Cute flower bear text face Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⡇⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠓⢦⣱⡺⠚⢉⡽⠃⠀⠀⢾⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣻⠶⣶⠯⠶⠶⠤⣤⣿⣋⣩⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠙⠺⠏⠀⠀⢀⣀⠀⠈⣦⠀⢠⠔⠒⠦⡄⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠦⣼⠀⠀⠀⠀⢠⠄⠀⠀⢠⠇⢀⠿⢤⠇⢠⠖⠆⠸⠶⠒⠦⡴⠋⠁⠈⠙⢦
⠀⠀⠀⠀⠀⣀⡤⠤⣄⡀⠑⢤⡸⠆⠀⡄⠀⢯⣘⣳⠀⣀⠠⡇⠀⠀⠀⠈⡎⢀⣀⠲⠄⠀⢹⠞⠉⠙⣆⠈⡇
⠀⠀⠀⠀⡼⠁⢀⣠⣄⡉⢦⡎⠀⠀⠀⢧⡀⠀⠉⠁⢀⣨⠇⠳⣄⡀⢸⡀⠓⠤⠋⠀⠀⣀⣮⡀⠀⠀⡜⢠⠇
⠀⠀⠀⠀⣇⠀⡏⠀⠀⠙⢦⣧⡀⠀⢀⣠⡀⠀⠀⠑⢋⣤⣀⡠⢞⢻⡀⢉⡳⠚⠀⢨⠏⠁⠀⠈⠳⢜⡡⠋
⠀⠀⠀⠀⠘⣄⠱⣄⠀⡠⠊⠀⠈⠉⠉⠀⠑⠦⠤⠴⢻⠲⠀⠷⠈⢠⡌⠉⡏⠓⠚⠉⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠈⠓⢬⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠰⠀⡄⢀⠐⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⣠⡄⢀⠘⡄⡏⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢸⠀⠀⢧⢀⡘⢃⣁⠇⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⣠⡟⠂⠀⠸⣀⡁⢨⢹⠀⠀⠚⣧⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠹⠄⠉⠀⠀⡠⠗⠛⠛⠚⢄⠀⠈⠁⠝⠙⠏⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢧⣀⣀⣀⣀⡼⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⣆⢸⣇⡾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⣠⠇⠀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠚⠛⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠚⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⡾⠛⢷⣄⠀⣠⣴⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⣠⣴⠾⠛⠛⠛⠛⠻⠷⣾⣧⠀⠀⢻⣶⡟⠁⠀⣽⡇⠀⠀⠀⠀⣀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠙⠻⣶⣄
⠀⢠⣾⠏⠁⠀⠀⠀⠀⣠⣶⠶⠾⢿⣧⣀⢸⡿⠀⣀⣼⣟⣠⣶⠿⣿⣿⠿⠿⠋⣿⣀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⢰⡿⠁⠀⠀⠀⠀⠀⠀⢿⣅⡀⠀⠀⢈⣿⡟⢻⡟⠛⠉⠛⠛⢷⣆⠀⠀⠀⠀⠀⠉⠛⠛⠷⢶⣦⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⡿⠟⠉⣿⡟⠻⣶⣤⣤⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⣠⣿⡇⠀⠈⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼
⢹⣇⠀⠀⠀⠀⠀⠀⣰⡿⠋⠘⢷⣤⡾⠟⠈⢿⣄⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⢰⡿
⠀⢻⣦⡀⠀⠀⢠⣾⠋⠀⠀⠀⢠⣶⠶⠶⠾⢶⣏⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠿⠿⢷⡄⠀⠀⠀⠹⣷⡀⠀⢀⣴⡟⠁
⠀⠀⠙⢿⣦⣰⡟⠁⠀⠀⠀⠀⠸⠷⠶⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⠿⠃⠀⠀⠀⠀⠘⢿⣶⠟⠋
⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣠⣶⠾⠟⠛⠛⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠛⠛⠛⠛⠷⣦⡀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⢠⣿⠁⠀⢠⣶⣦⡿⠋⠀⠀⠀⣠⣶⣶⣶⠌⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣵⣶⣷⡶⠀⠀⠀⠀⠈⢻⣶⣶⣄⠀⠘⣷⡀
⠀⠀⠀⣾⠇⠀⠀⠺⠿⣿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣦⣴⣿⡇⠀⢀⣀⣤⣤⣄⣀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣷⠀⠀⠀⠀⣿⡿⠟⠀⠀⢹⣇
⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠟⠉⠀⠀⠈⠙⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡿⠀⠀⠀⠀⠈⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣤⣶⣶⣶⣄⠀⠙⣿⣿⣿⣿⣿⣿⠟⠁⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⠾⠿⠟⢋⣾⠃⠀⣠⠘⠿⣦⣴⡾⠃⣤⠀⠈⣷⡈⠙⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠻⣧⣤⣾⢿⣦⣴⡟⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠶⠿⠛⠛⠉⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢰⡟⠛⢶⡀⣠⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⣛⣿⣧⠀⠈⣿⡏⠀⢀⡿⠀⣀⣤⣠⣤⣴⣦⡀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢰⡟⠋⠙⠛⢷⣤⣿⣤⣴⣿⣵⣾⡋⠙⠟⠙⠋⠸⢧⣤⣄⣀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣴⠾⢿⣾⢿⣄⡀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⣼⣇⠀⠹⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢀⣴⠟⠙⢷⣤⡾⠋⢻⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⣰⠟⠁⠀⠀⣠⡶⠶⠷⠷⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⢷⡆⠀⠀⠈⢿⡄⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⠏⠀⠀⠀⠀⠘⣛⣛⣛⣛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣛⡁⠀⠀⠀⠀⢻⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⡀⣠⡶⠛⠋⠉⠉⣉⡛⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣉⣁⡀⠀⠉⠙⢷⣄⢀⡀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣾⣿⡟⠀⠀⠀⣴⣿⣿⣿⣁⣸⣷⠀⠀⠀⣀⣀⠀⠀⠀⣾⣿⣿⣿⣿⣅⣠⠀⠀⠀⢹⣿⣿⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢹⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣠⡶⠛⠋⠉⠛⢷⣄⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⡏⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣄⡀⠀⠻⣿⣿⣿⣿⣿⡿⠋⠀⣤⣤⣤⣤⡀⠙⢿⣿⣿⣿⣿⡿⠏⠀⣀⣴⠟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠾⠿⠛⢩⡿⠁⢀⡌⠻⣦⣴⠟⢡⡄⠈⢿⡈⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠷⣦⠾⠻⠶⠾⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠶⠶⠶⣦⣴⠶⠶⠶⠶⠾⠛⠛⠋⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣀⡀⢇⣠⢞⣠⠤⢤⠀⠀⠀⢸⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠙⣬⡷⠋⢀⠔⠁⠀⠀⠀⢸⣞⣁⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⢼⣏⡽⠗⠚⠉⠛⠒⢶⡿⠥⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠙⠋⠀⠀⠀⣠⣄⠀⠀⢳⠀⢀⡴⠚⠓⠲⣄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠲⢤⡇⠀⠀⠀⠀⢀⡄⠀⠀⠀⣸⠃⢀⡼⠤⡼⠀⡴⠒⠄⠘⠶⠒⠦⣤⠞⠁⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠙⢦⣀⣹⠄⠀⡤⠀⢸⡀⠛⡆⠀⡀⠀⡏⠀⠀⠀⠀⢡⠎⢀⡀⠰⡄⠀⠈⣦⠞⠉⠓⣄⠀⣧
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠙⢦⣰⠋⠀⠀⠀⣇⠀⠀⠙⠋⠁⠀⢹⡆⢧⡀⠀⢀⡆⠘⢦⣩⠟⠀⠀⠀⢠⠃⠀⠀⠀⣽⠀⡏
⠀⠀⠀⠀⢸⠁⢀⡞⠉⠉⠳⣄⢻⠀⠀⠀⠀⠈⠁⠀⠀⠰⠤⠟⠉⠀⠀⣹⢳⠀⠑⠲⣄⡴⠀⠀⡖⠚⠉⠙⠲⣄⣠⢃⡼⠁
⠀⠀⠀⠀⠘⣇⠘⣇⠀⠀⠀⣨⠟⠓⠦⠤⠖⠛⢦⡀⠀⠀⣀⡜⣝⠛⣫⠁⠎⠓⠶⠶⡦⣄⣠⠴⠃⠀⠀⠀⠀⠈⠑⣏
⠀⠀⠀⠀⠀⠈⢦⡈⠢⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢳⠉⠀⠉⠀⠀⠇⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠙⠀⠆⢠⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡴⡆⠀⡈⢡⢸⠁⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⠀⡀⠃⣀⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⢀⣼⠓⠀⠀⢸⡀⡁⢀⡁⡇⠀⠀⠞⣦⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠙⡏⠈⠃⠀⠀⣠⠷⠒⠚⠲⢧⡀⠀⠘⠉⣹⠒⢾⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠀⠀⠀⠀⠀⣱⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠉⠓⠒⡖⠒⠉⠁⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⡀⢠⡇⢀⡄⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠈⢳⣬⣧⡾⠃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⡀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⣃⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠖⠶⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉

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

⠀⠀⠀⠀⠀⣤⡴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢫
⠀⠐⢂⠀⠒⠻⣷⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⡀⠈
⠀⠈⠁⠓⠣⠖⠦⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⢤⡄⠀⣀⠤⢄⣀⠀⠐⢴⣄⠤⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⣼⣋⡅⣤⡁⢠⣞⡟⢃⣄⣀⢢⡄⢸⠃⡀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⣀⣔⡉⣵⣇⡀⡟⠋⣀⢌⣼⢇⢽⣏⠉⠿⡜⡟⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠰⣽⣦⡙⠻⠵⠁⠀⠉⠀⠨⠤⠀⠀⢈⣡⣹⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢧⠋⡟⣿⠧⠀⣂⣀⠀⣀⡀⢾⣾⠃⠀⡯⠛⠛⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⠀⠆⡙⠓⠃⠆⠀⠙⠿⠁⢿⡿⠀⠀⢀⡴⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢦⣤⣴⠀⠘⠌⠢⣄⣀⠀⠐⢁⠀⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠠⠀⠈⣿⣶⡆⠀⠣⣤⣄⡀⠀⢰⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠁⠰⡀⠀⠈⡵⠨⠡⠀⡠⡇⠀⡔⠀⠉⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠈⡆⡠⢚⠁⠀⡁⣁⣦⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⠤⢋⣴⡇⠀⣰⠃⣻⡃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢈⡝⠒⢡⣀⣄⣴⠋⠁⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⣠⠿⠛⠛⠉⠉⡟⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣶⡄⠀⠀⠀⣶⣶⣾⣷⣶⡄⠀⠀⢀⣶⣶⣿⣶⣶⡄⠀⠀⢀⣶⣶⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠈⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠁⣀⣀⣀⣴⣿⠶⠾⢶⡄⣠⡾⠛⠛⠛⢷⣤⣤⡶⣦⡀⠀⣤⣤⣤⣴⠶⢶⠶⠶⣶⣶⠾⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠛⠛⢻⣯⣿⠀⢀⣾⢻⡟⠀⣴⢶⡆⠀⢿⣇⠁⢸⣿⠻⣿⠀⢸⣿⠀⢠⣤⡤⣿⣧⠀⣠⣶⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣶⣶⡾⢹⡟⠀⢸⡿⢾⣧⠀⠻⣾⠟⠀⣸⣿⡆⠀⠁⠀⠀⢀⣾⣿⠀⠀⣤⣤⣿⣿⠀⢁⠀⠠⣴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣸⣿⠀⠀⢸⣇⣀⣀⣀⣸⡿⣦⣀⣀⣠⣾⠏⠘⣷⣀⣀⣷⣀⣼⢿⣯⣀⣀⣀⣀⣸⣿⣀⣨⣦⣀⣼⠟
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠙⠉⠉⠉⠉⠀⢈⣉⣉⣉⣁⡀⠀⠈⠉⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠁
⠀⠀⢰⡟⠉⠙⣿⢀⣠⣤⣤⣤⣀⣀⣠⣠⣤⣤⡀⠀⠀⠀⣴⠟⠋⠉⠉⠉⠛⣷⣤⣤⣤⣤⡀⢀⣀⣀⣤⣤⣄⡀⠀⣠⣤⣤⡀⠀⠀⢀⣠⣀⣀⣀⣄⡀
⠀⠀⢸⣇⠀⠀⣿⡿⠉⢁⡀⠈⣹⡏⠉⢉⠈⢉⣿⠀⠀⢸⡏⠀⣴⡾⢷⣤⣾⣟⠁⠀⣀⠈⠻⣿⡉⠉⡉⠉⣹⣧⣾⠋⠁⠈⢻⣆⢀⣿⠉⠙⣿⠋⠙⣷
⠀⠀⢸⡟⠀⠀⣿⡇⢰⣟⣻⣿⣿⣧⠀⠈⠙⠉⣿⠀⠀⢸⡇⠀⢻⣦⣴⠿⣾⣿⠀⠚⠋⠀⣀⣿⡇⠀⠉⠋⢹⣿⡇⢠⠿⠆⠀⢿⣾⠇⠀⣀⠀⣀⠀⢹⣇
⠀⠀⢸⡇⠀⠀⢻⣧⡀⠙⠋⠉⣿⡇⠀⠈⠉⠛⢻⡇⠀⠘⢿⣄⠀⠉⠅⠀⣼⣿⠀⠰⡀⠈⢙⣿⠁⠀⠉⠙⠋⣿⠃⢰⣶⣷⠀⢸⣯⠀⣸⡿⠶⢿⣆⠀⢻⡆
⠀⠀⠈⠻⠿⠶⠿⠛⠻⠶⠶⠾⠛⠿⠿⠿⠻⠷⠿⠃⠀⠀⠈⠙⠻⠷⠾⠟⠋⠹⠷⠿⠻⠾⠟⠻⠿⠿⠛⠿⠶⠟⠷⠾⠏⠙⠛⠛⠻⠶⠟⠀⠀⠀⠻⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠤⠀⠀⠠⠈⢀⠢
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩
⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠃
⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠚⣷⡆⠀⠀⠀⢠⡞⣿⣆
⠀⠁⠁⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⢀⠀⢀⠈⠿⠿⠏
⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠈⠀⠀⠠⠤⠀⠀⠐
⠀⠀⠀⠁⠈⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⢰⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡜⠠⢒⣠⠠⣤⢄⠠⢤⡄⢤⣤⠤⣤⠄⣀⠀⢠⠂⢲⢄⢤⠄⢤⢤⣀⠐⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡰⠀⠲⠩⠷⠩⠦⠸⠎⠡⠧⠼⠼⠤⠴⠌⠽⠀⠸⠤⠴⠌⠔⠌⠼⠤⠅⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡘⣾⣇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢸⡷⠄
⠀⢀⣉⢄⢀⠙⠛⠯⣂⠠⣁⠀⠀⠀⠀⠀⣶⡄⢄⠀⠀⢀⣀⣤⣬⡿⢦⣈⣹⡿⠛⣰⠖⠲⣤⡤⣤⣿⡄⣀⡄
⠀⠀⠀⠈⠚⠒⠟⠣⠸⠑⠈⢀⣠⢤⣄⡀⢥⢬⣳⠗⣺⣫⢴⠶⠾⢶⠲⢭⣏⣀⣴⠁⠀⢀⠀⢹⡄⢹⣿⢻⡧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡤⣤⡛⢟⡲⠦⣽⠀⠿⣅⡎⢶⡻⡺⣷⠚⠁⠀⢈⣳⣼⣿⣦⡀⢰⠠⡄⢡⣤⠤⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠃⢸⣿⣤⣉⡑⡺⣮⠠⣟⢷⡻⢷⣥⢻⣦⠀⠀⠈⢻⣿⣿⣷⣇⠈⠣⣄⡸⠷⡟⣡⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠐⢾⣿⠋⣼⣞⠵⡯⣑⢌⣓⢾⠛⣓⡵⢻⡷⢆⠲⡏⠈⡟⠉⢋⠉⠈⣸⢧⣤⡟⠉⠛⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⡇⠀⠁⠀⠈⠁⣈⡑⠓⠚⠛⠖⠒⠁⠑⢄⣁⣱⣆⠀⣠⢦⣀⣴⢡⡟⣠⣿⢀⣠⣼⡁⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⡄⠀⠀⠀⠀⠈⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢹⠀⣉⣼⣞⣼⣿⡿⠃⠀⣿⠙⠩⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⢸⣇⠀⠀⠀⠀⠐⢌⣛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⣛⣡⠎⠉⠁⡅⠉⠟⢀⠳⣶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣴⠇⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢁⠀⢻⠀⠀⠀⡀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠀⠀⠀⠹⠀⢀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⠀⢇⠀⠀⠀⠊⠀⢀⣀⣀⣀⣀⡀⠀⠈⠀⠀⠀⡰⠀⠀⢰⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⣷⡀⠀⠈⠢⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠘⠁⠀⢀⣾⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠀⠘⣧⡀⠀⠀⠀⠰⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⡀⠀⠀⠀⢀⣼⠇⠀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢷⣆⡌⠛⠦⣄⠀⠀⢆⠀⠀⠉⢻⣟⠋⠀⠀⡰⠁⠀⣀⠴⠛⢁⣤⡶⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠈⠛⠷⣴⣌⠓⠄⠈⢳⡀⠉⠉⠉⠉⢀⡾⠁⠠⠞⣡⣶⠾⠟⠉⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠳⠀⠀⠀⠉⠓⠒⠒⠚⠋⠀⠀⠀⠜⠙⠁⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠈⠉⠋⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⣶⣀⣠⡆⠄⢀⡀⠀⠀⣠⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠟⠻⠿⠓⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠚⠿⠟⠻⠿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠀⠀⠀⠐⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢠⣾⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⣿⣿⠋⠙⣿⡟⠀⠀⠀⠀⢸⣿⠋⠉⣿⣿⣆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣿⣏⣹⣶⣴⡟⠁⢠⣤⣤⡄⠀⠻⣶⣴⣿⣙⣿⠄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠉⡏⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⢠⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡀⠀⠀⠀⣜⡀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠒⠓⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠚⠒⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠉⠙⢿⡇⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣾⠃⠒⠒⠒⠒⠒⠚⠛⢿⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠳⣦⡀⠀⣀⣠⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⣠⡶⠛⠛⠛⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣨⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣼⠃⠀⠾⠿⢿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠟⠿⠷⠀⢻⡄
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣼⣿⣿⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡶⠛⠉⢀⣠⣤⣤⣤⣤⣀⠈⠙⠳⣦⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠏⠀⠀⠀⣿⣿⣿⣿⣶⠄⣽⠇⠀⠀⠈⢿⡄⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢸⡏⠀⢀⠀⠀⠘⢿⣿⣿⣿⣾⠟⠀⠀⠀⠀⠈⣿⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢸⡇⠀⠹⣧⡀⠀⠀⠉⠉⠉⠁⠀⠀⢀⣾⠇⠀⣿⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣌⣷⠀⠀⠙⠿⣦⣄⣀⣀⣀⣠⣤⡶⠟⠋⠀⣰⣿⠾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠈⠛⠷⢦⣤⣀⣀⠉⠉⠉⠉⠉⣀⣀⣤⡴⠞⠋⠁⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⢀⣤⠄⠀⠀⠉⠉⠉⠉⠋⠉⠉⠉⠉⠀⠀⠀⢤⡀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⣿⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣼⣷⣀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⢀⣿⠃⠀⢀⣴⠟⠋⠉⢀⣼⠟⠉⠙⠛⠷⣦⣀⠀⢀⣤⣶⠟⠋⠉⠙⢷⣄⠀⠉⠙⢷⣄⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡏⠀⢀⡾⠃⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣿⠙⣷⠟⠙⣯⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠻⣆⠀⠈⣿
⠀⠀⠀⠀⣿⠇⠀⣾⠁⢀⣤⠾⠛⠋⠛⠛⢶⣄⠀⢰⠏⢸⡏⠀⠀⢿⡄⢀⣴⠞⠛⠉⠛⠻⢶⡀⠀⢹⡆⠀⢿⡇
⠀⠀⠀⢀⣿⠀⢸⡏⢀⣾⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠸⣧⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢹⣆⠈⣿⠀⢸⡇
⠀⠀⠀⢸⣿⠀⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⣿⣧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡇⢸⣿
⢀⣴⠾⠛⠿⠀⡏⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣠⡿⠁⠻⣧⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⡇⠸⠟⠻⢦⣄
⣿⠃⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣴⠏⠀⠀⠀⠈⢷⡄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢻
⢻⣦⣀⡀⠀⢸⡇⠈⣷⠀⠀⠀⠀⠀⣠⡾⠋⣠⡾⠃⠀⠀⠀⠀⠀⠀⠻⣦⡈⠻⣦⡀⠀⠀⠀⠀⢰⡏⠀⣿⠀⠀⣀⣠⣾
⠀⠈⠙⠛⠛⠛⣧⠀⠹⣧⣤⣤⡴⠞⠋⣠⡾⠋⠛⠿⠶⠶⠶⠶⠾⠿⠛⠋⠻⣦⡈⠛⠶⣤⣤⣤⡿⠁⢠⡟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⣀⣀⣠⣴⠟
⣶⣶⡶⢶⡶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀⠀⠀⠀⠀⠠⡀⢆⣀⣙⣦⡤⢤⣤⣤⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣴⣾⣷⣦⡵⠶⠞⢌⣶⣿⣿⣿⣿⡿⡷⡜⣿⠟⡗⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⢻⡿⣋⣤⠶⣤⣦⣼⠦⣿⣿⣜⣿⣥⡗⡞⠿⢻⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠏⠀⠉⠀⠀⠊⣭⠏⣵⣷⡍⣽⠽⠇⣨⣤⣼⡁⡼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠀⢠⡖⠀⠞⢡⣴⣿⣧⡝⡟⣯⣿⠦⢸⣿⣿⣿⣿⢠⡖⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⣻⠂⢀⠀⣼⣿⡿⠁⠀⠙⣿⣷⣶⠎⢻⠿⡿⠻⡤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠅⠀⢼⡆⢸⡄⠈⠏⢀⣤⣤⣄⣿⣿⣿⣶⣽⣄⣾⡦⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠹⡆⠈⢶⣷⠞⢀⣽⣎⣻⣿⣻⣾⣿⣿⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠿⣧⠀⠑⢤⣴⣳⣤⠼⡏⠍⣿⣾⢛⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⢀⠀⠘⠿⣌⠻⠛⠓⣶⣯⢿⣛⣧⣻⡿⡋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠈⠠⣄⡴⢛⣰⠿⡟⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣆⠙⣴⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠾⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣷⣿⣻⣟⣴⢿⣻⣿⣷⡟⠀⠸⠐⠄⠯⠖⠿⠘⠦⠄⠸⠷⠾⠰⠣⠿⠆⠺⠐⠳⠮⠸⠇⠸⠵⠺⠈⠧⠖⠥⠚⠆
⣶⣶⣶⣶⣶⣶⣶⣾⣟⣛⣛⣛⣛⣋⣽⣋⣿⣛⣻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⠿⢿⣿⣿⢿⠿⣿⡟⣿⣿⡿⣿⣿⢿⣿⣿⣿⠿⡿⢿⣟⣿⣿⣿⠿⠿⢿⣿⣿⣿⣻⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣾⣷⣿⣷⣿⣿⣾⣷⣿⣷⣿⣿⣿⣾⣶⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠠⠀⠀⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⣤⡔⠀⠀⠀⢠⠤⠹⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣇⣢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠋⠀⠀⠀⡘⡐⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⡀⠀⠀⠀⠠⢠⠄⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠒⠀⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⠆⡄⢀⠀⠀⠄⠀⠀⠀⣀⣀⣀⠀⠀⠠⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠀⠀⠂⢀⡠⠤⠠⠤⡈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⠔⠊⠉⠉⠑⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡎⠀⠀⠀⠀⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠂⠳⢎⣠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢄⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡇⠀⠀⠀⠀⡞⡆⢀⣀⠠⠤⠄⠒⠒⠒⠒⠒⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠲⢜⡾⠒⡸⢂⡠⠴⡴⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣼⣗⠞⠒⠛⠒⢞⠉⠐⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠎⠀⠀⠁⠀⠀⢒⡆⢨⣀⡎⣠⠌⠳⡠⢄⡠⠒⠂⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⢀⡀⣀⡈⠢⣈⠧⠀⠄⢸⣐⡆⢀⣰⠁⠀⠀⢱⠂⣄⠢⠀⢱⠊⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⢠⠃⡠⠤⢌⢲⠁⠀⠀⠢⠀⠀⣀⠤⠃⠓⣤⠸⢌⣑⠁⢠⠤⠛⢤⣀⢎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠘⡄⢇⠀⠀⡱⠓⠤⠔⠲⢄⣀⡠⣾⠒⡏⠊⡒⢲⠧⠤⠊⠀⠀⠀⠈⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠈⠪⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⢱⠠⢠⠀⡁⡚⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠶⠄⣄⠤⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠇
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⢄⠀⠀⢀⡮⠀⠸⠐⠀⢲⠀⠠⣇⠀⠀⢀⡴⠀⠀⠀⠈⡃⢀⠎⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⠚⠏⠁⠀⢠⠟⠒⠚⢄⠀⠉⠛⠚⠉⠀⠀⠀⠀⢀⡅⢸⠀⠀⠀⠀⠀⠀⡀⠀⠈⠋⠀⠈⠁⠀⡶⡄
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠓⠤⣤⠤⠚⠒⠤⡀⠀⠀⠀⠀⠀⠀⡰⠀⠸⡀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠠⠀⠀⢠⠃⠘⡀
⠀⠀⠀⠀⠀⠱⡀⠀⠀⢀⣀⡀⣠⣃⠀⠀⠀⡄⣿⢠⠄⢀⡀⠼⠦⠤⢀⡀⠀⡰⢁⡠⠤⠷⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⢇⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠈⡲⠊⠁⠀⠀⠀⠀⠈⢢⠀⠙⠛⠋⡔⠁⠀⠀⠀⠀⠀⠈⢫⡠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢇⠀⣀⡀⠀⢀⣀⣀⡴⠒⠒⠒⠒⠧⣀⡠⣀⣀⡠⠤⠤⠴⠁⠱⣄⠀⠀⠀⠀⠀⢀⡠⠖⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠉⠁

⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⣦⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⢄⡀
⠀⢀⣾⢉⠀⠀⠀⠈⠻⣿⠿⣿⠿⣿⢿⠿⢿⣿⢿⡿⡿⡿⠿⣧⠀⠠⣿⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⡿⢷⠟⠛⢟⡄
⠀⢸⣿⡆⠀⠠⠀⠀⣴⣿⣀⣈⣘⣧⣜⣨⣹⣯⣤⣣⣅⣇⣧⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠇⠘⠀⠄⢹⡟
⠓⢺⣿⣦⡀⠀⠀⢠⣼⣿⢀⡇⢿⡏⡌⡍⠋⡅⣰⡏⠒⡭⡨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣿⢻⡟⠁
⠀⠀⠻⣿⡅⣠⡀⣸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠋⠙⠉⠉⢉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣦⡀
⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⡀⠃⠀⢀⠀⠀⠀⠀⢰⡿⡏⠇⣈⠁⠚⣷
⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠁⠜⢧⣶⣷⣿⣶⣶⡗⠂
⠀⠀⠐⢀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠙⠛⠛⠛⠅⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⣶⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠠⠀⢰⠟⠻⢻⡟⡟⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⣴⣤⣬⣦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢬⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠙⠿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠠⡶⠋⠀⠀⠉⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠸⡅⠀⠀⠀⠀⠀⡷⣤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⢀⣠⡼⠃

⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠠⡄⠀⢤⣼⣿⢄⠀⡸⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣻⡖⣼⣿⠧⣤⣄⠼⣿⣤⣷
⠀⠀⠔⢖⣤⣀⣌⠡⣄⡣⢀⣠⡾⠍⠁⠀⠉⠙⠲⣼⣯⣬⣉⡏⢀⡞⠀⠀⠈⠷⣊⠛⠢⣀⠤⡴⠖⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠉⠀⠉⠁⢠⣏⠄⢀⡄⠀⡀⣀⡔⣋⠉⠷⣒⢺⡔⠚⠓⣤⣿⣷⣆⠘⠌⣃⡙⢺⣱⢿⣿⠃⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢈⠯⠽⣾⢹⣞⢼⢥⡃⡹⣏⡀⠀⠐⠛⡿⣿⠿⠖⠐⠉⣷⡶⢣⡀⢀⣷⣀⠲⠄⠐⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠀⠐⠻⣞⣒⣺⣄⠈⣟⢾⣛⣶⡼⡻⡶⠆⡛⣀⠈⠀⣨⣀⡾⣸⣤⣿⡷⠁⢻⣿⣶⣞⡢⢤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⣴⣈⣼⣿⡻⣹⣕⠪⢭⠟⣤⢊⠕⠉⠒⠴⠞⠓⠖⢳⣀⣡⠿⠾⠏⢷⠴⣞⣹⠛⡆⠈⢹⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡅⠀⣼⡿⢹⣿⣿⣿⠄⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣐⣄⡰⠁⢣⠘⠇⢡⣧⢠⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⢿⢁⣾⡵⡟⠛⠀⠈⢉⣩⣉⠀⠀⠀⠀⠀⠀⠀⠀⣉⡥⢬⣁⠀⠀⠈⡆⠀⢠⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢥⣤⡇⠀⠀⠀⣿⣣⣼⣷⠀⠀⣠⣤⣄⠀⢰⣿⣷⣞⡿⠀⠀⠀⢻⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠙⢿⣿⠿⠀⢸⣿⣿⣿⡇⠈⠻⠿⠛⠁⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⢤⣀⣨⢿⣁⣀⡴⠀⠀⠀⣠⣤⠾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡉⠛⠲⢤⣀⡀⠀⠀⠀⠀⢀⣀⡤⠴⠋⠉⡀⣆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⣇⣤⡀⡀⠀⠉⠉⠉⠉⠉⠉⠁⢀⠀⣴⠼⣷⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠏⠙⠳⣤⡄⠀⠀⠀⠀⠀⣀⡞⠚⠁⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡀⠀⠀⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣤⣄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡠⢀⣀⣀⣀⣀⣀⣀⠀⠀⣾⣿⡿⠛⠛⠿⢿⣿⡿⢿⣿⣯⠉⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⢀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠄⣿⣿⣿⠟⠙⠛⠻⠿⢿⣿⣿⡿⣿⠇⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠏⠋⠙⠁⠈⠁⠀⠈⠛⣿⣿⣿
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠐⠃⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟
⠀⠀⠀⠀⢸⢳⠀⠀⠀⠠⡄⠀⠀⠀⣤⠀⠳⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⡇⢄⣄⣠⠄⠀⡄⠀⠆⠀⠀⠀⠰⠀⠀⠀⠀⣏⠉
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢄⠀⡂⠀⠀⢘⠈⠀⠀⠀⢀⠀⢀⣀⢠⠔⠁⠀⠿⢉⡩⡀⠘⡀⠀⠀⠢⠀⠐⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⠀⠀⠀⠀⣀⡠⠂⠀⠀⠀⢀⡜⠀⢢⣀⠂⠀⢀⠂⠀⠀⠈⠂⢁⠀⢤⡀⢀⡀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠤⢻⣿⣿⣿⠀⠀⠀⠀⠣⡈⡠⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠁⠘⠚⠐⠳⠀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠄⠀⠀⢻⣿⣿⡇⠀⠀⠂⠀⠀⠁⠨⡒⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠢⣜⠂
⠀⠀⠀⠀⠻⠿⠿⢿⢋⠋⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⠀⠀⠀⠀⠀⠀⠠⠂⠀⢠⠆⠀⠀⡠⢤⠡⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠏⠀⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠀⣀⡀⢀⢠⠀⠀⠦⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠚⠗⠀⠀⠀⠀⠀⠺⠓⠃⠠⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠡⠐⢋⡉⣂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡠⠂⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠂⠀⠀⠀⠔⠁⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡂⠐⡂⡖⠀⠁⠚⠲⡆⠀⠀⠀⠀⠀⠑⢈⣱⠐⡆⠀⠀⠀⠀⠀⣀⣠⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡅⠀⢩⢅⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠞⠁⠀⠘⠚⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⠀⠀⠀⠐⢠⠖⡐⡄⠀⠀⠀⠀⠀⠄⠀⠐⠛⠁⠀⠀⣀⠶⠂⠀⢠⠀⡆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⣠
⣟⣧⣷⠀⠀⠀⠄⠀⠉⠉⠀⠀⠀⠘⠀⠉⠀⠀⠀⠂⠀⠁⠀⠉⠀⠀⠀⠘⠊⠀⢰⣟⣻⣛⣤⣧⠀⠀⠠
⢾⣃⣿⠀⠠⠰⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⠀⢠⣦⡀⢶⣶⣤⠀⠀⠀⢸⣯⡻⣟⣠⣿⠀⠄⠲
⠛⠛⠃⠀⢀⣴⢾⠓⠲⣶⡆⠀⠀⢸⣀⣿⠋⣨⡇⠀⠀⣿⣽⡟⡶⡬⣥⣶⠃⠀⣀⠛⠛⠛⠛⠀⠀⢀⡴⢞⠓
⠀⠀⠀⠀⢸⠻⠾⠷⠿⢏⣰⠀⠀⠙⠟⢿⣧⣼⠇⠀⠀⠙⠻⢧⣿⣯⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⣝⠳⠾⠾
⢠⡀⠀⠀⠘⠷⠤⠄⠀⠜⠃⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⣤⠀⠂⠀⠹⠶⠤
⠙⠁⢀⠀⢠⡂⠀⠀⠀⠀⠓⠁⠀⢧⣳⠄⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠚⠛⠀⠠⠀⣔⡀
⠀⠀⢥⠄⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣜⡄⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠈⡤⠄⠀⠀⢂
⣀⡀⣀⠀⠀⠀⠈⠰⢯⣎⠃⠀⠁⢀⠀⢄⠑⠀⠀⠀⠀⠐⠀⠮⠋⠀⠀⢰⡠⠃⠀⣀⣀⣀⠀⡀⠀⠀⠀⠁⠸
⢯⡟⢿⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡀⠀⣀⣀⠀⠀⠀⠀⢸⣯⣼⣽⠿⣿⠀⠀⡈⠀⠄
⣽⣴⡿⠀⠐⠚⣁⣀⣀⣀⠀⠀⠀⢠⠶⣶⣶⠶⡄⠀⠀⣰⣵⢄⠛⠿⠗⢀⡄⠀⠘⣷⣌⣯⣼⠿⠀⠒⢊⣀⣀
⠈⠀⠀⠀⢠⣾⣹⡍⣭⡽⠃⠀⠀⢼⣶⣻⡄⢶⡇⠀⠀⢿⣿⡯⣟⣯⣻⡿⠁⠀⣢⠀⠈⠈⠀⠀⠀⣰⣏⢩⢉
⠈⠀⠀⠀⢸⡉⠉⠉⠉⢱⡾⠀⠀⠈⠁⠛⠛⠛⠁⠀⠀⣀⡉⠛⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠉⠉
⣸⡄⠀⠀⠀⡙⠓⠒⠐⠋⣄⡠⠀⡤⡀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⢤⣃⣷⠀⠁⠀⠈⠛⠒
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣿⡶⣶⣶⣶⡶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣴⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠈⠉⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⠤⠀⠀⣄⣀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢰⠂⠐⠺⠗⠂⠈⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠓⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠐⠀⠀⠀⣠⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⣤⣤⣶⠟⠁⠀⡟⠛⠛⠛⠛⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠝⠋⠁⠀⠀⠀⢧⣤⣤⣤⣤⣤⣤⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠁⠀⢀⠀⠤⠀⠂⠁⠙⢛⣿⣿⠿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣴⣾⣧⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠈⠉⠙⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣄⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⠀⠀⠀⢀⡀⢰⠇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠰⡆⢽⢿⢀⣀⡀⢸⠅⡿⠀⡿⠀⠀⠀⢀⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣆⢠⣀⡄⢻⢸⣿⣸⣿⣯⣾⢰⠃⢰⣇⣤⣦⢄⣾⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⣟⣎⣻⣾⣿⣤⡏⣿⣿⣿⢷⡎⣶⣼⣿⣿⣯⢞⢟⡼⠁⠀⠀⠀⢀⡄
⠀⠀⢀⣶⣄⡀⢀⣤⢆⣷⣜⣎⢻⣿⣿⡜⡇⢸⣿⡟⡿⢠⡇⣸⣿⣿⠏⣼⣾⣶⣷⡶⣠⣴⣯⠞
⠀⠀⠀⡙⠻⣝⡮⣝⣿⣿⣿⡻⣇⠹⣿⠇⢣⠸⠉⠀⠃⠸⠁⠜⣿⢃⡞⣽⣿⣿⣯⢞⡵⢋⣡⠆
⠀⠀⠀⠉⠓⢦⣙⠮⣙⠿⣿⣿⡊⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠸⣿⠟⠫⢖⣥⣶⣩⣀
⠀⠀⠀⢀⣼⣶⣿⣿⣟⡦⣌⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣤⣾⣿⣿⡿⢛⣀⣤⣴⣶
⠶⢤⣶⣶⣬⣽⣿⣿⣿⣿⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠿⠿⣛⣻⠭⠿⠚⣋⣉
⠀⠰⠦⠤⢭⣭⣉⡛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣏⡍⠁
⠀⠀⠀⢰⣾⣿⣿⣿⣿⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣿⣿⣿⣿⠿⠿
⣀⣀⣠⣬⠭⢽⣿⣿⣿⣿⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣶⠦⢶⡗⠞⠯⠽⢿⣿⣿
⠹⠶⠛⣛⣋⡭⣵⣿⣽⣶⣷⣦⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢿⣿⣿⣿⣿⣏⡛⠒⠲
⠀⠀⠈⠉⠀⢲⣿⣿⣿⡿⣋⣠⢖⣡⣀⢄⠀⠀⠀⠀⠀⠀⠀⡄⠠⣄⣬⣝⢦⣬⣛⠿⣛⠿⠇
⠀⠀⠀⠀⠀⣈⡵⣾⠵⣪⣿⣵⣿⣿⢫⢎⣰⣴⣀⡄⡇⢲⣠⣜⢦⠘⢿⣿⣷⣿⣦⣝⠻⣽⣲⣄⣀
⠀⠀⠀⠴⣿⠷⢋⣥⠞⣹⣻⣿⣿⢷⣯⣾⣿⣼⣿⣧⢷⠘⣿⣿⣯⣿⢮⢿⡿⣿⡷⠈⠳⠆⠉⠛⠉
⠀⠀⠀⠀⠁⠀⠉⠀⠀⠘⠟⣴⢋⡾⣿⣿⢇⣿⣿⣿⣿⢦⢻⣿⣿⡿⣦⠳⣵⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡟⠀⠻⡿⢸⢼⣿⡟⢻⠸⡿⡜⡿⠛⠈⢧⡙⢮⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⣿⠈⠁⠀⢸⡄⢷⣷⠀⠀⠀⠀⠀⠈⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣏⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣤⣤⣤⣤⣴⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢠⠀⢴⠒⠛⠙⣆⣁⣀⠀⠀⣤⠀⠀⠠⠀⠠⡤⠀⠀⢀⡀⣠⢟⠛⠒⡦⠀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠓⠀⡃⠀⢰⠈⠈⢋⣁⡀⠀⠉⠀⠀⠀⠈⠀⠀⣀⡉⠀⠈⣌⠀⠀⠁⠜⠁⠀⠀⠀⠈⠻⠃⢸⣿⣿⣿⡥⣶⠀⠀⢰⡦⣿⣿⣿⣿⡇⠙⠛⠁
⠀⠀⠀⠀⠀⠁⠀⡘⠀⣴⣿⣿⣹⡄⠀⠀⠀⠀⠀⢀⣾⣿⣹⢷⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⡀⠐⠃⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠀⢧⠈⠿⢋⡀⠀⠀⠀⠀⠀⠈⡁⠿⠛⡸⠃⡚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠉⠀⢰⣾⠿⢛⡢⠀⠈⠁⠈⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠙⠶⠊⠁⠀⠀⠀⠂⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢶⣆⡄⠀⠀⠀⠀⠀⢤⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠲⠄⠀⠠⠔⠊⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠔⠀⠀⠀⠢⠀⠄⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⡀⠀⣀⡀⡰⢹⠀⠀⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⡎⠀⢣⣤⠙⡙⢧⢸⡄⠀⡰⠋⡘⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠢⣘⡉⠢⣼⠁⢰⠃⠀⠳⡇⠀⢻⣇⠜⠀⠀⣇⡴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡄⠤⠤⢼⣄⡀⠀⠈⡇⠀⠀⢱⠏⠀⠀⠀⠙⣆⠀⢿⠀⣀⢰⠋⠀⢀⣸⠤⠤⢀⡶⠂
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣈⠢⣄⠀⠀⠉⠙⠲⣿⢀⣀⡼⠀⠀⠀⠀⠀⢹⣀⠜⠋⣽⡼⠛⠉⠁⠀⢀⠔⢉⣀⣀⠀⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠈⠉⠙⢦⡀⠀⠀⠀⠸⡄⠈⠑⢦⡀⠀⠀⢠⠜⠁⠀⢀⡇⠀⠀⠀⢀⡾⠓⠉⠁⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣠⡤⠤⠶⠛⣒⠶⠶⠦⠿⣄⡀⠀⠙⢆⣠⠃⠀⠀⢀⣼⠷⠾⢶⣒⠛⠒⠦⢤⣄⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⣦⡀⠀⠈⠛⠶⣄⡀⠀⠀⢈⠓⣄⣸⣏⣀⡤⠊⠁⢀⣤⠖⠋⠁⠀⠀⣠⠾⠉⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠥⠤⠤⠶⡿⠶⣄⠑⢀⣠⠟⠓⠦⣴⠋⠁⠀⣠⣞⠱⡦⠚⠛⠦⣀⡠⠂⣠⠾⢟⠒⠒⠒⠦⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣨⣷⠞⠁⠀⠀⢠⣁⡠⠴⠊⠁⠈⠦⣣⠀⠀⠀⠈⠳⣾⢅⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣀⣠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⢄⣀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠉⠁⠾⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡖⢻⣷⣆⠀⠀⠀⠀⠀⢀⡖⢻⣷⣦⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠉⠉⠀⢀⡀⠘⠀⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⠓⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠠⠚⠉⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠦⠤⣄⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⠁⢀⣀⠀⠠⠠⢰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠀⠀⠉⠉⠋⠉⠉⠉⠀⠸⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⠦⠤⠤⠤⡤⡤⠤⠤⠤⠤⠴⠶⠒⠋

⠀⠠⠠⠀⡌⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡄⣦⠀⢰⠄⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢸⠀⠎⢹
⡇⠈⠄⠘⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡦⠃⣠⠃
⠰⠀⠀⠀⠀⠒⠲⠖⢀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠉⠚⡇⠀⠀⠈⠁⣀
⠀⠙⡄⠀⠀⠀⠀⢀⠟⠀⠁⠀⠀⠀⠀⠀⠈⢿⡁⢤⠀⠀⠶⠈⠉⣳⠜⢳⡄⠀⠀⠀⠀⠈⢱⠀⠰⢄⠀⠀⢀⣄⡐
⠀⠀⠈⠳⢦⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠗⠀⠀⠀⠀⠀⠀⠁⠀⠀⠳⠀⣀⠀⠀⠀⠘⣄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⡄⠈⡇⠀⠀⠀⠀⠀⠀⢠⡄⢉⡀⣠⣤⣤⡀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⡨⠃⠰⠖⠋
⠀⠀⠀⠀⠀⢧⠀⢹⡄⠀⠀⠀⠀⣠⠔⠛⠉⠁⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠳⣀⠀⠀⢀⠎⠀⢀⠟
⠀⠀⠀⠀⠀⠸⡇⠀⢷⠀⠀⡤⠊⠁⠀⠠⠄⠀⠀⠀⠠⢤⠀⠀⠀⠈⢢⠀⠀⠀⠉⠀⣰⠏⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣴⡀⠴⢧⡞⠁⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⣠⡄⠀⠀⢇⠀⠀⣦⠴⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⢡⡆⠀⠀⠘⣇⠀⣿⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠻⡀⠀⡇⠀⠀⠀⣾⣿⠉⠉⠉⠉⠁⢀⣤⣴⣿⠃⠀⠀⠀⠀⣹⠷⣤⡰⠏
⠀⠀⠀⠀⠀⠀⠀⢇⠀⢁⠀⠀⠀⢹⣿⣶⣶⣶⡶⠋⠉⠀⣹⠏⠀⠀⠀⣹⠊⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⡀⠀⠀⠀⠹⢿⡟⠉⠁⢉⣡⠜⠁⠀⠀⢀⣴⠃⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠹⢆⠀⠀⠀⠈⠁⠐⠂⠉⠁⠀⠀⢀⣠⠞⠁⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⠛⠶⢦⣀⣀⣀⣀⣀⣠⠶⠞⠋⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠘⣇⡠⢤⠤⠤⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⡍⠉⠉⠛⠓⠒⠤⠤⠤⣄⣀⣀⣀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠉⢉⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠐⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠱⢄⣀⡠⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡤⠲⠶⠶⠶⠖⠙⣧⣤⣄⣀⣀⠀⣀⠀⢀⣠⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⢸⠁⠈⠉⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⡴⠀⠀⠀⠀⠀⠀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⢻⠀⠀⠀⢀⡠⠊⠀⠀⢰⡀
⠀⢀⡀⠀⠀⢠⡴⠚⠁⠀⠀⠀⡀⢻⣄⠰⠊⠁⠀⠀⠀⡠⠺
⠀⢨⠑⠀⠠⠄⠤⠀⠀⠀⣠⡔⠉⠁⠈⠡⠄⠀⠀⠀⣄⠁⢼
⠀⠀⠉⠐⠒⠒⠒⠒⠒⠀⠓⠌⠀⠂⠀⡀⠺⠀⠒⠂⠉⠐⠂
⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⠂⡀⠄
⠀⡀⠠⠶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣸⣿⠼⡄
⠛⠱⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣷⠕⠿⣆⣦⣤⣄
⠀⠒⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡰⣦⣿⡟⣟⠋
⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡶⢷⠉⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡎⣀⡏⣿⣿⣾⣾⣷⣾⣷⡴⠂⠴⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢂⠀⠶⠮⠁⠀⠀⢻⣿⣿⣿⠛⣻⣿⣿⠃⠀⠀⡉⠉⣴⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠚⠏⠁⣿⣇⣶⣿⢷⣿⠝⠀⠀⠀⠁⠀⠀⠈⠉⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⢈⣻⡆⠀⣀⠉⠀⠀⠉⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠐⠀⠀⠀⠒⠊⠥⣦⣾⠅⠀⠀⠀⠠⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣆
⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⡀⠙⣹⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁


⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⠀⠀⠁⠀⠍⢉⠳⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠞⡉⠩⠀⠈⠀⠀⡆
⠀⠀⠈⡆⠀⠀⠀⠂⠈⢣⡙⡀⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⣁⠏⡼⠁⠐⠀⠀⠀⢰⠁
⠀⠀⠀⣷⣰⡄⠈⠳⠖⣯⡷⣌⣗⣳⣦⡐⡀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣺⣺⣣⠾⣝⠲⠞⠁⢀⣆⡾
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⣷⡮⢀⣸⡛⠚⠶⣆⠀⣦⣴⠀⣰⠶⠚⢛⣇⡄⡱⣾⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠃⢀⡀⢀⣀⣿⣿⣿⣿⣥⣵⣼⣾⣆⣿⣿⣰⣿⣦⣧⣮⣿⣿⣿⣿⣀⡀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⢻⣧
⠀⠀⠀⠀⠀⠀⠹⢷⣿⣿⣿⢭⣿⣿⣟⡽⣿⣿⣿⣿⣿⣿⣿⣿⢯⣻⣿⣿⡭⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣁⣼⠿⣿⣿⣿⢿⣿⡟⢿⡿⢻⣿⡯⣿⢿⡿⡿⣧⣈⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠟⠀⣎⡿⡶⢬⣎⡄⠀⠀⢐⢱⡅⢶⢿⣹⠀⠻⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣆⠀⠙⠿⠃⠀⢹⠇⠀⠀⠘⡏⠀⠘⠿⠏⠀⣰⡓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣦⣀⣀⣠⣴⡇⠀⠀⠀⠀⢸⣦⣄⣀⣀⣴⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠿⠻⣤⠇⠀⠀⠀⠀⠸⢄⠟⠿⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢁⣤⣄⡉⠻⣷⡄⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣾⠟⢉⣠⣄⡉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣸⡟⠉⠙⢿⡆⠸⣷⣶⠾⠟⠛⠛⠛⠛⠛⠛⠻⠷⣶⣾⠇⢰⡿⠉⠉⢻⣧⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠹⣧⣄⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⣠⣼⠏⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣈⠉⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠉⣁⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠟⠀⠀⣠⡿⠋⠁⠀⣙⣿⡆⠀⠀⢰⣿⣋⡀⠈⠙⢿⣄⠀⠀⠻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢰⣿⠁⠀⢀⡀⠙⣿⣿⠀⠀⣿⣿⠋⢁⡀⠀⠈⢿⡆⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⣇⠀⠀⠘⢷⣶⣿⠇⠀⠀⠸⣿⣶⡾⠃⠀⠀⣸⡇⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⣦⣄⣠⣴⡿⠋⠀⠀⠀⠀⠙⢿⣦⣤⣠⣴⡿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⣤⣴⣤⣤⡀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⣀⣀⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠛⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠛⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣤⣤⣶⠿⠛⠁⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠈⠛⠿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣶⠿⠛⠁⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠟





⣿⠚⠛⣿⠷⠷⢶⠿⠶⣷⡟⠾⠿⠿⢿⠿⠷⠶⢶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠿⠿⠿⠿⠿⢶⣶⡶⠾⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⣀
⠀⠀⠀⠀⠀⠐⣾⣧⣀⣠⡟⠤⣀⢴⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣴⠷⠔⠀⣴⣶⣴⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⢻⢂⣬⣒⡟⢸⡇
⠀⠀⠀⠀⢮⣶⣿⣿⣿⣿⣇⢀⠀⣸⣿⣶⣵⠆⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⢀⣀⣀⣻⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠈⢿⠋⠉⠛⠿⠷⠶⠒⠉⠙⢿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⠀⠀⠉⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⣹⠋⣡⣤⣈⠉⣀⣴⣌⠹⣏
⠀⠀⠀⠀⢠⡇⠀⣼⣷⡄⠀⠠⣾⣷⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣏⢀⣾⣿⠖⠉⢶⣿⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⣿⡿⣉⣤⡙⢿⣿⠄⢹⡀
⠀⠀⠀⠀⢸⣇⠸⣿⠇⢴⣶⡦⠘⣿⠇⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⢻⠃⠶⡶⠆⢻⠋⠀⡏⠀⠀⠀⠀⠀⠀⠀⠚⣴⡀⠙⣇⢉⣛⡁⣸⠋⢠⣬⠃
⠀⠀⠀⠀⠈⢻⣶⣠⡗⠐⠺⠂⢲⣅⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣆⡘⠛⣀⣼⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣮⣥⣤⣬⣵⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣤⡼⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⢿⣿⡿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡖⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣆⠀⠀⠂⠀⢀⣖⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢉⡀⢀⡆
⠀⠀⠀⠀⢀⡐⠇⣘⣣⣼⣷⡷⣔⣇⣰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣉⠁⡄⢈⣉⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⣧⠤⠦⣼⣿⣿⣿⣖⢦
⠀⠀⠀⠀⠈⣵⣞⣿⣿⣿⣿⣿⣿⢿⣻⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣖⠂⣶⠐⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⠉⠙⠛⠉⠉⠙⢻⠟
⠀⠀⠀⠀⠀⢸⡿⠛⠉⠉⠉⠉⠉⠙⠺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠛⠒⠓⠚⠛⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣦⣤⠀⣤⣶⡄⠐⣗
⠀⠀⠀⠀⠀⢰⠀⢸⣿⠆⠀⠰⣿⣇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠲⣶⠆⠀⢲⣶⠆⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⡋⠰⣿⡟⠁⠀⠈⢿⣿⠂⢹
⠀⠀⠀⠀⠀⣷⠀⠛⠃⢠⣴⡤⠈⠻⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣰⠏⠶⡶⠆⢳⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠹⠀⠻⠿⠛⠈⠋⢀⡿⠂
⠀⠀⠀⠀⠀⠘⢧⣄⠣⠤⠽⠄⠔⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣾⣄⢉⣨⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⣷⣈⠋⣀⣾⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⡿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣩⣛⣍⣍⣉⣯⣏⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⠴⠖⢦⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡏⠀⠀⠀⠀⠙⡆⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣠⡀⡄⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠳⣄⠀⢀⠚⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣦⢾⡇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⠶⠶⠶⠾⠛⠛⠛⠛⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠲⠶⣤⡀⠠⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⡞⠛⢲⣶⣌⠙⢦⡀⠀⠀⢀⡞⣉⠀⠀⣶⣶⣦⠀⠹⣦⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣾⢼⣿⣿⣿⣿⡿⠀⠀⣿⠀⠀⣿⢰⣿⣷⣾⣿⣿⣿⠀⠀⣿⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠈⠷⠿⠿⠛⠁⠀⠀⣾⠀⠀⣧⠈⠻⢿⣭⡭⠟⠁⠀⠀⣾⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⠘⢧⡀⠀⠀⠀⠀⣀⣼⡏⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢋⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣨⠁⠀⠀⠉⠛⠶⠶⠟⠋⢠⡇⠀⠀⠀⠈⠻⠦⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⣉⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⣠⠶⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠰⣷⡆⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⠀⢻⠓⠓⣠⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⢉⣧
⠀⠀⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠂⠀⠉⠉⠉⠀⢀⠔⠋⠹⣆
⠀⠀⠈⢻⡈⣷⠀⠀⠀⠀⠀⠀⢠⡶⠛⢦⣈⡙⠛⠒⠲⠦⠶⠖⠊⠉⠙⢲⣦⣤⡴⠚⠁⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠘⡅⢘⠀⠀⠀⠀⠀⢀⡼⠄⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣦⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢷⠀⡇⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣄⣀⣾⡁⠀⢹⣆⣀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠸⡆⣧⠀⣴⠋⠉⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣷⢸⣴⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠸⡀⠛⠀⢀⣤⡶⢿⠀⠀⠀⠀⠒⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⡇⢠⡴⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠳⠋⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠂⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠅⠀⠀⡸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣾⣶⣶⣴⣷⣶⣶
⣿⣛⣻⣛⣛⣛⣛⣃⣙⣛⣿⣛⣛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣭⣭⣽⣿⣯⣭⣭⣽⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠀⡌⠀⢤⠀⠀⢠⡄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠈⠀⠄⠀⠀⠈⠃⠸⠃⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠰⡤⠀⠀⠀⠀⠀⡀⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⢀⣤⠁⢱⣤⣀⣀⡀⠀⠀⠀⠀⢸⡇⢠⡀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠹⣷⡄⠀⠀⠀⠀⠀⠿⠟⠀⠀⠘⣏⣀⡅⠀⠀⠀⠀⠠⠁⠈⠙⠁⠀⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⣛⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⢰⣶⡄⠀⠀⠀⠀⢰⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡇⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣯⡄⠀⢠⣶⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡻⢇⡀⠀⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠩⣄⡇⠀⠈⠙⢦⣄⢠⡄⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⢃⠘⠀⠀⠀⠁⠀⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠀⠀⠙⢦⡁⣀⣠⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⣿⡀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠔⠂
⠀⠀⠠⠀⠀⢀⣴⠶⣤⠀⠀⠀⠀⠐⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠆
⠀⠀⠀⠀⠀⠹⣧⣀⡼⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⡶⠃⠀⠀⠀⠀⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡍⠻⡟⠁⠀⠀⢀⣴⠞⢻⡟⠻⡆⠀⠀⢠⡀⢀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠰⠆⡀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⢀⠀⡴⠀⠙⡇⠀⢻⠀⠀⠸⣷⠏⠁
⠀⠁⢠⡴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠁⠀⠀⠀⠀⠀⢀⡆⠃⠀⠀⠜⠁⠀⠀⠀⠀⠐⠀⠣⠀⠀⠁⠀⠀⠠⡄⠲⠀⡄⠀⠀⠀⢐⠀⠤⢣
⠀⠀⢻⣄⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⢿⠀⠀⠀⠀⠀⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠿⠶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣴⣶⣶⣶⣶⣦⣤⣉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠙⠛⠛⠛⠛⠛⠟⠻⠿⣿⠂⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠈⠉⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢇
⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⡞⢙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣀⡄⠀⠀⠀⠀⠀⠠⢬⣤⡄⠀⠀⠀⠀⠀⠀⣴⡆⢰⡤⢧⣦
⠀⠀⠀⣀⣢⡷⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠛⠤⢀⡠⣦⡶⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠧⠘⠀⠐⠛
⠀⠀⠀⠐⠋⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠌⣁⠠⡉⠁⢴⣤⣤⣤⡀⠀⣠⣤⣶⣾⠟⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠑⠀⡁⠂⢁⠂⠄⢀⠀⠀⠀⠀⢀⠀⠀⠠⡊⠄⢈⠀⠊⠀⠀⠀⠐⢀⡘⠙⠛⠣⠄⠻⠋⠁⢡⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠂⠀⢀⠤⣀⠨⣀⠄⠆⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠂⠀⠀⠀⠐⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠁⠀⠃⠀⠖⢂⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠠⠐⠻⣀⠇
⠀⠀⠀⠀⠀⠀⡔⣀⣡⠉⠑⠐⠀⠀⠀⠀⠐⠒⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠮⡄⢨
⠀⠀⠀⠀⠀⠀⠃⠘⠁⠑⢀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⢣⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠂⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⣄⠁
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠡⠀⠀⠀⠀⢹⡀⠀⠀⠐⠂⠀⠀⢀⡀⠀⠸⡋⠁⠋
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠉⠃⠀⠘⠠⠤⢀⠄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⢀⡄⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⢠⡞⠃⠀⠀⠤
⠰⠒⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠮⠒⠃⠀⠀⠀⠁⠀⠀⠀⢰⣞⣵⣋⣒⠀⠈
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡔⠊⠙⡐⠀⢰⡗⠞⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡤⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⣶⢖⡶⠶⠶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⡄⢀⡀⠀⠀⠀⡀⠀⠰⡄⠀⠆⡦⢀⠔⡂⠀⣰⠀⠀⠂⠀⠀⡦⠀⠀⠠⠄⡀⠆⠀⢄⠀⠀⠀⠄⠀⢠⡀⠄⠐
⢠⠔⡋⠍⣀⢉⠠⠊⡀⠈⡰⠑⡌⢰⠗⢁⠔⠑⢄⠀⠀⢤⠀⢀⢠⠁⠈⠐⠀⡠⠁⡄⠀⠌⢑⡈⠰⡔⢴⡋⠒⢂⠨
⢀⠜⠁⣂⠅⠁⡀⠊⢀⠎⣀⠀⡴⠃⡐⠁⠀⠀⢆⠀⠈⠀⢀⡙⣬⠐⢀⡀⠈⢀⠼⠤⣋⣨⣁⣐⠈⠀⢈⡠⠚⣉⠉
⠀⠂⠉⢐⠄⢊⡤⠖⢩⠀⢁⡠⡡⠚⢉⠅⢊⠝⢈⡦⢀⣀⣀⡤⢻⣯⡁⠄⠀⡉⢢⠀⢎⢠⠀⠉⠨⢢⡜⠠⠊⡠⠒
⠀⠲⡖⠁⡐⠉⡄⠀⠀⠇⠈⠀⡠⢂⠤⠊⡠⢂⠎⠀⠄⠀⢸⠀⠁⠚⠘⢆⠀⢀⡴⡘⡀⠀⠁⢂⠀⡙⡅⢀⠘⠁⡰
⠐⠆⠘⠀⠀⠌⣄⠠⣠⡴⠒⠚⠉⠀⠀⠉⢔⡩⡄⢀⣀⡃⠘⠀⠃⠀⠀⠈⡇⡎⠀⠌⠢⢌⠁⠢⣤⡇⠃⠸⠀⡉⠄
⢠⠤⢀⠡⡀⠀⠀⠃⢉⠠⢈⠣⢄⠀⠲⠆⡁⠀⠀⢀⠄⠱⡄⠑⡬⣀⡁⠈⠐⡄⡰⢠⠀⢀⢅⠂⠌⣣⠀⣠⠚⠁⡠
⠈⢢⠀⠑⠹⢄⠆⠀⡘⠀⠀⠗⠠⠚⢄⡀⠄⠀⢄⠓⠀⠀⡴⠀⢰⠈⡁⣀⢠⠞⢠⡀⠙⠡⠀⠈⠐⠘⢿⠃⠤⢀⣀
⠀⠀⠐⠢⢅⣸⡎⠜⢀⠀⠈⠀⠀⠀⡘⣠⠉⠂⠀⠑⠄⠘⠀⠀⠀⡰⠁⣠⠯⢠⡀⠀⡇⢀⠁⡀⠀⣀⠂⢇⠀⠢⠔
⠀⠀⣉⠔⢂⡽⠻⢋⠙⠳⡄⠀⠶⡉⠀⠃⢀⡀⠠⣆⡈⠀⣀⠤⡮⠤⠒⠁⠑⢤⡑⢠⢡⡞⠈⠠⠀⠩⠁⢸⡇⠤⢈
⢀⠔⠁⠀⢀⡎⠰⡄⠀⠀⢘⡐⡀⠘⠀⠑⣤⠄⠂⠛⣳⣾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠙⠝⠂⢄⠤⡳⡄⠘⢧⢀
⠀⣎⢐⡀⠘⠠⠀⠛⢐⠐⠊⡀⠈⢲⠀⡐⠀⠀⠠⠈⠁⠈⠳⢄⠁⠂⢄⠳⠔⠀⠉⠑⢄⠂⠀⢀⢼⣀⣀⠪⣲⡌⠠
⠘⣶⠀⠜⣰⡀⡼⠓⠢⣕⠰⣄⠀⠈⠀⢷⢁⡄⢀⠁⢀⠃⠁⢠⠑⡀⠈⠂⠸⡔⠂⢀⠄⠛⠀⠀⢈⠁⠢⠄⠸⢀⡩
⠀⡙⠠⠀⠟⠐⢁⠊⠠⠊⢱⠄⠃⠐⠢⠀⢹⡀⠀⡰⠙⠀⠢⡈⢀⡁⠴⡚⠠⣄⠀⢸⠀⠀⠃⠀⠈⠑⡠⠨⠆⠥⠄
⠐⣡⢡⢊⠀⢀⠀⠀⠋⡀⡠⠀⡉⢁⠀⡗⠀⡡⡌⠀⠀⠀⢀⡽⠎⠀⠀⠈⢂⠈⠢⡌⢠⠇⠀⣠⣶⠋⠀⠀⡈⠒⢉
⠀⠁⡠⠐⠁⠘⢄⠀⠁⢀⢀⠀⡙⡀⠘⠁⠄⠐⠌⠴⣦⢔⡃⠀⢦⡸⠤⢥⢈⡀⣂⢕⣤⠀⠥⠊⡀⠁⠂⢈⣠⠐⢃
⢀⠵⠦⠉⠙⢢⡬⠒⡈⠀⠀⠤⠼⣷⢔⠀⠀⠀⠀⣠⠎⠀⡈⠹⠛⠧⠈⡔⠁⠀⠴⠚⢃⠀⠂⢤⠈⠣⡉⠀⣨⣘
⠀⠤⠄⣀⠤⠊⠀⠦⢅⠀⠒⠉⠁⡣⠀⢠⢂⠠⠆⠇⠠⠀⢃⠁⠄⡘⠈⡇⠀⡒⠀⢀⠆⠢⣀⠀⠈⢀⠄⠈⢀⢁
⠀⢙⡉⠄⢀⠔⢃⡀⠀⠀⠀⠠⠖⠁⠀⠈⠆⠈⠛⡆⠀⠀⠙⣄⠜⠀⢀⠓⣄⠁⢰⠃⠑⠄⠀⠩⠙⠁⢄⢀⠢⠀⠑
⢀⡁⠀⣀⡿⠁⠀⠙⢌⠁⠛⢢⠇⠢⣀⠀⣄⠁⠀⠈⠺⣆⠀⢉⠀⠔⠁⠀⠘⠃⠘⢁⠀⡐⠀⡗⢗⠢⣔⠦⠑⠀⠑
⠀⠀⠐⠣⠁⠀⠀⢈⡌⠇⠀⢸⢤⠀⢀⡑⢽⡄⠐⠀⠒⣈⣷⡏⣠⡅⠀⠀⡠⠇⠀⠀⢠⠁⠘⠀⢰⡎⢈⣌⠐⢌⢠
⠀⠐⠂⠀⠀⠀⠃⠘⠀⠘⠓⠨⠐⠅⠀⠐⠃⠈⠀⠀⠀⠒⠟⠀⠀⠀⠈⠙⠠⠐⠀⠐⠘⠀⠀⠀⠐⠀⠐⠂⠑⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣶⣿⣿⣿⣗⠲⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⢻⡏⠉⠉⠉⠉⠁⠉⠁⠸⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⢠⣶⣿⣯⣙⡂⢸⣿⣧⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠧⠀⠀⠀⠈⠙⠛⠋⠋⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢦⡀⠻⠏⠭⠃⠀⢀⣀⢺⣿⡆⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣄⣀⣤⣴⡿⠁⢘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣉⣿⠟⠀⠀⣸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⡟⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠿⣿⠯⠟⠉⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣤⣀⣀⣀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣖⠁⠀⠀⢓⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠉⠉⠈⠁⠀⠈⠙⢦⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠺⣅⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠄⠀⠀⢣⢸⡆⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⣿⠁⠘⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠊⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⡐⠉⢻⣷⡀⠀⠀⡟⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⠇⠀⢀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⣸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢱⣄⣀⠀⢀⣠⡞⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⢿⡀⠙⠲⠶⢬⣧⡀⠀⠀⠀⠀⠈⢿⠛⠉⠛⡿⠁⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠢⠀⠀⠙⠢⢌⣂⠀⠀⠀⠀⢀⣀⣠⠔⠋⠀⠀⠀⠀⠂⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠢⡀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡠⠔⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠶⢦⣤⣤⣄⣀⣀⣐⣤⣥⡴⠶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠋⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋

⠟⢻⣿⣿⣿⣿⠇⢉⣼⣿⣷⡾⠀⠀⠀⢠⡼⠋⢀⣿⢻⠀⠚⠠⣶⣠⣤⠀⠀⠀⠀⠀⢻⣿⡷⠰⢾⣴⣿⣦⢿⡿⣿⣿⣷⣛⣿⣿⣭⣿⣿
⣀⣀⠉⢻⣿⣘⡆⠷⣨⣼⣿⡇⠀⠀⠀⢸⠷⣿⡛⢈⣮⠄⠀⠠⠻⣿⣯⡴⠀⠀⠀⠀⠀⠀⠒⠀⠺⠿⡿⠛⣠⣶⡝⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣿⢏⠁⠐⠈⠋⢻⠃⠀⢙⠿⡾⠿⣿⣿⢙⡶⠛⠀⡶⠒⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠠⢴⣿⣿⠟⠘⠈⣿⣿⣿⣿⡤⢻
⠈⠋⠙⠛⠀⠈⠀⠂⠀⠀⠀⠀⠀⣰⡏⢡⡠⣻⣍⣿⣷⣾⡓⢶⣆⠐⡀⣙⠛⠒⢄⡁⡀⠀⠀⠀⠀⠀⠀⠀⠙⣋⣄⠀⢴⣏⠀⠁⢸⡅⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠰⣿⣋⠁⠀⠀⠀⠀⠨⣷⢵⣻⣿⣟⡄⠌⣩⢧⠀⠀⠀⠀⠀⠀⠀⠛⠛⠐⠋⠃⢰⡄⠯⠟⢇
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⡦⣄⡀⠀⠀⠀⠀⠈⢿⣷⣽⢷⡐⠟⡄⠹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢼⣶⠙
⣠⡾⠃⢸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣙⣷⠁⠀⠈⠛⠁⠀⠀⠀⠀⠀⠑⠝⢫⢷⠑⡀⠬⠞⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⣿⣾
⠛⡁⠠⡼⠦⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢸⣏⠀⠀⠀⠀⠀⠀⠀⠸⢿⠦⠀⠁⢸⣿⡗⡉⡀⢀⡸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠉⠅
⠖⢺⠂⠀⠀⢀⡔⠃⠀⠀⠀⢀⡀⠛⢾⣹⣿⠀⠠⣦⣄⠀⠀⠀⠀⠀⠀⢀⣄⣾⢹⣻⡗⡁⠠⠁⣴⠆⠀⡉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠
⣦⣎⠠⠀⠀⠀⠒⠀⠂⠠⠄⠈⣅⠡⣄⣭⣤⢀⡀⠈⠉⠀⠀⠀⠀⠀⠀⢾⣿⣿⠈⣯⠙⢇⢀⠀⢀⢈⠂⣁⠀⠀⠀⠀⡤⣺⣿⠟⡀⠀⠘
⡿⣿⣇⡧⠀⠀⠐⠆⠉⢄⣀⣻⣤⣴⡟⠉⡐⠀⠸⡓⠲⠂⠀⠀⠀⠀⠀⢺⡿⢿⡆⢹⡄⢙⣘⢆⣀⠀⢀⡀⢁⠀⠀⠀⠀⠀⠉⢀⣤⣶⣾
⠷⠄⠀⠀⠀⠀⠀⣠⣾⣿⢷⡾⠙⡋⢹⠉⠱⠆⠖⠏⠱⠀⠀⠀⠀⠀⠀⢥⣷⣬⣿⡌⢷⡀⠈⠿⣍⢢⣤⡀⠀⢀⠠⠀⢀⡀⠀⠀⠐⠛⠛
⠀⠀⠀⣀⢀⢰⠂⢱⢎⢉⣀⣙⡊⢙⡈⢹⠦⡐⢀⢜⡀⠀⠀⠀⠀⠀⢀⡸⣿⣹⣿⣿⣌⠻⣦⣄⣈⠙⠷⢭⣿⡢⣤⣶⣄⣤⣤⣇⣠⣴⢖
⠀⠀⠀⡮⠊⣀⠺⢁⣵⢈⣹⡠⠽⣿⠼⠋⠐⢿⣌⠠⠿⠂⣏⠒⢀⠃⣎⠹⢎⣛⢿⣯⣿⣷⣌⡉⠛⠻⠶⣤⣄⣉⣉⣋⣙⣙⣛⣨⣉⡁⠊
⡆⠀⠀⠀⠒⠉⠗⠸⠆⣸⣍⢰⡜⣻⢂⠀⠀⠀⠉⠳⠶⢤⣤⣤⣬⣤⠶⠞⠋⠉⠅⣻⣿⡿⣿⣿⣶⣤⣀⠀⠀⠈⠉⠈⠉⠙⠋⠉⠁
⠁⣠⠀⠀⠀⠀⠠⢸⣿⣿⣿⡜⢲⣿⠻⢦⣄⢀⣀⣀⡀⠴⠚⠠⠎⢀⠀⢀⠀⣠⣴⠇⡾⠎⣨⣿⣿⣽⣿⣿⣶⣶⣤⣤⣤⣤⣀⣀⣤⡤⣶
⣿⠁⠀⠀⠀⠀⠀⠈⢁⣛⣿⣿⠘⢛⣴⣦⣭⣥⢍⠉⠴⡃⠀⢣⠀⠠⣛⣊⡝⠶⡶⢞⠛⣹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⢀⠂⠀⣰⠄
⠀⠀⠀⠀⡀⠢⠀⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠋⠛⠇⠈⠡
⠀⠀⠀⠀⠣⡀⠐⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⠘⠣⠤⠤⡀⠈
⠀⠘⣄⠐⢄⠡⠄⢡⠶⠈⠀⠀⠊⢠⠊⠀⠀⠀⠀⠀⠐⡀⠀⠀⠁⠀⡆
⠀⠀⠀⠑⣤⡁⠋⠀⡀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣀⠀⠁
⠀⠀⠒⠀⠀⢠⡀⠈⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈⢀
⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣻⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⡀⣣⠀⢃⠀⠀⢀⣀⣀⣀⠠⠤⠔⠚⠉⠀⠀⠉⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⡄⠀⠀⠀⠀⢀⣠⠋⠉⠛⠀⠉⠉⠉⠉⠛⠻⢇⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠐⡀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢙⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⣴⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⢀⠉⠠⣤⠀⠀⣠⣤⡤⠶⠒⠉⠁⣀⣼⣿⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠡⣄⣀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⡦⢀⣀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⢸⠂⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠈⠻⣿⣿⠋⠀⢈⠀⠸⠟⣿⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠙⠶⠂⣀⣀⡠⠞⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⢶⠖⠤⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⣶⣶⠖⠚⢹⠉⠲⡄⣘⡀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢸⢣⠀⡸⠀⠀⠀⠉⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠢⠤⠤⠤⠀⠚⠉⠀⠀⠀⠀⡄⠾⠃⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠻⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠚⠉⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢰⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣡⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠢⣄⣠⠎⣄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠖⢉⣡⠶⠛⢧⡀⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣴⠃⢀⣰⠃⠀⠀⠀⡀⣠⣤⡴⠒⠉⠁⠀⠀⠀⠀⠻⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢆⠈⠉⠉⠉⠉⠉⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠡⡀⠀⠀⠀⠀⢠⡆⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠓⠤⠤⠴⠋⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠠⠤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠁⡰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠤⠄⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠒⠂⠄⡀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠑⠶⠚⠁⢀⣄⠐⠁⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠐⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢰⠁⡌⠀⠀⠆⠀⠈⠉⠉⠉⠀⠉⢉⠇⠀⠐⡏⠀⠀⠀⠀⠙⠢⠤⠤⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⡤⠼⢧⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⠦⣀⣉⣁⡤⠚⠁⠀⠀⠀⠀⢈⡴
⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠶⠉
⠐⠀⡱⠐⠒⠈⠀⠀⠀⠁⠒⠠⠤⣩⣐⠠⢄⣀⡙⠦⣄⣀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⢀⠠⢐⡠⠆⠑⢄⡀⠀⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠥⣁⣉⡹⢛⣛⡻⠛⢛⡋⠀⠤⠤⠄⠒⠂⠉⠁⠀⠀⠀⠀⠉⠈⠃⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⢠⡄⢀⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⠶⠤⠤⠴⠖⠋⠡⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣤⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢠⡆⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣾⡇⠀⠀⣾⡇⠀⢠⣿⠀⠀⢠⣾⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠸⣿⡄⠀⢻⢿⡄⠀⣟⣧⠀⡼⣿⠀⢀⣿⡏⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⢢⣄⠀⠀⠹⣿⣄⠀⢹⣟⠢⡈⣯⠹⢦⡏⠈⠿⠡⣏⡴⠏⡿⠁⣠⣾⡿⠀⠀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⠙⣿⠙⠢⣯⣠⣼⣷⣶⣿⣷⣷⣶⣶⣿⣤⣹⡷⠊⢡⡞⣀⣤⣾⡿⠁
⠀⠀⠀⠀⠐⣦⣄⡀⠀⠈⠾⣯⠉⢻⣦⣾⣿⣿⡿⢿⡿⠟⠏⠿⠙⢻⠿⡿⣿⣿⣷⣾⡉⢠⡴⠋⠀⣀⣴⣾⠋
⠀⠀⠀⠀⠀⠈⠻⠿⣖⡶⠂⢹⣶⣿⡿⠟⠉⠁⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠈⠋⠻⣿⣿⣾⡓⠙⣋⡽⠛⠁⠀⣀⣀
⠀⠀⠈⠻⣷⣦⣤⣤⠌⢻⣤⣿⣿⠿⠀⠀⣴⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣆⠀⠀⠛⣿⣿⣾⠃⠴⠶⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠷⣆⣰⣿⡿⠟⠀⢠⠎⠁⣀⣀⣀⠀⠀⠠⠈⠀⠀⠀⣀⡀⠈⢱⡄⠀⠻⣿⣿⣦⡞⠋⠁⠀⠀⣀⣀⡀
⠀⠘⠻⢿⣶⣶⣖⠋⠉⣿⣿⠟⠀⠀⢈⣾⣟⣿⣿⣿⣿⣦⡀⢀⣴⣿⣿⣭⣍⠛⢦⠁⠀⠀⠿⣿⣿⡀⣯⣽⡿⠿⠛⠁
⠀⠀⠀⠀⠀⢀⣉⠝⢾⣿⠏⠀⠀⠀⢸⣿⣿⣗⣚⣶⣿⣿⡇⢸⡿⣟⣶⣲⣻⡷⠀⠀⠀⠀⠀⢻⣿⡟⠓⢤⣄⣀⣀⣀⣀
⠐⠒⠿⢿⡿⠿⠯⣤⣸⣿⡇⠀⠀⠀⢨⣿⡋⠛⠛⠋⢹⣿⠇⢸⡇⠈⠁⠉⠉⠀⣀⡀⠂⠀⠀⢹⣿⡧⣾⠓⠛⠟⠛⠋⠉
⠀⠀⠀⠀⠀⣠⡴⢊⠹⣿⣷⡀⠀⢑⠐⢿⣷⡄⠀⢀⣼⠛⣄⠈⠛⡆⠀⠀⢀⣘⡿⠀⠈⠀⣠⣾⣿⣃⣀⡙⣦⣤⣤⣀⡀
⠀⠐⠚⠿⠿⠟⠛⢙⠟⢿⣿⣿⣦⠀⠀⠀⠀⠀⣴⠟⠉⠓⣿⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠉⢦⡈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⣀⣠⣴⣧⡴⢬⣿⣿⣿⡄⠀⠀⠀⠰⣧⣶⡶⠿⠿⠿⠗⣖⣴⡄⠀⠀⠀⠀⢠⣿⣿⡿⠷⠖⠦⣿⣶⣤⣄⡀
⠀⠀⠐⠛⠛⠛⠉⠁⣠⣇⣈⣻⣿⣿⣆⠀⠀⠰⠀⠀⠿⠷⠖⠲⠾⠿⠀⠀⠆⠀⠀⣴⣿⣿⣿⣥⣄⣷⣄⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⢡⡋⢘⣿⣿⣧⡀⠀⠀⠀⣠⡤⡶⠲⠤⡀⠀⠀⠀⣀⣾⣿⣿⣅⡈⣧⠈⠛⠿⢷⣦⡀
⠀⠀⠀⠀⠐⠉⠉⠀⠀⣠⣾⡷⠋⡍⡈⣙⡿⣿⣦⣀⠀⠀⠁⠀⠀⢀⣀⣴⣿⠿⣿⣁⠘⡆⠳⣾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⢠⣗⡞⠉⣧⣄⡼⡏⢙⣿⠛⡛⡿⣏⠉⡿⣄⠄⡇⠙⣦⣧⡀⠀⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣿⠋⠀⢀⣿⡟⠀⢷⣾⠁⢷⣹⡇⢹⣰⠇⠈⣷⣷⠀⠈⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢀⣾⠟⠀⠀⣸⣿⠀⢸⣿⡇⠸⣿⡄⠀⠈⠻⣧⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⠃⠀⠸⡿⠀⠀⠙⡇⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠑⠀⠀⠀⠘⠉⠃⠛⠘⠐⠃⠘⠚⠐⠂⠀⠁⠀⠐⠃

⠀⠀⠀⠀⠀⠀⡐⠉⡝⢳⡠⡀
⠀⠀⠀⠀⠀⠀⡄⢸⣧⠀⠁⠹⡄
⠀⠀⠀⠀⠀⠀⡇⣸⣏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡁⣿⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⢱⣿⣧⢀⡀⠄⠠
⠀⠀⠀⠀⠀⢸⣎⣿⣟⠿⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠶
⠀⠀⠀⠀⠀⢸⡇⣿⡿⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡗
⠀⠀⠀⠀⠀⠘⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣣⣿⠋⢸
⠀⠀⠀⠀⢠⠁⣾⡅⠀⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣰⣿⣿⡅⠂
⠀⠀⠀⠀⢰⠸⣿⣷⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢼⡏⠻⠛⢀⠔
⠀⠀⠀⠀⢸⢠⣿⣿⣿⡆⠠⣇⢄⣢⣄⣲⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⡜⠉
⠀⠀⠀⠀⣸⠈⣿⠇⠁⠂⠸⣧⣾⠟⠙⢿⣿⡀⢢⠀⠀⠀⠀⠀⠀⠀⠀⡰⢪⣼⣿⠁⠀⠀⡰
⠀⠀⠀⠀⡿⢠⡇⠀⠀⠀⠀⣿⣿⡄⣀⡼⠛⠛⡄⢳⣤⣠⣤⠠⡀⠀⡼⣥⣿⣿⡿⡁⢀⡾⠁
⠀⠀⠀⢀⠃⣼⣷⠀⠀⠀⢰⣿⡿⡿⠁⠀⠀⢀⢸⡀⢿⡟⢿⣇⠰⡞⣴⣟⡉⠉⠁⣴⠋
⠀⠀⠀⠆⣶⣿⡟⠛⣠⣤⣬⠷⢩⠆⠀⠀⠀⢸⣼⣧⠘⣧⠘⣿⡆⢿⣿⡿⠀⠀⢀⠁
⠀⠀⠰⣀⢿⣰⣇⣾⡿⢻⡧⠀⠀⠀⠀⠀⣠⠋⠀⢿⡄⢿⣆⢻⣿⡘⣿⡇⠀⣰⠃
⠀⠀⠀⣿⣸⠋⠙⠁⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⢀⡲⠁⣸⣯⡍⠙⠇⠙⠋⡼⠃
⠀⠀⡼⣼⡟⠀⠀⠀⠴⢤⣤⣶⠟⢋⣁⣀⣨⣿⡿⣁⢼⠧⠀⠤⣈⡇⠘⢈⡁
⠀⡼⢱⡟⠁⠀⡀⠀⢀⡾⢻⣿⣾⣾⠿⣿⠿⡋⠐⠉⠏⠀⢀⣺⡾⢁⠄⣸⠁
⡘⣴⡟⠀⠀⢀⡃⠀⠾⠁⢸⣿⠋⣈⣶⣡⡾⠁⣠⣴⣶⣶⣿⠟⣡⠟⣼⠃
⡇⣿⠀⠀⠀⠘⠁⠀⠀⠀⠁⠈⣿⣏⣵⣿⣷⡾⠋⣦⡽⢋⣴⣿⠋⢀⡅
⠇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠻⣿⣿⣅⣰⢋⣴⠟⠉⠀⠃⠈⡇
⠰⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠘⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⣧
⠀⠹⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠁⢘⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣿⣿⣞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡙⣿⣿⣿⣷⣾⠶⡷⠀⠐⣿⡿⠠⠏⢻⣷⣶⡀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⡟⢈⡻⣿⣿⣿⣷⣆⠀⠀⣟⠃⠡⣄⣈⠻⢿⣷⣦⣤⠖⣩⠎
⠀⠀⠀⠀⡇⠰⣿⣶⣿⣿⣿⣿⣿⡷⠒⠒⣿⡟⠛⠃⠂⣀⣀⣠⠞⠁
⠀⠀⠀⠀⡧⡀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡟⠀⡰⠁⠀⠀⡾⠁
⠀⠀⠀⠀⢸⠱⣼⣿⣿⠋⢿⣿⣿⠃⠀⢸⠃⣰⠁⠐⠀⢰⠁
⠀⠀⠀⠀⢸⡄⣿⣿⣿⠀⠀⠀⠁⠀⠀⢹⠀⡏⠀⠀⠀⡎
⠀⠀⠀⠀⠈⡇⢻⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡆⠀⠀⠀⢻⣿⣿⣇⠀⠀⠘⣿⣿⣇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⠁⢀⣿⣿⡟⠀⠀⠀⣰⣿⣿⠏⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿
⣿⣿⡀⠀⠀⠈⣿⣿⣿⡀⠀⠀⢻⣿⣿⠀⠀⠘⣿⣿⡇⠀⠀⣾⣿⡏⠀⣼⣿⡟⠀⠀⠀⣰⣿⡿⠃⠀⣠⣾⣿⡿⠋⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠋
⣿⣿⣧⠀⠀⠀⠘⣿⣿⣧⠀⠀⠘⣿⣿⡆⠀⠀⣿⣿⡇⠀⠀⣿⣿⠇⢀⣿⣿⠁⠀⠀⣰⣿⡿⠁⢀⣾⣿⡿⠋⠀⠀⢀⣤⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⣀⣠
⢿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣆⠀⠀⢹⣿⣷⠀⠀⢻⣿⡇⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⢰⣿⡟⠀⣠⣿⡿⠋⠀⠀⣠⣾⣿⡿⠟⠋⠁⠀⠀⣀⣤⣴⣾⣿⣿⣿
⠀⢻⣿⣿⣧⠀⠀⠀⠙⣿⣿⡆⠀⠀⢿⣿⡆⠀⠘⣿⣇⠀⠀⣿⣿⠀⣼⣿⠀⠀⢀⣿⡟⠀⣴⣿⠟⠀⠀⣠⣾⡿⠟⠉⠀⠀⣀⣤⣶⣿⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠹⣿⣿⣧⡀⠀⠀⠘⣿⣿⣆⠀⠈⢿⣿⡀⠀⢻⣿⠀⠀⣿⣿⠀⣿⡟⠀⠀⣼⡿⠁⣼⣿⠃⠀⣠⣾⡿⠋⠀⠀⣠⣴⣾⣿⠿⠛⠉⠁
⣄⠀⠀⠈⢿⣿⣷⡄⠀⠀⠈⢿⣿⣆⠀⠈⢿⣷⠀⠘⣿⡇⠀⢹⣿⠀⣿⡇⠀⢠⣿⠃⣸⡿⠁⢀⣾⡿⠋⠀⢀⣴⣾⡿⠟⠉⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿
⣿⣧⡀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠹⣿⣧⡀⠈⢿⣧⠀⠹⣿⡀⠸⣿⠀⣿⡇⠀⢸⡟⢠⡿⠁⣠⡿⠋⠀⣀⣴⡿⠛⠁⠀⠀⣀⣠⣴⣾⣿⣿⡿⠿⠿⠛⠛⠛
⢿⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⠀⠀⠈⢻⣷⣄⠀⢻⣧⡀⢻⣧⠀⢿⡆⢹⡇⠀⣿⠁⣿⠁⣴⠟⠁⢀⣼⠟⠉⠀⢀⣠⣶⣿⠿⠟⠛⠉⠁⠀⢀⣀⣀⣀⣀⣀
⣀⠉⠻⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⡀⠀⠙⢿⣦⡀⠙⣷⡄⢻⣆⠸⣇⢸⡇⠀⡟⣸⠇⣼⠏⢀⣴⠟⠁⢀⣤⡾⠟⠋⢉⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⡈⠛⢿⣿⣶⣄⠀⠀⠉⠻⢿⣦⣀⠀⠙⠻⣦⡈⠻⣆⠹⣆⢻⡀⣇⠀⡇⡟⣸⠃⣠⠟⢁⣠⠾⢛⣩⣴⡶⠿⠛⠛⠋⠉⠉
⠙⠿⣿⣿⣶⣤⡈⠛⠿⣿⣦⣄⡀⠀⠉⠻⢷⣤⣀⠈⠻⢦⡈⢷⡜⢦⢳⢹⠀⣿⢱⢃⡼⢁⡴⣋⡥⠾⢛⣩⣤⣤⣶⡶⠾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⣉⠛⠿⣷⣦⣄⣀⠈⠙⠳⢦⣄⡙⠲⢌⡪⡣⡷⡀⣻⠁⢊⣴⣿⣪⠵⠖⢛⣉⣉⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛
⣤⣄⡀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣶⣦⣤⣍⣙⠛⠶⠶⢤⣤⣉⣙⡒⠍⠊⠐⣥⣇⡴⠋⠊⢑⣒⣛⣉⣉⣉⠉⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣶⣶⣤⣄⣀
⠿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠒⠒⠒⠛⢛⣛⠊⢉⠴⢛⠉⠒⠶⠶⣤⣭⣭⣉⣉⠙⠛⠛⠷⢶⣶⣤⣄⣀⠀⠀⠉⠙⠻⠿⣿⣿⣶
⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⣿⣿⣶⣶⣶⣶⣶⠶⠶⠶⠶⠒⠛⣉⡥⣒⣾⠏⡔⠀⡇⣦⡢⣍⠲⢍⡙⠻⣯⣛⠷⢶⣤⣀⡀⠉⠛⠻⢿⣷⣦⣄⡀⠀⠀⠉⠻
⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠖⢛⡥⢞⡕⣡⢣⠃⡇⣿⠰⡹⣌⠳⣄⠙⠷⣄⠉⠻⢶⣬⡙⠻⣷⣦⣄⡀⠈⠙⠿⣿⣷⣦⣄
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⠿⠿⠛⠛⢉⣡⣴⠞⣫⡴⢋⡴⢃⡟⢰⠇⣿⡆⢳⠘⣦⠘⢷⡀⠈⢳⣦⡀⠙⠻⣷⣄⠙⠻⣿⣶⣄⡀⠈⠙⠿⣿⣿
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣤⣤⣶⠿⠛⣉⣴⠞⠋⣠⡟⢁⡾⠁⣾⠀⣿⣿⠘⣧⠘⣧⠀⢻⣦⠀⠙⢿⣆⠀⠈⠻⣿⣦⡈⠙⢿⣿⣦⣄⠀⠈⠻
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠟⠛⢉⣠⣴⡿⠛⠁⣠⡾⠋⢠⡿⠁⢰⡏⠀⣿⣿⡀⢿⡄⠹⣧⠀⠻⣧⡀⠈⢻⣷⡄⠀⠈⢿⣿⣦⠀⠙⢿⣿⣷⣄
⠛⠛⠛⠛⠛⠛⠉⠉⠉⢁⣀⣠⣤⣶⣿⠿⠛⠁⠀⣠⣾⠟⠁⣰⡿⠁⢀⣿⠁⢰⡟⣼⡇⢸⣧⠀⢻⣧⠀⢻⣷⡀⠀⠹⣿⣆⠀⠀⠙⣿⣷⣄⠀⠙⢿⣿⣷
⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⡿⠟⠛⠉⠀⠀⣀⣴⣿⠟⠁⣠⣾⠟⠀⢀⣾⠇⠀⣾⡇⣿⡇⢸⣿⠀⠈⣿⡆⠀⢿⣷⡀⠀⠹⣿⣧⠀⠀⠈⢿⣿⣦⠀⠀⠻⣿
⣿⣿⡿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁⢀⣴⡿⠋⠀⢀⣾⡏⠀⣰⣿⠀⣿⡇⠘⣿⡆⠀⢹⣿⡀⠘⣿⣧⠀⠀⠹⣿⣧⠀⠀⠈⢻⣿⣷⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠟⠉⠀⣠⣶⣿⠟⠁⠀⣠⣿⡟⠀⢠⣿⡇⢸⣿⠇⢰⣿⡇⠀⠈⣿⣇⠀⢹⣿⡆⠀⠀⢻⣿⣧⠀⠀⠀⢻⣿⣿⡄
⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⡿⠛⠉⠀⢀⣴⣾⣿⠟⠁⠀⢀⣴⣿⠏⠀⢠⣿⡟⠀⣾⣿⠀⢸⣿⡇⠀⠀⣿⣿⠀⠸⣿⣷⠀⠀⠈⣿⣿⣇⠀⠀⠀⢿⣿⣿⡄
⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⣀⣴⣾⣿⡿⠛⠁⠀⠀⣠⣾⣿⠋⠀⢠⣾⣿⠁⢠⣿⡟⠀⣸⣿⡇⠀⠀⢻⣿⡇⠀⣿⣿⡇⠀⠀⢸⣿⣿⡄⠀⠀⠈⣿⣿⣿
⠛⠛⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⣠⣾⣿⡟⠁⠀⣠⣿⣿⠃⠀⣾⣿⠃⠀⣿⣿⠃⠀⠀⢸⣿⡇⠀⣿⣿⣧⠀⠀⠀⣿⣿⣷⠀⠀⠀⠸⣿⣿
⠀⢀⣀⣤⣴⣾⣿⣿⣿⡿⠟⠋⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⢀⣴⣿⡿⠃⠀⣼⣿⡟⠀⢸⣿⣿⠀⠀⠀⣾⣿⡇⠀⢹⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋⠀⠀⣠⣾⣿⡟⠁⠀⣰⣿⣿⠁⠀⣾⣿⡟⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⡀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠘⣿

⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢄⠀⠀⢀⠇
⠘⢻⣿⣾⠒⠒⠉⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⢠⣤⣤⣾⣷⣶⣦⡀⠀⠀⠀⠀⠀⡀⢠⡀⡀
⠀⣺⣿⣿⡇⠀⠀⠀⠀⠞⠛⠛⢿⣿⣧⡄⠀⣠⣼⣿⣿⣿⡿⠟⠛⢻⣷⣦⡄⠀⠠⣰⠿⠻⣿⣶⣦⣤⠀⢄⡀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠈⢿⣿⣿⠟⠃⠀⠀⠀⠀⣿⡟⠁⠀⠀⠁⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⠀⠀⠘⠿⢿⠧⢀⠑⠀⠊⠘⠋⠀⠀⠀⠀⠀⣄⣀⠀⢀⣽⠿⢋⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢃⠀⠀⠀⠀⠀⢀⣠⣾⣿⣧⣤⣦⡄⠀⠀⣴⡄⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣀⣼⠀⠀⠀⠀⠐⣿⣿⣿⣿⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠿⠀⠀⠀⠀⠀⠈⠛⠛⠿⠛⠛⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠲⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣴⣶⠖⠛⠻⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠈⠁⢳⡦⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣹⡗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⢀⣸⣿⠆⡀⣀⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠐⠳⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣏⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠤⠤⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠙⠻⠿⠟

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⠆⠀⠀⢠⠖⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠘⠻⣿⣿⠟⠛⠉⠉⠉⢉⠛⠷⣦⡀⠀⠀⠀⠀⣀⣴⡶⠿⠛⠻⠷⢶⣦⣤⣤⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠉⠲⢤⡀⢣⠀⠈⢻⣦⢠⡷⣾⠟⠁⠀⠞⣀⡤⠐⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⢄⠀⠀⠀⠀⠹⣧⠐⠊⠉⠙⠻⢄⡘⠀⢻⣿⢀⡞⠁⣀⡼⠛⠉⠐⠂⣼⡟⠀⠀⠀⠀⠀⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡁⠀⡀⢣⡀⠀⠀⠀⠹⣷⣄⠀⠊⠉⠈⠻⣄⣸⡇⢸⣁⡼⠋⠉⠉⠂⣠⣾⠏⠀⠀⠀⠀⢀⠞⠄⠀⢨⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢧⠚⠀⠄⢣⠀⠀⣴⠀⠈⢙⣿⣷⣶⣶⣶⣿⣿⡇⢸⣿⣶⣶⣶⣾⣿⣛⠁⠀⠀⠈⠃⠀⡎⢀⠈⠢⡎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠺⣦⠊⠄⣸⠀⠀⢀⣤⣾⠿⠛⠋⠉⠉⠙⠻⢿⣧⣾⡿⠛⠋⠉⠉⠙⠛⠿⣶⣄⠀⠀⠀⡇⠀⠱⡴⠒⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣐⣘⣦⡴⠃⠀⣰⡿⠋⢀⡴⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠓⢤⡈⠻⣷⣄⠀⠙⣤⣾⣀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠳⣾⡟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠙⢆⠈⢿⣦⠊⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⣿⡟⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠈⣿⡏⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢤⡠⢶⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⣀⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⡙⠀⣾⣿⠀⠀⠀⠀⠀⢀⠚⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⣿⣦⠀⠀⠀⠀⠀⢈⣿⡇⠈⠍⠐⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢀⣸⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢿⣇⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⣤⡄⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣼⡿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣤⣤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣄⠳⡄⠀⠀⠀⠀⠀⠀⠈⠻⠥⠽⠋⠀⠀⠀⠀⠀⠀⠀⣠⠏⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⣡⣾⡟⠁⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⣶⣶⣶⣶⣶⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠖⠁⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⡴⠁⣰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣠⠞⣛⣉⠉⠉⠉⠉⠛⠳⢦⣄
⠀⠀⠀⠀⣰⠏⠀⠀⣸⠃⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡍⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢠⡏⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢻⣄⡀⠉⠒⢦⣄⣀⠀⠀⠀⠀⢸⡷⠒⣟⣠⡴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠘⠓⠚⠛⢿⠛⣷⣿⣶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣽⣶⡿⢿⣟⢦⠀⠀⠀⠉⠙⠛⠲⠶⢾⡷⢦⣸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⢿⣿⣷⢟⡿⠁⣿⠀⠀⠸⣿⣿⣿⣷⣶⡟⡸⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⣤⣤⠴⠞⠁⠀⠜⢷⣄⠀⠙⠻⠿⠿⢛⣜⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⠋⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠠⡶⠂⠀⠀⠀⠝⠛⠶⣦⠶⠾⡋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢋⠀⠀⡆⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠳⢤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⡇⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡟⠀⣸⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣀⣤⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠃⢠⠇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠦⠤⠤⠝⠉⣏⡿⠉⠙⠓⠶⠶⠖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⡆⢀⠎⠀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⣀⣀⠀⠀⣠⡀⠀⡠⢤⡰⡛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢰⠀⡞⠀⢠⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠉⢀⡏⠀⠑⠊⠀⠈⠉⠀⢸⡀⠉⠳⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡘⡄⣇⠀⠸⡀⢻⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⠤⣊⠷⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⣴⡞⣅⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⡄⠀⠱⢤⣑⣦⣀⣀
⣔⠂⡀⠙⠀⠈⡂⠬⠴⠒⠋⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⢮⣑⠦⣄⡀⠀⢀⡴⢂⠄⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠾⠿⠛⠋
⠠⢪⠄⡤⠀⠐⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⠙⠲⠭⢭⡁⠀⠂⠘⢃⠶
⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⡐⡂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣱⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣦⢤⠶⡶⣾⠛⠲⠶⠤⣤⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠸⢤⠇⡿⠀⠊⢋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⢀⠋⠂⠑⡌⡰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢌⠀⠀⢠⡇⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢈⡑⠒⠲⠟⠶⣶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠰⢿⣿⣿⣿⣿⣿⣯⣿⣟⠛⢿⡟⢻⠟⠉⠉⠿⣿⣿⡋⠁⠀⠉⣿⡿⣿⠟⢹⣿⣿⣿⣿⡿⢿⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠛⠚⠉⠉⢱⣾⣤⢿⡀⠀⠀⢠⣿⣿⣀⠀⢀⣨⡟⢧⡘⠶⠾⣷⡉⣿⡟⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠈⣿⠖⢷⣿⠦⢷⢉⣿⡺⣟⠳⢦⣉⣑⣾⣿⣯⡅⡿⣗⣚⣛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡦⠟⣂⠁⠀⠈⢧⣀⣰⣾⡟⠛⠛⠁⠀⢠⣾⠋⠙⢷⢶⣡⢏⣧⣙⡟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣰⠿⠃⠀⠀⠀⠈⢿⡋⠈⡇⠀⠀⠀⠀⠀⣿⠀⢀⣾⠀⠁⠘⠛⠥⢖⡴⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⣩⠔⠀⠀⠀⠀⠀⣠⣾⣽⡿⠁⠀⠀⠀⠀⣀⢹⣿⢏⡏⠀⠀⠀⠀⠀⠨⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠛⠈⠁⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣶⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢻⣿⠉⠉⢻⣿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠚⠋⠀⠀⠺⠛⠀⠀⠈⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡄⠀⠀⡜⠃⡀⠀⠀⢀⠤⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠦⠤⠤⠤⣤⣤⡀⠀⠀⢇⢠⡸⠀⠀⢈⡴⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣆⠀⠄⡀⠀⠀⠙⢧⣀⡀⠩⠀⠀⠀⠈⠉⠀⢀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣆⠀⠈⠑⠢⡄⢾⣿⡇⢀⣠⠶⠒⠛⠛⠛⡉⣹⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠢⡀⠀⠀⠹⣆⠈⠻⣤⣀⣀⣈⣻⣿⣷⠟⠁⠀⠊⢀⡤⠊⣴⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⣄⢰⡝⠰⠵⠀⠈⠳⠦⣤⣬⣭⠽⢿⣿⣿⡴⠔⠚⠚⢁⣰⠞⠁⠀⠀⠀⠄⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⠁⠈⠀⠀⢀⣤⣶⣿⡿⢿⣿⣶⣼⣿⣿⣽⣿⡿⠿⢿⣷⣦⣄⡀⠀⠘⠃⠐
⠀⠀⠀⠀⠀⣤⣊⠡⠀⠐⠾⡧⣀⢀⣴⣿⠟⠉⠀⠀⠀⠈⠙⠻⠿⠟⠋⠁⠀⠀⠀⠈⢙⠻⣿⣦⠀⠀⠀⠀⣰⣋⠁⠍⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⢿⣧⠀⠀⠈⠈⠢⠴⠖⠁
⠀⠀⠀⠀⠀⠀⡴⠚⣢⡀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⢀⣜⣀⣉⡩⠉⠀⢀⣿⡇⠀⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⢹⣿⠀⢬⠄⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⢸⣿⡇⠀⠀⠀⠀⢠⣈⣷⡆⠀⠀⠀⠀⠀⠀⣄⣙⣷⡄⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⣼⡿⠀⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⠤⠤⠤⠴⡶⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢃⡄⠂⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠙⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡟⠉⠀⢨⡔⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣭⣿⡿⠿⣷⣦⣶⣾⠿⣿⣯⣭⡾⠃⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡆⢹⣿⣿⣿⠠⠏⢀⣼⣿⣡⠏⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⣿⣿⣿⠃⠀⣾⣿⠘⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢸⡇⢸⣽⣿⡏⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⡠⣾⡟⠀⠀⣿⣿⣿⠏⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣳⠀⡇⠈⣿⣿⠀⠀⢺⣿⡏⠀⠀⠀⠀⠀⠀⣠⠞⣱⡟⠀⠀⠀⣟⠻⠏⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⢇⢂⣿⣿⡄⢀⠀⢸⡆⠀⠀⠀⠀⠀⣰⡏⣾⣿⡅⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⡜⢿⣿⣄⢢⠀⠣⠀⠀⠀⠀⠀⢿⡅⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣷⠘⢮⡻⣿⣦⡱⡄⠁⠀⠀⠀⠀⠸⣧⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠿⠟⠃⠀⠳⣌⠻⣿⣾⢆⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣂⣷⠀⠀⠀⠀⠀⠀⢹⡄⠈⢻⣯⢆⠀⠀⠀⠀⣸⣿⣿⣿⣯⢷⡕⢤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⣼⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡙⠷⣝⡢⡀⠀⠀⠀⠀⠙⢿⣷⠦⢄⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⡜⠀⠀⠀⣿⣟⠀⠀⢀⣾⣿⣿⣿⡿⢻⣿⣿⣷⡈⠹⢮⣦⡀⠀⠀⠀⠀⠙⢄⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠞⠀⠀⠀⢠⣿⡆⠀⢠⣿⣿⣵⣿⣯⣤⣌⢿⣿⣿⣇⣀⣈⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⢠⣿⡟⠀⠀⣾⣯⣾⣿⣿⣷⣄⠙⣮⢿⣿⣿⣿⣿⣿⣷⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⣰⢟⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠘⡎⢿⣿⣿⣿⣿⣿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠈⢿⣿⣿⡁⠀⠁⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⣤⣴⣶⡾⠿⠿⠛⠛⠋⠉⠀⠀⠀⣠⣾⠟⣿⠋⠀⠈⠉⠛⣿⣿⣿⠀⠀⠈⣿⣿⣿⢀⠀⠻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⣋⣙⣻⣤⣶⣲⢶⣦⡀⠘⣿⣿⡇⠀⠀⠘⣿⡇⠀⠀⢠⠈⠉⠈⠙⡄
⠀⠀⠀⠀⠀⣰⠟⢁⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⡇⠀⠀⢠⣿⣶⣷⡀
⠀⢀⠀⠀⣰⡏⢠⣿⣿⠟⠁⠀⠀⠀⠀⣠⣶⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀⣿⣿⣿⣿⡆
⠀⡘⠀⢰⡟⢠⣿⣿⠃⠀⠀⠀⢀⣠⣾⢟⣩⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⣿⣿⣿⣿⡇⢠⡿⠀⠀⠀⠀⠙⠛⣻⠆⠛
⠀⡇⠀⣿⠃⣼⣿⠇⠀⠀⢀⣴⡿⢛⣵⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⡼⠃⠀⠀⠀⠀⠀⠀⠛
⠀⡇⠀⣿⠀⣿⣿⠀⠀⣰⣿⠟⢡⣾⣿⣿⣿⣿⣿⣿⠟⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡇⠀⣿⢸⣿⣿⠀⢸⣿⠏⢀⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⡴⠀⠀⣀⡀⠀⠀⠀⣀⠀⢸
⠀⡇⠀⡏⢸⣿⣿⠀⣼⡇⠀⣸⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⡟⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⢎⣤⠞⠋⠉⢻⣴⣶⣯⢽⣤⡼
⣴⠃⢰⠇⠀⣿⣿⡄⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠇⠀⣠⡾⠟⠛⢻⡄⠘⣿⣿⠏⠁⠀⠀⠀⠈⠉⠉⠀⠀⣿⠏
⠏⠀⠸⠀⠀⢹⣿⡇⣿⠀⣸⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⡿⠀⡾⠋⠀⠀⠀⢸⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⠛⠃⣸⣇⠀⠀⠀⠀⠀⠉⠻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⡀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⣿⣻⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣴⢻⣿⣧⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢀⠈⣜⣾⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⠞⢛⡉⠉⢩⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣩⠼⣧⡿⣡⠞⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⢻⣆⢹⣷⣫⣴⠾⠿⠷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣻⠥⠀⠀⠀⠀⠈⣿⣦⣿⣯⣤⣤⣤⣤⣤⡉⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠈⠁⠀⠀⠀⠀⠀⠀⠉⠋⠙⠷⣤⣄⣀⣠⣤⣴⠾⠛⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠷⢶⣄⠀⠀⠀⠸⡀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿⣿⣧⣤⣾⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣼⣿⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠟⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⣠⠴⠶⢤⡀⠀⠀⢰⣤⣀⠀⠀⣀⣤⡆⠀⠀⠀⣤⠴⠦⢤⡀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⠛⠚⠋⠀⠀⠀⠸⣧⣍⣉⣉⣩⣴⡇⠀⠀⠀⠉⠓⠚⠋⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠹⣟⡋⠉⣻⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣀⡤⠚⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠶⢦⣤⣤⣤⣤⣤⣤⣶⠶⠛⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠛⠀⠀⠀⠀⠀⠀⠹⣆⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⡀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠋⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⣼⣿⣿⣿⣧⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣶⣦⣤⣭⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣠⡬⠛
⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉⣽⢏⣀⠈⢹⡄⠈⠉⠻⣿⣯⢿⡄⠀⠀⠀⢰⠋⢩⠟⠉⠉⠻⣌⣷⡶
⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠙⢦⣌⣭⣞⠁⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⣿⠀⢻⡒⣶⡞⢛⡟⠙⣇
⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⡀⠀⠀⠀⢈⣷⣄⡀⠀⠀⣿⠀⠈⠛⠶⠶⠋⠀⠀⠙⡆
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⢙⡷⠀⠀⢻⡄⠀⠀⢀⡔⠢⢲⠀⡟⠁
⠈⠛⠶⢤⣤⣤⣤⣤⣤⣶⠶⠚⠃⠀⠀⣠⠃⠀⠀⠀⠘⢷⡞⠁⠀⠀⠈⢷⡀⠀⠈⢗⠒⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⣤⠤⠖⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠻⣄⡀⠈⠙⠉⠀⡇
⠀⠀⠀⠀⠀⠸⣿⣿⡟⢸⡇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣬⠟⠂⠀⠀⠀⡟⣿⣿⣿⠃
⠀⠀⠀⠀⢀⣠⣼⠇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣶⣤⣴⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⡇⠀⢺⣥⣀
⠀⠀⠀⡴⠋⠁⢀⣠⣼⣧⣤⣤⣀⣀⣀⣀⣤⣤⣤⣤⣾⠁⠀⠀⣼⠷⠶⠶⠶⠤⠤⣄⡀⢤⣀⡟⠶⣄⡀⠈⠙
⠀⠀⠀⠛⠛⠛⠉⢡⡏⠡⡱⡴⠋⠙⣄⣠⠋⡔⠁⠀⠸⡇⠀⢸⡇⠀⠀⠀⠀⢠⡄⠀⠉⠛⠛⠀⢀⡿⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠱⡙⣆⣀⠞⡡⠊⠀⠀⡆⠀⢿⢀⣼⠗⠀⡦⠀⠀⠀⠙⠶⠶⠞⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠘⢌⡡⠊⠀⠀⠀⠀⣧⠀⢸⡟⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣃⣀⠀⠀⠀⠈⠀⠀⢀⣀⣀⣀⣿⣠⣤⣇⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⡿⠉⠉⠉⠉⠙⡟⠉⢿⡀⣰⣾⣿⡉⣻⠛⠛⢻⡟⠛⣿⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣤⢤⠤⣀⣧⠀⠀⠀⠀⢸⣇⠠⣬⣉⠉⠀⠈⠉⠁⠀⣀⣼⢇⢠⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠘⠳⠴⠤⠶⣌⠧⠀⠀⢠⣋⡶⠤⠤⠼⠃⠀⠀⠀⡔⣊⠭⠚⡼⠘⠼⠒⠤⠥⠖

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢇⣟⣤⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣗⣀⣀⣄⣀⣀⡀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⢋⣼⣻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣯⠸⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣏⠰⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣽⣿⣿⡿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⠘⠉⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⠿⣿⡿⢷⣷⣯⢿⡿⣟⡿⢿⣶⣶⣥⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⡿⢰⣾⣷⡝⣿⣿⣿⡗⢿⣏⣿⣿⣿⣿⣿⣿⣙⠚⠛⠛⠟⠁⠚⠁⣿⢻⣿⡿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⣿⡷⣆⣻⣷⣿⠿⣿⣳⡾⣿⣿⣿⠿⣿⣿⣭⣝⣿⡗⠂⠀⣀⣶⣯⣴⣼⣿⣤⣼⠞⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠙⠓⣿⡈⢻⢻⣇⡘⠋⠻⠸⣿⣟⠿⣿⣿⣿⣟⡛⠛⢿⣿⡽⠿⠿⠿⠿⠯⠝⠛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⠚⣿⡻⢰⣟⣷⠆⠀⢿⣯⢻⣼⣦⣾⣦⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⡷⠾⠗⠛⠈⠻⠇⠐⣾⡝⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠈⠃⠁⠉⡐⠃⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⢐⡢⠀⢮⠆⠠⣒⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠰⣧⠀⠘⠷⡂⠀⣬⠆⣠⡄
⠀⠀⠀⠀⠀⣴⣮⣧⣤⣷⣶⣿⣶⣾⣧⣤⣯⣶⡄⠀⠀⠀⠀⠀⣻⣦⣾⣷⣾⡇⠙⢺⣷⣴⣟⡁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣗⣿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣹⣿⠿⠛⠛⠻⠛⠉⠻⢿⣿⠀⠀⠀⠀⠀⠀⢘⠏⠉⠉⠙⠛⠷⠗⠋⠉⠉⠹⡏
⠀⠀⠀⠀⠀⢰⣿⠃⣴⣶⡄⠀⠀⣴⣶⠌⢻⣷⠀⠀⠀⠀⢐⡿⠂⢀⣾⣿⠇⠀⠐⣿⣷⡄⠀⢿⡂
⠀⠀⠀⠀⢀⣿⣿⠀⢿⡿⠁⠀⠀⠹⣿⠆⢸⣿⡇⠀⠀⠀⢠⣷⡆⠀⢹⠏⣠⣤⣤⠸⡏⠁⢀⣿⡅
⠀⠀⠀⠀⠠⢿⣿⣷⣿⠁⠙⢿⠟⠁⣹⣷⣿⣿⠧⠀⠀⠀⠸⣿⣿⣤⣈⡄⣈⣽⣁⢠⣃⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣖⣛⣓⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠛⢟⣿⡿⣷⣤⣀⣤⣾⡿⣿⣻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠏⢿⡿⣿⡿⣿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠾⣟⣿⣻⠷⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⠁⠚⠛⠀⠀⠀⠀⢀⣴⣶⣾⣷⣶⣄⠘⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡜⠁⣀⣤⣤⠖⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⠿⠋⣡⠆⠀⢠⣿⣿⣿⣿⣿⡿⢿⠟⠉⠉⠡⣤⣾⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠀⠶⠟⠋⠀⠀⣸⣿⣿⣿⣿⣿⣷⡄⢱⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠀⠲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢸⠂⠀⠀⠀⠀⣿⠟⣛⣛⠻⣿⣿⡇⠀⠀⢤⣼⣷⣦⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠔⢁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠆⡾⠀⠀⠀⠀⣸⠃⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠭⣉⡁⠁⣼
⠀⠀⠀⠀⠀⠀⠀⣿⠐⣡⣾⡟⠀⠀⣿⣿⣟⣿⣿⣿⣯⠞⣡⠞⠀⠀⠀⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣾⡗⢐⠸⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠉⠀⠀⣸⣯⣿⣿⡿⠟⢋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡼⠃⢀⣿⠿⠛⠥⠖⠚⢉⢉⣠⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⡀⢼⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡁⠀⢚⢅⣾⠂⠀⢀⡤⠛⠋⠻⠛⠛⠓⠶⣤⡀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⢻⡀⠀⣼⡿⠀⢠⣿⣶⣖⡀⠀⠀⠀⠀⠀⠀⢙⣦⠴⠒⠒⠒⢦⣬⣭⣿⣻⣿⣿⣿⣿⣇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⡇⠐⠛⠛⠛⠉⠀⠀⠀⠀⣀⣤⡴⠈⠈⠆⠀⢀⠀⠀⢸⠉⠉⢢⣽⣿⣿⣿⣿⡏⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣏⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⠟⠁⠄⠠⠆⠀⣸⣷⡀⠀⣇⡴⠋⠀⣻⣿⣧⠈⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡅⢦⠄⠀⠀⢿⣿⣷⢀⡟⠀⢀⠜⠉⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡈⠛⢿⡶⠤⣤⣤⡤⠴⠋⠈⠣⢄⠀⢸⠇⠘⣿⢇⡞⣠⠴⠋⠀⣠⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡄⠀⠹⣷⠀⣌⠓⠶⣤⣤⣀⣀⣀⣠⣤⠖⣋⣀⣼⡿⠿⢚⡁⠀⠀⠼⠛⠀⣸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠛⠻⠿⠯⠭⢭⣉⣠⠴⠾⢿⣿⣷⡄⠀⠀⠀⠉⠀⢻⣿⠋⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠀⠉⠉⢉⡉⠉⠁⠴⢄⣀⠀⢀⡠⠤⠄⣀⡀⠀⠀⠀⠀⠀⢀⣀⠠⠦⠀⠀⠀⠠⠴⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠙⠣⠀⠀⠀⠀⠀⠛⠀⠤⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠐⠒⠠⢄⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠘⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⢀⠋⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⢣⡀⠀⠈⠑⢤⡀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠘⠶⣄⡀⠀⠙⠦⡀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠿⣦⠀⠙⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠳⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢇⠀⠰⠆⠢
⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠈⠀⠃⠀⠀⠀⠀⢸⠇⠀⢸⠀⡇
⠀⠈⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡄⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⢀⡄⠸⡁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⡃⠰⡁⠢⡈⠁⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠈⠀⠐⠛⠋⠀⠀⠀⠀⣀⠀⠀⠀⢀⡴⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄
⠀⠸⠀⡆⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠓⠶⠘⠁⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⢏⡀
⠀⠀⠃⣰⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠙⠲⠦⣀⡀⣀⠠⠴⠴⠞⠛⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡈⠃
⠀⠀⠀⢁⠶⠀⠀⠀⠀⠀⠀⠛⢄⡀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⢤⣄⠁⠀⠀⡀⠀⠀⠘⣠⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣀⠙
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠈⠀⠀⠀⣀⡀⠀⠀⠠⠀⠈⠉⠒⠤⠿⣀⡴⠊⠡⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⣴⠛⡆
⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠠⠂⡰⠀⠀⠀⠀⠀⠀⠉⠀⠸⡆⠃⡀⠙⠢⣤⣤⣤⡤⣤⠒⠉⠀⠄⢀⡌⢣⠀⡇⢀⡄
⠀⠀⠀⠂⠀⠂⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⢀⠄⢊⡐⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠆⠐⡀⠀⠀⠀⠀⠀⠈⠲⠐⠛⠒⠉⠀⠀⠢⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠀⠀⠀⠰⠎⠁⡀⠒⣁⠖⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢡⠀⢆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡠⠖⢉⡴⠋⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠣⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⡤⠖⠲
⠀⠇⠀⠀⠀⠀⠀⠀⣀⠴⠃⠙⠉⢁⡠⠞⠁⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣄⠀⠑⢄⡀⠀⠀⢀⣆⠀⠀⢀⠂⠀⢦⡈⠲⡄
⠙⠀⠀⠈⠢⡀⠀⠀⠈⣀⡀⠀⡟⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠳⢄⡀⠀⠛⠀⣶⠘⢦⣠⠂⠀⠈⡀⠀⠂⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⡇⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠙⠢⢤⣀⣤⠀⠀⠁⠀⠚⢁⡠⠔⠁
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠁⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣀⠘⠓⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⠤⢀⣉⣀⡠⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠤⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⡟⠛⠠⠤⠄⢒⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠀⠀⢹⡅⠈⠀⠀⠀⠐⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠤⡿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠛⠠⠀⠀⠀⠀⠀⠠⣧⠤⠤⢤⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡄⠒⠒⠒⠫⣆⡀⠀⠀⣴⠀⠀⠀⠀⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢣⡄⢀⠁⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢳⡄⠀⠀⠀⠀⠈⡄⢻⣆⠀⠀⠀⣠⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⢦⣄⣀⣤⡾⠁⢘⠇⠉⠲⠚⢁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⢀⣼⣦⣀⣀⣤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀
⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠙⠛⠻⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⠿⣿⣿⡟⠉⠉⠁
⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⢿⠏⠀⠘⣿⣄⣿⡉⠻
⠈⠛⣸⣿⣿⣿⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀
⠀⠀⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀
⠀⠼⠟⠀⠀⠿⠇⠀⠀⠀⠀⠀⠼⠿⠈⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠋⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣠⣾⣿⣦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⢻⣿⣿⡿⢻⣿⡏
⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⠿⠃⠘⣿⣿⣿⠛⠋⣿⣿⣿⡿⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠘⢿⣿⡁⠀⢿⣧⡀
⠀⠀⠀⢠⣾⣿⠋⠉⠉⢿⣿⠻⣷⠀⠀⠀⠸⠿⠿⠧⠀⠀⠀⠹⠿⠿⠷⡦⠻⣿⡿⣤⣤⡀⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠐⠞⠃⠀⠀⠀⠾⠟⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣴⣶⣶⣿⡿⠷⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠻⣿⡟⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⠛⣿⡿⠉⢻⣿⡟⠟⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠷⠀⠻⠷⠀⠀⠀⠀⠀⠀⠈⠏⠀⠘⠿⠦⠀⠻⠧⠀⠀⠙⠷⠶⠀⠀⠀⠀⠙⠛⠙⠛⠉⠙⠛⠋⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣤⣧⣿⣼⣴⣿⣼⣶⣽⣤⣦⣶⣴⣼⣧⣷⣷⣿⣧⣼⣾⣾⣧⣿⣼⣼⣦⣶⣴⣧⣧⣾⣯⣧⣿⣦⣾⣼⣤⣧⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣷⣶⣾⢿⣿⣿⣷⣿⣿⣯⠓⠄⠈⠣⠄
⣿⣿⣿⣛⠀⠋⠍⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⣠⡝⠿⠟⠙⣿⡟⠀⠀⠀⢠⣤
⣿⣿⣿⣯⠀⠀⠘⠃⠀⠉⠛⢷⣎⠉⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠹⠹⢿⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⣰⠆⠻⠁⠀⢀⡼⠛⣻⡆
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠙⠻⠿⢿⣶⣤⣀⡠⢄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⠇⢰⣾⠋⠀⠃⠀⠀⠿⠇⠈⠿⠁
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣤⠀⠀⠀⠙⠿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣿⡷⠀⠀⠀⣠⡀
⣿⣿⣿⣿⣿⣇⢠⣶⠟⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⠙⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⢠⣿⣿⡃⠀⡀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣮⣻⣿⠟⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣿⣿⠉⢻⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡷⣦⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢸⣿⣿⣷⠾⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣍⠻⣷⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⡟⠁
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣷⣶⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⢸⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣧⠀⠹⣿⣿⠿⠶⠤⣤⡀⠀⠀⠀⢠⡀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀
⠀⢿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠘⢟⢷⣄⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠉⠙⠛⢷⡄⠉⠀⠀⢸⡿⣿⣷⣦⣄⠈⢆⠙⠳⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠈⢿⣿⣿⣷⡄⠣⡀⠀⠈⠑⠉⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡴⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣾⣵⣿⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⢿⡄⠀⠀⠀⠀⠀⠀⠂⠀⣠⣾⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⢻⣿⣿⡇⠈⣿⠀⠀⠀⠀⠀⠀⠇⣴⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣾⣿⣿⣟⣿⡇⣸⣿⣿⢃⣼⠋⠀⠀⠀⠀⠀⣸⣸⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⢀⣴⣄⣴⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⠷⠟⠓⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⡿⢿⣿⢃⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣏⡡⠄⠀⠀⠀⠀⠀⠀⢤⣶⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠿⠖⠀⠀⠀⠀⠒⠀⠀⠹⠃⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⡀⠀⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠄⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠻⠿⠛⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠊⠰⢦⡀⢸⡀⢀⣰⣤⣤⣬⣤⣤⣤⣂⡀⢸⠀⣠⠴⠆⠂⢾⣿⣿⣿⣿⣿⣿⠒⠒⠓⠒⢼⣿⣿⣿⣿⣿⣿⠆
⠀⠰⠂⠁⠀⢹⣶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣽⠇⠀⠁⠰⠀⠙⠻⠋⣿⣿⣿⣾⠂⠀⢾⣾⣿⣿⡏⠻⠟⠁
⠀⠀⠀⠀⠁⡘⡇⣀⣠⣴⡆⠀⠀⠀⠀⣶⣤⣄⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠈⠎⠈⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠸⢹⣿⣿⠳⠂⠀⠀⠰⠹⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡀⠈⣽⠃⣠⡍⣭⡀⠸⡎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠓⡔⠁⠀⠈⢱⡊⠀⠀⠙⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⣊⣉⣉⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣲⣦⣤⣶⣶⣶⣶⣄⠀⠀⣴⣮⣉⠉⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⢸⣿⣿⣿⡗⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠋⣶⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣴⣾⠿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡿⢿⡉⠙⡛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⡟⣩⣽⣿⣿⣿⣿⣿⣟⠳⢶⣷⠀⣱⡤⢼⡌⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣩⡾⠟⠋⡿⠃⣿⣿⣿⠿⠿⠛⢿⣥⣿⣷⠠⠭⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡰⣶⣶⡶⠶⠾⢿⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣌⡁⠀⠰⠋⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡃⣀⣀⡀⣨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡇⢀⢀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠿⣷⣾⣿⣿⣿⣿⡿⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡰⣷⣿⣿⣿⣿⣿⡋⣱⣾⣧
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢰⣷⣿⣿⣿⣿⢛⡛⡙⠟⣮⡁
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣯⣿⣿⣿⣧⣾⣿⡷⢷⣎⣻⠻⣆
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⣿⣿⣿⣟⣿⣿⣿⣦⣤⣿⣏⣤⣿⣨⡆
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣏⡀
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡷⣼⡽
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠋⠉⠻⣿⣿⣿⣿⣝⡛⠗⠁
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⢀⣄⣷⠁⠀⠙⣿⣿⣿⣷⣦⣄⡀
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡷⣏⠈⠁⢀⣴⠿⣿⠿⡟⣧⠈⢻⣦⡀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢀⠴⠟⠁⣰⠋⠀⡇⢻⣧⡀⢿⠉⣦⡀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣡⣴⣾⠏⠀⢀⡇⠀⠉⢳⣼⣦⠙⠿⣆
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣽⢏⠀⠀⣸⣿⡄⠀⢸⣿⣿⢷⡤⣄⣱⠄
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣳⣼⢻⣄⣴⣿⣹⢿⡀⢿⡻⣿⡀⢿⡸⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠛⢻⡛⣟⣏⠛⢳⠸⣷⣌⠛⢳⡌⢹⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠒⠾⠇⣼⠋⠙⠻⣷⣿⠂⠀⢘⣃⠀⠙⢿⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠻⡄⣾⠀⠀⠛⠷⡄⠈⠽⠃⠀⠀⠀⠈⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢇⠀⠀⠐⠃⠀⢀⠀⠀⠀⠀⢊⣀⣤⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢶⣤⣄⣀⣀⣀⣀⣀⡤⣺⠜⠀⠘⢿⣦⡀⠀⠀⠀⢀⣠⡾⠃⢱⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⠀⠀⠉⠁⠚⠛⠓⠊⠉⠀⠀⠀⠀⠀⠉⠛⠼⠿⠯⠟⠈⠀⠀⠀⢿⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣍⡒⠠⡤⣤⣤⡶⠿⣽⠃
⠀⢦⡠⣤⣤⣤⣠⣴⣖⠜⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⢀⣎⡃
⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣄
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣳⣄⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠺⣳⣦⣤
⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⠟⠉
⠀⠀⠀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⢋⠃
⢀⣴⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠄⠀⠔⠗⠠⠤⠚⠃⠤⠤⡄⠀⠀⠀⠀⠀⢀⠨⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⣟
⠋⠛⠓⠂⠊⠭⣓⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠡⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⡄
⠀⠀⠀⠀⠀⠀⠀⢳⢱⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠡⠀⠀⢤⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⡽⠟⠋⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠠⠗⠀⠉⠰⠄⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡽⠁
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠄⠀⠀⠀⠠⠸⠀⠠⠀⡄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇
⠀⠀⠀⠀⠀⢐⣛⣧⠫⠮⣕⢦⡀⠀⠀⠀⠀⠑⠀⠅⠀⠀⠀⡥⠄⠩⠌⠄⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡠⣴⣤⣤⣤⣀⢻⣿⡄
⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠈⢣⢳⠀⠀⠀⠀⠀⡀⠁⠀⠀⠘⠃⠀⠰⠀⢰⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⣚⡛⠋⠉⠉⠉⠛⠛⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⣀⣀⠱⣄⠀⠀⠀⠇⠀⠀⠘⢨⠀⠀⢔⡐⠀⡀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢗⡮⠕⠒⠐⠋⠈⣿⢲⠒⠆⠀⠐⠖⢊⣀⣸⡿⠀⠋⠓⠛⠵⣦⣀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠉⠀⠀⠀⠀⠀⠀⡷⠖⠖⠂⠈⠉⠛⠁⠀⣉⡥⠀⠀⠀⠀⠀⠈⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⢶⢶⠆⠐⠂⠿⠁⠀⢋⣢⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⠀⠤⠶⠒⠈⢛⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣀⣤⣀⠠⠤⠖⠆⠘⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣭⣤⣄⡀⠤⠶⠶⢚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⣶⣦⣶⠞⠃⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠠⠔⠒⠒⠒⠀⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠤⠀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠆⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⡄
⠀⠀⠀⡐⠁⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠑
⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡄⠀⠀⠀⡏⠁
⠀⠀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⢈⢛⠃⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⢂⠀⠀⠀⠀⢈⡤⢶⣲⣤⣄⠀⠉⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠋⠀⠁⠀⠀⠂⠀⠀⠀⠘⠦⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⢰⡀⡠⠤⠤⠤⣀⠔⠙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡔⠁
⠀⢠⠀⠀⠀⠀⠀⠀⢙⣋⠀⠀⠀⠀⠈⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠉⡑⠂⠄⡀
⠀⢨⡠⠀⢀⠀⠀⠈⠀⠙⠦⠤⠔⠊⠁⠁⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠐⠁⠁⠀⠀⠀⡀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠙⠒⠤⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠉⠉⠒⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠦⠀⠀⠀⠠⠄⠒⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⣀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠿⢿⡿⠟⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣧⣽⣽⣿⣿⣿⡿⣿⣾⣿⣛⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⡿⣻⡿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⢶⠉⣩⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠈⠙⢿⣿⣿⣿⣷⣤⣉⠛⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⣤⡀⠠⡐⢌⠢⠀⠀⠀⠙⠲⣄⡀⠀⠀⠙⠯⣿⣿⣿⣶⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣴⣿⣿⣆⠙⢆⠑⢄⠢⣀⠀⠀⠙⠻⣧⣶⣤⠂⣌⡙⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⡈⠳⠀⠱⣌⢷⣄⠀⠀⠈⠻⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣄⠈⢦⡈⠳⣝⠓⣄⡀⠹⡞⢋⣳⣿⢿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠻⣦⡈⠳⣝⢿⣦⡈⠛⢻⣿⣾⣿⣟⣿⣻⡯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⠓⢝⢷⣝⢻⣶⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣷⡙⢷⣝⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢽⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⣀⣰⣿⣿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⣀⢠⠁⠀⠀⢹⣿⣿⠟⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠁⠀⠀⠀⠸⣿⡏⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⠐⠿⠿⠶⡶⠀⠀⣤⣤⣤⣄⠀⠈⡉⠋⠉⠉⠙⠻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⠐⠀⠆⠀⠀⠀⢠⠍⡉⠉⠀⠘⠀⠀⠀⡃⠀⠀⠉⠀⢈⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⠠⢤⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠘⠀⠀⡂⠀⢀⡁⢀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠋⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠈⠀⢀⠈⠐⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠄⡁⠀⠀⡀⠀⠀⠀⠀⢖⠛⣓⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠄⠀⠎⠀⢠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠐⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠬⡀⠀⠀⠀⠰⠀⠀⠀⢁⠊⠙⢿⠟
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⠀⠄⣀⡀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⠀⠊⠀⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠌⠀⠎⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⣀⣀⠀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠤⠀⠤⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠉⠁⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣶⣶⣾⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣠⣤⠤⠤⠤⢤⣄⣀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣀⠔⠋⠀⣀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⣁⡈⠉⠒⢄⠀⢀⣼⣿⣿⣿⣿⣿⣿⡏⠁⣉⣉⠉⢉⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠘⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢱⠘⠻⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⢰⠀⠀⠀⠀⠀⢸⠀⣶⣶⠀⠀⠀⠀⠀⣰⣶⡄⣸⠀⠀⠀⠀⠀⠘⠀⠀⠈⠛⠁⣿⣿⣿⡇⡓⠀⠀⢋⢺⣿⣿⣿⠈⠛⠉
⠀⠀⠀⠣⣀⠀⠀⠀⠈⢇⠈⠙⠀⠀⠀⠀⠀⡛⠉⢠⠇⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⡡⠀⠠⠩⣸⣿⣿⣿
⠀⠀⠀⠀⠈⠣⣀⠀⠀⣨⣮⡎⠀⠀⠀⠀⠀⠘⣧⣏⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣄⣦⣈⣵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠋⢡⢧⠏⣷⠀⠀⠀⢸⡈⣆⠆⠉⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠊⠸⡀⠀⠀⡇⠘⠪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⣧⠀⠀⢿⠋⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣦⡠⠟⢢⣀⢀⣠⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠸⣅⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠄⠀⠀⠀⠀⠀⠀⠀⠘⠤⠔⠃⠀⠀⠀⠀⠀⠀⠠⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⣾⠿⠓⠀⠀⠀⠀⠀⠘⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⡡⠂⠀⠀⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡠⠚⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡔⠁⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢐⣷⠀⠀⢰⠠⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣠⠾⣀⡠⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠛⠀⠀⡸⡀⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠸⡇⠀⣀⠱⡠⠖⠙
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⠄⠀⠀⠘⠦⢀⣀⣀⠔⠁⠈⠐⠀⠂⠁⠀⠀⠀⡐⠀⠀⠀⠀⢠⡟⠀⠀⠀⢹⣂⠀⣀⣱⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⡈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠠⠀⠀⠀⠈⡛⠀⠀⢐⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢣⠦⠤⠤⠦⠤⠤⠼⢤⠄⠂⠀⠀⠀⠀⠀⠀⢀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠳⡀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢷⡀⠀⠈⠲⣄⣠⠂⠉⣃⡀⠷⠐⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠾⣄
⠀⠀⠀⢀⠤⠐⠚⠹⡏⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⣤
⣠⠖⠚⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⣀⣀⠆
⠓⣲⠃⠀⠀⢠⠔⠢⣀⠉⡷⠀⠀⠀⠀⠀⡷⠒⠖⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⡆
⠀⢧⡠⢦⠀⡸⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠣⠤⣤⠤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠒⢒⡶⠋⠉
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⢀⣀⡤⠖⠋

⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶
⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻
⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⡀
⠁⠀⠀⠀⣀⡀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⣀⡀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠈⠉
⣀⣀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠝⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⠀⠙⠋⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣄⣀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢼⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⣁⢠⡀⣤⣿⡶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣼⣷⣶⣦⡀⡀⠻⢿⣿⡌⢛⣿⣓⣄⣭⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀⣀⡀⠼⠿⠋⠉⠛⠛⣿⣿⣿⣿⣇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣧⣤⣿⣿⣤⣴⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡩⠻⡟⠻⣯⡉⠉⠁⠈⢀⣌⣿⣿⣿⡛⣟⠉⠈⣿⣧⡿⠁⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⣼⡿⢀⢷⡎⠁⠘⠃⣿⡿⢧⡀⢹⡏⠀⠄⠁⢢⡜⠀⠀⠀⢄⣀⢠
⠀⠀⠀⠀⠀⠀⠀⣾⣛⣠⣼⣉⣀⣀⣼⣾⠻⣶⡶⠀⢨⣍⠉⠃⢀⠀⠀⢤⣰⣾⣦⣿⡃⡀⠸⠁⠰⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠋⢀⣻⡟⠁⠀⠀⠀⠀⠉⠀⠀⠈⠛⠃⢴⡈⢰⣯⣷⠙⠛⣶⠒⠄⠈
⠀⠀⠀⠀⠀⠀⠠⠿⣿⡿⠃⠀⠐⠊⠉⠀⠀⠀⠀⢀⡀⠀⡀⢀⣠⠠⡤⢘⣿⡜⠛⠛⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠶⠛⢷⡆⠀⠀⠀⠀⠀⠛⢠⡀⠰⢋⡤⢀⡾⠿⡀⠀⠂⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⣶⣿⣄⠄⠠⠀⠀⠐⠀⠀⠛⢋⡽⠿⠋⠁⠀⠁⠀⣠⣶⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⠻⠀⠀⠁⠄⠁⠀⠀⣸⣷⡀⠑⠒⠘⣀⠀⠀⠀⠹⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣒⠾⠀⠀⠀⠀⠘⠿⠧⠿⣿⣶⡀⠀⠀⠤⣴⣦⣤⡀⠸⡤
⣒⣒⣒⣒⣒⣒⣲⣺⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣒⣒⣺⣷⣾⣿⣿⣿⣶⣒⣚⣿⣿⣿⣷⣶⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠟⢉⣻⣍⠉⠉⠟⠉⡉⢿⣿⣿⡟⡉⢩⡉⠛⠻⣿⣿⣿⣿⡟⣉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡉⠉⠀⣀⠀⠸⢷⡾⠻⡏⢠⣿⡄⣰⣄⣀⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣎⣥⡄⠀⠈⡀⠀⠙⠧⠘⡿⢶⣿⣾⣿⡁⠀⣸⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣌⡑⢨⣄⣀⣄⣀⣀⡠⠶⣺⡥⣽⡦⣌⠹⢿⣾⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⣸⣿⡟⠋⠉⣉⠋⠿⢡⡆⠀⠈⠋⠙⠀⣤⣤⡟⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⡉⣿⡷⣮⣿⣄⡦⠘⠃⠀⠀⡀⢠⣾⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⣠⣿⣿⣻⡃⢐⣶⢶⣿⣿⠻⢯⣨⡍⠹⠋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣷⣤⣿⣿⣿⣿⡟⠻⣿⣧⡉⣹⣿⣿⠻⠓
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣏⣽⣷⣾⣾⣶⣾⣯⣿⣿⣯⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠻⢿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠇⣻⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠛⠃⣀⠹⡿⠟⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⣀⣤⣶⣀⣤⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⢿⣿⠿⢿⣿⠿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠉⠀⠙⠃⠉⠛⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣩⡙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣹⣭⡙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⣐⡼⠆⡴⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠋⡁⠗⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠗⠀⠀⠄⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⢿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠠⡑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠠⠐⢀⠜⠂⡀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢀⠂⢀⠄⢊⠔⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠑⠠⠄⡉⠐⡀⠀⢠⡚⢂⢠⠁⠀⠁⠠⠂⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠙⡈⠁⠁⢘⠁⠀⡢⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢀⠠⠢⠄⠀⠑⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⢀⠀⠀⠀⠀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⢄⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⡀⠅⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⡈⠀⠠⠉⠁⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡔⠠⢨⠛⠀⠴⠈⠀⠂⠠⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠘⢀⡘⠉⠢⡀⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠈⣁⡰⠉⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠢⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠡⡀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⣸⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡚⠎⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠹⠊⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣁⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠤⠐⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣂⣥⡶⠶⠛⠷⠶⣦⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⣾⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠄
⠀⠀⠀⠀⠀⠀⠐⣈⣤⡴⠶⠶⢦⣤⣀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈
⠀⠀⠀⠀⠀⢡⡾⠋⠀⠀⠀⠀⠀⠈⠙⠳⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁
⠀⠀⠀⠠⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠛⢶⣄⣾⠁
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠈⣿⠃⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠌⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⣶⠾⠛⢉⡉⠛⢷⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠨⢙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠗⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⡛⠷⣦⣄⣻⡆⠀⠀⠀⠀⠀⣀⣀⣤⠶⢛⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠌⡙⢿⣤⣴⠶⠾⠛⠋⠩⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠅⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠉⡉⠉⠉⢀⠀⠉⠻⣶⣲⣶⣾⢟⣽⢏⣫⡝⠛⠿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠓⠲⣶⡷⢤⣶⣿⣟⢿⣿⣿⣛⣻⣿⣛⠛⢋⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢤⠀⠀⠀⠀⣀⠴⠛⢿⣦⡀⠉⠁⠀⡤⠜⢻⣿⣿⣿⣷⣯⣬⣬⣽⣶⡿⠋⠙⠢⣄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠀⠀⣠⠞⠁⢀⣠⣴⡿⠿⢷⣶⣤⣴⡶⢿⣿⢿⣿⠉⠉⠉⠛⠛⠻⢷⣶⣤⡀⠈⠑⢄⠀⠀⠺⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⣴⡿⠋⠁⠀⠀⠀⠶⠶⢶⣦⣼⣿⣿⣯⣤⣶⠶⠶⠆⠀⠀⠀⠙⠿⣦⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⡿⠋⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢿⣦⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡜⠀⢰⣿⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢻⣧⠀⢱⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠃⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣃⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣿⢷⣾⣿⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⣿⣷⢿⠻⢍⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⡾⠛⣿⡄⠀⠀⠀⠀⠸⣿⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⡟⠳⡶⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢻⣧⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⢸⡿⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⡀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣤⡜⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⣿⠿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠑⢤⡀⠙⠻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⣠⠿⢷⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠲⢄⡀⠉⠛⠻⠿⠷⣶⣶⣶⣶⡶⠿⠿⠛⠉⢀⣠⠴⠊⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠑⠲⠦⠤⣄⣀⣀⣀⣀⣠⣤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚

⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣦⣀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠙⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠸⣿⣧
⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠛⠻⣿⣿⡇⠀⠀⠀⠀⢻⣿⣧⡀
⠀⠀⠚⢻⣿⠁⠀⠀⠀⢠⣿⣿⡇⠀⣾⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⣤⠀⢸⣿⣿⡄⠀⠀⠀⠈⣿⡟⠓
⠀⠀⠀⣿⡏⠀⠀⠀⠀⣸⣿⣿⣿⣤⣀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⣀⣤⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿
⠀⠀⢸⣿⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣶⣿⡇
⠀⠀⡿⠟⣿⡇⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⢸⣿⠻⢿
⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⣠⣿⠇⠀⠀⠀⠀⣠⣶⣶⣦⣤⣀⣠⣤⣴⣶⣶⣄⠀⠀⠀⠀⢸⣿⡄⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣆⣾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣷⣸⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠈⠻⠿⠿⠿⣿⣿⠿⠿⠿⠟⠁⠀⠀⢰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⣀⣀⣀⣀⣤⣼⣧⣤⣀⣀⣀⣀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣟⡛⠛⠙⢛⣻⣿⡿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠞⠻⡏⠉⠉⠉⠉⠉⠙⠛⠳⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢂⣤⠶⠛⠛⠛⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⣰⠃⣴⡂⠀⠀⠀⢹⣿⣻⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠋⠀⠀⣠⣤⠄⠀⠀⢤⣈⠳⡀⠀⠀⠀⠀⡇⣼⣿⣧⣀⠀⣀⣼⣿⣿⣿⣇⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⣴⣿⣏⠀⠀⠀⠀⣿⣵⡌⠀⠀⠀⠀⡄⣿⣿⣯⣀⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⣿⣿⡟⢢⣤⣤⣴⣿⣿⣿⡀⠀⠀⠀⢇⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢆⠑⢽⣻⠿⠿⠿⣟⡿⠏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⢯⠻⣿⣽⣿⣿⣿⣿⢿⡟⢀⠀⠀⠀⠀⠈⢣⡀⠈⠉⠉⠉⠉⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠙⠮⢽⣟⣻⠯⠗⠋⢀⡾⠀⠙⠶⠚⠀⠀⠙⠳⢦⣤⣀⣠⣤⣴⣾⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⣿⣿⣿⣿⡿⢿⣿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢟⠟⢿⣿⣷⣶⣦⣤⣤⣶⣶⠿⠿⠶⠶⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⢸⣿⣿⣏⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠈⠈⢿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠐⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⣄⡍⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡁⣤⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⣸⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣾⠿⠿⠛⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⣿⠷⣤⣄⣀⣤⣶⣶⣤⣀⣤⡶⠿⣿⡾⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠛⠛⠛⠛⠛⠙⠛⠉⠓⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢆⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠈⡄⠘⡀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣰⠀⠥⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠉⠆⠀⠀⠀⢠⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠄⢠⠁⢎⡠⠐⠈⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⡇⠀⠉⠑⠓⢀⡠⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠻⢄⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⠀⠱⠀⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣀⣠⠔⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⠀⠀⠀⢀⠎⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢡⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠉⠳⢦⡎⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢣⠀⠈⣤⠴⠖⠚⠛⠛⠛⠓⠒⠶⢤⣀⠱⡀⠀⠀⠀⠀⠹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⡷⠋⡡⢄⠀⠀⠔⠢⢄⠀⠀⠀⠀⠀⠙⠣⣄⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢉⣿⠦⡀⠀⠘⢆⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢂⣿⡇⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣸⠀⠀⠀⠈⣏⡁⠀⠒⠒⠛⢉⣁⣤⣾⣿⡿⠀⠀⠀⠀⠀⣤⣈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠟⠛⢿⡿⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⠿⣿⣁⠀⠀⣠⡴⠞⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠗⠲⠤⠤⣤⣤⡤⣤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣰⠃
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠁⡠⣀⡀⠰⢄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠹⡄⠀⠀⠀⠘⢄⠀⠀⠀⠄⠘⠀⠀⠙⠆⠀⠑⠄⡀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠘⢦⡠⠎⠀⠀⠑⢤⡀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠈⠂⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠳⣌⠢⡀⠀⠀⠈⡳⠋⠳⡀⠀⠈⢤⣀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠳⢤⡑⠠⡔⠀⠀⠀⡇⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⣠⠞⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠂⠬⢙⠲⢤⣀⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡞⠁⠀⠀⠀⠀⠐⢤⡑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠈⠉⠛⠚⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢙⠒⢄⠀⠀⠀⠀⠈⠢⣈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠳⡄⠀⠀⠀⠀⣹⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠊⢀⠞⠀⠀⠀⠘⢦⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⠋⠉⠒⠒⠦⠤⠴⠒⠁⠀⠀⠀⠀⠀⠀⠙⠶⠤⣤⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠀⠐⠪⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣛⣭⣽⣶⣶⣯⣥⠤⠤⢤⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡵⠻⠋⠙⠉⢀⣤⣀⠀⠀⠀⠀⠀⠈⣯⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠀⠀⠀⢤⠀⠠⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠴⠄⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡣⠁⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠏⠉⠀⠀⣀⠴⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢇⠀⠀⡀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠄⠀⠀⠀⠀⢤⠤⠖⠊⠁⣠⠇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡐⡄⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⢦⠔⠒⡩⡾⠀⠀⠀⠀⢀⡞⠀⠀⠀⡠⢊⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⣠⠏⠀⣀⢤⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⣀⣀⡤⠔⡟⠓⠒⢉⡡⠴⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⣀⡠⠔⠋⠑⠤⠤⠃⢋⠉
⠀⠀⠀⠀⠒⠀⠀⠇⠀⠀⢠⣀⠀⣀⣐⣒⣯⢀⣀⠤⠖⡛⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠐⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡀⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠈⠙⠲⠤⣈⡙⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⠉⠉⠉⠉⠃⠤⣀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢱⡒⣦⠤⠤⠆⣈⣁⠤
⠀⠀⡀⠀⠀⠀⠀⠀⡠⢊⡤⠒⠙⢧⠤⠴⠖⠒⠶⠄⣉⠉⠛⠒⠶⠤⠴⣂⣀⠀⠀⠀⣸⢁⠇
⠠⡀⡀⠀⠠⢄⣀⠜⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢶⡀⠀⠀⢠⡏⣀⠠⢐⡣⠊
⠀⠑⢌⠢⡀⠀⠈⠓⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡼⠒⠒⠊⠁
⠀⠀⠀⠑⠮⡓⠄⡰⠁

⢼⣿⠿⠋⢀⣤⣺⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡻⣿⣿⣿⣿⠷⠋⠀⠀⠀⠀⠀⢨
⠀⠀⣀⣤⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣾
⣿⣿⡾⠫⠟⡛⠛⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⡀⠀⠀⠀⠸⣿
⠀⠉⠀⠀⠀⠈⠙⣁⢠⣶⣶⡶⠂⠀⠀⣀⣤⣄⠀⣤⡄⠀⣠⣄⢠⣤⣤⣤⣤⣤⢀⣤⣤⣤⠀⢠⣫⠏⠈⠀⣤⣷⣸⣷⣤⠴⠛
⡀⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⠀⠀⢰⣿⠋⠛⢱⣿⡇⠀⣿⣿⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠁⠀⠸⣆⢘⣿⣿⠋
⢹⣦⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠸⣿⡇⢀⣿⣿⠀⠀⢸⣿⠀⠀⢸⣿⠶⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⡿⠂⢿⣧⣼⣿⣿⡄⠀⢸⣿⠀⠀⠸⣿⣴⡶⠂
⠀⠀⣀⣀⣀⣀⣀⢀⣀⣀⣀⢀⣀⣀⡀⠀⢀⣀⣀⠀⢀⣀⠀⢈⣀⠀⠀⠁⢀⣀⣀⠀⠀⣀⣀⣀⡀⠀⢀⣀⠀⠀⣀⣀⡀
⠀⠀⠉⢹⣿⡏⠉⢸⣿⠉⠉⢸⣿⠙⣿⡆⢸⣿⠹⣷⡜⣿⡆⣼⡟⠀⠀⠀⢸⣿⢻⣷⢰⣿⡏⠉⠀⠀⣾⣿⡆⠀⣿⡟⣿⡆
⠀⠀⠀⢸⣿⡇⠀⢸⣿⡤⠀⢸⣿⠀⣿⣿⢸⣿⠀⣿⡇⠸⣿⣿⠁⠀⠀⠀⢸⣿⣾⣟⢸⣿⡧⠀⠀⣸⡿⢻⣿⠀⣿⣧⣿⠇
⠀⠀⠀⢸⣿⡇⠀⢸⣿⣤⣶⢸⣿⣴⡿⠃⢸⣿⣼⡿⠁⠀⣿⡇⠀⠀⠀⠀⢸⣿⣸⡿⠘⣿⣧⣶⢤⣿⠛⢻⣿⡄⣿⡿⣷⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠁⠈⠉⠀⠀⠉⠀⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⣉⠉⠘⢻⣿⣧
⠿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⢉⠖⠀⠀⣿⡿⠂