦⣤⠤⠱⠊⡀⣸
⠀⠀⠀⠀⢸⡇⡃⢹⢈⣏⠳⣝⢸⠀⢀⣇⣸⢀⣸⢐⡎⣘⡗⡇⠀⠀⠀⠀⠀⠀⣸⢀⣠⣄⣉⣈⡅⠀⢛⣹⡁⠿⠤⠆⠀⣋⣈⣀⠀⠘⣿⢉
⠀⠀⠀⠀⠀⡇⣻⡛⠟⢓⠟⣒⢿⢘⣿⡞⢛⠸⢧⠻⢇⠹⣯⣇⠀⠀⠀⠀⠀⠀⢢⡴⢻⠟⣻⣿⣿⣄⣾⣏⡁⢤⡀⢀⣾⣿⣿⠟⠻⢿⢿⡇
⠀⠀⠀⠀⠀⡿⢷⡸⣌⡷⣤⡍⣴⢼⣶⣷⣾⢲⡿⣾⡗⣿⡿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣉⠐⠋⠛⠻⢿⣿⣿⣷⣾⢿⣿⣿⣷⣶⣾⣿⠿⠿⣷
⠀⠀⠀⠀⠈⣷⢸⣧⣿⣧⣿⣧⣿⣿⣿⣿⣿⣼⣿⣿⣧⣿⣷⣷⠀⠀⠀⠀⠀⠠⠚⣿⣿⣷⣄⠀⠀⠀⠉⠉⠋⠉⠛⠿⠿⠿⣿⣿⣿⣻⣷⡟
⠀⠀⠀⠀⠐⣿⢸⣟⣻⣟⣿⡟⣿⡟⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⠀⠀⠀⠀⠀⠘⢄⠋⠙⠻⢿⣧⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠠⠀⠈⠻⠿⠿⢄
⣀⣀⠀⠀⠨⣿⢸⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⡄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠙⠐⠂
⠁⠈⠉⠛⠛⠿⣼⣿⣽⣿⠟⠛⢝⣛⣿⡟⣿⣿⣿⢼⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣠⠾⠛⠛⠁⠈⢉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠒⠒⠒⠂⠀⠀⠢⠤⣀
⠀⠀⠀⠀⠀⣠⣀⣠⠴⠒⠋⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠠
⠆⠀⠄⠀⠀⠀⠉⠀⠀⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣒⣽⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠐⠒⣚⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⣯⣯⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣷⡽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠙⣿⠹⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠄⠛⠀⠀⢿⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⣿⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣤⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣾⢯⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⡀⣨⡿⠁⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠹⠿⠛⠁⠀⠂⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⣻⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⡟⠻⢿⡿⠛⢻⠿⠿⡿⢿⠻⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣼⣦⣬⣥⣤⣤⣴⣶⣷⣬⣴⣿⣥⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣴⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⠀⠀⠀⠀⢴⣿⣿⣾⣟⡉⠁⠀⠀⢰⡀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⣿⣿⡄⢀⠀⠀⠻⣿⣿⣿⣿⣀⣀⢀⠀⣸⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠽⠟⢻⣿⣿⣿⣷⣾⢺⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡟⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⣹⣿⠿⣯⣿⣿⣿⣷⣤⣿⣿⣟⡛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠀⠀⠀⠀⠉⠀⠀⠈⠛⠋⠙⠛⠃⠀⠉⠉⠉⠉⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠉⠐⠀⠤⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣤⠴⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⣄⠀⢈⣶⠄⠀⣤⠟⠁⠀⠀⠀⣄⠀⠀⠠⠀⠀⠈⠋⢼⡧⢠⡉⢏⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢈⡉⠀⠈⠛⣠⡄⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠠⢁⠈⠃⠀⢀⡀⢈⡀⠀⠸⠃⠀⠀⡈⠃⠀⢠⣀⡅⠀⢀⡙⠀⠀⠶⠇⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣀⠺⠇⠀⠀⠈⠃⠈⠀⠀⠀⠀⠀⠚⠛⠀⠀⣴⠄⠠⠄⠀⠀⠉⠀⠀⠀⠰⠋⠡⢾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡤⠰⠛⠁⠀⡀⠤⣀⠀⠉⠀⠙⡴⠀⠲⡶⠂⠀⠀⠀⠀⢲⡆⣶⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⠇⠀⠀⠘⢿⠇⠀⠈⠀⣀⠀⠀⠀⠀⠦⠀⠀⠀⡶⠀⠀⢠⠀⠀⠀⠀⠁⠀⠜⠻⠀⠀⠈⣹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠑⠂⣀⠀⠀⠀⠀⢀⣤⡀⠉⠀⠀⠀⠀⡄⠀⠀⠈⠀⢀⡀⠸⢴⣦⠀⠠⣤⠀⠀⠀⠀⢲⠆⠁⢽⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣦⠦⠘⠃⠀⢤⡈⠳⠄⠀⢀⡀⠀⠛⠀⠀⠀⠁⠀⠀⠀⢰⣏⠁⠀⠈⠓⠀⠀⠈⢰⣤⣄⠀⠀⠀⠀⢚⢿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⠧⢀⣰⣞⣣⡔⠀⠁⠶⠒⠀⠈⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠓⣤⣄⠀⠀⡞⠉⢉⡐⢡⠤⢀⡌⢲⣾⣿⡆
⠀⣀⠼⣷⣾⣿⡁⢿⡦⣿⣿⣟⠿⠃⠀⠀⠀⠀⠠⣤⠀⠀⠈⠀⠀⠠⣴⠀⠀⠸⠃⠠⠀⠀⠀⠀⠹⠀⠀⢠⠤⠀⢽⣷⢶⣶⣤⢛⣿⣿⣷⣄⣰⢄⣀
⣎⠁⠀⠈⢹⡿⣿⣾⡷⣿⣿⣿⣿⣀⣠⣷⣦⣤⡤⠈⠀⠀⢴⣿⠀⠀⠉⠀⠀⠀⣤⣀⠴⣶⡀⠀⠀⠀⠀⣀⣤⠀⠀⢈⣿⣿⣿⣴⣿⣿⣾⡿⠏⠀⠉⠛⠦
⣿⠑⠒⠤⠄⣀⡚⠛⢳⣾⣿⣿⣿⡿⢿⣟⣛⠉⠉⠐⠀⡀⠈⠃⠀⢀⣀⠀⠀⠀⢹⡋⠀⠉⠀⣰⣦⠝⢿⡿⣿⣶⣿⣿⣿⣿⣏⣿⣿⡿⠛⠁⠀⠀⠀⠀⣠
⡇⠀⠀⠀⠀⠀⠈⠙⠛⠲⠾⠤⢬⣥⣀⠀⡉⠀⠉⠀⠈⠁⠀⠀⠒⠛⠟⠳⠆⠀⠈⠡⠄⠾⠻⠿⠿⠷⠶⠤⠿⠟⠿⠛⠻⠟⠛⠁⢀⣤⠀⠐⠂⠀⠈⠛⢿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠒⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠙⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾
⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠒⠒⠂⠀⠀⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠀⠀⠐⠒⠒⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣄⡀⢀⣀⣀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠻⠿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⢀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠛⢒⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠈⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠚⠉⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠉⠃⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⢀⣀⣀⣀⣀⣀⣀⣠⠤⠶⠶⠛⠋⠁

⠀⠀⠀⠘⢓⡲⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⣀⣀⣀⠈⠓⢦⣉⠻⢛⡷⣶⣶⣿⣿⣶⣶⣶⣶⣤⣄⡉⠓⠦⣄
⠀⠀⠀⠉⠛⠿⣷⣶⡙⠷⣄⡉⠻⠉⠉⠁⠉⠉⠙⠛⠿⢿⣿⣿⣦⣤⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢟⠛⠺⡤⠀⠆⠀⠁⢰⣿⣿⣷⠀⠈⠻⣿⣿⣿⣦⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⡀⠀⠀⠀⠖⡘⠿⠅⠈⣰⣿⣦⠈⢿⣿⣿⣿⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠂⣀⠀⠀⠀⠻⣶⣿⣿⣿⣿⣷⡌⣿⣿⣿⣿⣿⣶⣯⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠈⢀⡠⡀⠀⠀⠹⣿⣿⣿⣯⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⡀⢠⡄⠀⠀⠈⠩⠙⡋⠈⠄⢤⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠐⠄⡈⢦⠀⠂⠢⠄⡬⠀⢀⠀⠀⠙⠻⠿⠿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣌⠐⠈⠀⠀⠈⠂⠀⠀⠀⠀⠐⠢⠐⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠙⠀⠢⠀⠄⠀⠠⠁⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠷⠀⢷⡄⠄⠀⡑⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠹⡆⠡⡄⢄⠈⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⢀⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣍⢠⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣶⡆⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢾⣷⣹⣿⣷⡇⡿⢸⣿⡇⣿⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⡠⡏⣰⡗⠀⣀⠀⠀⠈⠛⠳⠿⠅⢓⣃⣬⡿⠧⠟⠃⠀⠀⠠⠆⢸⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠄⣰⡿⣿⠇⠐⡿⠓⡄⠀⠀⢄⣀⠀⠀⠀⣀⡀⠀⠀⠤⠖⢰⣿⣦⢸⣿⠈⠻⡄
⠀⠀⠀⠀⢀⠀⣴⠟⢠⡏⣰⠀⢱⠀⢠⡿⡆⠀⣏⠀⣤⣦⡈⠇⢠⣾⣦⡀⢸⣿⡀⠂⢻⣧⠀⢿⣆⠀⡀
⠀⠀⢀⣴⣽⣿⠏⢠⣾⡠⠃⠀⣹⡆⢸⠁⢹⠀⡏⣸⣿⢻⣷⠀⣸⡿⣿⣇⠘⣿⣧⣀⢠⢿⣿⡄⠹⣷⡴⣄
⠀⠀⠘⣿⣿⣯⣠⣾⣿⠃⠀⠀⣿⣷⠇⠀⢸⡇⠁⢹⠉⣹⣿⠀⣾⣧⠈⢹⡀⢿⣿⡧⠈⢾⣿⣷⡄⠙⣿⡿⠃
⠀⠀⠀⠈⣿⣥⣿⣿⡇⠀⠀⢠⣿⣿⠀⢀⢻⡇⠀⢸⠀⠀⢿⡇⣿⡿⠀⠀⢇⠸⣿⣧⡀⠸⣿⣿⣷⣷⡞
⠀⠀⠀⠀⠈⠻⣿⣿⡀⠄⠀⣴⣿⡏⠀⠨⣿⣧⠀⢸⠄⣈⣼⡇⣿⣿⠀⠀⢸⡄⣿⣿⣷⣄⣽⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣼⣮⣱⣿⣿⣧⠀⣹⣿⡏⠀⣾⠀⣐⣾⡇⣿⣿⠇⠀⠸⣷⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⣧⣤⣿⣿⡇⠀⡟⢂⣹⣿⣧⣿⣿⣯⣤⣴⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠈⠙⠛⠛⠛⠛⠋⠙⠋⠉




⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣟⣿⣿⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠏⢷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡇⠀⠀⡇⠀⠀⠀⠳⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⡋⠩⠍⢸⣇⠀⠀⢇⠀⠀⢀⣶⣂⡀⠉⢉⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠊⢁⣀⡤⠒⠊⠉⠨⠖⠈⠁⠲⣎⠉⠀⠐⠠⣄⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⢙⠋⠀⣠⠎⠒⢲⡗⢠⠖⠐⢦⡜⠀⢀⡀⣠⢀⠑⠀⡆⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡎⢀⡼⠕⠀⠀⣾⠇⡼⠖⠀⠀⢿⡄⢺⡀⠉⠀⢩⠆⠹⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡞⠁⢸⡀⠀⠀⠠⡏⠀⠀⠀⠀⠀⢈⡇⠸⡧⠄⠀⠈⠾⡀⠿⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠃⡤⠞⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⢦⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠻⡬⠃⠀⠀⠀⠀⢰⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠃⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣏⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣼⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⠠⠷⣦⢤⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡃⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣄⣀⡀⠀⠀⠹⠶⣶⣤⣄⣀⢀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⣀⣀⣀⡠⠞⠚⠉⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠈⠙⠉⠉⠓⠶⠶⣶⡶⠶⠶⠛⠋⠉⠙⠋⠉⢁⣤⠶⠶⠚⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠒⠉⠉⠙⢾⡀⠀⠀⣀⣀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠓⠶⠤⠉⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⠏⢠⡿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡎⢀⣾⠃⣶⠀⡆⣠⠖⢸⡇⢠⡖⢰⣿⢰⡆⣴⢀⢰⡆⣠⡖⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⣿⠀⡇⣿⠀⣾⡇⣾⠃⣼⡇⢸⡇⢿⡏⢸⡇⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠙⠛⠁⠙⠋⠸⠇⠘⠛⠙⠇⠘⠇⠘⠁⠘⠃⠙⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠁⠀⠈⠁⠁⠀⠀⠂⠀⠀⠁⠈⠀⠀⠀⠁⠉⠀⠀⠁

⠀⠀⠐⠀⠀⡀⠒⠒⠀⠀⠀⠀⠘⠁⠀⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⠀⠀⠀⢀⡿
⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣀⣀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠻⢶⣄⢀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⣼⣯
⠣⠄⢠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠂⠐
⢄⠀⠺⡇⠠⠀⠤⠀⠂⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣤⠀⠀⠊⢱⡆⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠘⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢀⠈⠂⠰⠋⠁
⠛⢇⠈⢀⠀⠋⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣌⠁⠈⡀
⠑⠈⢂⡼⠦⠈⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠘⠇⠀⠐⠃⠀⠀⠚⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠄⠀⠀⠄⠀⠀⠀⠀⠐
⠀⠀⠈⠀⠀⢂⡀⣭⡀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠐⠛⡄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠠⠀⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠀⠐⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣤⡤⠴⠶⠖⠒⠚⠶⠶⠤⠄
⠀⠀⠀⠄⠀⠈⠀⠀⠆⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠑⠀⠐⠀⢰⡄⠀⠀⠈⠀⠀⠀⠀⢣⠀⡟⠀⢀⠀⣶⠀⠞⠋⠈⠀⠀⠀⠀⠀⠀⠄⠀⠠⠨⠉
⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠀⠀⠀⠀⡶⠀⠀⠂⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡉⠛⢡⡤⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⡐⠂⠁
⠀⠀⢶⠀⠀⠀⠰⣆⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⢀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⣴⢉⡙⢄⠁⠆⠈⠁⠀⠀⠀⠀⠀⡀⢰⠆⠀⠈⠁⠀⠀⠈
⢴⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢷⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⠃⠂⡈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⣘⢠⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⢈⡀⠀⠀⠀⠀⠁
⠀⢠⡀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⢄
⠢⠄⠀⠀⠀⠀⡀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈
⠃⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠸⡆⠈⠀⠀⠁
⠀⠀⠀⠀⠙⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⢀⣄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⢦⡄⠀⠀⠀⠀⠀⠴⠻
⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠁⠀⠀⠀⠐⠀⠀⠉
⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁⠀⠸⣇⠐⠤⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⠐⠀⠀⠀⠀⢶⠄
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡁
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠰⠀⢶⡋⠒⠄⠈⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣼⣥⠀⠀⠀⠀⠈⠁⡀⣀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠒⠛⢷⡤⠀⠀⢀⠠⣤⣀⣀⠀⠀⡴⠀⠘⠋⠀⠀⠀⠀⠀⠐⠛⠁⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠀⠉⠱⡄⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠒⠃⠙⡉⠐⠋⣴⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠠⠈⠀⣨⢀⡀⠀⣀⡀⣠⠀⠀⠀⠙
⠀⠈⠤⢁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠐⠊⠀⠁⠀⠉⠁
⠐⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠀⠀⠀⣤⡀⠀⠀⠀⠀⠚⠀⠀⢠
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠹⠦⠀⠀⠀⠃⠀⠛⠉⡱⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠻⣿⡿⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠶⢦⣤⣄⣀⠀⠀⠠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⡀⠀⠉⠉⠉⠉⠉⡉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠙⢳⣄⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣴⠿⣿⣿⣴⣿⡶⠿⠧⠾⠿⠿⣿⠿⣿⠆⡀⢠⠆⠉⠀⠀⡏⢼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢱⣾⡀⣶⣹⣞⣿⣷⡇⢚⣭⣿⣭⣽⣮⡅⣺⠄⢺⡀⠀⢠⠀⡇⣼⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⣿⣿⠫⣿⣟⣿⣿⢓⡿⣿⣿⢿⣿⠿⣿⡇⣸⡇⠀⠈⡄⣿⣿⠃
⠀⠀⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣗⣀⣗⣹⣿⣾⠑⣾⣫⣽⣿⣪⣯⣧⢉⣸⡻⣇⠀⢀⣧⣿
⠀⣴⣀⣄⣀⣀⠀⡀⢀⡀⢀⣄⣠⣄⣴⡄⠀⠀⠀⡀⣿⣿⡗⠟⣻⣿⣿⡿⢿⣿⣿⣿⣿⠉⠽⣿⣬⣿⠃⠙⢿⣿⡿⢿
⠀⣿⣿⣿⠋⢟⣻⣿⠿⠿⢻⣿⣿⠿⣿⡇⠀⠀⠀⡎⢻⣿⡗⢰⡿⣵⠻⣴⣷⣚⣿⣽⠩⠾⢫⣽⣽⡏⢲⣤⣢⣴⣖⢺
⠀⣿⣿⣿⡿⡛⣽⣇⣤⣶⣾⣾⣿⣷⣿⡇⠀⠀⠀⡇⠨⠙⡇⣾⡷⣿⠷⠛⠋⠁⠀⠀⠀⠀⠈⣉⡛⡙⠟⡻⠟⢛⣣⢸
⠀⣿⣿⣿⣿⠗⣿⣥⣿⣿⣿⠟⢋⣉⣽⡇⠀⠀⠀⣇⠐⣣⢻⣎⡕⠁⠀⣮⣷⠈⡁⠠⣤⡀⣠⢹⠀⠀⠊⠻⠧⣷⡷⢻
⠀⣿⣿⣟⠿⢷⡿⣿⡿⢋⣤⣩⡵⣲⣾⣷⣶⣶⣾⣽⣋⣿⣿⣿⡀⠀⠀⠛⠛⠁⠃⠀⠋⠀⠓⠚⡅⠀⠀⢛⣥⡟⡔⣻
⠀⣿⡗⢎⠙⢻⣛⠱⠖⠁⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢧⡀⠀⣈⣫⢰⣴⡄⢾⣽⠠⣜⡇⢀⢜⣿⠏⣾⡄⣿
⠀⣿⣿⣆⣦⣭⠁⠀⢀⣀⣤⣤⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣹⣶⣬⣁⣀⣁⢀⣀⣀⡠⢤⣴⣴⡚⠻⠠⠿⡇⣿
⠀⣿⣿⣿⣽⢻⡀⠹⠿⠟⠋⠉⣁⣼⣿⣿⣿⡿⠓⠂⠀⠉⠘⠋⢹⣗⣚⣻⣶⠶⣤⣤⣤⣤⡀⣨⣤⣦⡀⢰⣿⢾⢟⠏
⠀⠻⠿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⡟⠛⠉⠁⠀⠀⠠⠀⠀⡀⠀⢨⡉⢻⣿⣿⣦⣿⣭⣭⣿⣷⣤⣁⣭⣀⣨⣥⣴⠏
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠃⠀⢀⢀⠀⠀⠀⠀⢀⣨⣴⣾⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠋⠻⠙⠉⠉⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣬⡤⠔⠲⠅⠂⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠛⠛⠛⠛⠛⠉⢉⣩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡀⠀⠠⡔⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣄
⠉⠐⠀⠈⠀⢤⠀⠈⠍⠥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠚⠛⠓⠂⠀⠀⠀⠀⠀⠢⠀⣀⠀⠀⠀⣿⣿⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠏⠰
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⢀⠀⣀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⢀⡀⢀⡀⠀⢀⠀⡀⠀⢀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⢸⠀⡇⢸⠀⢸⠀⢸⡇⣇⠀⢸⡇⡁⠀⠀⢸⠀⢸⡇⠀⢸⠘⡇⠀⣼⢸⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢆⢸⠛⠀⢸⠀⣼⠀⢸⡇⠘⡆⢸⡇⡇⠀⠀⢸⠀⢸⡇⠀⢸⠀⠹⡄⣿⢸⢇⡄⡏⠀⠀⠠⠶⡟⠓⠿⠛⠃⠀⠖
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣇⡼⠸⠀⠀⠸⠀⢿⠀⢸⠁⢀⡿⠸⠁⠇⠀⠀⠸⠄⠀⠇⠄⢸⠀⢀⡇⠿⠸⠀⠇⡇⠀⠀⠉⠉⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⣀⠀⠀⠐⠫
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠐⣦⣀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⡀⣄⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣴⣾⣶⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤
⣿⣿⣍⣬⣋⣤⣏⣭⣍⣼⣏⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⢺⠹⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠌⢋⠔⢀⠋⡄⠈⠮⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠁⡠⠃⠀⡜⠀⢳⠀⠀⠈⠲⡕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢌⠀⣸⠀⢠⠃⠀⢰⡇⠀⠈⣧⠤⢤⡐⠉⠛⣗⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠈⠢⡸⢤⣸⣆⠀⠀⣧⡀⣐⠱⠕⠀⣿⠰⢲⡜⠀⠀⠀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡌⠙⠲⠤⣄⣀⡀⠀⠀⠀⠈⠙⠛⠉⠉⠉⠢⠤⠖⢋⣉⣉⣠⡤⠤⠖⠋⠁⠸⡄
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠢⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠑⠐⠋⠀⠀⠀⠘⢄⠀⠀⠀⢻⡄
⠀⠀⠀⢀⡇⠀⢀⡴⠒⠢⠤⠔⠋⠀⠀⢣⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠔⠛⡇
⠀⠀⠀⡸⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣿⠙⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣦⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡇⠀⣸⣿⣿⣿⣆⣀⣀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡇⠐⠛⠻⣿⣿⣿⣿⣿⣿⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣿⣧⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢈⣹⣛⠋⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣿⣿⣿⣧⠀⢸⣿⣿⣇⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡴⠦⠤⣄⣀⡤⠴⠶⠤⣀⣠⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠁⣀⣀⣈⣉⣉⡒⠦⣝⢦⠀⠀⣠⠋⢀⡠⠖⣛⣉⣉⣉⣙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠴⠋⠁⠀⣠⠴⠚⠛⠛⠛⢻⡶⠛⠛⠓⢾⡛⠉⠉⠛⠢⣄⠉⠉⠓⢦⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠑⣄⠀⠀⠈⢦⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡴⠃⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠹⡄⠹⣄
⠀⠀⠀⠀⠀⠀⡼⠁⢀⡞⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠙⣆⠘⣆
⠀⠀⠀⠀⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠘⣆⠈⢧
⠀⠀⠀⠀⢰⠃⢀⡞⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣆⠈⢧
⠀⠀⠀⢠⠏⢀⡞⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⣆⠈⢧
⠀⠀⠀⡟⢀⡞⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⣆⠘⡇
⠀⠀⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⣤⠇
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣀⡼
⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⣀⣀⡤⠤⠖⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠲⠤⢤⣀⣀⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠖⠒⠋⠉





⡿⠿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢰⡏⠉⠹⡆
⠀⠀⠀⠀⠀⠀⢳⡄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢻⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡹⣆⠀⢻⡸⣿⣭⡭⠭⠭⠿⠿⠿⠿⠭⠭⢭⣭⣟⣓⡲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⣴⢞⡿⠜⣦⠀⢷⡠⡖⠖⠒⠛⠚⠛⠛⠓⠛⠒⠲⠲⠤⣬⣉⡛⠲⢭⡳⣦
⠀⠀⠀⠀⠀⢸⡇⣏⠀⠀⣈⣓⣚⣃⣉⡷⠀⠶⠾⠿⠿⠛⠛⠿⠿⠷⠂⠀⠈⣹⠆⠀⣹⢸⡇
⠀⠀⠀⠀⠀⢠⡻⣬⡳⢦⣌⣙⡳⠦⠤⣤⣤⣤⣀⣀⣠⣤⣤⡤⠤⠴⠖⢚⣋⣡⡴⢞⣥⢿⡄
⠀⠀⠀⠀⠀⢸⡟⠶⣭⣛⡲⠯⣭⣟⣛⣒⣲⡶⠶⠶⠶⠶⢶⣖⣒⣛⣻⣭⠽⣶⣛⡭⠖⢻⡇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠉⠙⠓⠲⠾⠿⠭⠭⠭⠭⡭⠭⠭⠭⠿⠷⠖⠛⠋⠉⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠚⠁⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⡀⢤⡆⢤⡀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠉⣾⠁⠀⢸⠇
⠘⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣼⣖⡀⣀⣤
⢠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⠀⠄⠀⣀⣤⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣴⢿⣿⣯⠭⢿⣿⣿⡀⣧
⠀⣿⣿⣿⠀⣀⣀⠠⠀⣀⣈⣰⣾⠟⠻⢳⣴⣆⠀⠙⠷⠤⣶⣄⠄⠉⠀⠀⢤⣀⠈⠋⠀⠿⣿⣘⣀⣿⡿⢱⣷⢒
⠀⠿⣿⣿⣿⣿⣿⣧⢸⣇⣨⡿⠀⠀⠀⠈⠻⣿⣿⣷⣶⣄⣀⠀⠐⣦⠇⠀⢀⣉⢾⣷⠤⠠⠤⠻⣿⣍⣱⣿⣿⡆
⠀⢀⣙⣻⣿⣿⣶⠓⢻⣿⣿⣷⣄⡀⣀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣗⡊⠀⢨⣤⠚⢿⣿⣿⣦⣀⣸⠟⠛⠿⢿⣿⡦
⠘⠿⠿⠿⠿⠿⠿⣛⣻⣿⣿⣛⠻⠿⠛⠋⠉⠉⠉⠀⣨⣭⢙⠉⠉⢿⣽⣿⣿⣟⣠⠉⣿⣿⣿⢏⣽⠂⠀⠀⣀⣟⣃⣐⣶⣄
⣾⣷⠄⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣀⠑⢀⠀⠀⢻⣿⣿⣿⣿⡄⠈⡧⣦⣄⣁⣀⠶⣴⡟⣻⠛⠁
⢹⣭⣶⣷⣄⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣷⣦⣾⠉⣿⣿⡿⠁⠐⠁⡹⠩⠜⣩⡄⠹⡬⣷⡅
⢸⣧⣿⣿⣿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠉⠟⠣⣤⣭⢳⣷⡀⠺⠿⠁⢿⣷⣯⠀⡢
⠈⡻⢿⣿⣿⣿⠆⠀⠀⠀⠊⣽⣿⣿⣿⣿⣿⣿⣛⡛⠻⢿⡿⢿⣿⣿⣿⣿⡿⠂⠀⠀⠀⣾⣿⣷⣤⡄⠀⠈⠉⠁⠄⠃
⠸⣿⣿⣿⡿⡿⣠⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⢉⣿⣿⣷⣶⣶⣶⣿⠿⢿⣓⡴⠖⠀⠀⠀⣿⣿⣿⣿⣿⣀⡠⠼⡄⠈
⢸⣻⣾⣯⣟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⣿⣿⣿⣦⡝⣫⡧⠀⠀⠀⢠⣿⡟⠉⠀⠀⠉⡀
⣠⣭⡿⢿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⢮⣿⣷⣤⣴⣿⣿⡔⠄⠀⠀⠀⠀⠀⠀⠀⡀
⢻⣿⣿⣿⣿⣿⣷⢸⠛⠛⠿⠻⠀⠀⠀⠉⠉⠉⠉⠙⠛⢿⣷⣌⡻⠿⠷⠞⠛⠒⠚⠻⠯⣿⣿⣶⡴⠧⣸⣄⣠⠔
⠀⠙⠿⣿⣿⢼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠼⠿⣯⣀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠟⠛⠛⠛⠛⠻⠷⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠙⠿⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠿⠋⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣀⣤⡶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢶⣤⣀
⠀⢀⣴⠟⠋⠁⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⠙⠻⣦⡀
⣰⡟⠁⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣄⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣠⣤⣶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠙⠛⢷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡾⠛⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣮⣍⣙⡛⠛⠿⠿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾⠿⠿⠟⢛⣋⣩⣵⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣟⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⡄⠀⠀⢀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠁⠿⢿⣴⡿
⠀⠀⠀⠀⠀⠀⢉⣁⣂⣀⣀⣠⣤⡾⠟⠛⠛⣿⣿⣿⣿⣿⣶⣶⣦⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⣻⠷⠀⠀⠀⠀⠀⠐⠰
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⣰⡿⠀⠀⠘⠛⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⢐⡆⢠⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣅⣸⣿⡟⠋⠀⠛⠿⠖⣾⣦⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠘⠃⠈⠁
⠀⠀⠀⠀⠻⡿⣻⡿⠿⠆⢹⣿⢋⣿⣶⣶⣠⣤⡞⢿⣿⣷⣼⣿⠈⠈⠉⣿⣿⣿⣿⣴⣿⠿⡛⠋⣉⣿⣿⣿⣿⣿⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠐⠋⠰⣿⣤⣟⣿⣿⣿⣿⣿⣟⣹⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡗⣿⣟⠋⠈⡿⠾⠛⢿⠃
⠀⠀⠀⠀⠈⠀⠸⣶⣷⣿⣻⣿⢿⠟⠛⢿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣅⠈⠁⠀⠀⠀⠀⠀⢠⣤⣼⡇⠠⣄⡀⠀⡀⠀⡀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠋⠀⠀⠐⠘⠛⠉⠓⠋⠉⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠑⠂⠀⠘⠿⠿⠷⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠑⠀⠀⠀⠊⠑⡴⠛⢖⠲⠘⣆⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⣠⣤⡀⠉⢐⣀⣀⡀⠠⠖⠀⠀⠀⠰⡴⠟⠀⠠⠃⠀⠀⠀⠙⠻⠤⣤⣄⣀⡀⠠⠀⣠⣄⡀⠀⠜⠃
⠀⠀⠀⣤⣸⡖⠀⠀⠀⠈⠂⠀⠉⠁⠀⠀⣤⣄⡀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠐⠒⠒⠦
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⣠⠆⠀⢠⣄⢠⢢⠆⢤⢦⡄⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡏⢹⢿⡿⣶⣤⣀⣀⠀⠸⢄⣀⡄⠀⠀⠁⠀⠀⠈⠀⠋⠀⠀⠀⠀⠸⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣃⡏⢻⢾⣇⣟⢹⢟⣿⣷⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣿⣿⣭⡗⣿⢼⣇⡏⢻⢿⣿⠀⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣢⡟⠁⠀⣿⣿⢳⡧⣿⣺⠈⡏⢻⢾⣿⠀⠀⢰⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢈⣿⠗⣲⡶⢿⣿⢺⣇⣇⢸⢙⡗⣾⣼⣿⠀⠀⠀⠀⠀⠛⢿⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣶⡀⢐⣫⣀⡠⠹⣾⣷⡏⢹⢺⡧⣽⣸⣟⠀⠀⠀⠀⣠⣶⣭⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⢼⣽⡟⣺⢼⣟⣿⢸⡏⠀⠀⢨⣠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢰⣿⠿⣿⣾⣇⣿⢸⡇⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣸⠋⠀⠀⠉⠛⠿⣿⣇⣠⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡘⣧⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢿⣿⡇⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⢿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⠻⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠻⢶⣤⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⡀⠀⠀⢹⣧⣼⠟⠉⠀⣩⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠿⠛⠛⠋⠉⠛⠿⠶⠶⠿⠿⠶⠾⠟⠋⠉⠛⠛⠻⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠙⠛⠷⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠟⠛⠉⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡿⠁⢀⣤⣶⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠶⣶⣦⣤⣀⣀
⠀⠀⢀⣠⣴⠾⠟⠋⠉⠀⣰⡿⠿⠶⠟⠋⠀⠹⣷⡀⣠⡾⠟⠛⠻⣦⠀⠀⠀⠀⣠⡾⠛⠙⠻⢷⣄⠀⠀⠀⣀⣴⠟⣿⡄⠀⠀⠉⠉⠛⠿⢶⣦⣄⡀
⢀⣴⠟⠋⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠙⢷⣤⣤⡾⠋⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠁⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⠶⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠉⠛⠷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⠶⠾⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠐⠀⡇⠀⠉⠙⠋⠉⠈⠉⠛⠛⠛⠋⠛⠛⠉
⠀⠀⠀⠀⠀⣠⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⣀⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠐⠂⠋⠓⠀⠉⠚⠢⡇⠖⣀
⠀⠀⠀⠈⠙⣲⣦⣥⣤⣀⣀⣀⣀⣀⣀⣀⣠⣠⢿⣷⣀⡉⣙⣇⡀⠀⠀⠀⠰⠛⠦⢇⡲⠭⢗⣮⠉⠄⣀
⢠⣤⣶⡒⣯⣭⣶⡿⣿⠋⠉⠙⠃⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡶⣦⢴⢞⣿⣷⠀⠈⢀⣄⠀⠀⠈⡙
⠀⠉⠛⠛⠈⠻⠻⠿⠿⢶⣀⢀⣚⣲⣤⣭⠿⠍⠻⠟⠛⢋⠀⠀⠤⢶⣿⣼⠈⠀⠀⣨⡛⠋⣉⡰⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠁

⢠⠀⠀⢐⡀⡀⠀⣀⡀⠀⡀⣀⡀⢀⠀⠀⢀⠀⡀⠀⠐⠀⣀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠢⠀⠓⠃⠙⠃⠅⠳⠀⠂⠈⠛⠃⠚⠊⠦⠀⠀⠘⠲⠸⠊⠘⡁⢇⡀⠀⠻⢠⡀⠀⠘⠀⠀⠀⡍⠀⠀⠀⠈⠉⠉⠉⠉⠉⡛
⠀⠦⠤⠀⠀⡀⠀⠀⠀⣎⡱⠼⢴⢰⡀⢲⠄⠀⠐⣿⠀⡆⠲⡆⠀⢶⠂⡒⠀⠂⠀⢀⡀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠠⠤⠄⠀⣀⣀⣈⣀⣀⣐⣒⣒⣂⡐⠀⠀⠀⠀⠚
⠀⠀⠀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡿⠯⠍⠡⠄⣀⣀⣉⣉⣉⣉⣉⡉⢉⡙⠿⡿⠗⢲⣄⣀
⠀⠀⠀⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠇⠀⢀⣖⣄⢠⢄⡀⠀⣠⢀⠈⢁⢉⠉⢉⢉⢉⠉⡋⠈⠉⠉⠉⠛⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⢉⣀⠑⠈⠙⡛⠚⠂⠉⠂⠉⠀⠙⠉⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠨⢄⠇⣇⠀⠉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠟⠃⡆⡀⣟⡆⣓⠄⡐⣆⣂⠊⡀
⠀⠀⠀⠙⠉⠐⠒⠒⠒⠒⠒⠒⠂⠒⠒⠏⠙⠓⠲⠶⠤⠤⠬⠥⠬⠤⠥⠤⣥⡬⢥⠉⠤⠰⡧⠤⠤⠤⠤⠤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⡄⢂⠀⡠⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠉⠉⠉⠉⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠺⠦⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠤⠤⠤⠤⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠖⢀⠀⢀⣀⢀⣠⠀⠀⠀⢠⡄⠙⢠⣀⠄⡄⠀⡠⠈⢉⠅⠀⡡⣉⣈⡌⣡⠀⢲
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠁⣤⠈⠈⠀⠉⠀⠁⢉⣁⣁⠀⠁⠉⠉⠁⠈⠠⠰
⠀⠀⠀⠘⠲⠤⣄⣄⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣄⣀⣀⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠛⠛⠳⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⢴⠚⣛⢫⣀⡤⠀⠀⣖⣰⣲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠝⠁⠘⠢⠴⠚⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣋⣉⡙⠛⣋⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⣤⣤⣴⣦⣄⠀⠾⣿⣿⣿⢿⣿⣿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢯⠉⠲⢤⣤⣄⣀⣀⣀⣁⣴⡞⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⣿⣿⣿⠉⡉⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⢿⡿⠷⣤⣼⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠁⢾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⡟⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢿⣾⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠘⠶⡤⣄⣰⣀⣀⣰⡄⠀⠀⠀⠀⠀⠐⢏⣳⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠫⣽⣿⣿⣤⡙⠳⣀⡀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣟⠻⠀⠀⣀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣿⣯⡾⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣶⡞⢧⡄⠀⠀⠀⠀⠈⢻⣿⣷⣤⣦⡀⠀⠀⠀⠙⢿⣿⣿⢛⣿⣿⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⡉⠃⣀⡄⠀⠠⣀⠁⠈⢻⣿⣿⣄⠀⠀⢠⠾⣿⣿⣿⡿⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣧⣄⠀⠈⠛⠓⠬⠙⠿⣿⣿⡞⠻⢷⡈⢿⠌⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣦⣌⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠺⡷⡄⠻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦⣆⠀⠀⠀⠙⠢⣌⣷⡙⠲⢜⣿⡦⡘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣈⠓⣆⠀⠀⠀⠈⠈⢻⣶⢆⣿⡷⢮⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣌⡓⢤⣀⣀⢀⡎⢣⡈⠉⠁⠀⠉⠻⢿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⣀⠀⠀⠀⠙⠪⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠋⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢰⡆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣿⡄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠀⠀⠀⠀⠘⣟⢦⡀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠈⠳⣝⡢⣄⡈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⡠⠋⣴⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⡀⠀⠀⠀⠉⠓⠿⠷⠦⢤⠉⠒⠤⣀
⠀⠀⠀⢀⡞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠭⣗⣒⣲⠤⠤⣄⣀⣀⠀⠀⠀⠀⠉⠲⢤⣄⣀
⠀⣠⢴⠏⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠻⠿⣶⣤⡀⠀⠀⠀⠈⠙⢿⡲⢤⡀
⡜⠁⡞⠀⠀⠀⠀⠀⠈⠻⣗⡦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠙⢆⠙
⡿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠾⠯⠭⠭⠭⠭⠭⠭⠿⠿⠿⠷⢶⣤⣀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢸⡾
⡇⠀⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⢀⣀⡤⠴⠚⠁
⣧⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠲⠦⠤⠤⠤⠤⣤⣄⣀⣀⣀⣠⣤⣤⠤⠤⠤⠤⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⢠
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠒⠛⠉⠉⠀⠀⣨⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣓⣒⣶⣤⣤⣤⣤⣤⣤⣤⣴⣖⣒⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠛⠳⠶⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠑⠢⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⡆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⣀⡄⠠⡄⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⣄⠘⠉⠀⠀⠀⠈⠐⠒⠤⢀⠠⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠙⢦⡀⠐⠶⠓⠂⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠈⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠈⠛⠀⠀⢀⣤⢾⢠⠋⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠊⠁⢂⠇⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠎⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⡰⠀⠀⢀⣀⡤⠶⢶⣉⣽⠓⠒⠒⣳⣦
⠀⠀⠀⢀⣾⣘⣟⣛⣛⣻⣽⣧⡿⠟⠒⠀⣀⣠⠧⣖⣚⣩⠽⠒⠺⢉⣀⡠⠵⠲⠊⠁⠀⡆
⠀⠀⠀⢸⡏⠻⣿⠿⣛⡽⠏⠀⠁⠀⢰⡿⢥⣧⣖⡋⣉⣩⡶⡖⠒⠉⢹⠀⠂⠀⣇⠓⠀⢷
⠀⠀⠀⠈⣷⡀⠀⠚⠿⣄⠀⠀⠀⠀⠈⠁⠀⢻⠈⠹⡋⠀⠀⢛⠀⠀⠨⡦⠒⠊⢹⠀⠀⠘
⠀⠀⠀⠀⠘⣷⣠⣤⣤⣾⡿⣦⠀⠀⠀⠀⠀⣼⣤⣀⣧⠀⠐⠚⠋⠀⠀⢣⠀⠀⠀⡄⣀⡠⣗
⠀⠀⠀⠀⠀⠹⠛⣿⣿⣿⣹⣿⣇⠀⠀⠀⠀⠸⡆⠀⢸⠀⢀⠀⢇⠀⠀⣸⡤⠔⠒⢏⠀⢠⢺
⠀⠀⠀⠀⠀⠀⠐⣿⢿⣾⣟⣿⣟⠀⠀⠀⠀⠀⡇⠀⢈⣆⣈⠠⢼⡒⠉⠀⡇⠀⣀⠸⣀⡠⠼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⡀⠀⠀⠀⢠⣿⠉⠉⢹⠀⠀⠀⡇⠀⠀⣸⡤⠒⠈⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣿⣿⣿⡇⠀⠀⠀⣼⣉⡀⠀⢘⣆⣀⠤⢾⠊⠁⠈⡇⠀⠀⢀⣀⠄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⣿⡇⠀⠀⣰⡏⠈⡏⠉⠉⡏⠀⠀⠘⡆⠀⠀⣥⠴⠚⢻⡤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣿⣿⣧⡄⠉⠹⣟⣀⣓⡀⠀⢰⣀⣠⡤⢷⠊⣁⠼⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡿⣿⣿⣷⢰⠀⢯⣉⣹⣉⣉⣉⣏⠠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿

⠀⠀⠀⠀⠀⠀⠤⠆⣍⣀⡁⣠⡠⠀⠀⢀
⠀⠀⠀⠀⠀⢀⢘⡀⣀⡀⠛⣫⠤⠤⠤⠶⠠⠠⠠⠤⠠⠈⠀⠠⠤⠤⠤⠄⠂⠀⠤⠤⢬⠨⢅⠤⠤⠤⡬⠄⠀⠀⠄⢄⢉⠀⣄
⠀⠀⠀⠀⡠⠁⠈⠂⡬⠃⠀⢻⠀⠒⠓⠃⠐⠀⠐⠘⠐⠂⠀⠀⠂⠐⠀⡀⠀⡀⠁⠐⠒⣀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠨⠭⠀⢂⠁⠀⠀⠀⣸⠀⠀⡉⠀⠀⠀⠀⠀⠈⠀⠀⡄⠈⡬⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⢉⠀⢩⡙⠀⠀⠈⠀⠀⠁⠀⡇
⠀⠀⠀⠙⠓⠛⠙⠓⠦⠄⢤⡏⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠜⠐⠀⠒⠒⠀⠐⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠠⠀⠠⡠⠄⠄⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠆⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠀⠀⡄⢀⠀⠀⠐⠂⠒⠀⠀⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡈⠻⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⠔⠂⠉⠀⠀⠨⣀⢀⡒⠄⠈⣁⡘⠀⠀⠁⠀⠀⠁⢠⡞⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠛⠶⣦⠀⠀⡀⠀⠀⢲⠋⢁⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠉⠑⠄⠀⠀⠀⠀⠀⠘⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠐⠒⠓⢃⢈⡈⠬⣄⡿⠏⣩⠍⠭⠮⠉⠍⠉⠦⠀⣀⡁⠈⠈⠀⠁⠛⠘⡀⠐⠒⡒⠒⠂⢸⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⣚⢇⠒⠒⠚⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⡽⠀⠒⡀⢀⠃⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⣄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠂⠀⢸⡀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠉⢛⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠁⢀⠀⢸⢃⣠⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠗⣀⣀⠀⠄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠛⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡉⣀⡽⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠀⠤⢀⠙⠶⠷⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠑⠈⠉⠻⠂⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠴⡇⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠄⠀⠀⠠⠄⠀⠈⢢⠀⠀⠀⢀⠄⠀⠈⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠉⠀⠀⠀⠀⠀⣤⡴⢦⣤⣶⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠘⡗⠀⠀⠀⠘⠛⠳⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣞⣴⠟⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠍⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣐⣚⣻⣶⣭⣗⠒⠦⣄⣀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢿⠙⠶⣶⣖⣛⡍⣛⣦⣤⣩⣶⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⣅⣺⠀⠀⣿⠘⠉⢽⠛⠶⣶⠤⠿⢿⣷⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⢛⣿⣼⠟⠳⣾⣄⡃⣻⠀⠀⣗⠀⢠⠰⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣫⣴⣾⣿⢩⠎⡀⠁⣿⢀⡈⢻⠲⠤⣧⣤⡤⢤⡷⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⣡⣿⣤⡀⠁⠫⣈⡁⢸⠀⠀⣷⠀⠐⠀⣧⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⢾⣿⣿⣿⡟⣷⡀⢻⣭⢿⠳⠤⣿⣄⣨⣭⣷⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⣿⣿⣿⢻⣿⣧⠀⢹⣿⠄⠀⢹⡂⣀⠀⡧⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⣿⣧⣿⣿⣿⠀⢈⣿⣤⣅⣾⣀⣉⣠⣧⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⣿⣿⣿⣿⡇⠀⢸⣿⠛⠀⣿⠁⡀⠀⣷⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠃⣠⣾⣿⣀⡂⢺⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣯⣀⣹⠟⢸⠈⣉⢹⠛⠛⠛⡿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢇⣸⡈⠁⢸⡇⠠⠄⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠛⣿⣿⣿⣞⡍⠙⠓⠿⢤⠤⠤⠷⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⠃

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠐⠀⠀⠦⠀⠀⠀⢰⠁⠀⠈⢁⠔⠀⠀⠀⠈⠟⣉⡆⠀⠀⠀⠀⠀⠀⣴⠤⠀⠀⠠⠀⠀⠀⠀⡀⠔⠿⢧⠄
⠀⠀⣌⠑⠓⣾⣛⣷⠀⢰⣿⡿⢿⣆⣠⡄⠀⠀⡀⠀⠀⠀⢰⣦⠀⠀⠀⣿⣶⣬⣷⡖⣰⣆⠀⠀⠀⢰⣿⠓⠒⠊⠑⡆
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠈⠀⡈⣇⡏⡟⠀⠚⠀⠀⠘⠿⠅⠀⠙⠷⠠⣠⠄⢠⣷⢶⡤⠀⢰⡇
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠙⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠛⠛⠁⠀⠀⠂⠀⠀⣀⣀⠀⢀⣤⢤⣤⠄⢀⣇⣀⣁⠀⢈⡁
⠀⠀⠀⠀⢀⢐⠀⠠⢀⡢⠀⠀⠀⠀⣼⣟⣙⣻⠟⠁⠀⠀⠀⠀⠀⠀⠠⢭⠀⠿⠜⠶⠲⠶⠶⠶⠂⠀⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠸⣟⣟⡶⢶⠤⣥⡁⠀⠀⠐⠀⠤⠍⣉⣿⠀⠀⢀⢄⠂⠀⣠⣴⣲⠄⠀⠀⠀⠀⢀⣘⣃⡚⠛⢗⠂⣀⡆
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⣝⠀⠀⠯⣉⡓⠒⢤⣉⠁⠀⠈⠀⠀⠀⠰⣾⡟⠀⠀⠀⢠⣀⢈⣉⡉⢁⣀⡤⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠈⠙⠒⠟⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⠁⢀⣤⣤⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠀⢸⣇⡀⣴⣿⣿⣿⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣿⣿⡿⢛⣷⣼⠚⠿⢿⣿⣿⣿⣿⠉⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣾⡟⠀⠿⣿⠿⡆⣾⣶⣿⣿⣿⣿⡧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⣿⣿⡿⠃⢀⡀⣸⣶⣧⣸⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢶⣒⣶⣿⣿⣿⣿⣶⣤⣼⣿⡋⠅⡁⠃⠀⠉⠉⠻⡿⢿⣿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣊⣱⣿⠿⢿⣿⣿⣿⣿⣿⡃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⠴⠿⠿⣾⣯⣹⣋⣩⡿⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣠⢄⣼⣿⠋⠀⢠⣾⣿⣿⣿⣿⣿⣥⡂⢁⡀⠀⠀⠀⠀⠀⠀⣶⢊⡅⢶⣷⣶⣤⠈⠙⠉⠍⠐⠿⣿⣲⣄
⠀⠀⠀⠀⠀⠀⠈⣡⣼⠋⠉⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣄⠂⠀⠀⠀⣀⢚⣿⣮⣼⣾⣭⣿⣿⣿⡆⢀⠉⠀⠤⠀⢉⠛⠧
⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⣴⣯⣿⣿⣿⣿⣧⡙⠻⠟⠛⣿⡿⠏⠢⠀⣸⡿⢻⣿⣿⡟⠉⠉⠉⠉⠠⣾⣿⣇
⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⢸⣿⣷⣿⣿⣿⣿⡜⣇⠀⡃⠀⠈⠀⠀⣴⢿⣿⢧⣟⣿⣿⠛⠓⣶⠀⠀⠀⠈⠻⣟⣳⡄
⠀⠀⠀⣀⣼⣿⣿⠁⠀⢠⢿⠀⣿⣿⣿⣿⣯⢠⣿⡼⠀⠀⠀⢀⠰⠋⣼⣟⠈⣿⣿⢯⠉⠉⣿⣧⡀⠀⠀⠀⢽⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠂⠐⢸⣿⣿⣿⣿⡇⢸⡟⠀⠒⠋⠉⠀⠀⠀⣿⣿⠀⠘⣿⣿⡄⠈⢻⡁⣓⡀⠀⠉⠐⠻⢿⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢂⡀⢿⣿⣿⣿⣿⠏⡎⠀⠀⠀⠀⢀⠀⠀⢨⣿⣿⠀⠀⢹⣿⡟⠀⠀⠣⣭⣧⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⣿⣿⡿⣿⡆⡇⠀⠀⠀⠀⠀⠀⠀⡘⢿⣿⠆⠀⠘⣿⡇⠀⠀⠀⠹⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠎⠀⠘⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⣸⠆⠀⠀⢻⣿⠆⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⠂⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⢸⣿⡄⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⡇

⡰⠂⠈⠁⠀⠀⠀⠉⠉⠀⠐⠂⠀⠀⠀⠈⠉⠉⠉⠉⠒⡀
⠃⠀⠀⠀⠂
⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡶⠲⡴⣦⠀⣤⣤⣤⣤⣤⠀⠤⣤⣤⡄⠀⠠⣤⠀⣤⣄⡤⢰⣤⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⣤⠀⢠⡀⢠⡄⣤⣤⣤⣤⡄⣤⣤⣤⣤⣤⣤⣤⢀⣤⣤⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣄⠀⣀⢀⡀⢠⡄⢀⣀⣤⣄⠀⠀⣄⣀⣄⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣈⣁⣀⡀⢈⣀⣀⣀⣀⡀⢀⣀⣀⢀⣀⣀⡀⣀⣀⣀⢁⣀⣀⣀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣦⣴⣿⠇⠀⠀⠀⠀⢈⡉⣉⣉⣁⠈⢁⣉⣁⠉⠁⣈⢉⣁⡀⠉⣉⡀⠈⢉⣁⡈⠉⣉⣉⢉⡀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣦⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠉⢀⣈⣉⣉⠉⢁⣀⣉⠁⢀⠈⡉⢉⢀⡉⠉⣈⡁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠉⠈⠉⠀⠉⠀⠉⠁⠈⠉⠉⠉⠁⠉⠉⠉⠁⠉⠁⠉⠉⠈⠁⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠋⠉⠀⠈⠃⠀⠙⠋⠁⠀⠛⠋⠙⠛⠉⠋⠀⠀⠙⠛⠀⠀⠘⠛⠋⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠀⠃⠈⠛⠛⠁⠈⠛⠁⠘⠛⠀⠘⠛⠙⠁⠛⠀⠋⠛⠀⠛⠛⠛⠃
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠠⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣶⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣤⡀⠀⠀⠀⠀⠛⠛⠛⠛⠃
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠶⢦⣤⣤⣤⣤⣤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⡆
⠀⠀⢾⡟⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠚⠒⠛⠛⠂
⠀⠀⢸⡇⢹⡇⢻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠀⢀⣀⣀⣠⡤⠄
⠀⠀⠸⣷⡈⢣⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣵⣷⣿⣿⡟⠁
⠀⠀⠀⠘⣷⣄⠀⠀⢤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣸⠟⠃⢜⣼⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠈⠻⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⢐⣤⣿⣿⣿⣿⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣋⣥⣌⣠⣶⣿⣿⣿⠟⠻⠿⠿⣿⣶⣦⠠⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⣴⡖⠀⣿⠋⠉⣉⣻⡿⠁⣀⣠⡾⠛⣧⣤⣮⣉⣴⣶⣷⣄⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡐⢀⣿⡀⣾⣿⣟⣁⣼⡿⣿⡀⠺⢿⡿⣿⣿⡈⢹⣿⣿⣄⣸⣿⠵⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣄⠻⣧⣾⣿⣿⣿⠛⢉⣙⣻⣷⣿⣿⣦⣤⣠⣨⣯⣤⣾⢿⣿⠻⣿⣿⣶⡄⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠴⢶⣶⣯⣛⢁⣼⣿⡀⢿⣿⣿⣿⣿⣿⡋⠀⠚⠃⠈⢉⣉⣿⡇⠀⣿⢻⣿⣿⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣦⡀⠈⢉⣿⣿⣷⣿⠿⢿⣤⣿⡏⣭⡉⢿⣿⣷⣶⠶⢶⡾⣿⣿⣁⣴⣿⣴⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⣾⣿⣿⣿⣿⣟⠻⣿⡿⠛⢻⣷⣾⠿⣿⢶⣾⣿⣿⣿⣿⣆⡨⣿⣿⣷⣿⣿⣦⣄⣀⣀⣤⣼⣷⣿⣿⣿⠿⣩⣾⣿⣧⣤⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⣿⡇⠙⠃⠀⠈⠻⠿⣶⣦⣈⣩⣿⣿⣻⡟⢻⣿⣿⣿⣿⣿⣭⠒⠋⠩⠉⠩⠉⢹⣿⣿⣿⣿⣿⡿⠿⠉⠋⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠁⠀⠀⠀⠀⠘⣦⠈⢯⣽⣿⣿⣻⣿⡆⠉⢿⡟⠻⠿⠿⣿⣿⣶⣤⣤⣶⣾⠟⠉⢹⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡹⢿⣿⣽⣿⣿⢿⣶⣤⣤⣤⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠙
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣽⣿⣿⣌⠃⠽⢿⣿⣿
⠀⠀⠀⠀⠀⠘⣤⡀⠀⠀⠀⠐⠏⠽⢿⣷⣦⣴⣶⣴⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣶⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠴⣶⣶⡶⠀⣠⣴⢶⣤⣀⠀⣠⣶⣶⣦⡀⠀⠀⣴⡆⠀⠀⠀⠀⠉⠛⢿⣿⣿
⠀⠀⠄⠀⢰⣏⣹⣿⣇⠀⠀⣿⣿⡇⣸⣿⡇⠀⣿⣿⡆⢸⣿⣽⣿⠇⠀⣼⢿⣿⡄⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⢰⣿⠉⠋⢿⣿⡆⠀⣿⣿⡁⠘⢿⣧⣠⣿⠟⠁⢼⣿⢿⣷⡀⢸⠷⠼⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣤⣥⣀⣠⡀⠁⢀⣄⣀⣀⣀⣠⡀⠀⢈⣀⢀⣀⣀⣁⡄⠀⢀⣀⡀⣀⣌⣁⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠸⠿⣿⡇⠀⠿⠼⠷⠿⡼⢿⠇⠀⠸⣿⢿⣯⣿⡿⠃⠀⢘⡿⢧⣿⣧⠸⠇
⠀⠀⠀⢻⣷⡦⢤⣶⡶⠂⢰⡆⡰⠒⠶⠀⠲⠆⠐⠶⠀⠲⡶⠒⠀⡶⠲⣆⠤⣠⣶⠄
⠀⠀⠀⠉⠉⠿⠾⠿⠿⠇⠘⠋⠁⠰⠊⠉⠛⠆⠛⠂⠀⠘⠿⠁⠿⠋⠂⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣐⣒⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠾⢛⢹⡿⠀⢻⡿⣦⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣀⡴⠂⣠⡟⢸⠇⠀⠘⠃⢹⣧⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡴⠞⠋⢀⡴⠋⢠⡟⠀⢠⡶⠟⠛⠛⠻⣦⣼⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣠⡴⠋⠁⣠⠟⠀⢠⡟⠀⠀⠀⠀⠰⣾⣯⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠋⠁⠀⣠⠞⠉⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⣷⣤⠴⠆⠀⠀⠀⣠⡾⠃⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣾⢣⣄⠀⠀⠈⠙⠶⣦⣄⣀⣛⣁⣤⣶⣀⣹⣷⣤⣀⡀⠀⠀⠀⢀⣴⠟⠁⠈⣿
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠉⠛⠷⠶⣤⣤⣤⣈⣉⣉⣉⣉⠉⠉⠁⠀⠀⠉⠙⠻⣿⣛⣫⣥⡴⠟⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠃⠈⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⣸⠇⠀⠀⣀⡀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣦⡀⠀⢻⡆
⠀⠀⠀⢠⡿⠀⢀⡾⠋⣷⠀⠀⢠⡟⠈⣿⠀⠀⠀⢀⣾⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷⡀⣸⣧
⠀⠀⠀⣸⡇⣠⡾⠁⠀⠻⣦⡶⠟⠀⠀⢿⡀⠀⢀⣾⠃⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠈⠛⠋⢿⡀
⠀⠀⢀⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟
⠀⠀⠀⠉⠙⠛⠳⠶⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠞⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠴⠦⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠖⠚⠉⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣼⠀⠈⠉⠑⢦⠀⢀⡴⢢⠀⡠⣄⠀⠀⡔⠓⠒⠁⠀⠀⠀⢻⠉⠉⠙⠒⠲⠤⣀
⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⢀⡏⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠀⠘⡀⢀⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⡀⠀⠀⠈⠑⢦⡀
⠀⠀⣠⠞⠁⠀⠀⡠⠤⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⠀⢀⣨⠇⠀⠙⣦⠀⠀⠀⠀⢹⡄
⠀⢰⠃⠀⠀⠀⢸⡁⠀⠀⠣⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⢀⣤⠖⠃⠀⠀⠀⠀⣸⠁
⠀⠘⡆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠉⠙⠒⠲⠦⠤⠤⠤⣤⡤⠤⠤⠴⠒⠚⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠖⡭⠽⠯⡖⠶⣖⣒⣒⣒⣒⡒⣒⣒⣲⡄⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠉⠓⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠓⠭⠭⠴⠚⠉⠀⠀⠀⠀⠈⠉⠉⠉⢁⣀⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⠤⠤⠤⣤⣤⡤⠤⠤⠤⠴⠖⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢶⡟⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠟⠛⠛⠁⠀⠀⠉⠀⠀⠀⠀⠈⠛⠶⣶⣦⣄
⠀⠀⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠠⠘⠗⠀⠀⠠⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠢⢀⠀⠤⠂⠀⠈⠀⠈⣧⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠔⠈⠀⠌⠀⠀⠀⡀⠀⢐⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡯⠴⠶⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⢦⡁⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⢀⠀⠀⠀⠀⠀⢿⣞⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣤⣤⣶⠀⠀⠀⠉⢀⠈⠁⣀⣀⣀⣠⣴⠟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠈⠀⠁⠀⠀⠈⠛⠳⠶⠶⠶⠾⠛⠳⠶⣤⣤⣤⡴⠾⠛⠉⠉⠉⠁⠀⠘⣦⣀⣀⣠⡿⠛⠛⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣶⣦⣶⣶⣦⣍⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡉⠉⠈⠹⠋
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠉⠉⢀⣶⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈
⠀⠀⠀⠀⢀⣤⣶⠄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠿⢵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠁⠀⢀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠷⢿⣶⣿⣶⣴⡖⠋⠁⠁⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠛⢿⡿⠟⣸⣷⡄⠀⠈⠛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢃⡿⠁⠀⢺⠀⢈⣿⣦⣀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢣⣾⡁⠀⠀⠈⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⣿⡿⠃⠀⠀⠀⡼⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⢿⢿⣿⠇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠈
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠠⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⣀⠤⠄⠤⠤⠠⠤⠀⣀⠁⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⡀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠉⠓⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠔⠊⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡔⡫⠋⠉⠁⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡜⡼⠁⠀⠤⠒⠒⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡸⣰⠁⠀⠀⠀⢀⣀⡠⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢠⠇⡅⠀⠀⠀⠀⠀⢀⠤⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣜⠎⠀⠀⠀⠉⣆⠠⠃⢀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⡝⡠⢀⠄⢄⠀⠀⡀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⡎⠀⢀⠠⠔⠋⠁⠈⠔⠋⠀⢠⠐⠊⠀⣠⠃⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢃⡀⠄⠐⠀⢀⢀⡀⠀⠐⠈⠁⠀⠀⠊⠁⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠐⠒⠀⠀⠤⠂⠀⠀⠜⠁⠁⠀⠀⢀⠔⠁⠀⠀⢀⡴⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠈⠒⠀⠤⠀⠀⠀⠀⠀⢀⠠⡠⠔⠁⠁⠀⢠⠀⢀⠼⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠋
⠀⠀⠀⠀⠀⠐⠂⠠⢄⠀⠀⡎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⢀⢀⣀⣀⠀⠤⠄⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠂⠐⠓⢄⡀⣀⣀⠀⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁