Teapot Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠚⠃⠀⠀⠀⠀⠛⠲⠤⣀⡀
⠀⢀⣠⣤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣾⡛⠋⠉⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠿⠀⠀⠀⢀⣠⡶⠟⠛⠛⠛⢿⣦⡀
⠀⠉⠻⣦⠀⠀⠀⠈⢳⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⠤⠖⠋⠁⠀⣀⠠⠤⣀⠀⠹⣿⡄
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢀⠤⠀⠁⠀⠀⠀⠈⠢⠀⢹⣿
⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⢸⡄⠀⠀⠀⠀⢀⡜⢀⣾⡿
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢸⠇⠀⠀⢀⡤⠋⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⣿⠤⠄⠒⠉⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠛⠁⠀⠀⢀⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠉⠓⠒⠺⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠶⠛⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠋⠉⠉⠛⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢡⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢻⣿⣆⣴⣾⣫⣶⣶⣤⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⢟⣵⠿⣫⣾⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣀⣼⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣵⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⢿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⣲⣿⣽⣿⣿⣸⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡼⠋⠉⠉⠉⠻⢿⣧⢿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠛⠷⢾⣿⣿⣿⠿⣛⣵⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡀⠀⣧⠐⠛
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⣥⣤⣭⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⣿⣿⣿⣿⡿⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣻⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠘⠶⣶⣶⣶⣤⣭⣭⣭⣭⣭⣥⣴⣶⣶⡶⠚
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣛⣳⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣍⣨⡛⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣯⢇⡮⠄⡙⢎⢻⡻⡦⣄⣀⠀⠀⠀⠀⣰⠖⠒⢿⣧⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣶⣾⣔⣯⣁⣘⣀⢀⣄⣀⢄⣀⣀⣩⣀⣐⣲⡄⠀⢻⠀⠀⠀⠀⢩⣷⡄
⠀⠀⠘⠫⡱⣟⢣⡀⠀⠀⠀⠀⠀⢀⡴⢋⡿⠉⡽⠍⢹⡻⠛⠛⠛⠛⠛⢛⡟⠛⣿⡛⠻⣟⢷⣦⠟⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠘⡘⣆⠳⡄⠀⠀⣠⡖⠋⡱⠏⠀⡼⠃⠀⡞⠀⠁⠀⠀⠀⠀⠀⢷⠀⠈⢷⡀⠈⠣⡙⢧⣄⠀⠀⠀⠀⠈⣼⡇
⠀⠀⠀⠀⠀⠙⠘⠆⢹⡀⠘⢿⣿⣿⣿⣶⣾⣦⣄⣴⢅⣀⣴⣶⣦⡀⣄⣠⣬⣄⣤⣶⣿⣶⣾⣿⣿⣿⣷⠀⠀⠀⠀⢹⠅
⠀⠀⠀⠀⠀⠀⣵⢻⣷⢣⡄⢸⠀⠀⣿⠉⠉⠉⢹⠟⠛⠋⠉⠉⠉⠋⠙⠛⠛⡟⠛⠉⠉⢙⡏⠀⠀⣾⣿⠀⠀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⢸⢸⡧⠦⡇⢸⡄⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⣹⠀⠀⢸⣿⡏⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠈⣿⣾⢯⠻⡄⣇⠀⢻⡀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠀⠠⣠⡎⠀⣠⣾⡿⣒⣶⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣽⣎⢷⣝⣾⣦⠈⣧⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⢀⣸⡿⢁⢠⣾⣿⡞⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⡮⡿⣿⢻⢿⣷⣦⣶⣿⣦⣤⣤⣴⣦⣶⣶⣶⣿⣶⣿⡿⣷⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣄⢳⡀⣇⠀⡇⠀⡏⠉⡏⢩⡆⢠⠆⣸⠂⡼⣡⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣷⣼⣦⣿⣄⣷⣸⣇⣾⣣⣟⣴⣣⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⢯⣿⣭⣯⣿⣿⣽⣯⢿⣽⡿⠼⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣲⡀
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠖⠠⡀⠀⠀⢀⡤⠔⠒⠤⢄
⠀⠀⠀⠀⠈⢢⠀⠈⢦⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⢗⡻⣺⢦⣠⢣⠞⠉⠉⠳⡄⠱⡀
⠀⠀⠀⠀⠀⠘⡆⠀⠈⠣⣄⡀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢻⡴⠚⠳⣿⡀⠳⡄⠀⠀⢸⠀⢃
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣳⢤⢦⡼⢛⠒⠃⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣰⣧⣺⣭⣽⠀⠀⠀⠀⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⡾⢉⠴⠌⣿⣹⠀⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣦⣷⡘⠦⣵⣟⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡆⢰⡏⠐⣮⢻⡇⣼⠹⠣⣀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡑⣀⡙⠒⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⣀⣀⣐⣋⣀⣀⡹⣉⠉⠍


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⡷⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣶⣤⠀⣜⣠⡄
⠀⠀⠀⠀⠀⢀⣠⠎⣠⠤⠦⡄⠀⢀⠀⠀⠀⠀⡂⠈⠈⣻⣔⣬⣭⣤⣅⠀⠁⢄⠀⠀⢀⣤⣤⡶⠶⡤⠀⠀⠀⠀⣄⠀⠀⣀
⠀⠀⠀⠀⣰⠞⡠⠊⠀⠀⢶⡣⠀⠀⠳⣦⣝⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⠟⡿⠛⠛⡟⠉⠐⠁⠀⠀⠀⠀⠀⢀⡞⡉⡤⠚⠁
⠀⠀⢀⡞⠁⠈⠀⠀⠀⢀⡞⡱⠁⠀⢀⣾⣿⣿⡿⣩⣿⣿⡯⠄⠀⠀⠀⠀⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠝⣊
⠀⢀⡏⠀⠀⠀⠀⠀⠀⢸⣷⣇⣶⣴⣿⣿⡿⠛⣶⣿⣿⡿⠚⠒⠀⠀⠀⠀⠘⢒⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⠃⠀⠂
⠀⢸⠀⠀⠀⠀⠀⢀⡀⢨⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠴⢋⡟
⠀⢸⡆⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⠀⠈⠀⠀⠀⠋⠀⣰
⠀⠈⢿⣄⠀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣶⣲⣀⣀⢀⣠⣄⣴⣿⣿⣄⣀⣀⡴⠀⢀⢠⣶⡵⢃⡼
⠀⠀⠈⠛⢿⡽⣢⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣳⢟⣩⡴⠟⠁
⠀⠀⠀⠀⠸⣧⡿⠁⠀⠈⠙⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣰⣿⠏⢁⠞⠋⠀⠑⠋⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣽⡼⠀⠈⠻⣿⣿⣿⣿⣿⣿⣭⣍⣉⣤⣶⣏⣠⣴⣁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣴⣿⣿⣿⡿⠿⠛⢋⡿⠋⢍⠉⠉⠉⠉⠉⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡽⠋⣾⠟⠃⠠⠤⢐⣈⡐⠀⠀⣂⡀⠀⠀⠀⢀⠁⠀⢳⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠀⠀⠉⠃⠓⠓⠛⠁⠉⠑⠒⠂⠒⠉⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠂⠈⠈⠉⠉⠉⠙⠓⠒⠒⠦⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢭⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣻⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢹⠀⠀⢀⣀⣄⡜⠋⠉⠉⠙⢷⣤⣀⣄⡀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡼⢼⣬⢙⠻⠿⠧⠷⠶⠶⢿⢿⣿⣿⣿⣷⣯⣦⠄⢥⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡩⠶⠋⠀⠀⠐⠂⠀⠀⠀⠐⠚⠻⡿⣿⣿⣿⣽⣦⡀⠰⣵⣄⠀⠀⠀⠀⣠⠞⠁⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠛⣿⣿⣿⣧⡘⣮⢦⠀⢀⡼⠃⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣛⣿⣮⣿⣾⣧⣦⡾⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⣴⣿⣿⣿⣿⣿⡏⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣐⣿⢆⠀⣹⣿⣿⣿⣿⣿⣷⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠉⣸⣦⣸⡄⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠒⢠⠀⢼⣧⠠⢿⣿⣿⣿⣾⣿⣿⣿⣿⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣾⣥⡀⠐⠀⠤⠄⠀⠀⣀⣨⣬⣙⣻⣿⣤⣼⣿⡿⠿⢿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠒⠓⠤⠿⠿⠿⠷⠬⠴⠶⠾⠿⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⣠⠀⠀⣠
⠀⠀⠀⡇⠀⢘⠁
⠀⠀⠀⠈⢢⡈⠒⠤⡀
⠀⠀⠀⠀⠀⠈⡆⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⢢
⠀⠀⠀⠀⢀⠔⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡲⢦⢾⣻⠃
⠀⠀⠀⠀⡎⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠴⠶⠶⠛⢒⠿⠤⠤⢀⣀
⠀⠀⠀⠀⠈⠦⡑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⠩⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢢⠂⢄⠉⡓⠤⣄
⠀⠀⠀⠀⠀⠀⠈⢢⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⢢⢃⢎⠌⡐⡔⠀⡈⡱⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢀⠇⢀⡀⠀⠀⠀⠀⠀⠀⡔⠚⠓⠲⠦⠤⢭⣁⣁⣁⣂⣘⡙⠐⠑⠓⠡⠃⢊⣎⣜⣐⡰⠬⠵⢾⡲⢤⠀⣠⠤⣶⣶⣲⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣁⣡⣴⠟⠉⠳⡀⠀⠀⠀⠀⠈⣷⠦⢤⣴⣄⡤⢠⣀⣀⡀⢀⠉⡉⠉⠉⠉⠉⠅⣤⡀⣆⣒⣮⣼⣵⣴⢫⢞⡵⢋⡤⠤⠤⣌⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠻⠯⣁⢀⡀⠀⢱⡀⠀⠀⠀⠀⡟⠰⢠⡀⡈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡉⠩⡁⢄⢳⡏⡞⠰⠃⠀⠀⠀⠀⠱⡄⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⢧⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠂⠔⠓⡀⡄⢇⢢⠁⠀⣑⣌⢾⣦⣳⡁⠇⠀⠀⠀⠀⠀⠀⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⣆⠀⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠈⠀⠀⠐⣌⠻⣦⠱⣵⣵⡇⠀⠀⠀⠀⠀⠀⢸⡆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⡈⢧⢹⣣⠘⡏⢇⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢆⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢳⢡⠘⡆⢣⢣⢹⠸⡀⠀⠀⠀⠀⣜⡏⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠥⣂⠀⠀⠀⠀⠘⡆⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠘⠈⠀⡆⣆⠈⠈⡎⣆⡇⠀⠀⢀⣼⡞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡫⢐⡡⡢⢀⠄⡀⢣⠀⠐⠄⡄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⡄⢸⠀⠀⠀⠇⠟⠀⠃⡇⣿⠀⣀⣴⡿⠏⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠐⠥⢊⠔⡡⢊⠄⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡅⠇⠀⠰⢀⠇⡆⠰⢘⢰⠀⡆⠸⠀⠍⣿⣿⡿⠏⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠡⠊⡔⣪⢊⣏⠄⡢⠀⠀⠀⡀⠠⠀⢀⠂⠄⠁⢀⠀⠃⡘⠸⢀⠇⡍⠆⢰⢀⠆⡘⢰⣟⣦⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠲⠶⣊⠔⢈⠔⡡⢂⠈⠰⠁⠄⠌⠀⠀⢀⠂⠌⡰⢁⠃⡎⠰⢰⢀⠃⡜⡰⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠠⠚⡡⠊⡰⢁⢀⠀⠀⠀⠀⡰⡡⢃⠎⡰⢡⠃⡜⢠⢃⠃⡎⡴⠘⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠊⠔⠡⢊⠔⡠⢂⠜⡔⡡⢃⠜⣠⢃⡞⣰⢣⠆⠞⣘⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⢄⢴⡻⢿⣶⣤⣤⣀⣈⣀⣁⣈⣀⣁⣉⣀⣁⣤⢤⢤⢶⣲⣻⣽⣪⣔⠄⡠⢔⠠⣂⠄⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⠚⡩⢒⡩⢂⠔⡪⢖⡥⢊⠝⡳⡶⢭⡭⣙⣛⣓⠓⠚⠚⠛⡗⣗⣷⣻⣛⣏⣯⡯⢵⡷⢋⠔⡠⢒⠥⢊⠔⡨⢒⡡⢊⢔⡠⢢⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠁⠘⠉⠙⠉⠘⠡⠋⠑⠉⠔⠁⠘⠁⠊⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡔⢀⠦⠀⠀⠀⠀⠀⠀⢀⡤⢒⡀⢐⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢽⣅⠀⢙⡓⢈⠀⠀⠀⠀⠀⢀⠊⠀⠀⠁⠀⠀⠈⠎⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⡀⠈⠳⢶⠙⠄⠃⠀⠀⠀⠀⠀⢸⠀⠁⠀⠰⣳⠂⠀⣠⢘
⠀⠀⠀⠀⠀⡀⠠⠀⡄⠈⠁⠉⢳⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠲⠀⠀⠁⠀⡀⢀⠜⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠘⠁⢲⣟⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠙⠢⠬⠤⠤⠒⠉⠀⠀⠀⠀⠀⠈⣣⠘
⠀⠀⠀⠸⡁⠀⠀⣺⠃⠑⠠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠻⠀⢀⠙
⠀⠀⠀⠀⠑⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⢐⠁⢄⡠⣄⠸⢋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⠀⢀⠄⠀⠈⠒⠤⠄⢀⣀⣀⠤⠄⠐⠚⠁⠁⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⠄
⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠢⠠⠄⠢⣀⡴⢵⣒⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡰⠆⠚⠀⠀⠀⠀⡐⡀⠀⠀⠀⠉
⠀⠀⠀⢰⡀⠀⢡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⠄⠀⠃
⠀⠀⠀⠀⢧⣐⣾⠀⠀⠀⠀⠘⢄⡀⢠⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠘⠚
⠀⠀⠀⠀⠀⠹⣵⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⢠⡄⠂⠉⠁⠈⢑⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠢⢀⠀⣀⡠⠊⠙⠀⠀⠀⠀⢀⠼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠚⠒⠒⠂⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠤⣤⣤⣤⣤⣤⣤⡴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡾⠗⢢
⠀⠀⠀⠀⢀⠤⠀⠙⠒⠒⠦⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠠⠖⠋
⠀⠀⠀⠀⡇⠀⡄⠀⠛⠒⠧⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⡀
⠀⠀⠀⠀⠙⠀⠁⠀⠀⠀⠀⠈⠀⠀⠠⠤⠤⠐⢈⡇⠀⣀⣀⣻⣷⠾⣧⣴⡖⠀⠀⠀⠀⠶⢊⠅⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⠦⠤⠄⠾⣖⠂⠉⢒⡊⠀⠄⠊⠀⠀⠈⠛⣻⡯⢈⣺⣷⣦⡄⠀⠀⠀⣶⣁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⣵⡞⢿⡅⠀⠀⠀⠀⠀⠛⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⠐⠋⠹⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⣄⠀⢀⠀⣿⣏⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣔⡀⠀⠀⠁⠀⠈⠀⢙⣞⣿⣝⣻⣷⣦⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣁⡒⠒⠀⠀⠀⠀⠀⠁⠈⢹⣗⣛⣿⣿⣟⣀⠀⠀⠳⠤⠀⠀⠀⠀⠀⠀⢠
⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⢉⠉⠛⠛⠒⠒⠛⠚⠛⠛⢻⣿⣿⣿⣽⣍⣂⡤⠁⠈
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡘⢀⠂⠀⠀⠰⠀⠀⠀⠀⡀⠀⢠⠈⡇⠈⢿⣹⣷⣄
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢀⡰⡥⠃⡸⠀⠠⠁⡆⠀⠀⢀⠀⡇⠀⠀⡆⢸⠀⡘⢷⡹⣟⣷⣦⣀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⣿⣛⣙⡓⢒⣠⠥⠋⢁⡜⠁⠮⡂⢠⠁⠀⡈⠘⠀⡇⠀⠀⢂⠀⢇⡱⠃⢻⣌⠻⣷⣿⣿⠶⠀⣀⣦⠏
⠀⠀⠀⠀⢸⣯⣧⣀⣀⣀⣀⢰⠋⠀⡀⠄⠁⡜⠀⡄⠀⡄⠀⡇⠀⠀⢈⠀⠈⢧⣠⣢⡽⢇⣤⣍⣉⣥⣾⡿⠋
⠀⠀⠀⠀⠀⠙⠿⢿⡛⡿⣿⣦⣅⣈⣡⣤⣤⣘⠀⠐⠓⢀⣤⣁⣀⣁⣀⣠⣶⣶⣶⣦⣶⣿⣿⣿⣿⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢿⠿⡝⡟⡟⣿⡏⠻⡿⣿⣿⣿⣿⠉⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢻⣿⣦⣙⣿⣾⣷⣿⣠⣿⡾⣙⣿⣿⣿⣟⣛⣉⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣟⣛⣻⣿⣿⣿⣭⡿⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢤⣤⡿⠐⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠁⣴⣻⢠⡞⣣⠀⠈⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠀⠀⢴⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⠖⠛⠐⠈⠓⠛⠂
⠀⠀⠀⢀⠀⢀⢀⣀⠀⠈⢠⠀⠀⠀⠀⠈⠁⠀⠐⠀⢠⠀⠀⠈⠀⠀⠀⢀⣀⣰⣆⡄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠄
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠈⠉⣿⠁⢠⡅⣤⢰⡤⡄⣠⠖⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣄⠸⡇⡿⢸⠁⡧⠻⡨⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡓⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃
⠀⠀⠀⢠⢊⠄⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡴⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠳⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠓⠀⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠶⠤⢬⠤⠤⠤⢐⡂⠀⠀⠀⠀⠀⠀⠀⡀⠰⠦⠴⠦⠶⠃⣀⠀⢀⡀⠀⠤⢦⣴⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠒⠉⠩⠭⠭⠅⠚⠁⠀⠆⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠁⠀⠀⠈⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢘⠈⠓⣂⠀⠈⣶⢚⡄⠀⢸⣿⡆⣿⡗⠈⠐⠪⢹⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠈⢧⡸⢿⣦⠀⣿⡈⡇⠀⡞⢿⣿⣼⣾⣷⢄⠀⠈⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠀⠈⡇⠀⠻⣼⠁⢿⡖⣰⠃⠊⢻⣿⣶⣿⣶⣝⡀⢿⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣦⡈⠁⠀⠀⠀⣙⣧⡼⠿⠛⠋⠉⣉⣭⠜⣩⡽⢻⢿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠸⢾⣷⠥⠶⠶⠾⠯⠭⠤⠤⠤⠤⠴⠚⠛⠓⠛⠛⡐⠉⢾⡻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣤⣴⣤⣤⣥⣤⣤⣤⣤⣥⣄⣄⣠⣀⣁⣀⣀⡀⣸⡇⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠐⡇⠀⠀⠁⠈⠀⠀⠀⠈⠀⠏⠇⠀⠀⠀⠀⠀⠈⠀⢹⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⡄⠿⠜⢈⣧⡞⢷⠀⡦⠀⢠⡀⠀⠀⠐⠈⠀⠀⠀⢠⡇⣀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠐⠛⠀⠀⣨⣭⣽⣟⠀⣿⣉⣀⣿⣤⣤⣴⡀⠀⠀⢤⡜⣷⣙⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣧⣀⢹⡿⠁⠀⢸⠀⣿⠀⠀⢹⣴⠒⠛⢣⢶⠶⠒⠧⢌⠉⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢨⠄⡼⠈⣷⣒⣒⣾⡆⣷⠴⠄⡾⣣⣀⣀⣸⣿⣤⣤⣾⡟⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⡀⠂⠀⡇⣥⡌⠸⠗⠹⠀⠀⠁⢸⠇⠀⢹⠈⡏⠉⡏⠏⠹⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣺⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠴⢀⠀⢸⣿⡇⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⣠⣀⣀⠔⠀⠘⠛⠀⠀⠁⠀⠀⠀⣹⣿⡄⠘⣿⣿⡆⢀
⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠞⠉⢹⣶⢖⣴⠴⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠘⣿⣿⣎⠳⣦⡀⠀⠀⠀⠘⣧⣀
⢴⣿⣄⣰⡀⢀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠚⢛⣩⠴⠊⡀⢀⡄⣸⣧⡀⠈⠳⢀⡄⠀⠀⢹⡿⠷⠦⢙⠻⢷⣶⣄⣉⠛⠳⠦⡄⠀⠀⣦
⣿⣿⣿⣿⣧⣿⣼⡆⣸⣿⣿⣼⣀⠀⣠⣀⡄⠉⠁⣼⣦⣿⣸⣿⣿⣿⣷⣿⣄⣸⣿⢠⣤⣼⣧⣧⢠⣸⣇⣸⣧⣏⣿⣹⡄⠀⣰⣼⣾⣿⣷
⣿⠿⠛⠙⠛⠛⣛⠻⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⣙⡛⠉⠉⣉⣙⠿⠿⠿⠿⢿⣿⣿⣿⣷⣿⣿⠿⢿⣿⣿
⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠀⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠈

⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠟⠁⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡄
⠀⣰⣷⠀⠄⠠⠀⠀⠻⠶⠖⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡘⠅⢴⣶⣄
⠀⠈⠋⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁⠀⠠⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⢼⣿⣻⣋⠉⣀⣀⣰⣀
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠢⠀⠑⠦⠀⠈⠑⠦⠀⠀⠠⠶⠶⠚⠛⠛⠩⠽⠿⠟⠋⠽⠿⠿⠿⠿⠿⠿

⠀⠀⠠⡤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⢠⡌⠫⠤⣤⣤⠸⢧⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣛⢛⣉⡟⣫⣄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⢙⣏⣀⣀⣀⣀⣬⣥⣈⣏⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣛⣓⣲⣒⣶⣿⣿⣿⣾⣏⣉⣩⣽⣿⣿⠿⡿⠉
⠀⢸⣿⠿⠿⠟⠟⠟⠟⠿⠿⠿⠻⠻⠻⠶⠶⢤⡀⠀⠀⢿⠿⠿⠟⠟⠝⠝⠟⠯⠮⠮⠪⠫⠫⠫⠻⠳⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣶⡄⡀⠀⠀⠤⠈⠁⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣉⡀⠀⠒⢀⡀
⠘⢿⣧⣤⣤⣤⣤⣤⣴⡿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠿⡿⣿⣦⣤⣤⣿⣶⡆
⠰⠿⠿⠿⢿⣿⡟⠛⠛⠓⣼⣿⡄⠀⣀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠊⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠙⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢀⢠
⠀⣠⣾⣿⣦⣤⣴⣾⣏⣷⡄⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⣤⣦⣦⡄⠘⢺
⠀⠻⢿⣿⢟⣻⣻⣏⣿⣛⡇⣀⣤⣄⢰⣿⣿⡆⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⡶⢤⣤⣋⣼⣿⣿⣿⣿⣉⣿
⢠⣶⣴⣿⣾⣿⣿⣿⣿⠿⣻⣿⣿⣿⣄⣠⣄⣀⠀⠀⠀⠦⣀⣩⣷⢶⢶⢶⢶⢾⢿⢿⢿⢿⢿⣿⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠋⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠉⠙⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠤⠂⠊
⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⡤⠊⠀⠀⠴⠃
⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀
⠉⠉⠲⣄⠳⠀⠀⠀⢠⣻⡯⢄⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⣀
⠀⠀⠀⠈⠳⣤⠀⢀⣿⣿⠀⠀⡁⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⡄⠀⡀⠀⠀⠑⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣧⠏⠀⡀⠁⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⠀⠀⣴⣧⠀⠈⠉⠻⢄⠘⠦⠀⠀⠀⠰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣮⠀⣈⠴⠂⠀⣠⡄⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢀⣾⡏⠁⠀⠀⠀⠠⠿⠇⠀⠀⠀⠀⢀⡔⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠟⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢦⣤⣤⣀⣀
⠀⠀⢠⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠦⣄⡉⠉⠛⠳⠶⣤⣤⣀⣄⣀⣀⣀
⠀⢠⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠂⠀⠀⠀⠉⠉⠉
⣠⣿⣿⣿⣿⠲⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣶⣦⣤⣀⣀
⠈⠈⠉⠋⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢻⣿
⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠤

⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⢐⣮⣿⣴⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣮⣿
⠠⣮⣻⣿⣫⢖⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡺⣟⣿
⠺⣿⣿⣿⣶⣿⡿⠀⠀⠀⠀⠠⣾⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣾⣿
⣛⠷⣽⣿⣿⣿⠿⡃⠀⢀⠠⣜⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⣿⣿⣿
⣯⣷⣚⣿⣵⣶⡏⠀⢠⣿⣞⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢳⣶⣯⣿
⡝⣿⢿⣿⣹⠏⠁⣀⢿⣿⡿⡛⣻⡿⠿⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣗⡌⠻⣍⣿
⠙⣿⡻⣿⢀⡁⢠⣿⣥⣿⣿⣷⣾⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⣤⡹⡿⣫⣦⠀⣿
⠄⡇⢳⣯⢘⣃⣶⣭⣽⣧⣿⡿⠹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡠⢧⣽⡿⣿⣾⣿⡓⣿
⠀⠁⠀⣟⢻⠉⠀⠻⢹⣿⣿⡗⢶⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⣷⡾⣿⠿⣿⣾⣿⠿⣿
⠀⠀⠀⡯⠹⠤⠀⠀⡀⡏⠘⡇⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣛⡇⠈⠛⣻⠘⠁⠗⣿
⠀⠀⠀⡇⠀⠀⢰⠀⠙⡏⠁⠃⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠁⢀⡂⣠⠄⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠏⢿⠀⠀⠀⣿
⣀⣤⣦⣧⣴⣄⣠⣄⣸⡇⠀⣀⣸⣇⣀⡀⢀⣀⣀⣀⣀⣤⣄⣀⣀⣴⣤⣤⣄⣿⣤⣄⡄⣀⣼⢀⣀⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⣤⣤⣤⣶⣶⣿⣯⣭⣭⣭⣭⣭⣿⣿⣶⣶⣶⣦⣶⣾⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⠾⠟⠋⠉⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠛⠓⠮⣝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣸⢣⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠶⢤⣄⡀⠀⠀⣀⣀⣤⡤⠤⢴⣾⣿⣿⡶⠶⠦⠤⣤⣀⠀⠀⣠⣤⠤⢶⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⡶⢛⣁⣴⣿⣿⢛⣉⣀⠀⠀⠈⠉⠉⠀⠀⠉⠙⢷⣮⣝⣦⣉⡛⣦⢻⡁⠀⠀⠀⠀⠀⠀⣠⣶⠒⠛⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣧⢾⡯⣭⣭⣭⣝⣛⣛⣓⣒⣒⣒⣒⣒⣒⣛⣛⣻⡭⠭⠭⠽⠿⣼⢸⡀⠀⠀⠀⠀⠀⣸⡟⠁⣠⣬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡿⢋⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣝⢦⣵⡄⠀⠀⠀⢠⣿⠇⣰⡏
⠀⠀⠀⠀⠀⠀⠀⢠⡞⣵⡟⣱⠟⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢿⣷⣌⠳⡄⠀⠀⣼⡿⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣾⣸⡿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⢿⣿⣆⢹⣄⣴⣿⠃⣼⣿
⠀⠀⠀⠀⠀⢀⣾⣝⢼⡇⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡜⣿⣿⡴⣿⡟⠁⣰⢧⡏
⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣷⣖⣢⠤⠤⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⠿⣿⣒⣯⣿⣚⡿⢃⣴⢏⡾
⠀⠀⠀⠀⠀⠀⠀⠹⣆⢿⣍⠹⣿⣿⠿⠿⠷⢶⣾⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣷⡶⠿⠿⠿⢻⣿⣿⢏⣿⣶⣿⣫⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡻⣧⣙⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⣣⣮⡽⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢭⣷⠮⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣖⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⢶⣾⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠛⠛⠋⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣍⣫⣭⣉⣽⣫⣿⣻⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢉⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢄⠀⣤⡞⠀⠀⠀⠠⡠⢔⣨⠄⠀⢀⠐⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢩⡿⠱⡼⠃⣈⠀⢈⡑⡧⠀⠄⡛⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⣙⢿⡈⣭⠘⢛⠁⠐⢼⣧⡄⡢
⠀⠀⠀⠀⠐⠄⠠⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠐⠀⠀⣀⠑⠆⠈⠘⢻⠑⠬⡆⣘⠃⠈⡻⡁⠪⣅⡸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣬⣄⠀⠐⠀⠀⠼⡀⠐⠁⡀⢢⣤⡟⠃⡉⢳⢤⡓⠀⠾⠂⠅⠒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠸⣗⠦⢀⣂⡀⢿⠄⠲⣯⣼⣴⣤⡦⠾⠹⣊⢿⣿⣷⣁⣢⣈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠹⣆⠀⠘⠠⠁⢧⠙⣾⣸⠇⣿⣽⣿⣿⣿⣿⣼⣿⣿⡿⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⢸⣿⡐⠀⢹⣆⠀⠀⠀⠀⠣⣼⣿⠌⠉⠛⠙⠻⢿⣿⣾⠿⠀⢀⠘⠻⠁
⠀⠀⠀⠀⠀⠁⠈⠀⠒⢄⣀⣀⡀⡐⠀⠀⠀⠀⢸⣹⡀⠤⠀⢹⣦⠀⠀⠀⠀⠙⣀⠀⠲⡄⠀⠀⠈⠿⣇⠀⢰⠣⠤⠤⣄
⠀⠀⠀⠐⠐⠢⠖⣀⣠⣌⠉⠙⠑⢀⠆⠀⠀⠀⣈⣾⡇⠀⠀⠀⢻⣧⠂⠀⠀⠀⠈⢧⣠⠼⠖⡉⠰⢆⣀⣐⣏
⠀⠀⠀⠀⠀⠀⢠⣶⣥⣉⠙⣗⡀⠐⠀⠀⠀⠀⣿⣯⡇⠀⢀⠀⠀⢋⣶⡠⠀⠀⣀⣜⣳⣖⡀⠙⢦⠀⠀⡁⢀⡀⣀⣀⢅
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⢃⡨⠴⠓⠊⠚⠉⠡⠉⠃⠉⠉⠉⠙⠃⠀⠈⠱⠺⠋⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⢠⠂⠀⡰⠂
⠀⠀⠈⢄⠀⢄⡀
⠀⠀⠀⠀⠑⢄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀
⠀⠀⠀⠀⢀⠌⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢤⣠⡤⡷
⠀⠀⠀⢠⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠬⠗⠶⢏⣀⣀⣀
⠀⠀⠀⠀⠣⣐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠐⠐⡐⡈⡉⡒⢤⣀
⠀⠀⠀⠀⠀⠀⠑⡌⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⠀⠀⢀⠀⠀⡀⡀⡀⡀⠌⠔⡐⡰⡜⠀⣈⠳⡀
⠀⠀⠀⠀⠀⠀⢀⢣⠃⣀⣀⠀⠀⠀⠀⠀⢔⡉⠁⠒⠒⠠⠥⠭⠥⠬⢌⣉⣈⣘⣊⣊⣈⡬⠬⠬⠼⠔⡗⡟⠒⡄⡠⢔⡶⠶⠶⣒⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⠾⠋⠈⠳⡀⠀⠀⠀⠀⣿⠓⠲⠾⢶⣢⣦⣤⣤⣠⣀⣀⣀⣀⣀⣀⣔⣆⣧⣭⣴⡷⢷⣏⢞⡕⣡⠖⠒⠒⢤⡙⢿⣄
⠀⠀⠀⠀⠀⠀⠈⠛⠲⣵⡀⠀⢱⠀⠀⠀⢀⠏⠈⠐⠂⠀⠀⠠⠠⠈⠉⠉⠉⡉⢉⡉⡉⡉⣈⠅⠄⣐⢎⢆⢿⡞⢰⠁⠀⠀⠀⠀⢹⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⢇⠀⢀⠎⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⡰⠘⠌⠀⢀⠪⣦⡻⣳⣷⡸⠀⠀⠀⠀⠀⠈⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠱⡘⣷⡘⣿⢧⠀⠀⠀⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠄⠀⠀⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢇⢇⢡⠘⣱⡘⡘⡆⠀⠀⠀⢀⣾⠇⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⠩⡀⠀⠀⠀⠘⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠸⢸⢘⠀⡆⠁⠇⢡⡇⠀⠀⢀⣼⠏⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠨⢊⢄⠄⡀⡀⠃⠈⠀⢤⢀⠀⠠⠀⠀⠀⠀⠀⠰⠁⠀⠀⢈⠘⢹⢙⠃⡃⣹⣿⣿⡇⣀⣴⣿⣟⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠪⢖⡥⣪⢞⠔⣴⡀⠀⠀⠀⠀⠀⠀⠀⡄⠆⡄⠀⠀⢆⡅⡉⣈⣭⣉⢨⠁⡁⣩⣻⣯⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣁⠊⠵⠡⢢⡯⢄⠕⠀⠐⡱⠀⢀⢀⠡⠀⠀⡀⡈⠨⢠⢁⠃⠅⠃⡆⠸⢠⢁⣯⠧⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢛⠅⢊⠔⡪⢊⠄⠀⠁⠆⠀⢀⠀⡐⡐⠡⢁⠃⡌⡘⡜⠰⢠⢣⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠡⠊⡠⡡⢊⠄⡀⠀⢀⢊⠌⠜⡠⢡⢂⠜⡰⡰⣡⢣⢃⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣤⣀⠁⠁⠊⠔⠵⠡⠃⠊⠜⠀⠃⠊⠘⣁⣁⣥⣞⠅⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢄⠤⢔⡤⡠⢖⡡⣂⢕⡝⣪⢭⣓⡛⠫⠿⠶⣶⣲⣲⣶⣲⣿⡽⡽⠽⢾⢖⣛⣿⠟⡩⢂⠕⡨⢂⠕⡢⢂⢔⠠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠊⠀⠋⠊⠐⠁⠈⠁⠙⠁⠉⠙⠉⠓⠰⠒⠲⠒⠷⠃⠟⡻⠫⠟⡩⠋⠕⠋⠖⠑⠉⠐⠁⠋⠈⠁⠁⠈⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡏⡀
⠀⠀⠀⠀⠀⠀⢠⡗⠀⢠⣬⡷⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣍⣏⣶⡼⣶⣯⣖⣂⠀⠀⠀⠀⠀⡀⡀⠀⠄⠀⠀⢆⡀⠀⣀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⠷⠂⢰⣗
⠀⠀⠀⠀⢀⣉⣻⣿⣮⣿⡽⣷⣟⠿⡎⢁⣀⠐⠒⠚⢋⣉⣀⡀⢄⠀⠈⣹⡭⠀⠀⠨⠧⢄⠀⠀⠀⣀⡀⠀⢀⣨⣽⣯⡻⣷⣿⣷⣴⡇
⠀⠀⠀⠀⣉⡫⢞⣿⣿⣿⣹⣿⣿⣟⡛⠀⠀⠈⠀⠈⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⢬⣿⣯⣿⣿⣿⣿⣿⣿⡟⢃⡀
⠀⠀⠐⠺⢟⣳⣭⣧⣾⣿⢻⡟⣿⡶⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⡀⣀⠄⠙⠒⠀⢀⣰⠶⠞⠛⠋⠈⠀⠀⠢⣤⣴⣇⣳⣽⣟⣻⡟⡻⣷⣽⡇
⠀⠀⠀⠀⠀⢀⣺⡇⢛⠿⢤⡇⠙⢿⠣⣀⣶⣤⣀⣀⣬⣭⡬⠿⠛⠃⠀⠀⠀⠈⠉⠀⢀⠀⠀⡀⠉⢀⠈⠲⢦⣤⡉⣿⣙⣟⣻⣿⡷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣼⡷⠆⠀⠐⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠖⠲⠒⠒⠲⠶⣿⢭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠤⣿⡏⣿⢁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠶⠿⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⠩⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠀⠀⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡭⢶⠤⡀⠀⠀⠀⢀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠉⢯⠉⠉⢣⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣶⢶⡪⣦⡀⠰⢡⠖⠒⠒⢄⠉⢆
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠣⡀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢱⢎⡥⠷⣟⡇⠸⣄⠀⠀⠀⢣⠈⡆
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠁⠒⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡿⣄⣠⡈⡿⠦⡼⠃⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣞⡵⣩⣿⡧⡇⠀⠀⠀⠠⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⢎⡾⢛⣛⢿⡟⡇⠀⠀⢂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣾⡀⣏⠈⣨⣷⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣴⢟⡛⢿⣧⢈⡝⣿⠃⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⢇⠈⢧⣁⡸⠀⣿⠙⡃⠁⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⢠⡬⠀⠬⠴⠦⣬⡤⢞⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠚⠁⠐⠈


⠀⡃⠈

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⣀⣴⣞⣡⡄
⠀⠀⠀⠀⠀⠀⡔⣿⣿⣮⢞⡵⣫⠝⠁
⠀⠀⠀⠀⢠⢖⡣⣞⡿⠁⢀⣜⣡
⠀⠀⠀⠀⣎⣿⣿⣿⣷⣠⠜⠻⡀⠀⠀⢀⡀⠀⠀⠀⠈⠁⢀⣀⡀
⠀⠀⠀⠀⠙⠿⣿⣿⠿⣇⠀⠀⠱⣄⠀⢉⡤⢤⣀⠀⢀⠞⠁⠀⢸⠂
⠀⠀⠀⠀⠙⠓⣼⣅⠀⠀⠑⢢⡄⠀⠙⠺⣆⠀⠈⠳⣼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⡎⢻⣷⣄⠀⢀⣭⡓⢤⡀⠈⢣⡀⠀⠈⢳⡭⠥⠤⠤⠤⠤⠔⠒⠚⠉⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠳⢿⡈⢮⣑⢮⡀⠈⠙⢿⣦⡀⠙⠲⢤⠤⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⡤⢔⡛⠿⠆⠀⠀⠀⠃⠀⠀⢹⡉⠁⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠋⣉⠴⠚⢇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⠻⡖⠚⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠓⠿⣶⡄⢀⣤⣶⠿⠛⣁⣸⠾⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⡭⠞⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⣄⠀⠀⣾⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠷⢖⠤⣈⣋⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⡼⠂⠀⠙⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠔⣊⡥⠄⠒⠂⠀⠀⢲⡀⢱⠀⠁⠀⠱⢬⡑⢤⡀⠀⠀⠀⠀⠀⣈⡦⡇⠀⠀⠈⠳⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⠳⢄⡠⢊⡵⠊⠁⠀⠀⠀⠀⠀⢰⡣⠷⠞⠀⠀⠀⠀⠈⢯⠓⢬⡒⠒⣒⡩⠥⠒⠊⠹⣤⣀⡀⠠⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠑⣒⣻⡀⠀⣀⠉⣉⣉⡹⠂⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠕⠊⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣀⣀⣀⣀⣀⣀⢤⠤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠧⡔⠈⢋⠫⠏⠉⢖⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⠋⢀⢿⣾⣿⡛⠺⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⠷⠞⠿⢳⣾⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⡴⢩⠃⠀⠀⣠⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡀⠈⣛⣦⣀⡀⣀⣨⠇⣴⡉⠀⠀⢉⣑⣾⣖⠒⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣏⡫⢟⣽⡩⠊⠀⠀⠉⠒⠭⣓⠿⣏⡩⣟⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⠷⠟⠉

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⡀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⣀⣸⣿⣻⣖⢒⢠⣀⢀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣂⡤⠚⠻⠥⠤⠬⠥⠬⡟⢾⣍⡉⢻⢖⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⢀⠤⢤⣀⠀⠀⣀⣐⣬⣯⣄⡀⠀⠀⠀⠀⠀⠀⠙⣄⣩⣿⣃⠀⠵⣄⡀⢰⡞⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠙⣶⠊⠻⡠⢤⣷⡿⠋⠉⠀⠚⠡⠌⠰⠤⠴⠦⠿⠚⠛⠉⠀⢀⣀⠈⠱⡿⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣿⠿⣧⠀⠁⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢹⡏⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⣀⣩⣭⠿⢻⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣯⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣿⣿⣧⢸⡇⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⠸⠃⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⢠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣄⡀⠁⠀⠀⠀⠀⠠⠀⠄⠀⠄⠀⠀⠀⠀⠀⠤⠤⠄⠐⠢⠀⠀⠡⢀⡄⠓⠄
⠀⠀⠀⠀⠀⢀⠄⢀⡀⠠⡆⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡥⠤⠄⠀⡄
⠀⠀⠀⠀⠰⣅⡀⠀⠀⠀⠐⢄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⡠⠊⠀⠀⢠⠠⠬
⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⡤⠁⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠒⢀⢂⠙⠢⠄⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢑⠒⠀⠀⢠⠎⠀⢀⣾⣿⡄⣦⢧⠀⠀⠀⠀⠀⠦⠀⠎⠂⠀⠀⣐⠥⣀⠀⠀⠀⠀⠀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⣠⣿⣿⣿⡇⠈⠇⠂⠀⠀⢀⠀⠅⠁⠀⢐⡁⣠⠄⠀⠤⠄⢀⡀⠀⢀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠄⣈⣘⢦⡀⠘⡌⠂⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⢀⣀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣐⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠉⠛⠛⠛⠛⠛⠛⠙⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⣀⣿⡆⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠈⠙⢦⡈⠠⠀⠀⠀⠀⠀⠠⣴⣼⣀⣠⣴⡶⠿⣿⣿⣿⣶⣶⣤⣀⣷⣄⡄
⠀⠀⠀⠀⠀⠀⢳⣄⠐⢄⠀⠀⠀⢀⣼⣯⠓⠂⠀⠀⢀⣹⣿⣿⣿⣿⠿⣟⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠉⠂⠰⣿⣿⠟⠁⠀⠁⢴⣤⣦⣤⣶⣶⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣤⣿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣸⡿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠞⠿⢿⠇⠟⠇⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⣧⣶⡤⡄⢰⠄⢰⣾⠆⠐⡰⢼⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢛⠠⢌⢙⠀⠀⠈⠀⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⢐⣐⣂⣂⣂⣂⡀⠬⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣀⣛⣛⡛⠻⠿⢯⣛⠿⢦⠀⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢁⣀⠀⠀⠚⠋⣉⣩⣭⣟⠛⠶⠀⠈⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣿⣡⠴⠀⠀⠸⠟⣦⣀⣀⣠⣴⣶⡄⠀⠀⠀⠀⣠⡶⠶⣤⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡟⣡⠾⠋⠀⠀⠀⠀⢉⣩⢴⣿⡽⠂⠀⠀⠠⡾⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢸⠃⣠⠆⠀⠀⣀⣾⣯⣶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣴⠶⣠⣾⠃⠀⠀⠀⣉⡵⢞⣽⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⡶⠿⠦⠀⠙⢷⣄⠀⠀⣠⣄
⠀⠀⠀⣀⡴⠿⠀⠀⣠⢴⡟⠀⢸⠇⡿⠀⠀⠀⠀⠉⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⡟⠉⠻⢶⣤⡶⢶⣄⣀
⠀⠀⣾⠋⣰⠟⢡⣾⡟⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠙⠷⢾⣧⣽⡿⣦⠀⠀⣠⠶⡆
⠀⠸⣏⠀⠿⠀⡿⠘⠇⠀⠀⠰⣄⡀⠀⠀⠀⠲⣦⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣞⣡⠞
⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣤⣴⢿⣯⣩⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣙⠶⢤⣤⣤⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢧⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡖⢀⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠻⠶⠖⠂⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠿⣤⡌⠻⠓⢶⣦⣤⣀⡀⠀⠀⠀⢠⡏⢀⡾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠈⢻⡄⠀⠀⠓⠀⠈⣹⠟⠲⠦⣼⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⣶⣶⠶⠛⠁⠀⣀⣼⣄⣠⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⣿⠆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠛⠉⠈⠙⢷⣶⣶⣤⣴⣟⠉⠙⠛⠓⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠶⢦⣤⣄⣀⠀⠀⠙⠿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⠛⠂⠀⠀⣀⠀⠀⠈⠙⢦⠀⣤⣿⣧⡀⠀⣀⡠⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠴⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢶⣶⡉⣿⠟⢋⣡⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠗⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⢻⣽⡏⠀⡈⢻⡿⠳⠶⢦⣤⣤⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠛⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠛⣅⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣼⠂⠀⠀⠀⠀⢿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣗⠀⠈⠙⠷⣦⡀⠀⠀⢀⣴⣿⠋⠀⠚⠁⠀⠀⠀⠀⠀⠈⢿⡉⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⣷⠀⠈⠙⠆⣴⡟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢶⡶⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠿⡅⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⣀⡞⠁⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠈⢻⣷⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠾⠀⠀⠸⣦⣿⣏⠐⣂⠴⣯⠛⣿⣄⣼⡟⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠀⠀⠀⠹⠋⠁⣼⣏⠀⠙⣷⡉⡀⠉⠳⠻⣿⡻⠧⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣶⣶⠶⢤⣤⣶⣄⢀⠙⠃⠀⠢⠠⠑⠀⠀⠉⠀⠙⠛⠒⠀⣀
⠀⠀⠀⠁⡀⣤⣦⣶⣦⠾⠟⠛⠉⡉⠤⢀⣴⣄⣍⣉⣹⣿⣷⣴⣤⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤
⠀⠀⠀⠀⠙⢉⡀⢡⣆⣴⣴⣦⡈⠠⣾⡿⣿⣯⣿⡻⠿⣿⣿⢷⣾⣍⡛⣛⠷⢶⣴⣷⣶⣤⣀⣀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠙⠓⠺⠟⠒⠉⠙⠺⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠙⠓⠦⠴⡆



⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠸⣷⠀⡇⣽⠀⠀⢸⡆⠀⠀⣴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠀⡀⠀⢠⢰⣟⣿⡇⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⢀⠀⠀⠀⢀⣿⣼⣷⣴⣷⣾⣴⡔⣹⡇⢴⣧⢿⣾⡖⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣿⡇⡣⠀⣼⣼⣿⣿⣿⡃⠀⠀⠐⣢⣤⣼⣇⣸⣧⣼⡆⠀⠤⠬⢿⣿⡟⠉⢻⣿⣿⡇⣚⢻⣽⣿⣧⡿⢡⡛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⣿⣿⣿⣧⣨⡁⢻⣿⣿⡿⢿⠁⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⡿⠀⠀⠀⠙⣯⣥⢿⣾⣏⣺⣿⢕⣯⡄⠸⣷
⠀⠀⠀⠀⠀⠀⣀⣼⣾⣿⣿⣿⣿⣿⣫⡿⠀⠈⣿⣿⠇⠸⣀⡆⠀⠀⡌⠀⣻⣿⣿⠏⠁⠀⠛⡛⠓⣾⠃⠀⡀⡀⠐⠛⣥⡾⢻⣍⢹⣏⣴⠿⣿⠤⠿
⠀⠀⠀⢀⣷⣿⣿⡟⣿⣿⣿⣯⢿⡏⣼⠇⠀⠀⢹⡟⠄⠀⣿⡼⣷⡿⠄⠀⠂⣿⣿⣀⠀⠀⠈⠉⣠⠼⠃⠁⠀⠈⠒⠠⣿⣇⢈⣿⣿⡏⢿⣿⡉⡷⠄
⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⠿⠓⠛⠓⠏⠀⠀⠀⢸⠇⢀⡀⠘⣷⣽⢓⣀⣄⠠⠝⠿⠛⠳⠾⣿⢶⡇⠀⠀⢠⣠⣤⣀⣀⡜⢻⡿⣷⡿⡈⢼⣿⠳⢟
⠀⠀⠼⠿⠛⠉⣉⠁⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠋⠉⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠛⠉⠙⠗⠞⠃⠛⢂⠈⢠⣹⠆⠀⠃
⠀⠀⠀⠀⠀⠈⠽⠀⠂⠤⣤⣤⣧⠠⢠⣤⣤⡀⣀⠀⠤⠤⢀⣢⣄⣀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠶⠎⢉⣺⡟⣂⣉⣽⣷⣄⣀⣉⣱⡖⠀⠀⠀⠀⠀⠠⢶⣶⠤⢴⣈⡉⠷⣄⠀⠈⢻⡆
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠐⠺⠶⠶⠦⠶⠴⠶⠒⠛⠀⠠⠾⠷⠒⠒⠋⠉
⠀⠈⠀⠈⠁⢦⣴⣾⣿⣁⣀⣄⠀⣷⡄⠀⠀⣴⡄⠀⠀⠀⣆⠀⡀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣷⣷⡄⠹⣿⣤⣧⢾⡏⣧⣷⢠⢼⣷⡀⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣾⣿⡿⠿⠛⢿⣾⣷⣿⡇⠀⢁⠀⡆⡄⠀⡀⣼⣿⣿⠀⣆⣿⡆⠀⠀⢀⢸⡄⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠐⡻⢿⣿⡟⣿⠿⢿⣭⣥⠀⢘⠂⣻⢻⣧⣷⣿⣿⣿⡄⢸⢸⡇⠀⠀⠈⡄⣿⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠛⠁⠀⠒⠒⠀⠓⠄⠊⠀⡥⠜⠛⢛⠻⣿⣿⡗⡚⠉⢉⡠⠄⢠⣧⣿⡿⠴⠏⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠘⣿⠛⠏⠑⢿⠛⢛⢛⡻⢿⣧⣀⣀⣉⣭⡷⢶⣖⣚⣛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠙⠁⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡼⡓⢿⢷⣶⣴⣢⡄⠀⣠⣄⢠⣴⣶⣿⣿⣧⡄⠀⠐⠒⠶⠓⠲⠶⠶⠒⠲⠤⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡬⢝⠀⢁⠰⣼⣿⣿⣿⣯⣽⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠲⠘⠻⢿⠿⠿⡟⠛⣫⣁⢹⠷⢆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠉⢙⠓⠞⢦⣤⡛⣐⠃⡨⠁⣿⣦⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠿⢘⠳⠖⢾⠿⠛⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣟⣛⣉⣉⡉⠉⠉⠉⠉⠉⡉⡉⢉⠙⣛⣑⣶⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠿⠟⠛⠿⠿⠿⡻⣟⣻⣿⡿⠟⠻⠿⠿⠟⠛⠛⢿⠇⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣤⣤⣶⣖⣀⣶⡄⠀⠀⠀⠀⠀⠀⠀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠻⠿⢿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡖⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠤⠶⣶⣿⣿⣿⣿⣷⢶⣤⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠣⡀⠀⠀⠀⠀⠀⣶⣾⡷⠻⠤⣤⣀⠀⠈⠰⠿⠀⠀⠻⠀⠈⣉⣻⣶⣄⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⣰⣟⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠁⢻⡏⠀⠀⠀⠙⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⡤⣾⣿⣿⠟⠲⠶⠶⠤⠤⢤⣤⣏⣉⣁⣠⣀⣈⣡⣠⣠⠤⠤⠤⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠁⠀⠍⠀⠀⠀⠀⠀⠀⠘⠀⠸⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠋⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣼⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣆⡀⡀⠠⠠⠀⣭⢰⣶⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣴⣿⡿⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠤⢭⡍⠙⠘⠛⠶⠿⠾⠿⠿⠭⣤⣤⣤⡤⠤⠤⠴⠶⠾⠒⠛⠛⣉⣡⡵⠿⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠻⠷⠶⠶⠶⠰⠶⠤⠶⠴⠖⠒⠒⠋⠉⠉




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

⠀⠀⠀⠀⢀⣀⣀⣀⣠⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⡦
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⣖⢒⡇
⠀⠀⠀⠀⢸⠀⣴⡜⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠿⠯⢼
⠀⠀⠀⠀⠘⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂


⠀⠀⠀⠀⠀⣀⣀⣀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢠
⠀⠀⠀⠀⢰⠁⠀⠨⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠸⠘⠄
⠀⠀⠀⠀⢇⠀⠀⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⠓⡆
⠀⠀⠀⠀⠀⠁⠒⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⣰⣁⣰⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠄
⠀⠀⠀⠀⢸⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠱⠋⠉⠉⠉⠉⠙⡗⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠘⡀⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⣇⡇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠞

⡉⠉⠉⠀⠒⠀⠂⢉⣭⠁⢀⠒⢒⣠⡈⠅⠀⠀⢒⠀⠀⠠⠀⠒⠂⠠⠬⠁⢐⠒⠠⠬⠁⢒⡀⠬⢉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠈⠓⠘⠉⠛⠛⠒⠰⠾⠿⢶⠴⡖⠲⠑⢲⠁⠲⠀⠹⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠁
⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡄⢀⠀⣤⣧⢄⣤⠶⣆⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣄⡿⣾⣷⣿⠷⠆
⠀⢳⣾⠷⠞⢫⠾⢵⣶⡞⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⣶⣾⣿⣾⣯⣽⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⠄⣤⣄⣠⣤⣤⣤⣄⣤
⠀⠾⣿⣿⠳⣾⣷⡼⠻⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠠⣿⣿⣿⣿⢫⣮⠻⣿⡿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⣷⣤⣽⡿⣿⣿⣿⣯⣿⣿⣿⣾
⠀⠒⠻⠉⠀⢰⣀⡄⡰⠃⠀⠉⠉⠛⠖⠀⠀⢀⣦⣶⣷⣾⣿⣗⣬⣆⣸⣿⡁⢻⠽⠛⠋⠙⠝⠶⠖⠀⠀⠀⠠⣿⣯⣾⣿⣿⣿⣿⣿⣭⣬⣿⣿
⠀⣠⣀⡄⠙⢾⣾⣵⣯⡖⠀⠀⠀⠀⠀⠀⠀⢈⡝⠋⠩⣯⣤⠛⢿⢯⠝⡏⠚⡁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣷⣾⣿⡃⠜⣿⣿⣿⣏⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⢤⣶⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣹⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠛⣿⣿⣿⣿⣿⡷⠀⠙⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣧⣴⣶⣶⣿
⠀⠋⠙⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⠿⣿⠿⣿⣶⠆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣛⣿⣻⣿⣿⡿
⢀⣀⣠⣤⡤⠤⠄⠒⢒⣀⣀⣥⠴⠖⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⢀⣉⣉⣥⣬⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠘⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄⢠⣾⣶⡄⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠾⣟⡛⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠡⠀⠠⢴⡾⢶⣿⣿⣿⠛⠡⠤⢤⣙⢿⣿⣿⣿⡆⣿⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠠⠦⡌⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠒⠉⢀⡚⠒⠛⠳⢝⢿⣿⠰⠻⣡⡀⣘⡇
⠀⠀⠀⠀⠀⣰⠀⠘⣇⠹⣿⢿⢷⣶⣄⡀⢀⠀⠀⣰⡇⠰⠂⠈⠙⢦⣄⣀⣐⣄⣄⠀⢣⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢷⣤⣌⣳⣶⣤⠦⣉⠻⣿⣮⡟⠛⠟⠀⠀⠀⠀⢶⣄⣬⠉⠉⣿⣿⡄⠞⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠢⠌⠳⣦⣴⠾⢃⡀⠀⠀⠀⠀⠛⠯⠀⡀⢀⣿⣿⣧⠈⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣀⠀⠀⠀⠀⠁⠀⢤⡶⠟⠛⠶⠀⠀⠀⠤⠶⠾⠋⡼⢻⣿⣿⠀⣿⣿⡀⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡞⠁⣼⢿⡏⢠⡘⠿⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⢳⡄⠀⠀⠀⠀⢠⠞⣷⣦⡀⠀⠀⠀⠀⠀⢡⡌⢻⣁⣾⠧⣄⣙⠳⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠿⣧⠀⠀⠀⠀⠀⢤⠿⠛⠁⠀⠀⠀⠀⠀⢲⡄⢸⣿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠙⠂⠉⠀⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢫⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠠⣴⠶⠶⠦⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⠛⠛⠁⠀⠀⠀⣴⣊⠉⠁⠀⠀⠀⣀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣽⠀⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠾⣅⢘⠀⠀⠀⠀⠀⢀⡀⣀⠜⠚⢻⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠈⢿⡅⣀⣙⠀⠏⢉⡽⢁⠄⣠⠞⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡆⢀⣒⠚⠇⢹⣿⡗⠀⠉⢚⣿⠋⣠⠔⣡⠾⡄⠀⢀⡴⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⡟⠀⠀⠈⠙⣿⣾⣿⣿⣧⠰⢻⣷⡞⣡⠞⢁⣴⡷⠖⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⢠⡟⢰⡟⠀⠀⠀⠀⠀⢈⣿⣿⣋⠁⢀⠈⠹⣿⢧⠾⠋⣡⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⡟⠠⣾⣃⠀⠀⠀⠀⠀⠘⡿⠿⠟⠃⠘⠳⠟⠛⠃⢰⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠏⠀⠀⣈⣛⡛⣦⠀⠀⠀⠐⣿⣿⣽⣧⣿⣴⣷⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠈⣍⡉⠙⢧⠀⠀⠀⢻⣿⣄⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⣄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠟⠛⠿⢃⣠⠟
⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⣰⡟⠀⠀⠚⠋⠁
⠀⠀⢀⣀⣿⠃⠀⠀⣀⣤⡾⠋
⠀⠀⠛⣩⣿⣄⠀⠀⠈⣿
⠀⠀⠈⢧⠼⢿⣷⣤⣀⠁⣼⢿
⠀⠀⠀⠀⢶⣼⡟⢳⡇⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢉⠡⠄⢀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠑⠀⣠⠀⣤⠀⠀⠀⠀⠀⠠⣾⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠛⢀⣖⡢⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⠀⠀⣀⣾⡿⡇⠀⠂⣤⠀⠠⣄⡀⣀⣠⣾⠝⠓⡒⢛⡶⠛⢃⠠⠐
⠀⠀⠀⢠⠄⣀⠄⠀⠀⠀⠀⠀⠶⠂⠀⠀⠄⠀⠀⢸⣿⣷⣄⡉⠉⠂⠀⠀⠀⠙⠧⠂⡈⠟⠛⠁⠀⣀⣤⡿⠋⠀⠩⣀⡀⠀⠀⢀
⠀⠀⠀⠈⢶⣿⣷⣦⣄⠀⠀⠀⠐⠻⣶⣶⣬⣿⡥⢮⣽⣷⣾⣿⣦⡀⠀⣠⠶⠒⠒⠈⠁⠀⠴⠞⠛⢁⠀⠀⠤⠤⠐⠚⠃⠀⠊
⠀⠀⠀⠀⠘⢧⣙⠻⣿⡿⢷⣐⢶⣤⣭⣍⢉⣉⣉⣉⣉⣉⣉⣉⣉⠁⢀⡀⣀⢀⠀⢀⣤⣀⣀⣠⣿⣿⣇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⠉⠉⠁⠉⠀⠈⠉⠁
⠀⠀⠀⠀⢠⠤⠀⡀⠀⠀⠤⠄⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠈⠉⠀⠃
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⣤⣤⣤⣤⡶⠶⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣠⠞⠋⠉⠁⣐⣒⡒⠾⠿⣟⡶⢦⠠⣤⡇
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣁⡄⠀⠚⢉⣩⣭⠭⠛⠒⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⡞⠁⠀⠀⣴⡋⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠘⣇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢺⢗⣩⠄⠀⠁⠙⠲⢒⣯⣟⠇⠀⠀⣠⠞⠉⠙⠃⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⡞⢁⠄⠀⢀⣴⣾⣽⣫⠅⠀⠀⠀⠁⠀⠀⢶⠀⢻⡄
⠀⠀⠀⠀⣧⠀⠀⠀⣠⡶⢦⢶⠃⠀⠀⢈⡵⢫⡟⠁⠀⠀⠀⠀⠀⠳⠶⠾⠓⠀⠛⢦⡀⠀⣤⣄
⠀⠀⣠⠖⣻⢀⣠⢶⠏⠀⡏⠻⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠈⠛⢶⣛⣷⢶⣄⡀⠀⠀⢀⡀
⠀⢸⠇⢾⠁⡞⣿⠘⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠃⠀⠀⠀⠀⠉⠙⠻⣯⣷⣀⠔⡩⠃
⠀⠘⢧⡀⠈⠁⠀⠀⠀⠈⠛⠶⣤⣤⣬⣽⣟⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣤⡀
⠀⠀⠀⢻⠀⠀⠀⠀⣝⠶⠤⡤⠶⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣤⣤⣤⠤⠤⠤⠤⠤⢀⣠⣀⣀⡴⢀⡟
⠀⠀⠀⠘⣇⠀⠀⠀⠈⠙⠛⠁⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠶⡎⠋⠛⣶⠶⢤⣄⣀⠀⢼⢁⡞
⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣤⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢹⣦⠀⠀⢀⡴⠋⠉⠙⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⠙⠻⠛⠙⠳⣤⣤⣄⣰⡞⠒⠶⠦⢤⣤⣤⡶⠏⠀⠀⠀⠘⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠰⠶⣤⣄⣀⠀⠙⠿⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡀⠀⠀⠉⠛⠶⣄⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡴⠛⠉⠀⠀⠐⢦⡀⠀⠈⠁⢐⣛⢿⣤⡴⠆⡶⠀⠀⠀⠀⣼⠄⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⡄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⢿⣷⠇⠀⠶⡶⢤⣤⣤⣠⡷⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡟⠃⠀⠀⠀⠘⠃⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢠⣖⣒⡛⠡⣤⣀⠀⠀⠀⠀⢀⣠⠆⢀⠞⠀⠀⠀⠈⢿⣯⣤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⣤⣤⠙⠳⣄⢀⣴⠿⣧⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⢦⣤⣤⠘⢧⡀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⢿⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢰⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠸⠶⠃⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠉⢝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⣀⣤⣦⣤⣀⢸⣿⣆⠀⠀⠀⠀⠀⠈⡎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⣠⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣼⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡵⠶⠿⢿⣿⣧⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠋⠀⠀⠀⠀⠉⠻⣞⢷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠝⠶⣭⣿⣿⣿⣿⠿⣫⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⠀⣿⠐⠛
⠀⠀⠀⠀⠀⠀⠠⡤⠤⣤⣤⣤⣼⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢻⢠⣿⣿⣿⣿⣿⣿⠛⠁⡷
⠀⠀⠀⠀⠀⠀⠀⠸⡞⣿⣿⣿⣿⣿⣿⠴⠊⠁
⠀⠀⠀⠀⢤⣀⣀⣀⣙⣿⣿⣿⣿⣟⣁⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⡿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠈⠀⠀⠘⠂⡀⠀⠀⠀⠀⠀⠀⠙⠂⢀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⡀⢀⣠⡇⠀⢠⢀⡄⣠⠀⠀⣀⣦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⢀⣿⣼⣿⣿⣿⣾⣿⡧⣿⣿⣼⣿⣿⣷⣿⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠣⣼⠤
⠸⡿⢿⢿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠤⢽⣖⡃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣒⢻⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⣤⣀⠤⢾⣆⠠
⠀⠀⣄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣾⡀⢤⡥⠽⣿⠷⢒
⠠⣸⣿⣧⣶⣷⣾⣷⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡂⣨⣿⠤⠀⠙⠶⢾⡟⣋
⠀⣿⣿⣿⣿⣿⣿⣉⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⢂⠀⣑⣲⣿⣊⡁⠈⢳⣾⣟⣋
⠀⢿⣿⣿⣿⡿⠟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣼⣧⡄⠠⠽⣿⠆⠆⠤⣻⡿⣿⣋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠁⢀⠂⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠄⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠤⠤⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⠈⡁⠞⢻⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣨⣄⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠂⡂⢄⣐⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠓⠐⡀⠁⠄⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⡈⢃⡈⠤⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠤⠐⢂⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉