Boomerang Emojis & Symbols

⠀⠀⠀⠀⠀⢠⣴⣶⡶⣦⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢮⢻⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣥⢿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⢷⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣭⣶⣾⡌⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⢿⣛⡭⠶⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣩⡶⡾⢓⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣴⠶⠟⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠁⣤⡀⢠⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢠⣙⠿⠸⠃⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠉⠁⣀⣤⡶⠆⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡰⢟⣿⠛⠛⠛⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡙⠁⠀⢀⣠⣴⣶⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠞⣛⣭⣽⣿⣿⢿⣿⣿⣿⣽⣿⣿⠟⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⣴⠿⣯⣾⠏⠀⢠⣤⡀⠀⠉⠉⠛⠛⠛⢛⡋⡉⠍⢀⣦⡈⠃⠁⢿⣿⡟⣿⡚⣷⢿⡿⢿⣻⡵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠸⠟⠁⠀⣠⡟⣸⠇⠀⣾⡆⣾⡄⠀⣿⢿⡆⠀⢚⣭⣶⡆⠀⠀⠿⣷⠹⢟⣸⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⢰⣿⡟⠉⠀⢸⡟⣿⢿⡇⠀⣿⡾⣿⡀⠀⠲⠆⠀⠀⣀⣬⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⠈⠃⠀⠀⠾⠃⠁⢿⠀⠀⠻⢃⣙⢁⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣶⣤⣤⣤⣶⣶⣶⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣶⠶⡶⠶⠟⠻⣟⠛⢻⡛⠛⠻⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡾⠿⠟⠛⠛⠉⠉⠉⠀⠙⣆⠀⠹⡄⠀⠀⠸⡆⠀⢧⣀⣴⣿⠟⠁
⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⠀⠀⢀⣷⣴⠿⠛⠉
⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⣷⠾⠛⠉
⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠋⠁
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠋⠁
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⣀⡀
⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠳⣄
⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢤⡀⠀⠙⢿⣦⡀⠀⠀⠈⢳⣄
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢿⣦⡀⠀⠀⠙⢷⡀
⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠈⠻⣿⣄⠀⠀⠀⠻⣦⡀
⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠘⢿⣷⣄⠀⠀⠙⣿⣄
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠻⣿⣦⡀⠀⠈⢿⣦
⠀⠀⠀⠀⢹⣧⣀⣀⣀⣀⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠙⣿⣿⣄⠀⠈⢿⣧
⠀⠀⠀⠀⠘⣿⠀⠉⠉⠉⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠈⢿⣿⣆⠀⠸⣿
⠀⠀⠀⠀⠀⢻⡷⠤⠤⢤⣤⠤⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⢿⣿⣧⡀⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⢿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⢹⣧⣤⣀⣀⣠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠉⠉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠁
⣶⣶⣶⣶⣶⡖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡾⠷⠶⢶⣶⠶⠶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢲⡟⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁⠀⠙⣿⡄⢳⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢻⣷⣄⣠⡴⢿⣿⡈⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⢋⡷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡙⣦⡙⢿⣿⡀⢀⣿⣷⠘⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡾⢣⡟⣡⠏⣸⣿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣌⠳⣌⠻⣿⣏⢉⣿⠷⠛⠋⠉⠉⠉⠉⠛⠛⠻⠿⣧⣟⣱⠟⣴⠋⣴⠋⠉⠹⣿⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡘⢧⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠧⢾⣟⢦⣤⡼⢁⡾⢡⡟⣳⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢥⣞⣰⠟⣼⢏⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣾⣯⠿⠿⠷⠶⢾⠇
⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠚⠛⣿
⠀⠀⠀⠀⠀⠀⣿⣉⣉⣉⣉⣉⡟
⠀⠀⠀⠀⠀⠀⣿⢿⠋⠉⢹⡟⡇
⠀⠀⠀⠀⠀⠀⢻⣾⣦⣤⡾⢿⡇
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⢸⣟⣛⣛⣛⡻
⠀⠀⠀⠀⠀⠀⠀⢯⣭⣭⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⡚⠛⠛⢛⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠄⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠉⡳⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢞⠁⠂⠀⠀⠀⠀⠀⠠⢀⣡⠴⠚⠛⠉⠉⠛⠛⠶⢦⣄⡂⢀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⡀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡒⠀⡀⠀⠀⠀⠀⠈⡙⢦⡄
⠀⠀⢀⡴⠡⠈⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣥⣀⠂⢀⠀⠀⠀⠂⠹⡆
⠀⠀⡾⠀⠁⢀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣬⣄⣥⡴⠃
⠀⠀⠻⠶⠴⠶⠚⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⣛⠉⠉⠉⣥⠀⢀⠀⠀⣈⣩⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡛⠉⢰⣆⠲⠂⠹⡆⠘⠃⢹⡄⠙⠀⣏⠉⠰⠄⣯⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡋⢁⣀⣳⣾⣄⣤⣿⣤⣤⣬⡿⠤⠤⢤⣯⣤⣤⣿⠀⣀⣤⡼⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣀⣀⣀⣠⣤⣄⣀⣀⣀⠀⠉⠓⢿⡀⠀⠘⢁⣀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄⠈⠳⡟⠋⠋⣥⠁⠸⡄
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣯⣿⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⣏⣻⣿⣿⣷⡄⠙⣆⣀⣀⣤⡄⢷
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣯⠁⢠⡤⠘⡇
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣿⣿⣿⡆⠘⣧⣤⠴⠆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣛⣿⣿⡄⠘⣧⣀⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⠀⠘⣿⠶⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣻⣿⡆⠀⠘⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣻⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⠒⢿⡛⠛⠒⠲⠶⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣞⠉⠈⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠈⠳⣄⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⣛⣲⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠙⢦⡀⠀⠈⠳⣄⠀⠈⠳⣄⠀⠈⠻⣄⠀⠀⠀⠀⢀⡼⠁⠀⣠⠖⣋⣭⠤⠶⠦⢭⣛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢦⡀⠀⠀⠙⢦⡀⢀⣹⡶⠶⠒⠛⠛⠛⠛⠚⠳⠦⣤⣀⡞⠀⠀⡼⢡⠞⠉⠀⠀⠀⠀⠀⠈⠳⣌⢻
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢦⡀⠀⢳⡀⠀⠀⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⣥⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠹⡌⢷⠀⠀⢷⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣿⢸⡇⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠴⠞⠁
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡿⢸⠃⡼⠁
⠀⠀⣠⠏⠀⠀⠀⠀⢀⡾⢡⢏⡾⠁
⠀⣰⡟⠦⠤⠤⠶⢚⣩⠴⢋⡞
⢠⠏⠉⠛⠒⠒⠛⠉⠁⢀⡞
⢸⠲⠤⣤⣤⣤⡤⠴⢶⡟
⠘⢧⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠙⠓⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢎⣸⣽⣿⣻⣿⣾⣿⣷⣜⠛⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠺⠛⠂⠿⠿⠟⣽⣯⣭⡝⠯⠍⠻⣷⣄⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣀⣰⠶⠒⠁⠀⠀⠀⠀⠀⠐⠒⢦⣍⡙⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠙⠓⢄
⠀⠀⠀⠀⢀⣼⠛⡀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡃⠀⠀⠸⡧⡀
⠀⠀⠀⢠⡿⢏⣵⣦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡶⣪⡴⣿⡄
⠀⠀⠀⠸⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠛⠉⠉⠉⠉⠉⠛⠓⠒⠲⠦⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⣠⠚⠓⣦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⠻⣍⣙⣒⣶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡞⢁⡽⠚⣉⠛⢦⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣏⠳⢤⣭⠤⢬⣑⠦⠌⠭⢶⣦⡄
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠛⡟⢠⡏⣩⠽⠖⠛⠛⠉⠉⠉⠛⠒⠒⠒⠲⠧⠾⢭⣷⣶⣒⣛⠒⢬⣓⣾⠿⢷⣿⡿
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠹⣄⣷⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠒⠛⠁
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⠏
⠀⠀⢀⡟⠦⠤⣄⣀⢀⡏
⠀⠀⡸⣟⢳⡶⢤⢬⡟
⠀⢠⠇⡼⢈⡇⢸⡸⠁
⠀⣾⡞⣱⢋⡴⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀
⢠⡇⣧⢻⢸⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠉⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡟⠻⣿⣿⣶⣶⣤⣄⣀
⣼⣠⣣⣾⢼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⣠⣿⣿⣿⣷⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡉⠳⠤⠤⠶⢬⡛⠿⠿⠿⢶⣦
⣿⣷⣷⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⢻⣿⣿⣁⡬⠟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠲⠿⠿⢷⣶⣿⣿⣶⣭⣽⣿⣿⣿⣿
⠘⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⣬⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠻⠿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢳⠲⣦⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⣸⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⡞⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⡇⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣴⣥⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⣾⣿⠏
⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣠⣹⣿⣿⣋⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⢐⣶⣶⣶⣶⣶⣤⣤⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⣲⣾⣿⣗⠼⣿⡿⢻⡎⢿⡿⢻⡿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⠰⣷⣼⣿⡤⢿⣿⣿⣧⡸⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠹⠿⠿⠯⠼⠿⠿⠿⠧⠿⢟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢟⢿⣿⣿⣥⣿⡿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣴⣶⣶⣖⣶⣿⣿⣿⣿⣶⣶⣲⣦⣄⡀⠀⠀⠹⡟⣹⣥⣴⡶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡌⣿⡿⢿⡏⢺⣿⣋⣻⡀⣿⣏⣻⣿⣿⣿⣿⣿⢿⣿⣤⡀⠀⠈⢿⣿⣿⣷⡿⠿⠿
⠀⠀⠀⠀⢀⣠⣴⣶⣿⣾⣿⣿⣇⢻⣶⣾⣿⡞⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣷⣼⣷⣿⣿⣷⡄⠀⠀⢻⢫⣵⣤⣶⣷⣦
⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠿⠿⠿⠥⠛⠛⠛⠓⠚⠛⠛⠛⠚⠛⠭⠿⣷⣿⣿⣿⣿⣿⠿⣿⣿⣄⠀⠀⢻⣿⣿⣧⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⢿⣿⣿⣶⠿⠿⢏⡀⠀⠀⢉⣹⣭⣴⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣡⣾⣶⣶⠚⣿⣿⡄⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⣟⢧⠀⠀⠀⢻⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⣤⣷⣶⢾⣿⡆⠀⠀⠀⢻⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡴⠿⠟⠀⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢒⠄⣀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣀⣀⠀⣬⡭⡬⠦⡀
⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠶⢋⢩⢝⡆⡿⠈⠅⣿⠃⡇⠀⠸
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠀⢁⣲⠀⡤⣞⣴⣏⣵⠾⢠⣹⢸⡼⣿⡮⣻⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢂⣾⣪⣲⣟⠻⠿⠿⠁⠁⠸⠿⠾⠋⠿⠿⠭⠈⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣨⢼⣿⣼⡃
⠀⠀⠀⠀⠀⠈⠀⠀⣘⣩⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣾⣮⣶
⠀⠀⠀⠀⠀⠀⠀⠐⠒⢈⣉⢉⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠕⡀⠀⠀⠀⠀⠀⠠⠐⠚⠺⠄⠠⠬⠤⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠲⢤⣀⣠⠴⠋⠀⢀⣠⠤⠤⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢰⠟⢄⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⠲⠦⠴⠞⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠊⠉⠉⠁⣽
⠀⠀⠀⠀⣾⢁⣀⠤⠖⠋⢉⣀⡤⠤⠖⠒⠚⠉⠉⠀⡿
⠀⠀⠀⣸⠏⢉⣀⠤⠖⠚⠉⠁⠀⢀⣀⠤⠤⠐⠂⢸⡇
⠀⠀⢠⡟⠊⠉⠀⢀⣀⠤⠔⠒⠋⠁⠀⣀⣀⠤⠄⣾⠁
⠀⠀⣾⣀⡤⠖⠊⠉⣀⣠⠤⠖⠚⠉⠉⢀⠀⠀⠀⡟
⠀⢸⠋⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⢠⠟⢳⠀⢸⡇
⠀⡿⠚⠉⠁⠀⠀⠀⠀⢀⣤⠤⠤⠴⠋⠀⠀⠣⣸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢹⡇
⣼⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⢘⡇⠀⠀⢀⡀⠀⣸⢷⣄
⣿⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⣇⡴⠚⠉⠙⢶⠏⠠⠙⠷⣦⣀
⣿⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠁⣀⣀
⢹⡄⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⢋⣉⣁⠀⠀⠋⢉⣃⣀⡀
⠈⢷⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣡⠴⠚⠋⠉⠀⢀⣠⠞⠋⠁⣨⠟⠷⣄
⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡳⣄⠀⠀⠀⠈⢳⡀⠰⣏⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠙⢦⡀⠀⠀⠙⢦⡈⢷⡀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⡀⠀⠀⠀⠀⠀⣠⠴⢋⡴⠞⠁⠀⠀⠀⠀⣳⠄⠹⡄⠀⠀⠀⠀⠀⠀⠙⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡴⠚⢡⠔⠋⠀⠀⠀⢀⣠⠶⠋⢁⡴⠚⠁⠀⠀⠀⠀⠀⠀⢠⡃⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣤⣀⠀⠀⠔⠋⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡎⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣴⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⡇⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣤⣀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣴⣋⠀⠀⠀⣠⠟⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢵⡶⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣋⡡⣶⣾⣻⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠈⠛⠃⢈⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠡⠔⠦⠄⢀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣍⢠⡀⠈⠛⠶⠂⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢻⣀⠸⠂⣀⣀⣶⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣻⣗⣮⣍⡺⣏⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣃⣛⣃⣾⣯⣿⣿⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣏⣨⣯⣼⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿⠛⣻⣧⣼⣷⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡤⠟⣛⡩⢭⡵⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠥⣶⣉⣹⡷⢾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⠛⠛⣿⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣿⡶⢞⣫⡍⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⢀⣼⡿⣷⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢨⠉⠀⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠶⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠰⠆⢰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢣⠈⢻⣯⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⠷⠌⠛⠛⠛⠛⠷⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⣀⣄⣀⣀⡀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⡾⠟⠻⢿⡿⢿⡇⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣤⣤⣴⡿⣵⢾⣿⡀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣲⣦⣼⣷⣄⠀⠀⠀⠀⠀⠙⠓⠲⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⠾⠛⠋⠉⢿⡛⢻⣿⣃⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⠶⠶⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠛⠛⢿⣿⣿⡟⣫⣽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡁⣀⣤⣼⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⠀⠀⠀⢀⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠯⣛⢿⣿⣷⣤⣿⡶⠶⠷⠶⠶⠶⠶⢤⣌⡉⠀⠀⠴⠋⠼⢂⡁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⣤⣤⣠⠄⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢦


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⠈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠁⢹⠜⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⡏⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠇⣿⠀⢸⡖⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢸⠁⠠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠷⢹⡀⠀⢷⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⢠⠃⢀⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠆⠀⠐⠮⣅⠀⠚⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢤⠃⢀⠊⢀⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠐⠀⠀⣃⠱⠄⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡀⠀⠀⢲⠁⢀⠎⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠀⡀⢈⠀⠀⠈⠂⢲⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠀⠀⠀⠷⠁⡠⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠐⠃⠀⠀⠂⠀⠀⢫⣬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⡀⠌⠀⠠⠀⠄⣛⡀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢀⡠⠷⠀⠀⠘⡄⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⢋⡷⣦⡀⠀⠰⠀⠈⡅⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⡄⠔⠐⡂⠀⠁⠐⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣋⣼⣱⢣⢟⣦⡀⠠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢧⠀⠷⢀⠠⠉⡐⢨⠀⠑⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⠉⠈⠙⢮⡜⡼⢹⢄⢠⡇
⠀⠀⠀⠀⠀⠀⢀⠣⡑⡈⢇⠘⡆⠀⠀⠁⠰⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢙⠣⣄⠀⣠⠀⠘⢷⢋⠞⣾
⠀⠀⠀⠀⠀⢀⠦⢄⣱⣔⡈⢆⠐⣤⠊⠉⠳⡀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡀⠉⢻⡅⠀⠐⠀⠿⣾⡟
⠀⠀⠀⠀⠀⣜⠁⠒⠢⢄⣐⡈⢆⠻⠤⠀⠁⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠣⢄⠀⠒⠛⣆⢀⡄⠤⢹⡇
⠀⠀⠀⠀⢸⡣⠤⣍⠑⠲⠬⡙⠀⢂⠱⡀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠑⠄⠈⢆⡐⠂⠸⡇⠀⠠⠘⡇
⠀⠀⠀⠀⡿⢤⣀⣸⠔⠛⠂⢨⣑⠢⢧⠘⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠢⡀⠈⢠⠈⢧⠀⠀⣸⡀⠀⠀⠹⣄
⠀⠀⠀⢰⠏⠀⢀⡀⠓⢶⠯⠲⢨⡠⠂⡄⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠑⡄⠀⡅⠐⠂⠅⢰⡏⠁⠨⣀⡽⢧⡀
⠀⠀⠀⢸⠦⢤⣬⣄⡀⣸⠀⠉⠳⡄⢀⡆⠀⠚⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠇⠀⢸⠀⡋⠀⠰⡇⠈⢑⡄⣿⠬⢽⢦⡀
⠀⠀⠀⢻⠀⠀⢠⠀⠉⠳⠆⡀⣴⠀⠈⠢⡄⣠⠄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣇⠀⡈⠀⡅⠀⢠⡇⣐⡋⠀⣩⣝⣚⠎⠻⣦⡀
⠀⠀⠀⠘⣆⠈⠈⠒⠠⠔⡀⠈⠳⣄⠀⣁⠀⢱⣄⣠⠥⠘⢦⣄⠀⠀⠀⠀⠀⠀⠈⠳⢇⡸⠀⠂⢼⠃⠉⠀⠁⣓⠒⠶⣏⠐⠩⡛⢦
⠀⠀⠀⠀⠈⠫⡀⠁⠀⠀⠑⣤⠄⠈⢧⠀⠀⠀⠈⠧⡀⣠⣀⡬⠷⢤⡀⠀⠀⠀⠀⠀⠈⠙⢦⣲⡇⠀⠀⠆⣸⠫⠭⣙⠂⠄⠀⠱⡤⠽⣆
⠀⠀⠀⠀⠀⠀⠈⠲⡶⠄⠤⢼⡤⠤⠤⢷⢶⠖⠚⠚⠋⠁⠀⠀⠀⠂⠙⣢⣀⠀⠀⠀⠀⠀⠀⠙⠷⣍⠀⢸⢯⣍⡒⢖⠁⠀⡴⠀⠱⠦⠬⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢅⡀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⡠⣤⠦⢂⠀⠄⠈⠳⢄⡀⠀⠀⠀⠀⠀⠈⠳⣝⡳⢬⣙⠇⠀⠊⠅⠀⠀⠤⢤⣀⣈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣞⠚⠓⠒⡘⠓⠋⠋⠁⢄⡑⠒⠨⠀⠂⠀⠰⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠙⠦⣍⠀⠀⠀⣈⠒⠄⣀⡀⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⡴⠁⢠⣀⣠⠋⠁⠀⠉⡴⠊⠉⠉⠇⠘⠀⠀⣈⡷⣄⠀⠀⠀⠀⠀⠀⠈⠳⢦⡉⠀⠁⠀⢨⠀⠉⠓⠦⢄⡘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡘⢀⠀⠈⠘⠣⡀⢀⣀⣀⣠⡴⠟⠋⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠰⠖⢤⣀⠀⠀⠉⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣟⡛⠛⠛⠋⠉⠉⠀⠀⢀⣀⢤⢲⣫⠾⠷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠈⠙⢦⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡶⣒⣒⣒⣂⣬⣯⠶⠟⢉⡉⡔⠊⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠽⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠤⢭⣠⢆⡀⢃⣈⢢⣀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡄⣰⣶⡀⣶⣶⣦⢰⡆⣴⠆⠀⢰⡆⢰⡆⣶⢰⡆⣶⡄⣶⢴⣶⠆⣶⡶⢰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⢹⡇⣿⣆⣿⢸⣿⣿⠀⠀⢸⣧⣼⡇⣿⢸⡇⣿⣿⣿⠀⣿⠀⣿⣄⢸⡇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣿⢾⡗⣿⠉⣿⢸⣟⣿⣀⡀⢸⡏⢹⡇⣿⢸⡇⣿⢿⣿⠀⣿⠀⣿⠁⢸⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠟⠘⣧⡿⢖⣻⠽⡷⠾⠻⠭⠿⢷⡺⠇⠻⠿⠃⠻⠈⠟⠐⠿⠀⠿⠿⠸⠇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠈⠀⠉⣻⣿⠟⢿⣿⣿⡿⠚⠉⢀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⣀⣤⡶⢶⣾⡋⠁⠀⠀⠀⢀⠀⠀⠬⣝⣿⠻⠶⠭⠁⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣶⣿⣿⣤⣼⡟⠀⠀⠀⠀⠀⠀⠁⠀⠱⣮⣻⡂⠀⠀⠀⡠⠚⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣭⣿⣿⣿⣥⣦⡔⠀⠀⠀⠀⠀⡄⠀⠙⣝⣿⣦⠀⣾⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⢠⠀⠀⠀⠃⣠⢻⣎⢻⡎⢅⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣫⣿⣿⣾⡿⣿⣿⢿⢹⠀⠀⠘⠀⠀⣴⢀⣿⣿⣿⣦⣧⠈⣮⠻⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⢏⣼⣿⣿⣾⠈⠎⠀⣰⢃⣼⣿⡎⣿⣿⡿⣿⣿⣦⡉⣦⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⡩⢋⣿⣾⣿⣿⠟⠁⢠⡄⠀⣱⣿⣿⣟⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡤⠤⢂⣨⣿⣿⣿⣿⣼⣰⢟⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣙⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢤⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣢⣟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣏⣾⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠛⠛⠛⠛⠛⠛⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⢰⣼⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⣼⣦⡀⠀⠀⢾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣄⣘⣿⣿⣿⡆⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣦⣀⣄⠿⠛⠉⠀⢀⣤⣶⣤⣤⣤⣀⠘⢷⣄
⠀⠀⠀⣴⠟⠀⠀⠠⣆⠀⣶⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠻⣦
⠀⠀⣼⠏⠀⠀⠀⠀⠹⣿⣿⣧⡠⠖⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠛⠉⠁⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⣧
⠀⣸⡏⢀⠀⠀⠀⠀⠐⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠛⢉⡏⡰⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣇
⢠⡿⠀⢿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⢿
⣸⡇⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣷⣦⡀⢸
⣿⠀⢠⡀⣤⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣶⣦⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⠀⠈⢻⣿⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡄⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⡇⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⡿⣿⣿⣷⣀⣀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣷⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣽⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢻⣆⡄⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠻⣧⢸⡄⠀⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠙⢿⣇⢰⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣾⣿⡆⡆⡄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣧⣱⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣝⣻⣿⣿⣿⣿⣿⠛⠋⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠾⢿⣿⣤⣴⣴⣦⣶⡶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠛⠛⠛⠛⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠂⢉⣀⣀⣄⣀⣤⣄⣠⣄⡀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⠛⢋⣡⣤⡴⠶⠶⠶⢶⣶⠶⢬⣭⣱⠶⣤⡀⠀⠈⢳⡄⢠⡀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠀⠀⢈⡛⠉⠀⠀⠀⠀⠀⠘⠛⢷⡄⠀⠈⠙⢳⣎⢳⣦⡼⠇⠘⠃⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡇⠀⢀⣴⠖⠀⠀⣠⣤⣄⢻⡆⠀⠀⠀⢿⠋⠀⠀⠀⢸⠇⠾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠛⢉⣩⣶⣟⡁⣠⣄⣙⣿⡀⠀⠀⠈⣧⣠⣄⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠀⢸⠁⢻⣿⣿⡇⠀⢼⣿⣧⣿⠀⠀⠀⠀⠟⠀⣹⠀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⣄⠷⠦⠾⠏⠙⢦⣄⣩⣿⠟⠀⠀⠀⠀⣀⣤⠟⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢶⣄⠀⠀⠀⡋⠀⠀⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣠⣴⠟⠑⢦⡌⠈⠀⠀⢠⡇⠀⠀⢸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠶⠶⠶⠛⠛⠉⠀⠀⠀⠀⠈⢢⡀⠀⢸⠀⠀⠀⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡤⠶⠚⠁⠈⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠞⣶⡖⢠⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣄⣀⠀⠀⠀⣠⣴⠟⠉⣶⣤⡀⠀⣀⡀⢠⣤⣤⠾⠋⠀⢸⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡙⢋⠁⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⣠⡟⠀⠀⠀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠲⣤⣀⣀⠀⠀⠀⢀⣀⣤⡾⠋⠛⢧⡀⠀⡷⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⡇⠈⠉⠛⠛⠛⣿⠉⠀⠀⠀⢠⡖⢱⣄⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠶⠚⠃⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⠁⠃⠸⡁⢸
⠀⠀⣠⡴⠶⠒⠛⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢠⡇⠘⠀⠀⢻⣾
⠀⣾⠁⠀⠀⣠⡀⠀⠀⠀⢀⣀⣤⣴⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠶⠶⠀⠈⢿⡄
⠀⠻⣆⠀⠀⠉⠻⣯⡉⠉⠉⠉⣰⠏⠀⠸⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠸⡇⠀⡆⠀⠀⠘⠹⣦
⠀⠀⠘⢷⣄⠀⠀⠈⠙⣦⢀⡼⠋⠀⠀⠀⢹⡄⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣾⣥⣰⣂⣡⠀⡇⠀⠀⠀⡇⠈⢷⣄
⠀⠀⠀⠀⠙⣧⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠻⣀⣠⠋⠀⠀⠀⠀⠀⠈⢱⣯⠀⠉⠉⠁⠀⠑⢦⣀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⣸⠆⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠠⣎⠁⠀⠀⠀⠀⠀⠀⠈⣿⠉⠻⢦⣤⣀⣀⠉⢷⡄
⠀⠀⠀⠀⢸⡷⠒⢺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠛⢦⠀⠙⢦
⠀⠀⠀⠀⡞⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⠄⡀⢸⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⣀⣤⡤⠒⠾⣅⡀⢀⡀⠀⠀⢀⣀⣠⣤⡴
⢇⠘⠓⠈⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡇⠀⢩⠀⠀⠀⠀⠀⠉⢹⡏⠉⠁
⠈⠓⠶⠶⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠑⠒⠒⠒⠒⠒⠒⠉⠉⢹⡇⠀⠀⡄⠘⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠓⠶⠤⣤⣤⣤⣤⠶⠖⢺⡇⠀⠀⠐⣄⠡⣄⠀⠀⠘⣷
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢦⡈⠓⢤⣤⠿⣀
⠀⠀⠀⠘⠒⠒⠒⠒⠒⠲⢦⣤⣤⣤⣉⣉⣉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠒⠒⠖⠒⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠉⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⢶⡶⠦⣤⣤⣄⣀⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠙⡞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠛⠓⠒⠒⠒⠒⠀⠤⢶⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣧⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣟⠁⠙⠳⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⡶⠒⠒⠒⠒⠲⢤⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠔⠒⠛⠓⠛⠒⠀⠀⠀⠀⠈⠓⠚⠻⠛⠛⠋⠉⠉⠙⠛⠛⠻⠿⢶⣶⠶⠾⠃
⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠤⠤⢤⣤⡴⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣞⣀⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀
⠀⠀⠀⠀⠀⠀⢀⠯⣝⡦⣝⣿⡄
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠉⠙⠻⠷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⢘⠗⠲⢤⣀⡀⠀⠀⠀⠉⠛⠺⢭⣒⠦⢄⣀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⣹⣄⣤⣀⠀⠀⠀⠀⠈⠙⠒⠬⣧⣀⠀⡀
⠀⠀⠀⠀⠀⠙⠶⢤⣀⣀⡏⠀⠈⠙⠛⠦⣄⡀⠀⠀⠀⠀⠀⠉⠙⠻⢧⣞⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣗⡤⢄⡀⠀⠀⠀⠈⠑⠂⣤⢀⡤⣀⡀⠀⠀⠈⠉⠒⡦⢭⣒⠤⢄⡀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣝⡲⢤⡀⠀⠰⣇⣀⣽⢶⠯⢕⣲⠀⠀⢀⠁⡆⢸⢹⢲⠬⣵⣶⡍⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠧⣄⣀⠀⠉⠙⠛⠶⠼⠉⡗⠓⠾⣘⠁⣸⣸⢸⢰⠂⡏⡙⠒⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣼⠉⠙⠓⠲⠤⣼⡇⠈⠓⢤⣀⣿⠺⡇⠹⢿⣼⡁⡇⣧⠀⢰⣏⣉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢰⡇⠀⠀⠀⠀⡴⠁⠈⣳⠀⢀⡎⠁⠀⠈⠓⠢⠔⠛⠧⣟⠤⣼⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⣆⠀⠀⠐⠛⠒⠚⠋⢹⡄⠘⣆⠀⣀⣀⠀⠀⠀⠀⢀⣠⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢽⣷⣦⣄⡀⠀⠀⠀⢸⣇⣾⡁⠸⣟⣩⠇⠀⢀⡴⡯⠬⣥⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣒⡶⠞⠙⡶⠃⠀⠀⠀⠀⠀⡼⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠈⢧⡀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⢰⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡟⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⣀⣤⣄⠀⠘⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢇⣾⠀⠀⢷⣞⡽⠂⠀⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠬⣭⣓⣦⠬⣤⡀⢠⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠻⠶⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⢿⡟⠙⢿⣁⣹⣏⣈⣿⣀⣸⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢤⣜⠋⢾⡋⠙⣏⣉⣿⣅⣈⣿⣿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢾⣿⣷⣶⣶⣶⡶⢻⣆⣀⡿⣶⠞⢻⡟⠛⣿⠉⣿⠉⠉⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡿⠞⠋⠉⠉⠙⠛⢿⣷⡎⢉⣿⣠⡼⣧⡾⢷⡶⠻⣿⠛⢿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⡷⠋⢀⣤⣶⣦⠤⣤⣤⣿⣧⠟⢿⡁⣻⣀⣸⣧⣼⢧⣤⡿⣦⣼⣿⡟⠀⡆
⠀⠀⠀⠀⢀⣤⣾⣟⣻⡿⠟⣵⢶⣿⠷⠿⠓⠷⠶⡿⠿⠻⢶⠊⢻⣅⣹⣄⣸⣧⣀⣿⣀⣸⣇⣀⡇⣀⠁
⠀⠀⡠⢺⣿⡿⠟⠋⠁⢀⣠⣿⠏⠁⣀⣤⣀⣀⡀⢲⣼⣧⡼⢿⠋⢻⠉⢻⡏⢉⡏⠈⣿⠁⢹⣿⡇⡿⡀
⢀⣾⡿⠛⠉⢀⣠⣶⣿⣿⡿⢟⣥⣿⣿⣿⠿⣽⣿⣿⣯⣸⣦⡼⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠂⡇
⠸⡟⠁⣠⣾⣿⡿⠿⠋⠀⠀⣘⡿⠉⠀⣀⣀⠀⠈⣩⣝⠉⠖⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠤⣶⣶⡆⠀⡇
⠀⢡⣰⣿⠟⢁⣀⣸⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣷⣾⣿⢐⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠃⠀⣿
⠀⢸⣟⣡⣴⣿⣿⣿⡍⠀⠉⢽⡿⠋⢁⣀⠀⠈⠛⢛⣣⡏⠴⢃⣀⣤⣤⣤⣤⣤⣤⡤⠀⣤⣤⣶⡆
⠀⠀⢻⡟⠋⢀⣐⣿⣶⣿⣷⣿⣟⣻⣿⢭⣷⣶⣤⣸⣿⣷⣀⠻⠿⠿⠿⠿⠻⠟⠛⠓⠂⠛⠛⠛⡇⡀⣬
⠀⠀⣨⣴⣶⣿⣿⡉⠉⠉⢩⣽⣏⠁⠀⠈⠉⠙⠛⣛⣿⠋⣅⠀⣀⣀⣀⣠⣤⣤⣀⣠⣤⣤⣵⣴⡇⠁⣷
⠀⣼⠟⠋⣀⣺⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣶⣬⣿⣿⣶⣺⣿⣿⣿⣿⠿⠿⠿⠿⠿⠶⠿⠿⠿⡂⠀⡗
⠀⣧⣶⣿⡿⣿⣧⡀⠈⢉⣽⠟⣡⡀⠀⠈⠙⠛⣻⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠁
⠀⣿⢁⣀⣼⣿⠿⣿⣿⣾⣿⣶⣿⣿⣿⣷⣶⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢠
⢠⣿⠿⠿⣿⣟⡀⠀⣽⣿⠟⠉⠀⠀⠉⠛⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢸
⢸⣁⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⡿⠿⠿⠇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣤⣤⣤⣤⣤⣤⡄⡀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣰⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣴⣿⣿⠿⣿⣿⣻⣿⣟⣫⣿⣿⣿⣿⣿⣸⣽⣿⣿⣭⣟⣛⣿⣿⣛⣿⡇⣉⣉⣉⣉⣹⣷⣄⣀⣀⣀⣠⣿⣇⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠃⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠉⠁⠁
⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠁⠀⠀⣿⣿⡿⠃⠁⠀⠐⠟⢿⣿⣿⣿⡀
⠘⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣐⠶⢠⣴⠄⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣷⡄⠀⢠⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣿⣿⡿⢁⣀⡘⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⢨⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡷⠆⠉⠉⠩⠶⠿⠿⠿⠶⠉⠉⠁
⠀⠀⠀⢀⡀⢀⢻⣼⣷⢸⣿⣳⣿⡿⣿⣿⣿⣿⡿⠿⠟⠀⣀⣀⣀⣀⠈⠙⠛⠛⠛⠋⠁
⠀⣠⣾⣿⣠⣿⣷⡹⠿⣸⣿⣾⣿⣷⣄⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠁
⢸⣿⣿⣿⣿⢿⡿⢀⡘⠯
⢸⣿⣿⣿⣿⠀⠁⣼⡇
⢸⣿⣿⣿⡇⠀⠀⠉⢡⠆⠴⠾⠂
⢸⣿⣿⣿⣇⡀
⠘⣿⣿⣿⣿⡿⠁
⠀⢿⣿⣿⡿⠁
⣀⣘⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣖⣮⣭⣽⣭⣭⣵⣖⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣯⠧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⢉⣁⣠⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣽⣾⣿⣿⣿⣿⣿⣿⡿⠃⠙⠿⠟⠳⢯⣷⣿⣿⣿⣿⣿⣿⢟⠞
⠀⠀⠀⠀⠀⠀⠀⣸⣱⣿⣷⣿⣿⠋⠖⠈⠿⠋⢐⣦⣄⡀⠀⠀⠀⠀⠙⠻⢿⣿⣋⣚⣷⣶⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢾⣻⣿⣿⢿⡀⠀⠐⠀⠀⠀⠈⠋⠀⠀⠀⠀⠉⠀⠉⠘⠉⠉⠉⠉⠉⢹⣽⠀⠀⣠⣫⢿⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣓⣆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠋⢍⣍⡽⠲⣶⣶⣶⣞⡋⣎⣀⣰⣳⠃⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡴⣯⠭⠿⣭⣯⣷⣯⣽⠄⠤⠐⠀⠠⠵⠠⠤⠀⡴⢋⢪⠀⢆⠀⠀⡀⠀⠙⠒⠓⢲⠃⠐⡞⢷⣭⣢
⠀⠀⠀⢀⡤⣤⣴⣹⡇⠀⠀⢀⣀⡀⡠⠀⠀⠀⠀⠀⠐⠒⠀⡤⣴⢣⠈⠀⠀⠈⠂⠤⠄⠃⡴⣲⣒⣚⣦⣴⣷⣾⣟⡽
⠀⠀⡴⡵⠋⠉⠉⠉⠉⠁⠀⠀⠀⠰⠁⠀⠀⠀⠀⠉⠉⠠⢾⣥⣿⣷⣄⠀⠀⠀⠀⠀⣰⣞⣵⠁⠀⠀⠉⠉⠉⠉⠁
⠀⢸⣹⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣄⡀⠀⠀⣈⢀⣀⣾⣿⣿⣿⣿⣷⣤⠤⢤⡔⢿⣿⣮⢦⡀
⠀⠈⢫⡳⣤⣀⣀⣀⡠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⠙⢿⣷⡵⣄
⠀⠀⠀⠈⠓⠺⡽⣍⠉⠉⣹⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢿⣞⣆
⠀⠀⠀⠀⠀⠀⠙⢮⣲⣶⣛⡯⠗⠊⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⠠⠄⢀⣴⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡷⢝⡦⠤⣞⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡯⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠭⠽⢿⣿⣟⣿⣿⣿⠯⠭⠟⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣷⣲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠿⠷⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣃⣀⣼⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⢿⠋⠁⢸⠟⠛⠛⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠉⠨⡄⠀⠀⠀⠀⠰⠪⣶⣶⣶⣾⣭⣭⣤⣷⡶⠟⠛⠛⠛⠺⠞⠲⠒⣶⠚⠛⠛⠛⠛⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢤⡀⡀⠀⠠⠄⠓⠀⠀⢀⠀⠀⠀⠀⠐⣔⡪⠍⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣶⠶⠖⠛⡛⠉⠀⠠⣶⣚⣀⠈⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⢸⡀⠀⠀⠀⠀⢾⡁⣀⣤⣶⠋⠀⠀⠀⢀⣿⣿⣷⣶⣆⡀⡄⠤⠁⣀⣀⣠⣤⠴⠶
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠙⡯⡟⠁⠀⠀⠀⢀⣿⠏⠙⠛⠻⢻⣿⣿⣶⣼⡿⠋⠉⠈⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠃⠀⠙⢦⣄⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⢿⣦⣤⣴⣿⣿⡿⡇
⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠈⠙⠋⠻⣿⣿⡟⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠘⠂⠀⠀⠠⠄⠀⠀⠉⠁⠀⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢹⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠲⠖⠤⣤⣤⡾⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠩⠍⠐⡒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠢⡀⠀⠀⠀⣠⢤⣤⡤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⢢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣠⠿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠛⠃
⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣻⣏⣙⢂⠀⠀⠀⠠⠤⠤⠀⠒⠂⠁⠀⠀⠀⣠⡤⠤⣤
⢸⠀⠐⠀⠒⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⡀⠀⠀⠐⢻⡅⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀
⢸⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⣴⠀⠀⠀⠀⢀⡴⠒⢲⡇⠀⠐⠒⠒⠒⡖⠛⠛⠛⠁⢀⡟⠉⠉⠻⣦⡀⠀⠀⢿⣀⡾⠁⠀⠀⠀⠀⠀⠀⢠⡏
⠘⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠘⣿⠛⠛⠛⠛⠛⠀⠀⠠⡕
⡄⠀⢠⡿⠒⠒⠲⢾⡇⠀⠀⠀⣿⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠈
⡇⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⣴⠀⠀⠀⢙⡷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢿⣄⠀⢀⡾⠁⠀⠀⠀⠀⠛⠀⠀⠀⡠⠂
⡇⠀⠸⠃⠀⠀⠀⢸⠇⠀⠀⢰⡿⠀⠀⠀⠿⢶⣤⣤⠞⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⣀⡀⠠⠄⠂⠉
⠧⠀⠐⢆⣀⣀⣀⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣤⠤⠤⠤⠀⠐⠒⠒⠒⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠡⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⢸⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⢸⠀⠀⠔⠜⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⢀⠀⡇⠀⠀⠀⢸⠠⠀⠀⠀⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠂⠸⠧⢤⡬⠐⢠⠄⠉⠁⠂⠨⠁
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⣤⣤⣤⣤⣬⣽⠋⠁⠀⣾⣟⠢⣀⣶⠀⠀⠀⠘⣾⣿⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⣓⣿⣦⣤⣤⣤⣄⣀⣀⣀⣰⣟⣿⣿⣇
⠀⠀⣷⣶⣾⣿⣿⣿⣉⣉⣉⣩⣿⣿⣿⣻⣽⣧⣦⣤⣮⣤⣿⣶⠀⠀⣠⠤⠆⠁⠀⢀⣿⣷⣿⣯⣭⣭⣭⣿⣽⣯⣿⣿⣯⣽⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣶⣿⠻⠛⠛⠛⠻⠛⠋⠋⠛⠛⠉⠉⠋⠛⠛⠀⠀⠀⠩⠾⠿⢢⣶⠾⣿⣿⣿⣷⣶⣶⣶⣶⣾⣷⣶⣾⣷⣿⣿⣿⣿
⠀⠀⣿⣿⠉⢹⣿⡏⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⢉⣉⣿⣿⣿⣭⣭⡽⢯⣯⣿⠿⠿⠛⠉⠉
⠀⠀⠿⠃⠀⠘⣿⣗⠀⠀⠀⠀⠀⢼⣷⣂⣀⣉⢻⡅⢸⡿⠷⠿⡿⠉⣶⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣧⣼⣿⠁⠀⠀⠀⠀⣀⡀⡠⢠⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠈⣿⣍⣉⣝⣿⣛⣻⣿⢿⣿⣟⣃⡐⠦⢀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⣿⣿⣿⣿⡄⠀⠀⢠⠋⠁⢹⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠈⠈⠁⠀⣻⣦⢿⣿⣶⣶⡦⠋⠁⠀⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠘⢄⢀⣴⡽⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣶⡶⢶⡖⢲⣶⣶⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿⡇⠀⢀⡤⠛⣏⠰⡿⣿⣶⡀
⠀⠀⠀⠀⢀⣀⡶⣤⣴⣶⣶⣶⣦⡴⣆⣀⠀⠀⠀⠀⢻⣁⠀⣇⡿⢋⣽⣿⣷⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠀⠀⠘⠠⣤⣧⣬⡇⣿⣯⡿
⠀⠀⠀⢀⢿⣛⣋⡾⠿⠷⠰⠿⠿⣎⣛⣻⢇⠀⠀⠀⠀⠑⠓⠛⠁⠁⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣼⣀⣸⡇⣿⣿⣸⣷
⠀⠀⠀⠈⠛⠛⠛⣦⣤⡾⠿⣦⣤⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣷⠀⠀⣤⣤⣤⣶⣶⡀⠀⠀⠀⠀⠀⢸⠉⢿⠉⢩⡇⣭⣭⢫⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠶⢶⣦⠀⠘⢀⣻⣿⣿⡿⠟⠀⠀⠨⢻⣿⣿⣟⣧⠀⠀⠀⠀⠀⠌⠐⢺⠖⠶⡗⣛⣻⣚⠋
⠀⠀⠀⠀⣤⣀⣀⣤⣤⣤⣷⣷⣴⣤⣤⣤⣤⣶⣿⣒⣲⣶⣖⣾⣖⣯⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠃⠠⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠙⠙⠛⠛⠛⠛⢹⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⢿⣿⣿⣿⡇⠀⠀⠈⡟⣿⣿⣧⠙⡏⡝⠛⢑⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣸⢲⣎⣲⣛⡶⢿⠀⠀⠀⠀⠀⢸⣿⣿⡷⠾⠿⣿⣧⠀⠀⠀⠀⠀⠉⠙⠃⠀⠒⠟⠁⠘⠿⠿⠂⠳⠶⠶⠷⢶⣶⣶⣶⡤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠈⢻⣏⣉⣙⡟⠉⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣇⣨⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣒⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣤⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⢿⡟⠏⠉⣻⠉⠳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⢀⣠⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢠⣿⣿⢟⣷⣿⣿⣿⣿⣿⡄⠀⠈⠙⠧⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣟⠿⠛⠋⣿⣿⣿⣿⠀⠀⠀⠈⢹⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣄⠀⣼⣿⣿⣿⣿⠀⠀⢀⠀⠈⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣦⣻⣿⣿⣿⣿⢿⣿⣯⣭⢻⢿⣿⣿⣿⢛⡟⣿⡄⠘⢿⣿⣿⣿⠁⠀⠈⠃⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠾⣽⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣦⣤⣤⣿⠏⢸⠃⣿⣿⣤⣿⡿⣿⣿⣧⣀⡀⢀⣠⣴⠀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡘⠿⠶⢿⣷⣿⡇⠀⠀⠀⠉⢻⣿⣿⣿⡟⠀⡾⢀⡇⢿⣿⣿⢃⣿⡧⠀⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣷⣶⣿⣿⡗⠀⠀⠀⠀⣼⣿⣿⣿⠃⣼⠁⢸⠓⢸⣿⣿⣿⣿⢃⣨⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡹⣿⣿⢿⢿⣿⠀⠀⠀⢠⡿⢹⣿⡏⠀⠁⠀⠀⠀⣼⣻⣿⣿⢡⡿⠋⢀⣤⣶⡀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡘⢿⣾⡛⣿⡆⠀⠀⠸⠅⣼⡿⠀⠀⠀⠀⠁⣰⢯⣿⡿⠃⣾⣾⣟⢃⣶⣄⠃⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣎⠻⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣾⣿⣇⡸⣿⠁⠀⠈⢉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠻⣏⢿⣧⡄⢸⡇⠀⢀⡀⠀⠀⠀⠀⠀⡀⣰⣿⣶⣿⣷⣿⡗⣶⡛⠛⠢⠞⢴⠶⢴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠙⠳⠿⠇⢸⣷⣾⣿⣟⣿⡏⠀⠀⣸⣆⣻⣷⣿⣿⣿⣿⣿⣘⡇⠈⠁⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣶⣄⣀⣿⠏⠙⢿⣿⣿⣷⣀⣰⣿⣿⢿⡋⠉⠈⠿⠿⢻⣯⣿⣤⣤⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⠿⣿⡿⣻⣷⢟⣽⢟⡗⠘⠻⠻⠿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣷⣬⣴⣾⣿⣿⣿⡆⠀⠀⠀⠉⠉⠛⣿⡿⠟⠀⠈⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⣴⣿⣿⣯⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠀⢤⣄⠄⠀⠛⠻⠿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠄⣾⢻⠎⠒⠁⠀⠀⢻⣷⣶⠆
⠀⠀⣠⣴⣶⣾⣿⣏⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠚⠛⠛⠛⠚⠷⠆⣀⢰⣿⠟
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⣿⠛⠛⠛⢁⣬⡠⣦⠀⠀⠨⠾⠿⠚⠛⠛⠉
⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⡽⠶⣔⠺⣿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡉⠓⠀⠂⠘⢆⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠟⠁

⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⣀⣀⣠⣀⣀⠀⢀⣤⣤⣤⣤⡀⠀⠀⢀⡄⢀⠀⣤⡀⢠⡀
⠀⠠⣼⠄⠀⣼⡄⠀⢰⡆⠀⠀⣿⠀⠀⢸⡄⠀⠀⣿⠿⢿⠻⣿⠁⠸⢿⣿⣿⣿⠇⠀⠀⣿⣧⣸⣀⣿⡇⠈⢷⣄
⠀⠀⣿⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿⠀⠀⢸⡇⠀⠀⢿⠀⢸⠀⠿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡿⢻⠿⣾⡇⣤⢼⣿⡄
⠀⠀⣿⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⣀⣀⠀⢸⠀⠀⠠⠄⠀⢸⡇⠀⠀⠀⠀⠹⡇⢸⠀⡿⠃⡟⠛⣿⠇
⠀⠀⣿⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⣷⣺⠀⢺⠀⠀⢀⡀⠀⢸⡇⣰⣄⣰⣆⣠⡆⢸⠀⠀⠀⡟⢠⡟
⠀⠀⣿⠀⠀⢹⠀⠀⢸⡇⠀⠀⣿⠀⠀⠈⠁⠀⢿⡼⠀⢼⠀⠀⢹⡇⠀⢸⡇⢿⡿⢼⡧⢿⡇⢸⠀⠀⠀⡷⠋
⠀⠀⣿⠀⠀⣾⠀⠀⢸⡇⣀⠀⠀⠀⠊⠉⠓⣦⢸⡇⠀⢸⠀⠀⢸⡇⠀⢸⡇⠈⠀⢸⡇⠀⠁⢸⠀⠀⠀⣷
⠀⠀⠈⠀⢀⠉⠀⢀⠀⢰⣿⠀⠀⡄⠀⢀⠴⠋⢸⡇⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡷
⠀⢰⣧⢀⢸⡇⡀⣿⡄⢸⣿⠀⠀⡇⠀⢸⠀⠀⢸⡇⠀⢸⠀⠀⢸⡇⠀⠘⠃⠀⠀⢸⡇⠀⠀⠸⠀⠀⠀⣿
⠀⢸⡿⠈⢻⡏⠰⢿⠖⠸⣿⠀⠀⡇⠀⠈⠀⠀⢸⡇⠀⢸⠀⠀⢸⡇⢰⣷⣾⣶⡇⢸⡇⣤⣤⣤⣤⡄⠀⠘⠇
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡷⠀⠀⠁⠀⠀⢲⠀⢸⡇⠀⠀⢀⣀⣀⠀⢸⣿⣿⣿⡇⢸⡇⠿⠛⠋⢹⠁⣀⣸⣇⣰⡆
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢸⠂⠘⠃⠀⠀⢢⣽⣥⠀⠈⠋⢹⠉⠁⠀⠀⠀⣺⡆⢸⠀⠉⢹⡏⠙⠃
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣴⣶⢶⡄⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⢀⣼⣿⠁⢸⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⣤⢸⠀⠘⢿⠋⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⢀⣾⡿⠃⠀⢸⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠿⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣼⠟⠁⠀⠀⢸⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⡇⠀⢠⠀⠀⢸⠀⠀⠇⠀⠀⡀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⢽⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠽⠋⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢝⢦⡀⠀⢀⡤⡺⠛⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⣽⣿⡵⠋⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⢔⡫⠚⠛⢮⡢⡀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⣾⠗⠉⠀⠀⠀⠀⠙⢮⣢⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣯⣄⡉⠁⠀⠀⠀⠀⠀⠀⠙⠪⡲⣄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠨⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠈⠪⡳⣄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣈⠪⡳⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠾⣇⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠜⡿⡟⢙⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣤⣶⣵⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠈⠚
⠀⠀⠀⠀⠀⠀⢰⡿⣻⣯⣵⣿⣿⡏⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣠⣃⣤
⠀⠀⠀⠀⠀⠀⠸⣿⠻⣿⡿⣿⣿⢃⣾⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠏⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡾⠿⠿⠿⠊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠤⠴⠃⠈⠓⢢⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢁⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡟⡗⠚⡇⠀⠀⠀⠀⣠⡶⠶⠂⠐⣧⢒⡶⠃
⠀⠀⠀⠀⠀⠀⠀⢄⣏⠸⣇⣇⣀⣙⣲⡄⢸⣾⢟⣶⣄⣀⠚⢉⣀⣀⣀⣀⣀
⠀⣁⡀⠤⠒⠚⠃⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠀⠸⠖⠠⢀
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⡐⣄⠊⢧⡲⡀
⠀⠀⠀⡠⠔⠉⠀⠀⠀⠙⢦⣠⠵⠌⠃⠀⠁⠘⠄⠀⠀⢀⣀⣀⡀
⠀⣠⠎⠀⠀⠀⠀⠀⠀⢠⠎⠁⢀⣀⡀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣰⠁⠀⠀⠀⠀⠀⡴⠋⠈⠆⠴⠛⠛⠃⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄
⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢻⡄⠀⠈⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢣⡀
⠹⢄⡀⢀⡠⠞⠀⠀⠀⡀⠀⣀⠀⡱⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢳⠀⠰⠀⢢
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣣⡘⠿⢷⠀⢀⣤⡀⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠇⠀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣽⣿⣿⡆⠌⣛⠕⠁⠀⠀⢻⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⡀⠀⡇
⠀⡎⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠑⣄⠀⠀⠘⡗⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⣸⠁⠠⠁⢀
⠀⢣⡀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠄⠀⠀⠀⠀⠘⡄⠀⠀⠘⢦⡀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠒⠒⠶⠊⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠁⠒⠖⢲⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠉⠒⢤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠘⡿⠟⠛⠛⠿⠶⣶⣶⣾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠤⠜⠛⠁⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢇
⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠀⢀⣀⡠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡌⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⢦⡀⢀⡴⠁⠀⠀⢳⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠸⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠹⣄⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡗⠲⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠃⠀⠀⡙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠠⠚⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠠⠄⢀⠀⠀⠀⠀⠀⡿⢤⠄⠋⠁⠀⠀⠀⠉⠒⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢰⡤⠠⠀⣀⢀⣠⠖⠫⠉⠉⠘⢧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠂⠌⣎⡫⡕⠠⣀⠐⠂⡜⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⡽⠀⠈⣢⣄⣼⡓⢼⠦⡀⠁⠺⢄⠘⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⢲⣴⡋⠁⠀⠀⡽⠀⢀⡤⠓⠀⢀⠉⠪⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠧⠤⠴⠻⡙⠁⢀⣠⠞⠁⢀⡽⠀⠀⠀⢀⠰⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠀⠀⠀⠀⢀⠜⠀⠙⠋⠉⠀⠀⠀⢜⣣⣤⡑⣄⠸⠓⠢⢌⠮⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⡀⠀⡠⠔⠉⠢⡀⠀⠀⠀⠀⠀⣠⢈⣀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠑⠤⠤⠴⡒⠉⠀⠀⠀⠀⠈⠳⣄⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⡤⡎⢳⡀⠀⠀⠀⠀⠀⠀⠈⢢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠥⠲⠦⠒⠉⠀⢻⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠑⠢⣄⡦⣄⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⣠⠜⢉⠇⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⡆⠀⣠⠔⠊⠁⢠⠊⠑⠢⢤⡀
⡴⣦⣶⡄⠤⠄⠀⣀⠀⠀⢀⠤⣤⡀⢶⡒⠈⣠⣤⠹⠞⡀⠒⢄⣰⠃⠀⠀⠀⣸⡁
⠣⠻⣤⣇⣀⣀⣀⣀⢠⠚⡜⠶⣏⠉⠉⠉⠓⠃⠛⠀⠐⠛⠉⢰⡦⢾⣁⡦⠴⣟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⢆⣷⠤⣤⠠⢬⠿⠯⠥⠤⠉⠉⣉⣙⣟⠛⡟⠺⡄⠈⠉⢃⣠⠔⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠁⠐⠀⠠⡤⠤⢼⣏⢢⡈⠙⣟⢯⢮⠣⠄⠁⠈⠽⠵⡧⠛⠉⣶⠁⣔⣠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣔⡇⣰⢶⡟⡆⢅⠊⣿⡓⠋⠉⠒⠒⠒⠒⠚⢧⠀⠀⠈⠉⠉⠀⠈⠑⠾⠓⠢⢤⣀⡀
⠀⠀⠀⠀⢀⠤⣄⣤⢞⣦⢸⣧⢧⣇⣀⠽⢾⠭⠑⠒⠂⠠⠤⠤⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢠⠧⣠⡞⠪⠚⠉⠉⢈⡅⠁⠀⠀⠯⣄⣀⣀⣀⣠⡤⡾⡏⠙⡑⣄
⠀⠀⠀⠀⠑⠂⠭⠄⠀⢀⢉⣩⠇⠀⠀⠀⠀⠀⠀⠈⡏⠉⣹⣠⠇⣄⢰⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⣆⣊⠟⠀⣎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣁⢶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠠⢤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡛⠀⠀⠉⢳⠐⠞⢥⡈⠀⠀⣀⠀⡿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠢⢄⠀⠑⢳⣞⠳⡈⠑⠠⡀⣰⠃⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠚⠁⢀⣠⠵⠖⠺⣄⠑⠛⠂⢄⠀⠉⠢⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢈⣶⣿⠀⠀⠀⠀⡜⠀⢀⠄⠂⠁⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡬⠷⠤⠴⠛⢁⠁⠀⢀⡠⠊⠀⠀⡠⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⣃⣀⣀⠀⡀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠈⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠢⣀⣀⣀⡬⠔⠊⠁⠀⠀⠀⠀⠠⣀⠀⠀⠀⡴⠋⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣀⡀⣀⠴⠊⢹⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡆⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⢶⣤⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠤⠃⠨⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⠀⠀⣀⡤⠂⠁⠀⡀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⢀⢤⣤⢤⠄⡀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠠⠀⠀⠀⢠⡈⢷⡞⠁⠢⢄⣀⡔⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢨⠼⣇⢽⠂⠀⠀⠀⠀⠀⡀⢀⣠⣀⡀⠂⠘⠻⠦⠼⠱⠏⠈⣠⢟⣒⣂⣭⣡⡖⢠⣀⣠⡿⢣
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠐⠧⣌⢠⠁⣟⣒⣐⣒⣒⣒⣶⣂⡐⠒⠢⠰⠤⠿⣴⡶⣾⠤⣴⠛⠈⠗⢲⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⣵⠿⡀⠻⡦⣙⣯⢅⢠⠀⠋⠬⠉⠵⢶⣲⡦⣴⢇⣀⠁⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠉⢒⠓⣧⠁⢄⣀⢻⣅⡚⠌⣀⣀⠀⠒⠒⠁⢱⠀⠀⠀⠁⣠⠼⠴⠂⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠀⢿⡿⠉⡆⠰⣅⠀⢎⡀⠀⠀⠀⠀⠈⠉⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠂⠠⢄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢦⠠⡺⣍⡄⣿⢁⢠⣁⠠⠀⠘⠗⠀⠈⠙⠂⠀⠐⠒⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⣠⡎⠓⠒⠃⠈⠁⢀⠀⠀⠀⠀⠸⢤⣀⣀⣀⣀⣠⡴⢾⣭⠉⠫⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠍⢀⡐⣒⡒⠈⣩⠆⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⢹⣀⣜⢠⡀⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠙⣇⠤⣺⠇⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠈⠓⠤⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠪⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠂⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠈⢳⣤⣤⣤⣤⣤⣄⣴⠾⠿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⠀⠙⢿⣄⣤⣴⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠖⠂⠀⣠⣴⠶⠿⠿⠿⠿⠿⠿⢿⣷⣦⣄⣀⣼⠟⠋⠉⠀⠀⠈⠙⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣧⣄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⠀⠉⢻⡟⢁⣤⠶⣦⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠞⠀⣾⣡⣦⠘⡧⠀⠀⢀⡾⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⡼⠿⣿⣇⠀⠀⣸⣵⣶⡀⣸⠃⣀⣀⣀⣀⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⡶⠶⠶⠶⠶⣤⣿⠿⠛⠳⠶⠤⠀⠉⠙⠻⢏⣰⠿⠋⠉⠉⠀⠈⠉⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡿⠋⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⢀⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢋⡽⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣄⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⡶⠋⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠶⠦⠤⠤⠤⣤⣤⡿⢱⣶⣶⡄⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣿⣆⠀⠀⠀⢀⣀⡤⠶⣻⡽⣿⣿⡇⣴⡶⠶⠿⠛⠋⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡬⠿⣷⣖⣋⣩⡴⠖⣋⣡⢟⡶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠒⠒⠒⠚⠛⠋⠉⠉⢿⣆⠀⣀⡬⠟⠛⠛⠟⣻⠟⢁⣞⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠿⣧⣤⣀⣀⢀⣼⣁⣀⡼⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠙⡻⠋⠛⠉⢹⠇⠀⠀⠘⢿⢿⣷⣶⣤⣤⣤⣶⠟⠋⠉⠛⠿⢿⣷⣶⣦⣤⣤⣤⣤⣶⡾⠟⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣾⠀⠀⠀⠀⠈⢣⡈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠐⠒⠁⠂⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠈⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠐⠀⠀⠀⠀⢈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⢀⡠⠰⢀⠤⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⣠⠂⠁⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢌⠀⢠⠃⢜⡂⠀⠀⠠⠀⣠⠖⠊⠀⠂⠀⡀⠈⠠⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠢⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠉⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐
⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣟⣉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡮⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⠿⣝⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠚⠻⢕⣌⡓⢤⡀⠀⠀⠀⢶⠤⣀⠔⠉⠉⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⣀⠿⣮⠶⠭⣧⣀⠀⠀⢣⡄⠢⡀⠀⡠⠖⠋⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠀⠀⠹⠀⠀⠀⠈⣄⡄⠻⠀⢷⣄⠀⠉⠢⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⠤⠳⢶⣤⠔⠛⣯⣁⠀⣈⡿⢳⣦⣀⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣛⣲⣤⣄⣧⣷⡀⣈⣻⣷⣭⣴⢼⡛⠉⠉⠁⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠠⠽⣿⣿⠿⣛⡻⣄⠐⢄⠀⠉⠳⠘⢮⡉⠀⠀⢇
⠀⠀⠤⠤⢤⣀⣀⣀⣀⣤⠤⠤⠤⠤⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠢⢳⠈⠀⠀⠀⠀⠀⠳⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡒⠒⠚⠓⢤⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠓⠦⣉⠙⠲⠦⣭⣉⣙⠛⠛⠒⠒⠒⠂⠀⠀⣂⣉⣀⣀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠑⠲⢤⣀⠈⠹⣿⣿⣷⣶⣶⡀⠀⠀⠀⠘⡀⠀⠄⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⡀⠀⠀⠀⠀⢹⢦⠀⠀⠀⡀⠀⠀⠀⣿⠣⣀⡘⣆⠰⡄⠈⠙⠀⣿⠉⢿⡏⢿⣿⡶⢄⠀⠁⠐⠀⠘⡀⠀⠀⣧
⠰⠀⠂⢄⠀⡿⣀⠀⢹⠱⡙⢂⢠⣠⠀⢹⠀⢣⢠⡀⣿⣆⠈⠂⢸⠀⠙⠹⣿⢆⠃⠀⠀⣠⠟⠀⠀⢿⠈⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠉⠀⠉⠁⠂⠀⠉⠀⠃⠁⢐⡼⠀⠀⠷⠡⡿⠘⠇⠀⢺⠀⠀⠀⠁⠈⠃⠀⠀⣿⡀⠀⠀⠈⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣆⣀⣤⣤⣴⠶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠛⠛⠻⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠋⠀⣿⠋⠛⠀⠀⣰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣶⣴⣿⣦⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⠆⠀⠐⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⣿⣿⣿⣿⠟⠙⢤⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣄⠀⠰⠦⠤⠤⠤⡔⠋⠁⠈⠉⠉⠉⢻⡿⠁⠀⠀⠀⠉⠻⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⠬⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠗⠦⣬⣁⠀⢴⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠛⠓⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣞⡄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣡⣄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡜⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢋⡿⢻⣿⡿⠀⠀⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠃⠀⢻⣿⢿⠒⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠟⠳⣦⣤⣄⣀⠀⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⣿⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⡛⡆⠀⠀⠀⠀⠉⠀⠀⠴⢢⣄⣆⣸⡇⡀⠀⠀⠀⣀⡀⢦⣴⣾⡇⠀⠀⠘⣿⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣉⠛⠿⣇⣿⣴⣾⣦⣿⠹⠎⣿⣾⠁⠀⠀⠀⢿⣗⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣾⡟⠛⣁⣠⣠⣤⣤⣬⣿⣷⣄⠀⠀⠀⠘⠋⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠁⠉⠁⠀⠛⠛⠛⠛⠛⠁⢿⣿⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⣿⠻⠀⠀⠀⠀⢁⣬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⡇⠀⠀⠀⠐⣼⣾⡇⠀⠀⠀⠀⢸⡏⢸⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡷⠀⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠈⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⢸⡏⡗⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⢸⡄⠀⠀⠀⠀⠀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣾⠃⠀⡕⠀⡀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⠀⣹⠆⠀⢷⣀⠁⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢴⣶⣾⡇⠀⠀⠘⢧⠖⠀⢀⠀⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⠀⠀⠀⠀⠈⢷⣭⡥⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣿⠀⠀⠀⠀⠀⠀⢻⣷⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣇⣿⣿⠀⣠⡀⠀⠀⠀⠈⣿⡈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣾⠿⣿⣿⣿⣿⣿⣷⠀⡀⠀⠀⢸⣧⢹⣿⣇⢀⣶⣤⡆⠀⣀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⣿⣇⠰⣟⣵⣿⠟⠋⠛⠁⠀⠀⠀⠀⠀⢸⠟⣿⣿⣿⣾⣿⣿⣷⣿⠟⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣴⠈⠀⢺⣾⣿⠿⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣾⣧⣼⢿⣽⣿⣿⠿⠛⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡿⠋⣠⣿⡿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡟⢹⡿⢟⣿⣿⠟⠁



⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢂⠠⠂⢂⠀⠀⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠉⠀⢇⠈⠄⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣎⠢⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠂⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠉⠰⠛⡏⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⢁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠠⠤⢧⡀⠀⠲⣄⠘⡀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⣴⠃⠀⠀⠀⠈⠢⢀⠈⠳⠵⣄⣀⠀⠘⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠑⡀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠒⢀⡀⠀⠀⠑⠦⡀⠀⠀⠀⠀⣰⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠔⠈⣿⣿⣿⣿⣿⣷⣤⣴⡿⠁⠀⠢⣀⠀⠈⠢⡀⠀⣰⣿⡟⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⠀⠀⡌⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⠂⠁⢸⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠁⠀⡐⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡰⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠐⠁⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⡗⠈⠈⠁⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡋⠁⠐⠒⠒⠒⠚⢁⡀⠀⠔⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡟⠉⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⢼⣁⠀⠙⡙⠋⠙⠉⠉⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢀⡠⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⡤⠤⢀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢀⡲⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡀⠀⠀⣼⠀⠀⠀⣀⡠⠒⠉⠀⠉⢳⡀⡀⢀⡀⠤⢄
⠀⠀⣀⠠⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠠⠠⠄⠀⠀⠀⠉⠀⠀⢀⡨⠀⢠⠊⠀⡡⠤⠤⡀⠀⠈⠁⠈⡇⠀⠀⠀⠗⠢⡀
⠀⠉⠉⠁⠀⠀⠂⠀⠌⡑⠂⠤⢀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠒⠪⣀⠠⠔⠀⠀⢸⠀⠀⠓⠀⠀⠹⠀⠀⠀⠴⠃⢀⣀⠀⠀⠀⠚⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⢀⠈⠒⠠⠄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣣⣀⠠⠄⠐⠁⠀⠀⠀⢀⠀⠈⡸⠀⠀⠐⠀⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⣐⠀⠀⠄⢀⡀⠉⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⠀⠀⠈⠉⠉⠀⣠⣤⡤⠶⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠒⠤⠤⢌⣁⡀⠒⠒⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣒⡒⠒⠬⣔⠄⡀⠀⠀⢠⠀⠀⠀⠈⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠢⡀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠒⡶⠶⠦⠤⣄⡀⢀⣸⡄⠀⠈⡆⠀⠉⠉⠁⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠐⢤⡀⢀⠤⠶⠦⣄⡀⠀⠀⢱⠄⠀⠖⠀⡹⠁⠈⠳⠤⠖⠁⠠⣄⠀⠀⠈⡧⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠤⠉⠒⠀⠀⠒⢿⡀⠀⡆⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣆⠀⢀⡴⠄⠊⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠴⠦⠀⠤⠞⠉⠉







⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣋⣥⣥⣼⡒⠀⠀⠀⠀⠀⢄⠠⠀⢀⣄⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⢀⡀⢀⠤⠀⠀⠄⠠⠠⠀⣶⣽⣿⣻⣟⣻⣿⣿⣿⣧⣤⣤⣤⣭⣶⣏⣉⣥⣌⣥⣄⣩⣄⣹⠿⠿⠿⢯⣵⠦⠤⠼⣭⡵
⠀⠀⠎⠀⠀⠀⢀⣀⣠⣤⣶⣴⡶⠶⠟⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡋⠉⠉⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠃⣶⣿⣿⣿⣿⢟⠟⠋⠉⠀⠀⠀⣾⣿⣿⠀⠉⠋⠁⠉⢻⣿⣿⣷⡀
⠀⠀⠈⣛⠻⠿⠑⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⠉⠉⠙⠒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠯⢀⡈⠙⠦⣀⡄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣤⣄⡀⠀⠀⠉⠂⢄⠁⠂⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠉⠀⠁⠢⢄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣦⢂⣀⠀⠀⠀⠉⠒⢄⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠉⠁⠈⠋⠁⠀⠀⠀⠀⠀⠹⣦⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⡀⠀⠀⠀⠠⠀⠀⡀⠀⢈⠉⢣⠼⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠉⠛⠻⠿⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠤⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⡠⠀⠀⢇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⣀⡤⠖⡻⠁⠱⠀⢰⢶⠀⠁⠀⠀⡠⠊⠀⠐⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠃
⠀⣀⠤⠒⠉⠁⠀⠈⠑⠀⠀⢀⠋⠈⡇⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠄⠆
⠀⢆⠀⠀⠀⠀⠄⢲⠀⠀⠈⠀⠀⠀⠀⠐⠒⠒⠀⢠⢄⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠍⡘⠨
⠀⠀⠣⡀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⠐⠀⢰⠀⠉⠢⢄⡀⠀⠀⠀⠀⠑⣤⡀⠀⠀⡸⢰⢃⠃
⠀⠀⠀⠈⣀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠂⠀⠀⢣⡀⠀⠀⠉⠢⣄⠀⠀⢀⠆⢹⢀⠊⠑⢆⡌
⡦⠓⠲⠞⢹⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠑⢦⡊⢀⡃⠀⠀⢤⡜⠁
⠑⠄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⢯⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⠃⡼⠄⢍⠁
⠀⠀⠀⠀⡀⠈⠳⠶⢴⡦⠄⠠⠤⠶⠿⠛⠋⠁⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠰⠸
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠔⠀⠹⠀⢣⠃
⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠄⢰⠃⠀⠦⡀
⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⡜⠀⠉
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠂⠄⢀⣀⣀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣀⠀⠀⢀⠊
⠀⠀⢀⣀⠤⠄⠒⠘⠂⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠑⣤⠆
⠀⢮⣥⣤⣤⣤⣤⡤⠤⠴⠶⠂⠴⠤⠤⠤⠤⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⣠⡟⣆⣰⣿⣿⠿⠭⠭⠭⠭⠭⣿⣿⣷⣶⣶⣖⣶⣲⣶⣶⣦⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶
⠀⠀⢰⣿⣧⣠⣍⣭⣭⣭⣵⣿⣗⣶⠷⠶⠾⠶⢾⣶⣶⣶⣶⣶⣶⣶⣼⡍⠉⠉⠉⠉⠉⠙⢷⣬⣯⣽⣆⠀⠛⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠈⠻⣯⣿⣿⣿⣿⣿⠿⠿⢿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣼⣭⣭⣭⣥⣿⣿⣿⣿⣷⣿⣷⣾⡇⢿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⢸⣿⣆⣤⣥⣤⣽⣷⣶⣶⣿⣿⢏⢏⡏⡏⡟⡿⣹⢹⣿⣭⣭⣭⣯⣭⣭⣭⡍⢭⣭⢋⣷⣿⣿⡇⠀⠀⠀⠛⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠈⠛⠚⠛⠛⠻⠿⠿⣿⣟⣫⣏⡼⢼⡬⠥⠥⠥⠷⠚⠉⠉⠉⠉⠀⠀⠀⠘⢿⣘⢷⣸⣿⣿⠛⠁⠀⢀⣀⠀⠀⠀⠀⠸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢣⣤⠀⠀⠀⠀⠈⣯⣿⣽⣿⠀⠀⠀⡼⣿⣷⣦⣀⠀⢠⣿⣶⠀⡄
⠀⢀⣶⣆⠒⠂⠤⠄⠒⠒⠂⠉⠉⠉⢭⡢⣄⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣸⢱⣶⡄
⠀⠀⠻⠿⠿⠷⣶⣿⣶⠶⣶⣶⣴⣤⣦⣷⠈⠑⠦⣀⣠⣿⣷⣷⡄⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿⣿⣿⠟⠀⠀⣤⠀⠀⢸⣿⠿⣿⣿⣿⣿⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠪⣙⠻⢾⣭⣟⣿⣿⣾⣷⣶⣮⣭⣆⣙⡙⠣⠤⢤⠿⣿⣿⡆⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⣀⣀⣸⡷⣴⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣙⡻⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣷⣶⣴⣯⣉⢙⡒⠢⠤⣀⣀⣄⡀⢰⣾⣿⣿⣿⣿⣧⣿⣧⣿⣿⢸⠀⢸
⠀⠀⠀⠀⠀⢀⣀⠤⢀⣀⣀⣀⣀⣀⣀⠀⠤⣀⡀⠀⠀⠀⠀⢿⣟⡦⢬⠿⠿⣟⣢⣿⣿⣶⣶⣤⣽⣎⡆⢯⣿⠿⠛⠛⠛⠛⠛⣿⣿⣼⠷⠞
⠀⠀⠠⣤⣴⣧⠉⠀⢿⣿⡿⢟⡻⣿⣿⡿⠈⢩⣵⣦⣤⢀⠀⠸⣿⠗⢸⠀⠀⣿⡇⢸⠉⠉⠻⠿⡿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡟⠂
⠀⢈⠈⡿⢛⡛⠂⢺⣿⠿⣿⡂⢘⡿⠿⣿⠂⠘⢛⠛⣯⠀⡂⠀⣿⡇⢹⠀⠀⣿⡇⢸⠀⠀⠠⡀⠀⠀⠀⢠⠄⠀⢸⠀⡄⠀⠀⣿⣿⡇⠃
⠀⠸⣦⣆⢺⣿⣷⠙⠂⠀⢪⣴⣬⡐⡀⠐⠱⣿⣿⡇⣶⡾⠁⠀⣿⡇⢸⠀⠀⠉⠉⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢸⠁⡇⠀⠀⣿⣿⡇⠄
⠀⠀⠀⠈⠀⠀⠈⢲⣶⣸⡼⠛⠛⢼⣶⣶⠌⠀⠀⠈⠁⠀⠀⠀⠙⠋⠋⠀⠀⠀⠀⠀⡰⢤⠄⠀⠀⠀⣾⠁⡀⠀⣾⠀⡇⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠿⠗⠀⠀⢰⣿⠀⡇⠀⣿⠀⡇⠀⠀⠘⣿⣿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⠶⠼⣿⣿⣿⣿⠶⢶⢶⡆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠇⠀⢿⠀⡇⠀⠀⠀⣿⠛⠒⠛
⠀⠀⢀⣀⣀⣀⣀⣀⣤⣬⣽⣥⣭⣿⠾⠶⢌⣷⣷⣶⣿⣴⣼⣷⣾⣿⣮⡿⠤⠤⠤⠴⠶⠤⠄⠀⠀⠀⠛⠚⠁⠀⠘⠛⠃⠀⠀⠀⣿⡃
⠀⠀⠸⣟⣿⡿⠋⠉⠉⠉⢹⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣤⣶⡶⠆⠀⠀⣿⠁
⠀⠀⠀⠉⠉⠁⠀⠀⠀⣴⣿⠃⠀⠀⢿⣿⣧⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⣶⣶⡿⠿⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠉⠀⠁⠀⠁⠀⠃⠀⠂⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠉⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⢀⠤⡀
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠠⡆⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠔⠀⠈⠣⠀⢀⣀⣀⣀⡀⠤⢷⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⡄⠀⠀⠈⠁⢀⠀⠀⢀⠄⠙⡂
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⢀⣦⠶⠒⠃
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠐⢾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢦⡠⠖⠤⠀⠢⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⢠⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⣄⠰⠀⠀⠐⠒⠄⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠁⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢐⠀⠀⠸⠁⠨⠑⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢸⠄⠒⠶⠂⢖⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠈⠀⢈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠤⠠⠤⠤⠤⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠀⠀⣀⢀⣀⡀
⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠄⠘⡇
⠀⠀⠀⡟⣆⠀⠁⠒⠒⠒⠂⠐⠂⠤⠄⢀⣀⣀⣀⡀⠀⠠⠤⠤⠤⠤⠤⠄⠀⢀⣀⣀⠀⠀⠀⣀⠠⠐⠊⠁⠀⠀⣀⣀⣀⣠⠃
⠀⠀⠀⢣⣈⠓⠠⠤⠤⠤⠄⠤⠄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠁⠀⠀⢀⠎
⠀⠀⠀⠈⢦⡣⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠉⠲⣕⠄⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠜
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣁
⠀⠀⠀⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠃
⠀⠀⠀⠇⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣭⠉⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢀⡀⠒
⠀⠀⠉⠁⠀⠁⠀⠐⠁⠀⠀⢠⣀⠀⠤⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠠
⣀⣀⣀⣄⣘⣁⣀⣀⣀⣐⣒⣀⣀⣄⣀⣐⣛⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣐⣂⣒⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⠴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⣠⠞⠁⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢀⡴⠋⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡈⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠉⠲⣄⠈⠳⣄⠀⠀⢀⡴⠋⢀⡴⠊⢁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡈⠓⢤⡈⣱⠞⠁⣠⠔⠋⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡴⠋⢀⡤⠚⢁⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣠⠴⠋⣠⠶⢥⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡊⢁⡠⠞⢁⡴⠊⠉⠲⣄⠙⠦⣀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡩⠄⠙⢏⣠⠖⠁⠀⠀⠀⠀⠀⠑⢤⡈⠳⣄⡨⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡵⢊⡠⠊⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠞⠁⠔⠲⢝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡔⠋⠀⠀⠚⢁⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠑⢄⣑⠌⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⡑⢄⠀⣀⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⢹⢆⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆⡸⢏⣝⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⣢⣄⠔⢱⠌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⢳⠘⠈
⠀⠀⠀⠀⠀⠀⣠⠞⡩⡣⠂⡐⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣸⡦⢄⣀
⠀⠀⠀⠀⠀⡴⢃⠊⡔⠑⢊⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣔⢌⠫⡲⡌⢧⡀
⠀⠀⠀⢠⠞⡱⠁⠰⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠁⠱⡈⢢⠳⡄
⠀⠀⡰⠋⠰⠁⠀⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠡⠀⠱⠘⢦
⢠⠞⢰⠃⠂⠄⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢃⢠⠳⡄
⠣⣄⠐⠀⠀⠠⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠘⠀⠀⠇⠈
⠀⠀⠙⠲⢤⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠁⠀⠀⣠⠔

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣼⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⡓⠂⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣭⣴⣶⣾⠿⢿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠨⠙⠀⠀⠙⠁⣀⢄⣀⣀⣀⠤⠤⠦⣤⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠁⠀⠀⠀⠀⠁⠉⢻⠟⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠉⠀⠄⠚
⠀⠀⠀⢀⠀⠀⠀⠱⣄⣀⣀⣀⣠⠤⠴⠖⠀⢀⣤⠄⠘⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠂
⠀⠀⠀⢰⠀⠀⠀⠀⢸⠋⠉⣁⣤⠖⠀⠀⠀⢈⣿⣿⣤⡄⠀⡀⡀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠓⣿⡿⠃⠀⠀⠀⢰⣿⠛⠻⠿⣿⣿⣿⣅⣴⡿⠿⠋⠛⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠸⠀⠈⠲⣄⠀⠀⠀⠀⢀⣴⣿⡏
⠀⠀⠀⠀⡂⠀⠀⠀⠘⢿⣶⣤⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣟⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣛⡽⠿⡛⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠛⠛⠓⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠴⠶⠒⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⢳⢏⣠⡄⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠞⣉⠁⠀⢀⣤⣉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠀⠀⠀⢀⡎⠈⡇⢠⡏⠀⠘⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣠⠖⠒⠚⢿⣆⡇⢸⣦⣄⡠⠟⠋⠉⠁⠀⠈⠉⠂⠀⠀⠀⠐⠋⠉⠀⠀⠀⠈⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠉⠀⣇⠀⠀⠀⠀⠩⠤⢬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠘⢦⣀⡀⠠⢤⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠒⠀⠲⠤⠤⠀⠄⠀⡀⣾⣀⡀⠀⠀⣰⠛⠓⠚⠛⠃⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠨⣉⣡⡽⢀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠤⠤⢶⡀⠈⠁⠈⠳⠶⠛⠦⣤⣀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠂⠁⠁⠀⠀⠀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠙⠲⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⢤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣸⠷⣄⠀⠀⠀⠀⠀⣀⡤⠟⣆⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠶⠛⠁⠀⠈⠙⠲⠶⠒⠛⠉⠀⠀⠈⠓⠶⠤⠤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⣀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⠿⠿⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣿⣤⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⢠⣿⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠟⠉⣿⠉⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⠒⠀⠨⣿⠅⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣀⠀⡀⢀⣠⡀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣇⣀⠀⠀⠀⢿
⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⡟⠀⢰⣤⣿⣄⣀⠀⠀⠀⢹⣿⣿⣿⢏⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠋⠀⡏⠈⠙⠁⠀⢸⠀⠀⠀⡇⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⢺⡗⠂
⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠿⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⡇⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠿⠀⠀⠀⣀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣴⠿⠋⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⠉
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⢻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠗⠒⠒⠀⠀⠀⠀⠀⢹
⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣄⣀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠦⢌⡀⢼⣿⡄⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢫⣤⡀⠾⠗⢨⣟⣃⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⣴⣶⣾⣿⡿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣷⣿⣿⡟⠀⡽⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣛⣡⢾⣿⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣉⠑⡄
⠀⠀⠀⠀⢴⠖⠂⠀⠀⠀⠀⣆⡂⡀⠆⠐⠛⣿⣿⡿⠁⠻⣿⡄⠈⠋⠀⠀⠀⠀⠀⢀⡜⠁⠀⠙⢄⡀
⠀⠀⠀⠀⠈⢷⣄⣠⣤⣤⣤⣼⠿⠛⠘⡛⠖⠉⢠⠃⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠿⠛⠛⣏⠁⠀⠈⣰⡄⠀⠀⠀⠄⣸⠀⠀⠀⡸⠀⠠⠤⢀⠀⠀⠄⢰⣏⣀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠐⠛⠻⢃⡄⣠⣄⣸⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣴⡄⡀⠀⠀⢀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠙⠿⣿⣿⡇⠉⠀⢸⡀⠐⠐⠆⠤⠄⠀⠀⠀⠉⠉⡼⠉⡳⠂⠉⠁⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⢀⣼⠻⣷⠂⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠃⠀⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⣠⠆⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡶⠈⠀⠀⠀⢀⠀⠐⠶⠤⠄⠀⠀⢧⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠙⢻⣛⡭⢅⣠⣤⣶⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣶⣤⣀⠀⠀⠘⠄⠒⠻⢋⢁⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠈⠉⠉⠀⠈⠉⠉⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⡄⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⢻⢉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠢⠽⠞⠾⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠰⡉⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣠⠷⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠂⠉⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠉⠂⠘⣾⡀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⣑⣲⡚⣧⣤⠀⢀⠔⠉⠀⠀⠀⠀⠀⠠⡊⠉⠉⢹⡆⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢿⡍⠉⠁⢸⡴⠃⠀⠀⢀⠁⠀⠀⠀⠀⡀⠒⢒⣋⣤⣄⣀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣧⣸⠟⠳⣀⠞⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠁⡴⠋⠀⠀⠀⠈⠑⢆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⢫⡀⠀⠀⠀⢻⠀⠀⠀⠀⢰⡄⠤⠤⡀⠀⠀⢰⠁⠀⢀⣄⠀⠀⠀⠈⢧⠈⣧
⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢧⠀⠀⠀⠐⠀⠀⠀⡇⠘⡦⠘⠓⠢⣼⠛⠇⠀⠀⠀⠈⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠘⡆⠀⠀⠸⠀⠀⡸⠀⠀⡇⠀⠀⠀⠈⢣⠀⠀⠀⠀⢀⡏⠀⢠⠀⠀⠄⠀⠀⣠⠖⠉
⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠆⠀⠀⢣⠐⠁⠀⢠⡁⠀⠀⠀⠶⢼⠒⠒⠒⣒⣉⡴⠃⢨⠎⠀⢀⡴⠚⠁⠀⠀⢰
⠀⠀⢸⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⣄⠀⠈⢧⣀⠀⠈⠙⠦⠄⠀⠠⠎⠀⠀⠀⠉⠁⠀⡐⠁⠀⠘⠉⠀⠀⠀⠀⢀⡟
⠀⠀⠸⡄⠀⠀⣯⠙⡶⠶⠤⠤⢄⣀⣀⣀⣀⣰⠀⠀⣠⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠶⠶⠂⢀⡔⢹⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⡇⠀⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠃⠀⢀⣶⠀⡖⢄⠀⣀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⢁⠀⠀⠲⠷⣴⣤⠄⠀⠀⠀⠀⠀⠀⡇⠀⠟⠀⠀⣟⠸⠀⠇⠀⠑⠏⠱⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⢀⣠⡼⢦⣤⣄⣀⢷⣄⣀⣀⣀⡀⣀⣠⣀⢦⣀⣧⠀⠀⠋⠀⢠⠃⠀⠀⠀⠀⢷⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⡜⠉⠀⣠⠁⠨⠿⠓⢀⠿⣆⠀⣸⡧⢨⠔⢣⠀⠈⠹⠑⠦⠄⢰⠇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⢳⣤⣤⣼⣖⡢⠴⠂⠀⠀⠀⠈⠛⠳⠶⢶⠒⣠⣤⡾⠀⠀⠐⠷⠤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣥⠄
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⢤⣄⣀⣀⣀⣀⣀⣠⣤⠤⠖⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠂⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠇⣷⢰⡗⢰⡇⢿⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⡶⠿⠶⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠟⠈⠃⠘⠃⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⢻⡟⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠶⠶⠶⠶⠀⠀⠘⢷⣤⡾⠁⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⢸⡇⠀⢀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⠶⠶⠶⠶⠶⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⡿⠷⠶⠶⠿⣿⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⣀⡀⠀⠀⠀⢀⣤⡶⣿⠋⢿⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠸⠿⠟⢀⣤⠾⣯⠁⠀⠸⣧⣘⣧⠀⢀⣴⠿⠷⠶⠶⠶⠶⠶⠾⠋
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡾⠁⠀⠙⠷⣦⣄⣈⣿⣵⡾⠛⠁
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⢠⡟⠀⠀⢠⣶⣦⠀⠀⠀⠀⢹⡄
⠀⠀⣾⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠘⣷
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠃
⠀⠀⠈⠛⠻⠶⠶⠟⠛⠛⠛⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢻⡟⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⣤⡀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⣀⡀
⠀⠰⣾⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠐⠲⠤⠀⠀⣠⠔⠋⡏⣀⢤⢒⡈⠁⣦⠘⢸⠇⡈⠉⢍⡋⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⠧
⠀⠀⠉⣀⠀⠀⠀⠙⠋⠁⠀⠀⠘⣦⡀⠀⡠⠚⠁⠀⠀⡟⡰⢎⣌⢁⡃⣐⠶⢸⡄⠂⠂⠽⠋⣠⠄⠀⠀⠉⠻⠏⠉⠀⣤⡀
⠀⠀⠼⠧⠀⢰⣶⣶⣶⣶⣶⣶⣶⣼⣷⣌⠳⣄⡀⠀⠀⡏⠱⠆⣁⢈⢋⣍⠰⢸⡇⠀⢀⣤⠞⣁⣀⣠⡤⣤⢤⣶⣤⠀⠈⠁
⠀⠀⠀⢀⣀⠈⠛⠙⠻⠙⠻⠿⠻⣷⠋⠁⠀⠈⠙⠦⣄⣿⠛⠀⠭⠠⠎⣁⠲⢸⡇⠘⢿⣿⠭⠿⢿⣯⣿⣹⣿⣿⣿⠀⠶⠒⠒
⠀⣰⣾⣿⣿⣶⣶⣶⣿⡄⠀⠀⠞⠁⢀⣤⣠⣤⣶⠶⠶⠿⠄⠀⠀⠀⠀⠀⠉⢉⡁⠀⠀⠙⣦⡀⠀⣀⠈⠉⠉⠙⠻
⠀⠈⠙⠛⠿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⣿⣿⣿⣶⡄⠈⢁⣾⣿⣤⣤⣤⣄⣀⣀⡀⡀
⠀⠀⠀⢀⣀⠀⠀⢶⣦⣤⢼⡏⣹⠟⠋⠀⣠⣤⣴⣖⣂⣀⣀⣀⣈⣁⡀⠉⠀⠛⠛⠋⠉⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠇
⠀⢀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠛⠁⠀⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉⠉⠉⠉⠀⡀⠀⠀⠀⡀⠀⠠⣀⠈⠙⠂⠀⠀⢀⡀
⠀⢸⠿⠶⢶⣤⣄⣀⣈⣿⣷⣤⡀⠀⠀⠀⣠⣤⣴⣶⠯⠤⠤⠴⠶⠶⠿⠿⠿⠀⠀⠸⡷⠦⠤⠆⠑⠪⠇⠉⠉⠉⠀⠐⠚
⠀⢸⡇⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡿⠃⠀⠉⠉⠉⠛⠇⢀⣠⣴⣤⣤⠶⠶⠶⠦⠀⡀⠀⠀⠀⠀⠀⢀⡼⣃⣀⣤⣀⣀⣀⣀⡀
⠀⢸⣿⣤⣴⣶⣿⣿⠿⣿⣿⡿⠋⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⢉⣀⣀⡀⠀⠀⢤⣾⢷⣦⢲⣰⣠⡀⠻⣽⠾⠿⠸⠿⠿⠿⠟⠣
⠀⠾⠿⠛⠋⠉⠀⠀⠐⣿⠏⠀⠀⠈⠉⠙⠋⠁⠀⠀⢀⡀⠀⠈⠁⢀⡀⠀⠀⠀⠙⠇⠁⠈⢁⣩⠁⠀⠈⠂
⠀⠠⣤⣶⣯⣤⣤⠄⠀⠀⠠⡾⠶⠶⠶⠶⠆⠀⢀⣴⣿⣥⣤⣶⣾⡿⠗⠀⠀⠀⠀⠀⠀⠀⠻⣟⡛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣤⠦⠀⣀⣀⣀⠀⠙⠻⣿⠏⠁⠀⠀⠀⠀⠠⢶⣶⡿⠭⠀⠀⠀⠉⠀⠀⣤⣤⣄⣀⣐⣦⣄⡀
⠀⣠⣶⣦⣤⣴⣶⠀⠀⠈⠉⠈⠁⠀⠈⠙⠋⠉⣀⣤⣤⣤⣤⣀⣀⣀⣼⠳⣦⠀⠀⠉⠀⣀⡔⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠁
⠀⠙⠛⠿⠋⠉⢁⡀⠀⣀⡠⣤⣽⣿⣿⣦⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠁⠀⣀⠄⠘⠛⠋⠉⠉⠁⠀⠀⠀⠀⢀⣴⣠⢤
⠀⠀⠀⠀⠀⣰⠘⢛⣀⠀⠀⠈⠙⠛⠋⠉⠀⠾⠗⠒⠓⠀⠀⡤⣄⣀⠀⢦⡀⠈⠙⠻⠛⠛⠒⢒⡒⠃⠀⢀⠀⠀⠈⠛⠀⠈
⠀⠀⠀⠀⠈⠙⠛⠂⠀⠀⢀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⣇⣈⣩⣿⣶⡿⠆⠀⠀⠀⠀⠀⠸⠤⠛⠛⠟⠁
⠀⠂⢀⣭⠷⠶⠆⠀⠀⠘⠛⠿⠛⠓⠒⠃⠀⠉⠛⠉⠀⠀⠀⠉⠁⠀⠀⠏⠀⠀⠀⢰⡶⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤
⠀⠀⠤⠤⠴⠀⣤⣴⣶⣦⣄⠀⠀⠀⠀⠠⣤⣦⠤⠤⠀⠀⠀⠀⣀⣀⡄⣠⣀⣶⣦⣾⡇⠀⠉⠳⢦⡀⠀⢻⠓⠛⠛⠉
⠀⠀⢀⡠⠀⢀⣀⠈⠉⠀⣀⣠⠴⠀⠀⠀⣀⣀⣀⡀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡴⠚⠀⠀⢀⡀⠐⠒⠒⡯⠷⠖
⠀⠈⠛⠶⢿⡟⠛⠁⠀⠈⠛⠻⠿⣭⠭⠭⠭⣭⣬⣷⠀⠀⠀⠀⠁⠛⠙⠛⠻⠿⠻⠟⣧⠴⠋⠀⠀⠀⠠⣾⣥⣤⣤⣤⠴⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢁⡀⢄⣀⠄⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡿⠿⠿⠛⢦⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠻⠟⡂⠛⠋⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣼⣦⣴⣴⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠉⢉⣿⣿⣿⡷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣽⣿⣿⣿⣿⣿⠛⠀⣤⣾⣿⣿⣿⣋⣤⣤⡤⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠂⠈⠛⠛⠛⠛⠛⠻⢿⣼⠟⠉⠀⠀⠀⠈⠉⠉⢱⣧⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣿⡿⣾⣤⣤⣠⣀⣤⠀⠀⠀⣤⣻⣶⣶⣶⠶⢾⣶⣠⡧⣼⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣻⣿⣿⣿⣿⡾⠛⠋⠉⠁⠉⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⠀⣀⣠⣴⣶⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣵⣿⣿⣿⣿⣿⣿⣷⣤⣼⣶⣄⡀⣤⡤⣼⡆⢀⣴⣦⣶⣦⣤⣄⢾⣿⣿⣿⣿⣿⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣬⡍⠛⣿⣿⠟⠋⠀⢹⠟⡉⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠟⣉⣸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢿⡏⠀⠀⠀⢻⣆⣡⠆⡄⣄⣤⣤⢀⣀⣤⣴⣖⣿⠟⢛⡫⠈⠙⢍⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⡇⠀⠀⠀⠸⠛⠋⠉⠉⠉⠛⢿⡿⠟⠋⣉⣉⣤⣶⣿⠧⣀⠈⣀⣁⣼⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠾⣇⡀⠀⠀⠀⣶⡏⣤⣶⣯⣶⣞⣷⣾⣿⣿⠟⢛⡏⠀⢀⡀⣹⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⠟⠉⠉⠀⣤⣿⣿⣶⣿⣿⣿⣿⠿⠛⠉⢩⣼⣶⣿⣿⣿⡿⠰⠏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣶⣏⠻⣟⢁⣽⠏⠁⠀⠀⠀⠀⣀⣀⠟⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢾⣧⣴⢿⡷⢀⠀⢿⣯⡴⣦⣶⡄⣰⣆⣿⣿⠃⣌⣶⣐⣶⣿⡾
⠀⠀⠀⠀⠀⣀⠶⠛⢉⣠⣤⣾⣿⡟⠓⠈⠁⠀⠈⠛⠛⠉⠉⠹⠁⢉⣰⠃⡘⠉⠉⠉⠡⠁⠐
⠀⠀⠀⠀⠀⢣⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⠃⣴⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠿⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⢃⣼⡿⢱⡿⢻⣿⢿⣿⡿⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⣰⡿⠣⠊⠉⠀⠋⠀⠸⠋⠈⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢿⠢⠿⡛⠂⠿⠾⠥⠤⠤⣤⣤⠤⠇⢿⡶⣶⣦⠛⠻⠯⠤⣴⠎⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣧⣿⡇
⠀⢢⡀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠸⡄⠀⢠⡾⠊⣠⠇⢛⣛⡛⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⠁
⠀⡿⣬⣻⣿⣧⢿⡄⠀⢰⠀⠀⠀⠗⠒⠶⠒⠛⠋⠹⣿⠿⠿⠶⠛⢿⡀⠀⠀⠀⠀⢀⣄⣀⣿⢻⡅⣿⠄
⠀⢻⣬⣿⣿⣿⠸⢿⡄⢸⠀⠀⠀⣀⣤⣺⡇⠀⠀⠈⢿⡄⠈⠁⠀⠘⣧⠀⠀⠀⡀⢼⢻⣿⣿⣿⣿⣿
⠀⢈⡟⣿⣧⣾⣾⠘⣿⣿⣷⣿⢿⣿⡿⠻⡇⠀⠀⠀⢸⣿⣄⣀⣀⣀⣸⡇⠀⠠⡀⢈⣿⣿⣿⣿⣿⣿
⠀⢸⢹⣿⣿⣛⡃⣤⢹⡏⣧⡀⡘⡋⠃⠀⡇⠀⠀⠀⠀⠙⠛⠉⠛⠛⠋⠁⠀⢀⠈⣹⢿⣿⣷⠐⣿⣿⡄
⠀⣿⢸⣿⣿⡸⣿⢸⣿⣟⠛⢷⡖⠒⠒⠀⠃⠀⠀⠀⠀⠀⠀⣬⣭⣖⣤⣀⠀⠀⠀⢰⠸⢹⣿⡟⢫⣽⠇
⠀⢸⣾⣿⣿⣿⣝⣾⣿⠗⠀⠀⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡟⡞⣹⢳⢺⣵⣟⣿⣿⢿⣾⠁
⠀⠘⣿⣿⣯⣿⣿⣿⣿⡆⢠⡆⠊⣪⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⡿⢏⣯⢿⢻⣽⣰⣽⣾⣹⣿⡞⠉⡆
⠀⠀⠘⣿⡿⠿⢿⡿⠁⠀⣾⠇⠐⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣙⣛⡓⠛⠋⠉⠁⠀⠀⠈⠙⠁
⠀⠀⠀⣼⣿⠸⣿⣧⠀⠀⢹⡀⢠⡆⠈⠻⣆⠀⠀⠀⠀⡴⠁⢼⠀⠀⣹
⠀⠀⠀⣸⣿⠀⣿⣇⠀⠀⠀⢣⣈⠳⢄⠀⠘⠷⣤⣤⣐⣳⠐⢓⢛⡚⢿⣾⡦⠦⠶⠤⣤⡤⠤⠤⡤⠤
⠀⠀⠀⠈⣿⠑⣿⡇⠀⠀⠀⠀⠙⢿⣷⡠⠄⠄⢀⡇⢿⣿⣿⣿⣿⡇⡿⢟⡟⡛⠛⢛⣛⡛⢛⠛⠛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠠⠠⡄⢠⡽⢻⣿⣿⣿⣿⣿⣿⠟⢛⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠾⣇⠀⢠⣤⣼⣏⠲⣿⣿⡛⠛⢻⣿⡿⠎⣽⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠛⠐⢲⠝⠀⠠⠯⢌⣉⣉⣉⣉⣿⡶⢾⡶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠏⢠⠻⢋⣉⡉⡾⠿⠻⠿⠰⠿⠛⠿⡆⣉⣉⠻⠃
⠀⠀⠀⠀⠀⠀⣠⣴⠟⢂⠀⢠⣧⣼⣭⣭⣭⣭⣿⣦⣤⣿⠿⠿⠿⠿⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠻⣦⡀⣤⣶⣷⣦⡄⣠⡾⠟⠿⠿⠟
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣛⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠙⠛⠛⠁
⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⡿⠟⣻⠋⠙⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢠⣦⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠻⣿⡀⢿⣄⣠⡯⠁⠀⢀⢁⡄⠐⠃⡔⠓⠀⣈⠢⡄⢀⡤⠒⠒⠲⡄⠀⠀⢸⣿⣄⡀⠀⣠⢿⡟⢤⣀⡤⠻⡿⣄⠀⢀⣠⣾⡇
⠀⠀⣰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠙⠛⠉⠉⠀⠀⢠⠴⢾⡗⠚⠳⡟⠒⠲⡧⢤⡨⣟⢂⠀⡀⢀⣽⠀⠀⡜⣩⠶⢝⠟⣵⠋⠉⢻⠉⡔⠉⠉⣮⠛⡫⠤⢏⢣
⠀⠠⣿⣿⡿⢿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣠⣆⣀⣸⣧⣤⣤⣧⣤⣼⣧⣤⣤⣈⡹⣬⡶⠛⠛⠀⠸⡙⠧⣀⣨⠇⠸⠓⠒⠋⠀⢙⢒⡚⠃⠸⣇⣀⡼⢃⠇
⠀⠀⣿⣿⣿⣿⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷⢸⣶⣶⠀⣶⣶⡴⣶⣶⣾⣿⠇⠛⠛⠛⠛⠃⠀⠑⠦⠤⡵⠶⢟⣛⣿⠧⠤⠼⣛⣛⡛⠶⢦⠤⠽⠊
⠀⠀⠻⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⢸⣟⣛⡲⣟⣛⡛⣯⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠆⣯⣀⡀⠀⠀⠀⢀⣀⣽⠀⣞
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡀⠈⠙⠛⠃⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢤⣂⣉⣉⣉⣐⡬⠤⠒⠊
⠀⠀⢰⣍⣀⣀⣀⣀⣀⢀⣀⣀⣤⣀⣀⣀⣉⢭⡍⣉⣉⣉⣉⣉⣛⡑⠒⠒⠒⢒⣒⣒⣂⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠤⠠⠤⠤⠴⡒⡄
⠀⠀⠘⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠛⠻⠿⠭⠭⠉⠉⠛⠛⠿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠙⠛⠛⠛⠛⠛⠿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠐⠒⠒⠒⠒⠒⠒⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠉⠉⠉⠉⠉⠐⠦⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠁⠁⠀⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢰⣶⣶⣶⣶⡆⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢶⣶⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠚⠛⠛⡟⠉⠁⠀⣴⣶⣶⣶⣶⣶⡄⠀⠀⢠⣶⣶⣶⣶⣶⡆⠀⠘⠛⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢰⠁⡐⠁⠀⡆⠀⠀⠀⠈⠉⢉⣭⡉⠉⠀⠀⠀⠀⠉⣩⣭⡉⠉⠁⠀⠀⠀⠑⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠱⢀⠀⡇⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠠⠀⠀⠿⣿⠏⠀⠀⠀⠀⢀⡠⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⣀⡇⠀⠀⠀⠠⡠⠠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⡀⡄⠀⢠⣀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠒⠂⠀⠀⠀⠤⠀⠀⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠀⠐⠒⠂⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣲⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠤⠤⣼⣿⣿⣿⣧⣿⣦⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠠⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⣠⣴⡞⢿⣽⡀⠴⣏⢏⡶⠘⢿⣉⡛⠶⠆⠀⣀⠀⠀⠀⣏⣠⣄⣉⣍⣭⣭⣽⠓⠻
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⠫⣶⣿⣿⣷⠤⢬⠟⢿⠿⠿⣶⣾⠿⠠⠄⠁⠀⠒⠚⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⠭⠤⣄⠰⣿⠟⠋⠀⠀⠈⠑⠬⠤⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠘⣤⣼⣭⡄⣇
⠀⠀⠀⠀⠀⠀⠾⠟⠉⠉⠉⠁



⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢠⡀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⣿⣿⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⣾⣿⣿⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠜⠀⠀⠞⣻⣿⣿⣿⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⢄⣀⣄⢀⣆⠼⡧⠒⠿⠒⡶⠃⠀⢀⣴⣾⣿⣿⣿⣿⡿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠀⠀⠈⠛⠃⠁⠀⠀⠀⣴⣾⣴⠂⠀⣵⣿⣿⣿⣿⣿⣿⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠺⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡹⣿⣿⣿⣿⣿⢨⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠿⠀⠀⠀⠀⡤⢤⣄⣀⠀⠀⠀⠀⠻⢿⣿⣿⣟⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠃⠀⠉⡂⠀⠀⠀⠊⠀⠴⠆⠀⠉⢤⡀⠆⣀⠀⠀⠈⠉⠙⣁⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡻⢶⠻⣶⣈⡟⠀⠀⢀⣀⣠⣶⠿⠿⠷⣶⠤⠀⣀⣀⠀⠀⠀⠀⠠⠭⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠐⢤⡿⠁⠀⠀⠀⣿⣿⠧⠤⠤⠚⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡧⠐⠁⠀⠀⠀⡼⠋⠑⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⢶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡟⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠓⠀⠀⢀⣀⠀⢀⡀⠀⢶⡽⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠋⠀⠀⣀⠤⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡈⠓⢦⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⠒⢻⠃⠀⠀⠀⠉⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣝⢷⢦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⣤⡏⠀⠀⠀⠀⠀⣀⠔⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣧⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣬⠉⠒⠤⣤⣴⣚⣡⣴⣶⣿⣿⣿⣿⣷⡒⠤⣀⠀⠀⠀⠘⢦⣌⣻⢟⣆⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠛⢧⡀⠀⠁⠀⠀⠀⠈⢿⣿⡎⣿⣟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⡌⠇⠁⠈⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠈⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡀⢀⢹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡋⠻⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡘⡟⠇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢿⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠙

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⠀⠀⠀⠀⠀⠀⠘⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠠⠴⠐⠐⠚⠁⠉⠉⠉⠁⠉⠉⠁⠀⠐⠒⠀⠀⠤⠤⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠁⠈⠐⠀⠒⠒⠐⠂⠒⠒⠋⠉⢉⠅⠤
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠠⠴⢆⣀⣩⣭⣭⣶⣾⣿⣦⣴⣶⣽⠂⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠛⣛⣛⡁⠈⠙⠛⠁
⠀⠀⠀⣰⠶⣿⣛⣻⣦⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢺⡿⠿⠛⠛⠋⠉
⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⡏⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠙⠳⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣤⣤⣴⡿⠕⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢈⣉⡉⢀⣄⢠⣤⣰⣶⣶⡾⢿⣿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠻⡿⣼⣇⣸⡟⣿⠇⣿⡇⣼⡇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣶⡦⣿⡟⣿⣿⣿⢀⣿⠀⣿⡇⢠⣍
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣧⣾⠇⣿⠁⠿⠉⠻⠛⠋⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣨⡉⣠⠄⠴⠄⠼⠇⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣛⣋⣉⣉⣉⣩⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢒⠢⠄⠀⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢶⣶⣶⡶⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠠⠘⠄⡼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠂⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣄⠀⠀⠀⠳⣧⣄⠀⠀⠀⠀⠀⠀⡦⣄
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠄⡈⡇⠀⠀⠀⠀⠙⡗⠀⠀⠀⠀⠀⡉⠢⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠹⢂⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢘⣀⠀⠠⠌⢀⠁⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢀⠈⠁⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠐⠀⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠐⠁⠀⠘⠀⠀⢀⠀⠀⡄⠠⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠁⠉⠀⠀⠀⠀⢀⠀⠂⠀⠁⠤⠐⠧⠠⠠⢀⠨⢖⣩⣶⣾⡮⠧⣆⡉⠀⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢊⣍⡙⠚⠉⢀⡀⠈⠈⠐⠁⠻⡂⠀⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡀⠉⢤⠆⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣄⢀⠒⠐⡖⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠷⡿⠀⠀⠧⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄⡀⠀⢀⠀⢀⠄⠀⠗⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠁⠀⠈⠀⠘⠐⠀⠀⠉⠘⠐⠈

⠀⢀⣤⣤⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡷⣄⡀
⡤⡇⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠹⣧⣿⣉⢷⢤⣤⣤⢄
⣧⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠙⠛⠛⠛⠿⣿⣿⣿⣿⡯⠉⠉⢩⢩⠙⣿⠋⠉⠉⠉⠉⠉⠉⠁⡆⡇⡇⡆⡆⢐⢰⢴⡈⠉⠉⠛⠇⡠⠐⠀⠁
⠈⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣺⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣄⣀⣀⣎⣂⣻⣀⣀⣀⣀⣀⣀⣀⣀⣁⣃⣃⣃⣋⣉⣈⣈⣀⣀⣀⣀⣨⡇
⠀⠀⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⡖⠀⠿⠻⠿⠿⣏⣉⣉⣵⣾⣆⠠⣤⣭⣥⣭⡥⠠⠀⠀⣨⣷⣤⠀⠀⢀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠠⠀⠀⠀⠀⠀⠘⢻⣿⢿⢿⢿⡧⠀⠀⠱⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠒⠒⠒⠧⡠⢀⡾⠏⠀⠀⠀⠀⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢟⡛⣻⠿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣷⡜⢟⢛⢟⠒⡨⠍⠩⠭⠥⠖⠚⣻⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡁⠀⠀⠀⠀⠀⣧⢹⠯⠉⠻⣿⣿⡌⢦⠀⡪⠪⢀⢈⠪⠊⢔⠌⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠣⡀⠀⠀⠀⢀⡿⡾⠁⠀⠀⢹⣿⣿⠈⡖⠁⡐⠕⠕⡠⡀⠑⠁⡺⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡒⠤⣀⡛⠀⠀⠀⣀⡴⠻⠿⣟⣃⢰⠨⡊⢂⢀⠪⠊⢄⢌⠊⢀⠽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⠉⠉⠉⠁⠈⠀⠀⠙⣿⣆⢱⠀⡑⠕⡡⡢⡑⠅⡠⡠⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡄⢣⢂⢄⠈⠊⢒⢔⢌⠊⡐⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡈⡆⠑⠡⡠⡀⠁⠡⡠⠍⢀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠸⣀⢌⠊⢀⢕⢄⠈⠔⢕⠄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢃⠡⡨⡢⣑⠡⡪⡂⠁⠠⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠘⣀⠎⠀⢔⢔⠌⠐⢕⠕⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠇⠢⡢⠀⠁⠪⡢⢀⠨⠪⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣟⣀⣤⣬⣬⣤⣥⣬⣤⣵⣥⣤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣉⣁⠂⢀⣠⡤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⡧⢸⠁⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠓⠚⢁⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢁⡎⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣊⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠃⡘⠠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠶⠾⠁⠀⠉⠉⢹⡆⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢠⠄⠀⠀⠀⠀⠀⠀⢼⠁⠀⠲⠤⠀⠀⠀⢸⠷⠛⠛⠛⣦⠀⠈⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠙⡆⠀⠀⢀⡖⠻⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠸⠶⣄
⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠈⠓⠋⢁⠆⠀⢸⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⠾⢤⡀⠂⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠘⣆⣰⢠⠀⠀⠀⠀⠀⠀⡰⠋⢀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣀⢀⣴⣾⠶⠿⠓⠒⠦⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠉⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⢷⡄⠀⠀⠀⣸
⠀⠀⠀⠤⠤⠒⠚⠉⣀⠤⠒⠀⠀⠀⠈⠉⠑⠒⠲⠶⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠤⠐⠁⠀⠓⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⢀⡖⠀⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠐⠋⠒⠒⠶⠦⠤⠶⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⣀⠈⠀⣠⡟
⠀⠀⠀⠀⠀⡠⠔⠊⠁⢀⣀⠠⢤⣀⠀⠀⠀⠀⠒⠢⢄⣠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠺⡝⢠⣄⠈⢿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡙⢦⠀⠀⠀⠀⠀⠈⠑⠄⠀⠐⠶⠖⠂⠀⠀⠀⠀⠀⢹⡆⢸⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠀⢹⠄⠃⠀⠀⠀⢸⡋⠉⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣘⠒⠊⠀⠀⠀⠀⠀⠀⠻⣈⡠⢆⠀⠀⣶⡄⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⠹⣄⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣾⣿⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠙⢋⣛⣷⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⡞⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣻⡿⢿⣽⣶⣶⠄
⠀⠀⢀⣴⣿⣿⡟⠛⠛⢛⣻⣿⡿⠿⠟⠛⢿⣿⣿⣿⣿⡟⠛⢫⣿⢿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⢀⣽⣿⣪⣿⣵⣿⠻⢻⣿⠇
⠀⠀⠈⣿⣿⣿⣷⡾⠿⠛⠉⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⢀⣾⢟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡾⢯⡾⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠹⣿⣷⣠⣤⣦⡀⣴⣾⣿⣻⣿⣿⣿⣿⣧⡾⢿⣼⣿⣿⣿⡿⠃⠀⣠⣄⣀⣰⠟⠈⢻⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡟⠁⢀⣾⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣿⣷⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⡿⣳⣿⢯⠯⡿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡛⠉⠁⠀⠀⣰⣟⣼⣿⡧⢋⢴⣿⣿⣿⣿⣿⣦⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣴⢯⣼⠿⣋⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢡⣿⡿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠙⠻⢿⣿⣿⣿⣿⣵⣅⣤⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣳⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠁⠀⠀⠀⠀⠈⠙⠻⠿⠏

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⡀⠀⢀⢀⠀⡀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢠⠀⠀⢀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣏⢨⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠦⡷⠾⣾⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⣈⣀⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⡄⣞⣻⣾⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡁⣨⢧⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠙⠄⠱⣾⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⣲⣶⢻⣦⣄⠀⢀⡴⠋⠀⢠⠄⠀⠀⢠⡞⠉⠉⠙⡆⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣿⠉⠉⠁⣿⡴⠋⠀⠀⢠⠇⠀⠀⢀⠀⠀⠀⠒⣚⣁⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣆⣹⡿⢧⢀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠀⠌⠏⣠⠚⠁⠀⠀⠉⠓⢦⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠙⣏⠉⠀⠀⠈⢏⠀⠀⠀⠀⢸⣃⣤⣄⡀⠀⠀⢠⡇⠀⠀⣀⠀⠀⠀⠈⢳⡀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠈⢢⠀⠀⠀⠘⣆⠀⠀⠀⢸⠀⠀⠀⡇⠘⣦⠴⠷⠤⣸⡿⡇⠀⠀⠀⠀⢧⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠹⡄⠀⠀⢸⠂⠀⣸⠃⠀⡗⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⣸⠀⢸⡄⠀⣠⠀⠀⠀⣠⠞⠁⢸
⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⢳⡄⠀⠘⣧⡴⠃⠀⢠⡇⠀⠀⠀⣤⣼⡦⠤⠤⠴⠞⣡⡾⠀⣷⠊⣼⢀⡴⠋⠁⠀⠀⣼
⠀⠀⠀⠀⡏⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⠀⠘⣆⠀⠀⠈⠱⢤⣀⠀⣀⡽⠁⠀⠀⠛⠛⠉⢠⠞⠁⠀⠟⠉⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⣧⠀⠀⢹⡗⢲⡤⣄⣀⣀⡀⠀⠀⠀⠀⣼⠀⠀⣠⠟⠀⠀⠨⠋⠀⠀⠀⠀⠀⠭⢭⡤⠄⠀⣠⠞⡇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢻⠀⠀⠈⣇⢸⡇⠀⠀⠀⠉⠉⠉⠉⢹⠉⠀⢰⠏⠀⠀⣆⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢸⡄⠀⢠⣼⣤⣇⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⡞⢹⠀⡇⠈⠢⡟⢢⡀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⣀⣧⣀⣈⡁⢸⣏⠁⠀⠀⠀⠀⠀⠀⣘⣇⠀⡇⠀⠀⠷⠋⢠⡇⠀⠀⠀⠀⢧⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⢠⡶⠋⠉⡷⢭⣻⣿⣍⢽⣯⣉⠙⣱⢻⢟⡽⡋⠉⠙⢿⢤⣄⣀⣠⡎⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⢸⣄⣀⣈⣧⡠⢜⣪⠕⠋⠈⠙⠿⢷⣻⣯⣄⣼⣀⣀⣼⠀⠀⢀⣞⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡀
⠀⠀⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠛⠛⠋⠀⠀⠀⠶⢾⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠖⠂⠀⠐⠄⠂⠂⠐⠀⠠⠐⠀⠀⠀⠀⠀⠒⠒⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⠤⢤⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡤⢤⣨⠏⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠏⠀⣠⠦⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢶⠶⣞⣉⣻⠛⠉⠁⠘⠀⣰⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠐⠶⠶⠒⠒⠲⣿⣿⡃⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⡀⠈⠁⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣃⡀⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠖⠚⢁⢿⢹⡏⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣀⡔⢢⠀⠀⠀⠀⠀⠒⠒⠒⠀⢀⣬⣭⣄⡀⠀⠀⢦⡀⠀⠀⢸⢸⡜⡇⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠃⠤⠠⠠⠿⣄⣀⠀⠀⠀⠀⠀⠈⠙⢙⣥⣴⡶⠀⠀⠀⠀⠀⢘⠀⢃⣇⠀⠰⡇⠀⠀⠸⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠔⠠⠴⠟⠚⣍⣛⢿⣤⡀⠈⠉⠒⣰⣿⠀⣸⠋⠤⢀⡸⢦⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣾⢫⣀⠀⠭⣷⣶⣽⣿⣿⢿⣷⣶⣦⣬⣿⣿⡯⣌⢷⠀⠘⢧⢠⡓⡾⢅⠅
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠮⣷⣬⣿⡔⢿⡿⣛⣋⠉⣉⣉⠙⠛⠋⠻⠛⢿⡇⠉⠑⠘⢿⣧⣦⠖⠀⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠉⠀⠈⠀⠀⠓⠒⠰⠟⠏⠉⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⢸⣿⠯⢤⡄⢠⣤⡙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡆⠀⠀⠀⢹⡄⢀⣀⣀⣀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⣧⡋⠙⠉⢉⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⣀⣼⡿⠻⠶⠶⠊⠹⠆⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢻⣿⣿⣿⠷⠄⠀⠀⢀⠔⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⣄⣹⣿⣿⣤⣤⡌⢆⣤⣦⣤⣴⣦⣴⣴⠂⠘⡆⠀⠀⠀⠀⠀⠀⠐⢒⡠⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠙⣻⠟⠭⣉⠉⠁⠀⢻⠁⠀⠀⠀⠈⠉⣿⡖⠁⢘⠀⠀⠀⠀⠀⠀⠐⣄⣪⠉⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣃⠀⠸⡧⡀⠀⠌⣠⣤⣤⣼⣤⣤⣦⣤⣤⣄⣿⡦⠀⠈⢧⡀⠀⠀⠀⠀⡄⠛⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⣸⣧⠈⣸⡇⠛⠛⠛⢻⠛⠋⠛⠛⠛⠋⢻⣧⡀⠀⠀⢳⡀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣴⡾⠋⠙⢳⣿⡇⢸⣿⣧⣼⣤⣤⣠⣤⣠⣄⣿⣟⡽⢄⠀⠀⣿⣶⣼⣦⣳⠆⠀⠀⠀⠀⢐⣿⣿⡄⠀⠀⠀⠀⠀⣠⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠛⠉⠀⢀⣨⡿⠻⣿⠸⠟⠛⢻⡟⠛⠛⠛⠛⠟⠃⠘⣟⠁⠀⣿⣿⣿⣿⣿⣧⠂⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⣠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣯⣤⡀⠀⠀⣠⣿⣿⣿⣿⣿⢸⣶⣿⣾⣥⣴⣲⣦⣦⣶⡇⠀⠘⣦⣼⣿⣿⣿⣯⣿⡍⣮⠀⠀⠀⠀⠀⠘⢿⣿⣿⣰⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣠⣾⣿⠛⠿⠿⢻⡟⠿⠷⠟⠛⡿⠟⠛⠛⣿⣿⣷⣶⣶⣾⣽⣿⣿⣯⡛⠩⣧⣰⡄⠀⠀⠀⠀⣸⣿⣻⣿⣿⣿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠉⠛⠁⠀⢿⣿⣿⢱⣶⣶⣾⣷⣿⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢰⠋⠙⣁⠀⠀⠀⡘⢻⡕⢿⣿⣿⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣾⣿⣿⣿⡿⣾⢻⣷⠀⢠⡩⢹⡿⠿⣿⣿⣽⡋⠀⠀⣾⠀⠀⣿⣃⡀⠠⢿⠀⠈⠠⣛⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⣿⣿⣿⣯⣹⡹⠯⢤⣤⣶⣾⠀⠀⠀⠙⠻⠯⣠⡴⠋⠀⠀⠸⣿⡧⠀⢸⡀⠀⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢃⣬⣍⣝⠛⡍⠀⠰⠞⣋⣉⣽⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⣶⠛⠋⠉⢴⣶⣧⣤⣀⣾⣿⠿⢁⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣧⣴⣦⣤⣄⣈⣉⣉⣡⣤⣤⣄⣈⣉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣙⡩⠉⠉⣉⣩⣾⣁⣉⡉⢛⣉⣉⣉⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠿⠻⠾⠛⣩⣽⠃⠘⡿⠟⠛⠉⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⡐⠶⣶⠿⠛⡿⠀⠀⣿⠻⠿⠷⠤⢽⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⠷⠤⠐⠚⢳⡇⠀⠀⢻⣿⣷⣦⠄⣸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣴⣶⣶⣶⣼⠁⠀⠀⣾⠀⠶⢖⡚⣉⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠘⠀⠀⠀⢻⠀⠾⠛⠿⠿⠃⠻
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠒⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠾⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⠀⠀⠀⠀⠐⠒⠒⠐⠒⠀⠤⣀
⠀⠀⠀⣴⠶⠛⠻⠶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡵⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣠⣤⡤⠤⠍⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠓⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠘⢧⣄⡀⠀⠀⢀⠀⠤⠤⠶⠒⠒⠒⠂⠀⠀⠀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣄⣀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠃
⠀⠀⠀⠙⠲⠦⢤⣤⠤⠀⠀⠁⠀⠀⠀⠀⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢯⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣉⠓⢦⡀⠀⠀⠢⢤⣀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠀⠀⠁⠀⠀⢠⠞⣁⠀⠈⠳⡄⠙⡄⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠱⣀⣀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡒⠒⢉⡠