Unwind Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⢤⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⢀⣀⣀⢠⠀⠀⣤⠀⢠⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡆⢸⠀⠀⢸⠀⢠⡿⡆⠈⢧⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣞⠀⢸⠶⠆⢸⠀⣾⠛⢿⠁⢨⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠘⢦⠸⠦⠤⠸⠦⠤⠀⠸⡆⠟⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠌⢡⡤⢤⡀⠀⢀⣶⠀⠀⡇⠀⡉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢰⡏⠀⠀⣷⢀⣼⣹⣦⠀⣇⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠉⢳⠸⡇⠀⢀⡿⢠⡏⠀⣷⠀⡟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠋⢀⡙⠒⠛⠁⠘⠀⠀⡌⠀⠃⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⢸⡆⢸⡇⢷⠀⢠⣷⠀⢰⡇⣿⢸⡆⢸⡇⢹⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⢸⠻⣼⡇⠘⡆⣼⠘⡇⣾⠀⣿⢸⠻⣼⡇⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠇⢸⠀⢻⡇⠀⢻⡇⠀⢻⡇⠀⣿⢸⠀⢻⡇⣸⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⡾⠲⢶⡁⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⣩⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⡏⠉⢹⡏⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⠳⣤⣀⠀⠀⣀⣴⣿⣿⣿⣿⢗⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠉⠀⠂⢠⣿⣿⣿⣿⣿⠛⠛⠁⠃⣹⣿⣿⣷⣿⣿⣿⣿⣏⠠⣜⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣀⠀⣿⣿⣿⣿⣿⠀⠀⢀⣼⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡇⠀⠛⢿⣿⣿⣿⣠⣶⠟⠁⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⡖⠀⢿⣿⣿⣿⡟⠁⠀⣀⣀⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⣧⣾⣿⣿⣿⣿⣷⠀⠸⣿⣿⣿⣟⠛⠛⠛⢛⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⣿⣿⠛⠙⠛⢙⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⣿⣿⣿⣿⣿⣿⡀⠀⠂⠈⣯⠉⠉⡠⠀⠆⠀⣯⣼⣿⣿⣧⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠠⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⡤⠒⠉⢱⠤⡄
⠀⠀⠀⠀⢺⠖⠃⢠⠋⠀⢱⠀⠠⢋⣁⣀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⣴⣡⠀⠀⠫⣀⠀⠀⢳⡀⣇⠀⠈⠑⣄⠀⠀⡠⠖⠒⢢
⠀⠀⠀⣹⠁⣄⢠⣄⠙⢄⠀⠀⠑⢽⡄⠀⠀⠈⢧⠊⠀⣀⣀⣸
⠀⠀⠀⠷⠊⠘⠏⠀⠙⢾⣳⣄⠀⠀⠹⣄⡠⠴⡾⣯⣉⣠⣴⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢞⣦⠀⠀⠈⠲⣄⣰⡇⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣚⣛⠓⠀⠀⠀⠀⠊⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣀⣄⣢⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⢉⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣒⠠⠧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢢⡤⣀⡀⠉⠉⠐⠒⠲⠤⠤⢤⣄⣀⡴⠚⡮⣦
⠀⠀⢠⡖⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠈⠉⠒⠢⠤⣀⣀⠀⠀⢀⡞⠱⣄⡇⠹⡢⣄⠀⠀⠀⠀⠀⠀⣎⠲⡄⠀⣀
⢀⡀⠀⠉⢺⠍⠳⢀⡀⠀⠀⠀⠀⡜⠀⠀⢸⠃⠀⠀⠀⠀⠈⠉⠓⠚⠀⠀⡏⢣⣀⠱⡬⢧⣀⡀⠀⠀⢀⡼⢸⠁⠸⣟⠵
⡇⡜⡹⢲⠋⡠⠒⠒⠢⠭⣒⡒⠤⠟⢲⠲⠾⠀⠀⠀⠀⠀⠄⠀⠠⠤⠤⢾⠃⠈⢯⣈⡭⠦⠴⢖⣒⠒⠒⠒⠢⢍⡁⠉⡰
⠈⠣⠷⣨⠞⠀⠀⠀⠀⠀⠀⠀⠉⢲⠚⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⢒⣒⣾⠀⠀⠀⠑⣦⣐⡂⠉⣉⡹⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠒⠪⠟⠋⠁⠀⠙⣲⠤⣄⣀⠇⣀⢤⣖⣿⠋⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣄⡀⠀⠀⠀⣠⠔⠚⠛⠚⠳⢌⠫⢉⠀⠀⠀⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⢄⠉⠒⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠠⠈⠀⠈⢁⠐⠤⢓⠀⠀⠐⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠠⠡⢀⠀⡤⣈⣠⣤⣶⣦⣌⣄⣴⡶⠶⠶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠹⡋⠬⠀⠄⠐⡀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠂⣀⠔⠈⠀⠲⡈⠤⠐⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⣶⣴⣶⢶⣦⣴⡾⠦⠴⠀⠄⠠⠄⠢⢄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠉⠍⣁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠆⠄⡀⠠⠀⡀⢀⡀⠂⠊⠁⣀⠄⠀⠨⠞⢄⣁⠂⠀⠄⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⣀⣀⣴⣌⡀⢠⣌⠀⣠⣸⣿⠛⡏⠀⠐⠀⠁⢆⡸⠛⠻⢶⡤⠄⠀⠀⠐
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠉⠛⠙⠛⣿⣾⠿⠇⢉⣡⡅⠀⠳⣾⣴⠾⠶⠄⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠠⣤⡤⠀⢤⠀⠀⠀⠀⠀⠀⠂⠀⠰⠁⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣘⣷⣄⡀⠁⠶⡆⠠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠈⠉⠻⣷⣀⣰⣤⡀⠔⡂⠀⠀⢫⣈⣍⢂⡊⠂⢠⠀⠀⠁⠂⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠀⠈⠀⠁⠈⡋⠙⠿⣷⣆⡈⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢌⠢⣀⠉⢻⣷⠖⢘⢠⠔⠐⠠⠒⠂⠂⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⠀⢐⡠⠻⠧⠼⢆⣠⡀⢀⠀⢐⡀⠀⠀⠄⠡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠈⠀⠀⠀⣄⣀⡀⠀⠈⠻⠛⠻⣿⠿⢿⣶⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⣾⠃⣤⣾⣿⣿⣇⣄⣠⣄⡀⠠⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠛⠋⠈⠉⠙⣿⠿⠛⠛⠋⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠠⠀⢂⠔⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⢀⠑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠔⢀⡒⠀⠢⣀⠉⠂⠀⠌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠆⠀⠀⠀⠉⠀⠀⠀⠈⢆⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢰⠀⠀⠀⠀⢈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⣀⠀⠀⠀⠀⠀⡄⠚⠳⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡄⣴⠟⠛⠀⢸⣀⡄⣼⣏⠠⠙⢼⣯⠀⡶⣅⢠⠀⢰⢁⣔⣄⠠⠒⠀⢀⡀
⠀⠀⠀⠀⠀⠇⠀⠐⠢⡈⢂⣸⣸⢹⠀⢴⡇⡄⣼⣿⣿⣿⣧⡴⣿⣿⣤⣧⣏⢎⣾⠀⢰⡦⣿⣸⣼⣴⣿⢡⣥⠀⠀⢤
⠀⠀⠀⠀⢀⠺⠴⠤⡀⠙⣾⡿⠻⢾⣶⣮⣤⣿⣿⣿⣿⣿⡧⠩⠛⣿⣿⣿⡏⡾⣹⣼⣿⣷⣿⣿⣉⠶⣶⣶⣤⣤⢀⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠿⢤⡈⠨⢷⠙⢿⣿⣿⣿⢻⣿⡧⠶⡐⣾⣿⣿⣷⣥⣿⠟⠛⠁⠀⠘⠋⠷⣂⢬⣝⣯⣞⡔⢸⢃⠴⠒⠀⠀⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠑⠀⢁⠺⣟⡻⣭⠳⢰⣼⣿⣿⣽⡿⣯⣧⣄⣤⡶⢤⣤⣀⠀⣸⣿⣿⣿⣿⣧⣤⣷⣾⣍⣡⣤⡤⠋⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠚⣻⣿⠿⢿⣾⠿⠛⣻⠿⠟⣿⣿⣿⣿⢿⠿⣿⣿⣳⣿⣿⣿⣟⠉⠁⠀⠀⣀⡀⢀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠶⡿⠋⠀⠀⠉⠁⠀⢀⡀⣀⣬⣿⣋⣾⣽⠸⠦⠾⠷⠿⠿⣿⣍⢄⠀⠀⢀⡄⢀⠖⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠓⠐⢻⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠅⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠒⠒⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡂⢷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⢿⣧⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠈⢿⣧⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⠂⠀⠈⣿⡆⠀⠘⣿⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠸⣷⡄⠀⢿⡆⠀⠀⠀⠀⠀⠈⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⢻⡄⠀⢸⣷⠀⠀⠀⠀⠁⠀⡇⠉
⠀⠀⠀⢀⣦⠀⡄⠀⠀⠀⢺⣿⣿⣷⣂⡔⠀⠀⠘⣿⡄⠈⣿⡆⠀⠀⢰⡄⠀⡇
⠀⣿⣀⣼⣏⠀⠄⢀⡄⠀⢸⣿⣿⣿⣿⢀⠀⠀⠀⣿⣧⣤⣿⣷⣤⣶⣾⡆⠀⠃
⠀⣿⣿⣿⣿⣿⣦⣸⡿⠀⣸⣿⣿⣿⣟⣿⣿⣶⣿⣿⣿⣿⠟⣿⣿⠛⢹⣷
⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⠿⢟⣿⣿⣿⠟⣿⡟⠁⢰⣿⠃⢠⣿⣿⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡧⢸⣿⣧⡀⣼⡟⠀⣾⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣸⣿⣾⣥⣿⣇⣾⣿⣿⣿⣇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⠛⢹⣿⢸⣿⣿⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢿⣿⣸⡟⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⡇⣿⣇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⠿⠆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⢻⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠳⣸⣿⠀⢀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣽⣭⣶⣄
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂

⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠒⠒⠒⠒⣾⣿⣿⡿⠿⢿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⠿⢿⠶⠾⠶⣿⣿⣇⣀⡀⣀⠀⠀⠀⢀⣀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⢀⣀⣀⣴⣷⠀⠈⠉⠡⠠⠤⠖⠚⠒⠲⠢⢤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⣶⣛⣓⣒⡀⠀⠀⠉⠁⢩⠁⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣖⣤⠟⠁⠀⠀⠀⠉⠓⠦⠀⠠⠼⠿⢿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣿⣿⣿⣷⡿⠛⠛⠛⠟⠶⣤⡀⠀⢀⢀⣄⠠⣠⣙⣓⣒⣒⣒⣒⣒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⢿⣿⣿⣿⣿⣷⣤⠈⠛⠛⠛⠒⠶⠦⣀⡈⠁⠀⣼⣾⣿⣷⣿⣿⡛⠉⠉⠉⠉⠉⠉
⠀⠀⠉⠉⠉⠉⠉⠉⠛⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⠀⠀⠀⠀⠈⠙⠠⣾⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣦⣄⣀⠀⠐⠀⠈⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣿⣿⠧⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠲⠖⠶⠶⠖⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⣲⣒⣒⣒⣒⣚⣛⣛⣛⣛⣻⣿⣿⣿⣿⠿⠛⠛⠿⠿⢿⡿⠿⣿⡧⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⢤⠤⡤⠤⠤⠤⠤⠤⠤⣤⣤⣤⡿⠛⠋⠛⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⠟⠛⠟⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠿⢶⣤⣤⣤⣀⣠⣤⣴⠟⠉⠙⠓⠒⠒⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣄⣀⣀⣠⡤⠖⠲⠦⠤⠤⠤⠤⠴⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⠀⠀⠀⠀⣴⠖⠠⠀⠒⠒⠒⢒⠲⡾⠶⡶⠰⠶⠶⠶⠶⠤⠤⠤⠦⠤⢤⡤⢀⣀⣀⣀⣠⡄
⠀⠀⣙⡆⢀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢣⠠⠉⠣⠤⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⡀⢰⣿⠸
⠀⠀⢨⣥⡭⠄⠀⣼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠲⠷⠾⡉⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢺⣨⡇⢈⣦⣤⠄
⠀⠀⠰⡿⠛⠛⢻⠏⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠁⠉
⠀⠀⠀⠥⠀⠀⣼⠠⠀⢿⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠠⣴⠤⢠⠇⠀⠀⢸⡆⠀⠠⠀⠀⠀⠀⠀⠀⠘⠂⢸⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠒⠒⠐⡗⠀⠘⡖⠒⠢⠀⡀
⠀⠀⠀⡃⠀⡸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠨⠀⠀⠀⠈
⠀⠀⢀⠇⢀⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢻⡉⠀⠀⠀⠿⠂⠀⠀⠀⠀⠠⢧⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⢸
⠀⠀⠘⠧⢸⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣯⡉⡥⠖⠀⠀⠀⠀⠀⠀⠀⡣⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠉⠸⡎⠀⠀⢀⡀
⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠛⣿⣷⠒⠀⠀⠀⠀⠀⠀⠐⢲⠖⠂⠒⠂⠀⠀⢠⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⣠⣤⣬⣍⣀⠀⠀⠀⠀⠒⠒⠚⠛⠃⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⡒⠒⠀⣀⠀⠀⠁⠉⠉⠉⠍⠁⡀⠀⠀⠀⠀⣤⣤⠀⠀⠈⠙⠻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠉⠳⣄⠐⢦⡀⠀⠈⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠁⠀⣼⡿⠋⣿⡿⠉⠻⣷⠀⠀⠀⠀⠀⢠⣾⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠚⠁⠀⢀⡀
⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠃⣼⡿⠁⢀⣼⡿⢀⣠⣄⠀⢠⣿⣿⠞⠁⣀⣤⣀⡄⠀⣠⣄⠀⢀⣤⡀⠠⠔⠊⠁
⠀⠀⠀⠉⠳⢦⣌⠑⠢⠀⠀⠀⠀⣼⣿⣷⣶⠿⠋⣼⡟⣩⡿⠁⣾⡿⠁⢠⣾⠋⢹⣿⠃⢀⠙⣿⣶⡿⠋⢀⡀⠀⠀⣀⡤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠄⠀⠀⣰⣿⣿⡇⠀⠀⢸⣿⣟⠋⣀⣼⣿⣁⣴⣿⣇⣰⣿⣇⣴⣟⣠⣿⣿⣀⣰⡟⠀⠚⠉⢀⣀
⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⣰⣿⠇⠸⣿⣆⣀⣀⠙⠻⠟⠛⠙⠻⠟⠋⠛⠟⠋⠛⠟⠛⠻⠛⠁⠙⠟⠋⠀⠀⠀⠉⠁
⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠛⠋⠀⠀⠘⠻⠟⠃⠀⠀⠀⢀⣀⡀⠀⠀⢠⣤⣶⡄⠀⠐⣶⡶⢲⣶⡶⠀⠀⡔⡄⠀⠀⣀⣠⣄
⠉⢙⣿⣿⣿⣿⠟⡀⢀⣶⣦⢀⣀⡄⢀⣶⣿⠿⣷⡇⢀⣴⡿⠿⣿⣧⠀⢸⣿⣿⣧⠀⠀⣿⣧⣿⠟⠀⠀⠀⠈⠁⠰⠟⠛⠻⣿⣀⡀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠃⠸⣿⣧⣤⣈⠁⣸⣿⠀⠀⢸⣿⠀⣿⣏⣸⣿⠀⠀⣿⡿⣿⡆⠀⠀⣦⡄⠀⠀⠀⠀⣾⣿⣿⣷⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡴⡀⢠⣬⠙⠛⣿⣧⢻⣿⡀⢀⣿⡟⢸⣿⠿⢿⣿⣆⢠⣿⣇⣻⣿⡄⠈⠹⠻⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀
⠈⠻⢿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠛⠀⠸⠿⣿⣾⠿⠃⠈⠻⠿⠿⠋⠀⠛⠛⠁⠉⢉⣁⠈⠉⠁⠈⠉⠉⠀⠀⢀⣴⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⣤⣀⣤⡄⠀⣀⣤⣤⣾⠟⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣷⣶⣤⡤⠄⢸⣟⠁⢠⣿⠀⠀⢀⣿⠃⠀⢀⣀⠀⢠⡤⣠⡖⣰⣏⣾⠇⣼⣿⢟⣿⠃⣼⡟⢡⣿⠏⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠋⠉⢉⣀⠀⠀⠉⢀⣿⠏⠀⢀⣾⢇⣾⣷⢿⡿⢠⣿⢣⣿⣱⡟⣼⣯⣼⣿⠃⠸⣿⡾⢿⡶⢿⣿⡾⠋⠀⠀⠀⠻⠿⠿⠿⠿⠟⠋⠁
⠀⠀⢰⣿⣿⣿⡿⠋⣴⡀⠀⣾⡟⠀⢀⣾⡏⣼⣿⠃⣿⣧⢿⣷⠿⠿⠟⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣤⣧⠂
⠀⠀⠈⠛⠛⠉⠀⠀⢿⡇⠀⣿⣇⣠⣾⣿⡁⠙⠃⠀⠉⠁⣀⣤⡤⠴⠶⠶⠶⠤⢤⣤⣤⣤⣤⣤⠶⠟⠁⠀⠀⠉⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠙⠛⠀⠀⠀⡴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣦⣴⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠿⠿⣿⣿⣿⣟⣛⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠟⣍⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣠⣿⠖⢻⣿⠿⠟⠛⠛⠛⠛⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣷⡟⢁⣀⣀⡄⠀⠀⠀⣀⣀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⡿⠀⠈⣹⣿⣟⠂⠀⣼⣿⡤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠡⣿⣇⠀⡼⣻⠿⠟⠀⠀⠉⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⠁⠀⣰⠋⠀⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢀⡟⠀⠀⢀⡈⠉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣀⠀⠈⠙⠛⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⣤⣶⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠻⣿⣿⣀⢂⣀⡀⠐⡶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣮⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣹⠁⠈⣉⡉⠁⠈⣿⠼⣿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡙⠻⠿⣶⣶⣤⣤⣶⡿⠋⠀⠀⠀⠀⠈⠻⢇⢠⡧⡀⠷⠈⣿⣧
⠀⠀⠀⠀⢀⣾⣿⣿⡀⠀⠀⠀⠀⢀⡜⠻⡏⠀⢀⣈⣽⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣇⡅⣠⠞⣟⣿⣧⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⢀⠠⡏⠀⠀⠀⣠⠎⠁⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣋⣦⣾⡏⠉⠃⣰⡄
⠀⠀⠀⢸⣿⣿⢿⣿⣿⣧⢀⣸⢰⡇⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡍⣠⠞⠁⢹⣦
⠀⠀⠀⢁⢿⠀⣤⣿⣿⣿⡄⣿⣿⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⣿⣿⣿⣃⣤⣤⡎⠞⡹⢷⡀
⠀⠀⠘⠂⣼⡄⠘⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠈⠻⣿⣿⡏⢀⣀⣠⠀⣨⣽⣦
⠀⠀⣶⣄⡀⠉⠓⠀⠙⣿⣿⣿⣷⡶⠆⣁⣶⣿⣀⣀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣀⠀⠀⠀⠀⠙⣿⡟⣉⡕⠈⠉⢁⠘⠷⣄
⠀⢸⣿⣽⣿⣷⣶⣦⣤⣿⣿⣯⣷⡾⠿⢿⣄⣉⡉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣶⣦⣄⣀⠙⢿⣯⣔⣆⡬⠶⠶⠖⢈⣷
⠀⣶⣠⡌⣿⣿⣽⣿⣿⣿⣿⣏⡀⠀⠀⠀⠈⠀⠄⠀⠀⢀⣤⠈⠀⠀⠀⠀⠀⠀⠀⣼⡟⢨⣿⣿⢻⠿⣿⣿⣿⣾⣿⡿⠿⠛⠳⠶⢦⣌⣿
⡴⠿⣿⠛⡂⠀⠈⠉⣹⣿⣿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠉⠁⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣽⣿
⢃⣘⣛⣿⣿⣿⣛⣲⣿⣿⣿⣿⣶⣤⣤⣶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⢤⣾⡿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿
⡭⠐⢉⡁⠜⠿⠛⢿⣿⣿⣿⡛⠻⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠒⠀⢠⣾⣿⣿⠀⠀⠀⠀⣠⣭⣾⠏⠀⠀⠀⠀⢀⣴⡾⠟⠉⠁
⣠⠖⠁⠀⠀⢀⣼⠟⠙⠛⠿⣿⣷⣦⣀⢤⣄⣀⣀⣤⣤⣤⣶⣿⡟⠉⠛⠋⠹⢻⣿⣿⠀⣀⣶⡾⠿⢿⣽⣿⣄⢀⣠⣶⠿⠋
⠻⣦⣾⠀⣴⣿⡇⠀⡀⣠⣶⡿⠻⣿⣿⣷⣯⣭⣭⣵⡾⠟⠉⠁⣀⡤⠀⣠⣞⣼⣿⣿⣾⣿⣿⣵⣵⣶⡿⣿⣽⣿⡟⠉
⠀⠀⠹⣿⣿⣿⣷⣄⢤⣿⣿⣷⡀⠄⠙⠿⣿⣿⣿⣿⡀⣠⣼⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣽⣿⡟⠁
⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⣏⡈⡀⠈⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⡆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠂
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⣥⠒
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⣄⣩⠉⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⠇⢼⣆⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣦⣾⠈⣦⣿⣶⣾⣶⣄⣀⣠⡆
⠀⠀⠀⣴⢴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣭⡙⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⢶⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡄⠈⡟⢦⠀⣰⠋⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⢇⡐⠁⠈⣧⢿⠀⠀⠀⠀⠀⠘⠐⠒⣲⣠⠀⣻⠉⠙⢲⡀⠀⢰⢋⣀⠙⢦⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⡄⠀⠀⠐⠀⢀⡿⠔⠉⠫⠤⠶⠒⠶⠤⡖⠉⢹⠚⠁⠀⠀⠀⠉⡆⠈⢹⠈⢳⡘⣦⡞⢀⣄⠙⡦⣄
⠀⠀⠀⠀⠀⠀⡴⠋⠉⠁⠈⠉⠢⣀⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠜⣷⢠⠞⢀⡤⠾⠷⠖⠋⠀⢠⢧⣄⠙⢬⠶⠁⠈⠘⡆
⠀⠀⣠⣤⣀⢸⠁⠀⢀⡀⣀⠀⠀⠈⢧⣿⠀⠀⣠⡶⠿⠷⠦⢤⣄⣀⣀⣠⠴⢧⣼⡄⡎⢀⡖⠒⠒⠠⢔⡁⣾⢁⠀⠀⠀⠀⣀⡼⠗⠒⠲⢄
⢀⡞⠁⠀⠈⢻⡀⠀⠇⠀⡀⠱⡄⠀⢸⡏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡾⣧⡴⠋⠙⠄⢹⡌⠻⣦⡀⠿⣭⡏⠀⠀⠀⠀⠈⢧
⠈⠟⠉⢱⠀⠀⠳⣄⡀⢀⡟⠀⣷⠀⠸⠀⠀⢠⡇⠀⠀⢀⣄⠀⠀⠀⠀⣠⣀⣠⠶⡆⠀⠹⣮⣷⣯⣇⣠⠞⢁⣔⡁⠙⠚⠉⡇⠀⡴⠋⠉⠆⢸
⠀⣠⠚⠉⠉⢧⠀⠀⢉⣉⣀⡤⠟⠀⠀⠀⣠⠞⠀⣴⠒⠋⡸⠀⠀⠀⠀⠑⠈⠐⠋⠀⢀⡤⠞⠛⠒⠒⠮⡷⠄⣀⣹⡞⠉⠉⠙⣦⡇⠀⠀⠀⡼
⠀⡇⠀⢠⡖⠚⢱⠋⢉⡤⠤⢤⣀⣠⣴⠾⠥⠤⣤⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣶⣏⠀⠀⡴⠦⣄⠀⠈⢫⠀⠙⢧⡀⠤⠔⠁⢹⠤⠤⠞⠁
⠀⠙⢦⣀⣩⠇⠸⣄⠈⠁⠀⠀⣸⡏⠀⠀⠀⣀⠀⢹⣄⡤⠤⠤⠤⠤⠤⠖⣋⠥⠖⠁⠘⠦⣀⣠⠞⢸⡆⠀⢨⣗⡖⢺⠿⠶⠶⣖⣻⡤
⠀⠀⠀⠀⡴⠚⠋⠉⠉⠉⠛⢿⣹⡇⠀⠀⠘⢿⣒⣊⡤⠛⠛⠒⠶⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧⣢⠞⠀⠀⡼⠁⢻⡿⣀⣤⠀⣸⠃⢄
⠀⠀⠀⠸⡇⠀⠀⡤⠶⢶⠤⣀⠈⠑⣄⠀⠀⠀⠀⣠⠴⠒⠛⠓⢦⡀⠙⣄⣀⣤⣤⠾⠿⠟⠋⠁⠀⣀⣤⡚⠁⠀⠾⢻⡞⠁⠸⡁⠀⢈⡇
⠀⠀⠀⠀⢳⡀⠀⠃⠀⠀⢳⠘⡆⠀⢻⡶⠋⠓⡞⣡⠴⠦⠤⡀⠀⣷⠀⢹⣿⡟⠀⠀⠀⡠⠴⠖⠋⢀⡠⠙⡆⠀⣤⠞⠳⣄⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠙⠲⠤⣤⡤⠞⠀⢳⣀⠈⠓⣂⡤⠋⡇⠀⠀⠒⠼⢀⡟⠀⢸⣿⠀⠀⠀⠸⡅⣨⠑⣄⠸⡄⣠⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠙⢄⡀⠄⠤⠞⢀⡰⠃⠹⣄⠀⠀⠀⠉⠁⠀⡿⠀⠙⠦⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠉⠀⠀⠀⠈⠓⠦⠤⠤⠴⠋
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢖⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⡀⢐⠂⠴⠐⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⠀⡂⠀⡀
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⠀⠊⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢢⠀⠘⠀⠀⢲⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡠⠈⠀⠀⠀⠀⠀⢂⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠀⢸⣄⠀⡀⠃⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⣄⠀⠀⠀⠀⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠁⠙⣄⠀⠀⣠⡀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣤⡤⠀⠀⠉⠋⠉⢱⠀⠀⡰⢀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠒⠘⠒⠲⠀⢀⡀⠀⠄⠤⠚⠀⠐⠟⠈⠓⠂⠀⢀⠐⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠀⠀⠀⠀⠊⠐⢡⠀⠀⠀⠀⠀⠀⠰⠄⡃⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⣀⠀⠀⣟⠀⠀⠀⠀⠀⡠⠔⠒⠫⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠬⠥⠈⠁⠀⠤⠋⠁⠕⠒⢠⡄⡀⠃⡀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠤⠀⠄⠀⠀⠀⠠⠔⠐⠒⠈⠀⠀⠀⠑⡆⠀⠃⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐⠆⠄⠖⠈⠀⠀⠐⣄⠁⠀⠀⠀⡀⠀⠀⠈⠊⡀⠀⠀⠀⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢄⠀⡀⠂⠀⠀⠀⠀⠀⣌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠓⠀⠀⠀⠀⠸⠶⠃⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠴⠆

⠀⠀⠀⠀⠀⢀⡀⢀⠀⢒⣾⣾⣴⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣯⡭⠅
⠀⠀⠀⠀⡴⠛⢳⣟⣿⢣⣴⡿⠐⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⢏⣫⡙⠐⠀⢀⣴⡖⡂⣠⣤⣀
⠀⠀⠀⠀⠁⢸⡿⠹⠿⢛⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠃⡹⠅⠀⠀⠘⠈⢿⠈⠛⠹
⠀⠀⠀⠀⠀⡜⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⢄⠀⠀⠑⠢⡀
⠀⠀⠀⢠⠎⠀⢀⠞⠀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠑⠄
⠀⢠⡴⠁⣠⡾⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠈⠲⠄
⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⣶⠶⢶⣶⡶⣶⣶⠶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⣹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣤⣶⣤⡀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⣤⡀⠀⣠⣤⣄⠀⢀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠿⠿⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠇⣾⣷⣬⣹⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣛⣋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣛⣛⣛⣛⣃⡙⠿⠟⠛⣿⣿⣿⡿⠛⠿⠟⣁⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣙⣋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢰⣾⣦⢹⣿⣿⣿⣿⣿⡏⣴⣿⡆⢻⣿⣿⣿⣿⣿⢡⣾⣶⢸⣿⣿⣿⣿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠘⣿⣿⡀⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⡇⣸⣿⡿⢸⣿⣿⣿⠏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⢻⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢸⣿⣷⢸⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⢰⣿⣿⢁⣿⣿⣿⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠸⣿⣿⡈⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⡏⣸⣿⡿⢸⣿⣿⠟⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠂⠻⠿⠃⠻⠿⠟⠻⠃⠻⠛⠃⠸⠟⠛⠿⠃⠛⠻⠃⠺⠶⠶⠞⠋

⠀⠀⠀⣾⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡶
⠀⠰⠿⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⡶⠲⠶⠶⠶⠶⠶⠶⠶⢾⢿⡿⠿⠂
⠀⠀⠀⠿⠆⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠠⣿⣿⡟⠛⠛⠛⠛⣻⣯⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠐⣿⠃⢿⠀⠀⣠⡿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣀⣨⣀⣀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡍⠻⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉
⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⣀⢸⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⢩⢨⡇⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣶⡘⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠈⣻⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⢈⡃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣶⣆⣶⣤⣤⣦⣹⣿⣿⣷⡿⠁⠀⠀⠀⣾⣷⣾⣾⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢘⢉⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⠟⣻⠛⠁
⠀⠁⠀⠀⠀⠘⣿⣿⣿⠃⠙⠀⡁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⢠⠛⡄⠄
⠀⠄⠀⠀⠀⠀⠛⠛⠛⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⣴⣾⣿⣙⡋⠀⠀⠉⠀⠀⢈⣋⣹⣷⣶⣾⣾⣍⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠘⠮⠄⣀⡙⢋⣽⣶⣦⣶⣿⣍⣛⢁⡠⠬⠥⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⢄⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠙⢲⠏⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠄⠀⠀⠀⠘⡆⠀⠰⡦⢄⡉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⢹⣄⣈⠱⠦⠄⠈⢑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠁⢉⢏⠟⣄⠀⢀⣀⡤⠞⠓⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⠀⠈⠋⠉⠀⠀⠀⠀⢀⠠⢻⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡰⠋⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠀⠀⠀⠀⠀⣠⠊⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠎⠀⢠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⢠⠞⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠎⠀⢠⠃⠀⠈⠑⡦⠀⡞⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣕⢦⡀⠀⠀⢀⠔⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠎⠀⠀⣇⠀⠀⠀⡼⠀⣼⡃⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢝⣢⡴⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡎⠀⠀⠀⠈⠓⠢⠚⠁⡼⢹⠀⠀⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⡎⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡏⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⢎⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⢀⡞⡎⠀⠀⠀⠀⡀⠀⠀⠀⢠⠃⠀⡜⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⢀⣌⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠇⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠋⠙⠋⠋⠉⠉⠉⠙⠉⠉⠉⠙⠛⠛⠛⠋⠙⠉⠛⠙⠛⠉⠉⠉⠉⠉⠛⠙⠙⠛⢙⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣄⣉⠙⠛⠋⣹⠿⢷⣤⣤⣤⣤⠾⠿⡟⠟⠿⠿⠿⠛⠛⢩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣶⣿⡀⢘⣿⠿⠿⣧⣠⣄⣿⣶⣶⣶⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣶⣤⣄⣉⣉⣉⣭⣵⣶⣶⣮⣽⣭⣁⣉⣉⣉⡉⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢘⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡄⣠⠀⠀⠀⠀⢠⣶⠂⠀⠠⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⡀⢧⠀⠀⠀⠀⢠⣶⡆⠀⠔⠂⡀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⢤⠀⠀⠀⢈⠇⡸⢀⡇⠀⠀⠀⠀⠰⠿⢗⣤⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⣤⣶⣶⣿⣿⣶⣦⣤⣄⣀⣠⣤⣶⣶⣶⣶⣤⣀⣀⣀⣠⣤⣶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⠉⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣯⣿⣽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠙⠄⡀⠀⠀⠀⠀⠀⠀⠈⠆⠈⠑⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠊⠁⠰⠁⠀⠀⠀⠀⠀⠀⢀⠤⠋
⠀⠀⠀⠀⠐⠆⠀⠀⣀⡀⣤⠀⠀⠀⠀⠀⠐⡤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢠⠆⠀⠀⠀⠀⠀⣤⢀⣀⠀⠀⠰⠂⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠐⠄⡀⠀⠀⠀⠀⢀⠀⠂⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠁
⠀⠄⠤⢀⠀⠀⠀⢀⠀⠀⠀⠜⠁⠀⠐⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠊⠀⠈⠣⡀⠀⠀⡀⠀⠀⠀⡀⠄⠠
⠀⠀⠀⠀⢢⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠈⠈⠒⣤⣀⠀⠀⠀⣀⠀⢼⠀⠀⡇⠀⡀⠀⠀⠀⣀⣠⠚⠁⠉⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡔
⠀⠀⠀⠀⢠⠂⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⠣⠜⠀⠀⠀⠉⠀⠉⠀⠀⠁⠀⢨⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⡄
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢃⠈⠰⠄⣄⣠⡤⠀⠀⠀⠀⠀⠀⢤⣄⣠⠠⠖⠅⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡰⠁⠀⠀⡘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢃⠀⠀⠀⢆⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠐⡄
⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠈⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠑⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣀⠄⠒⠤⢤⣀⣈⣃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣘⣁⣀⡤⠰⠂⠠⡀
⠂⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲
⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠆⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠲⠤⠠⡔⠀⠉⠄⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠠⠀⠀⠋⠂⢢⠤⠤⠖
⠀⠀⠤⠒⠐⠂⠠⣠⠂⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠐⠀⠀⣀⠤⠼⠒⠒⠤
⠀⠆⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠰
⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠐⠃
⠄⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠈⠢⠤⠖⠚⠉⢉⡝⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡉⠉⠓⠒⠠⠐⠈
⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠱⡀⠀⠀⢡⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡌⠀⠀⢀⠎⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡌⢀⠰⠂⠋⠛⠓⠀⠀⠀⠀⠀⠀⠚⠋⠛⠐⠦⡀⢡⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⣀⠀⡀⠀⠀⠀⡔⢢⠀⠀⠀⢀⠀⣀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡜⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰⢀⢀⠤⠛⠁⠀⠀⠀⠈⠀⢸⠀⠀⡗⠀⠉⠀⠀⠀⠉⠙⢤⡀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠂⠒⠊⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⡰⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠈⢄⠀⢀⡔⠁⠀⠀⠁⠀⠀⠀⠁⠒⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠐⠁⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⢀⠠⠆⠀⠀⠉⠁⠛⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠚⠄⠀⠀⠀⠀⠀⠛⠈⠉⠀⠀⠰⠄
⠀⣠⠒⠁⠀⠀⠀⠀⠀⠀⢀⡆⢀⡀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⢄⡀⢰⡀⠀⠀⠀⠀⠀⠀⠈⠒⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠬⠧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠏⠁⠀⠀⠉⠦⠒⠒⠢⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⠂⠋⠀⠀⠀⠀⢀⠔⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣥⣤⣤⣤⣤⣮⣭⣭⣤⣤⣤⣀⡀⣤⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣀⣀⣠⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣷⣾⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠬⠇





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡰⢺⢴⡀⢦⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡁⢧⣎⣡⠋⡗⠀⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⢣⠁⠈⠘⠣⠄⡸⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡼⣅⠀⡀⢠⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠈⠂⠀⠘⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠄⠊⡐⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⡀⠀⠀⠀⡁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢠⠀⡘⠀⠀⠀⠀⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣀⠐⠀⠀⠀⢀⡌⢅⠂⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢡⠔⠈⠃⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⡃⠀⠀⠀⠄⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠁⢀⠀⠄⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠈⠀⠀⠀⡀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠢⢄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⡄⠀⠀⠈⢀⡁⢸⢡
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠰⣹⣿⣷⠡⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⠀⡀⡁⠀⢀⠔⡏⠀⠄⡐
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠉⠉⠙⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠀⣦⣄⠁⡠⠃⠠⠄⡐⡎⢰
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡠⢠⡞⠁⠀⠀⠀⠈⠄⠀⡰⠁⠀⠛⠁⢀⡴⠒⠹⣍⠢
⠀⠀⠀⠀⠀⠈⠐⠂⠤⢠⣀⣀⣴⠗⠋⠐⢂⣾⣿⣙⣾⠃⠀⡇⠀⠤⠤⠴⠻⣄⣦⣧⡌⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠤⢰⣶⡖⢣⣤⣤⡋⠈⠉⠻⣇⢄⣀⣀⣀⣀⣈⣿⡤⢧⣾⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠃⠚⠛⠣⠽⠿⠅⠈⠃⠀⠉⠉⠉⠉⠉⠙⠁⠛⠛⠚⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡴⠛⠉⠳⣄⠳⠟⠀⡤⢤⢰⡇⠀⠀⠘⡶⠦⡄⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠰⣇⣈⡇⣇⠀⠀⠀⡽⣠⠴⠚⢧⡼⠋⠳⣤⣤⠾⣅⣠⠏⠀⢿⣀⣸⢂⣀
⠀⠀⠀⠀⣰⠶⢶⣶⣶⡧⠤⣬⣥⣤⡾⣗⣒⣋⣁⣏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠋⣳⣀⣩⣥⣽⠼⢷⣶⣶⡶⠶⣆
⠀⠀⠀⠀⠙⠲⢦⣄⠉⠉⠛⠓⠶⠶⠿⣭⣭⣍⣉⣙⣶⣤⣞⣛⣛⣛⣛⣛⣉⣉⣩⣽⣭⠥⠶⠶⠚⠛⠉⠉⣠⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠞⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠳⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⢀⣽⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⣯⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠂⠀⠘⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢰⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣟⣿⣷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣟⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⢧⠀⠀⠀⠀⠀⠿⢔⠲⢄⠀⠀⠀⠀⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⣿⣿⣿⡵⠋⠀⠀⠀⠀⠀⠀⢰⡇⠈⢢⠀⠀⠀⠀⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⡟⠁⠀⠀⠀⠄⡀⢀⠀⠸⡇⠀⠀⢣⠀⠀⠀⢀⢺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⡏⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣆⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣿⣿⣧⡀⠀⣀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣾⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣳⠏
⠀⠀⠀⢀⣠⢴⣿⡿⣿⣿⣿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠴⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⣴⣿⣿⣿⣿⠛⠓⠻⠼⠛⠁⠀⠀⠀⣠⣤⡴⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢿⣿⣿⣿⡟⣆⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣽⠃⠈⠀⠀⠀⢀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⣿⣿⣿⣿⡿⣷⢦⣀⣀⣴⣿⣾⣿⣿⢻⡞⠁⠀⠀⡀⣠⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃
⠀⠀⠀⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣤⣞⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏
⠀⠀⠀⠀⠻⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠻⠿⡽⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠽⠟⠋⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠒⠻⠽⠿⠿⠗⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣠⣤⣤⣤⠤⣀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣉⠁⠛⠘⠧⠆⠀⡝⣷⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠗⣈⠁⠀⠀⠁⢁⠻⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣽⠇⡐⢉⡃⠀⠀⠘⠋⠡⢘⣻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢈⠘⡷⢨⠀⠀⠀⠀⠀⠀⠦⠾⠙⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⢧⡈⣁⠐⠟⠳⡤⢛⡗⠀⠤⠚⢹⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⣄⡀⣈⡶⢶⡐⠓⣠⢦⣀⣀⣠⠞⢋⠳⣦⢤⣤⣤⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢧⡈⠉⣁⠀⡈⠛⢛⠁⢀⢾⡿⠁⡀⠀⠈⠢⣀⢡⠶⠶⢤⡉⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢆⠀⠙⡆⠈⠙⠀⠀⢁⡔⣡⠋⠀⠈⠀⠀⡄⠀⠀⣝⠀⠀⠀⣕⠀⢇⢻⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢤⣄⠳⠀⠘⡄⠀⠀⠀⠀⣼⠁⣀⠔⠀⠀⢀⡇⠀⠐⡌⢳⡈⠂⠘⡄⢸⢠⠄⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⢣⠈⠂⠘⡄⠀⢀⡸⢣⡞⠁⠀⠀⠀⠉⢡⠀⢰⡌⡶⣌⣢⣑⡀⢸⡞⢀⡏⣵⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡂⠀⠀⠀⠘⣀⣀⠀⢀⣀⠜⠛⠁⠀⠀⠀⠀⠀⠀⠀⣇⠉⢇⠀⠘⣄⣜⣢⣀⢀⡜⡴⣣⠤⠿⣤⣀
⠀⠀⠀⠀⠀⠀⠤⠄⠦⢿⣿⣿⠃⠀⠀⠀⣄⣹⠛⠛⠻⠱⣦⠀⠀⢠⣀⣰⣤⣤⣤⣤⣿⣀⣨⣷⣠⣼⣿⣿⣿⣿⡆⠀⠁⠊⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡆⠈⠃⠀⣰⣇⣰⠃⡄⠀⣸⣿⣿⣿⠾⠍⠉⠙⠛⠛⠛⠛⠋⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠇⢀⠊⠀⠀⠀⠫⣤⠚⡓⠳⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢛⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠆⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢠⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣤⣄⠀⠀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣯⣿⣧⣤⡀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠸⣧⠀⢸⡏⣿⣿⣿⣿⣿⡏⢸⡇⢈⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⠀⠀⠙⠁⢸⡇⢹⡷⣿⠃⣿⣹⠸⣇⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⢀⣤⠞⠛⠉⠉⣿⠟⠳⣤⠀⣸⠇⠘⠃⢹⠀⠟⢿⠀⣿⡸⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⡆⢹⠄⠀⠀⠛⢇⠾⠖⠈⠙⠶⢄⠀⠀⠛⢁⢿⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⡀⢱⡎⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠈⣳⠀⠀⢸⠀⠇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠉⠉⠉⠉⠁⠈⠉⠻⣿⠿⡿⢿⡿⠛⠛⠛⠒⣿⠀⠀⢸⡷⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣿⣦⡀⠀⠀⣠⡴⠃⠀⠀⢸⡅⠀⠀⠉⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⣀⡴⠟⡙⠳⠶⠛⣉⣀⠀⠀⠀⠀⢸⣅⣴⠶⠛⢛⠛⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⠀⠀⠀⣸⠀⠉⢙⣷⠾⠛⠛⠉⠀⢰⣧⠀⠀⠀⢉⠁⠀⠀⠀⠀⠸⠋⢁⣴⠿⣿⠿⠆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠀⢀⣿⣤⠾⠋⠁⠀⡀⠀⠀⠀⣸⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣂⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣶⡿⢨⠀⠀⠀⠀⠠⣷⣤⣶⡄⢻⠈⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠘⡿⠾⢿⡟⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣶⠟⠋⠀⠙⠟⠀⠀⠀⢀⡄⢿⠁⣸⡇⢼⡆⠀⠀⢸⣄⡿⠀⠀⠀⠀⣶⠀⠀⣧⢄⣸⠃⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣸⢀⣿⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⡘⢧⠀⠀⣿⠀⠉⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣴⠿⠋⣿⠀⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠃⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⠀⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣰⡟⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⢠⡿⠀⠀⠀⢠⡄⠀⠀⠀⣼⠀⠀⠀⠙⠁⠀⠀⣿⠀⠀⠀⢰⡇⣹
⠀⠀⢰⣿⠀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⠀⠀⢠⡈⢠⣿⠃⠀⠀⠀⢸⡇⠀⠀⢀⠻⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⣤⣻⣷
⠀⠀⠘⣿⣀⣿⠀⠀⠀⠀⢰⡏⠀⠀⠀⣇⣠⢀⡶⠉⣠⡿⠃⠀⠀⠀⠀⣿⠁⠀⠀⣼⡀⡆⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠽⠿⣇
⠀⠀⠀⠹⡿⢇⡀⠀⠀⠀⡌⣣⠀⠀⠀⠛⠛⠁⢀⣴⠟⠁⠀⠀⠀⠀⠀⣹⡄⠀⠀⠙⠛⠀⠀⠀⡀⠀⠀⣸⡇⢰⣧⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⢠⣾⠻⠶⣦⣤⣷⣯⣤⣤⣤⣤⣤⡾⠟⢁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⣿⠁⢸⢹⠀⠀⢀⣤⣾⠋
⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠀⢸⡟⠀⣧⢸⡶⠞⠋⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⡄⣿⠃⠀⠙⠋⠀⡀⢀⣠⣴⠟
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠘⢿⣷⠶⣶⠶⠶⣾⣃⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠻⠇⣽⡟⠀⠀⠀⠀⠀⣿⠈⠉⠙⠶⣄⢀⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠏⠀⣿⠀⠀⠘⠛⠁⠙⠻⢿⣷⣶⣄⣀⠀⢹⡇⠀⠀⠀⠀⠀⣸⣟⠀⠀⠀⠀⠀⣠⡟⠀⠀⢀⣴⠏⢸⡇
⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⣘⣦⡀⢻⣆⠀⠀⠀⠀⠀⠀⠈⣿⠿⣠⣽⠿⢻⡇⠀⠀⠀⠀⣴⣿⣻⣶⠀⠀⠀⠀⡹⠀⠀⠀⠈⠙⣷⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⠚⣿⡆⠀⠀⠀⠀⠀⣾⠈⡀⠈⠻⣾⣤⠇⠀⠀⠀⣼⡟⢉⣻⣿⠃⠀⠀⠀⠻⠟⠀⠀⠀⣴⠟⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢘⣷⠶⠀⠸⣷⡀⠀⠀⠀⠀⢿⡴⠃⠀⠀⠀⠁⠀⠀⢠⣾⣿⣧⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⣅⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣹⢿⡟⣻⣿⣋⣀⣀⣀⣀⣀⣤⣀⣀⣠⣼⡇
⠀⠀⠀⠀⢸⡆⠀⠀⠀⣾⢡⠀⣾⠋⠀⠐⣦⣽⠗⢻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣸⡇⠘⣺⡋⢉⣟⠉⠉⠉⠉⠙⣿⠉⠉⠉⢻⡄
⠀⠀⠀⠀⠘⣿⠀⠀⠀⣷⡀⠰⣿⡀⠀⠀⡞⠉⡆⢸⡍⠛⣶⣤⣤⣤⣤⣴⠟⠁⠀⢠⡿⠀⢰⡿⠃⠈⠛⢻⡟⠻⡷⢿⢹⣶⠻⢶⣟⠁
⠀⠀⠀⢠⡆⢿⠀⠀⠀⠉⠁⠀⢽⣟⡛⢻⡇⠀⠑⢾⣦⡼⠛⣯⠀⢀⣿⢷⡄⠀⣀⣾⠃⣠⡟⠁⢐⡀⠀⢸⣯⠀⣷⣾⡘⢿⣄⠀⠉⢷⡀
⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⢠⡿⠋⢻⠃⠀⠀⢸⡇⠀⠀⢻⣤⡾⠃⠀⠹⣿⢿⡏⠰⠋⠀⠀⢸⣇⠀⢘⣿⣴⠟⢿⡇⢈⣿⣷⣤⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢺⡅⠀⣿⠀⠀⠀⢸⣧⣄⣀⣼⠛⣇⣀⣀⣠⣿⣿⠁⠀⠀⠀⠀⡄⢻⠀⠘⣿⠁⠀⠀⠛⠋⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⢸⣷⠀⠙⣿⡇⠀⠀⠀⡾⡏⠉⠉⣿⠀⡟⠉⠉⢙⢹⣿⠀⠀⠀⢀⠀⣧⡘⠀⢠⣾⠀⠀⠀⠀⢀⡸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡀⣿⠀⠀⠙⢷⣤⡀⢐⡇⠉⠀⣰⠏⣀⣽⠀⠀⢸⣼⣿⠀⠀⠀⢸⡀⠈⠁⠀⠀⢀⣠⣤⡶⠞⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⣧⡿⠀⠀⠀⠸⣇⠘⠛⠷⠀⣰⠏⠀⣿⡟⣀⠀⠀⠈⣿⣀⣀⣀⡸⣧⣤⡶⠶⠟⠛⠉⠀⠀⢸⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⢠⣾⠋⠀⠀⢸⡆⢿⡄⠀⠀⠈⠋⠉⢹⡁⣿⠁⠀⠀⠀⠠⢼⡿⠛⢛⣧⡄
⠀⠀⠀⠀⣠⣤⣤⣤⣤⡤⠴⠖⢶⣶⣶⣾⠃⠀⠀⠙⣧⡀⠀⢰⣼⠃⠈⣿⡄⠀⠀⠀⠀⠘⣧⠟⠀⠀⠀⠀⠀⠘⣿⠛⢿⣍
⣤⡾⠛⠛⠉⠀⠀⠀⠀⠀⠰⣿⣋⣈⣈⣿⣛⣋⣶⣶⣼⣿⣆⣀⣠⣴⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣶⣾⡛⠛⠛⠛⠻⠶⠶⢶⣦⣄⣀⡀
⠙⠻⠶⣶⣤⣤⣤⣤⣤⣤⣤⣀⣈⠁⢉⣉⠉⣉⣀⣤⣼⡇⢸⣿⣟⢉⣉⣿⣟⣛⣛⣻⣶⣶⣦⣤⣤⣤⣤⣤⣤⣷⣦⢀⣨⣿⣆⣀⣤⣤⣤⣤⣤⣤⣬⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠛⠱⣯⡁⠀⣀⣀⣤⣤⣤⣼⠄⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣅⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣼⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡤⠤⣄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⡆⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠃⠀⠀⠈⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡤⠞⠀⠀⠀⡏⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡖⢲⡀⡇⠀⡇⠀⣀⡀⠸⣥⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠒⢦⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣀⣸⣇⣠⣇⣇⣀⣇⢸⠁⢸⠀⠀⢰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢳⠀⢀⡖⠛⢲⣤⠤⣄⠀⠀⢠⠏⠉⢹⡄
⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠶⠤⠬⣯⣅⣀⣀⣀⣀⣀⣀⣀⣀⣧⣠⣤⣤⠤⠤⠾⠶⠾⢦⣀⡼⠁⠀⠈⡿⠉⠉⠳⠤⠾⡄
⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠴⠃⣀⡀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠉⢳⠲⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⢼⣉⣹⢲⠏⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣇⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⡼⠙⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠁⢹⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢻⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⠀⠀⠀⠀⠀⢀⠴⡄
⣿⣿⣿⣿⣿⣿⣧⢿⣿⣶⣿⡿⢼⢭⣿⣿⣷⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⢸⣓⡇⠀⠀⠉⠁⠀⡜
⣿⣿⣿⣿⣿⣿⣿⡼⣿⢿⣻⣛⠿⡾⢟⣟⢫⣝⠿⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣆⢀⡠⠴⢬⣈⣁⠤⢤⡜⢢⣠⠇
⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠿⢷⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠈⠀⢀⣀⠙⠉⡼
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⠭⣿⣿⣷⣭⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢴⣲⠀⠀⠘⠚⠁⢀⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣛⣛⣛⣛⣛⣛⣛⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠤⠤⠤⠤⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⣶⡶⠶⠶⢶⣶⠶⠶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠿⢶⡶⠟⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣀⠀⠀⢸⣧⣤⣤⣤⣄⣴⡿⠛⢿⣾⡇⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡘⠛⣠⣤⡿⠛⠉⠉⠉⠙⠛⠀⠀⠀⠿⠟⠿⣶⣄⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣏⣼⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⣿⣛⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦⣄⣤⣾⠟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⢠⠄⠀⢤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠄⢀⠄⠁⠀⠀⠀⠀⢀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠄⠃⠀⠠⠀⢀⠀⠀⠀⠀⠀⠐⡰⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡎⠀⠀⠀⠀⠀⠀⠀⡄⣄⠘⠀⠀⠉⠁⠠⠀⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣸⠀⠀⢰⠳⡈⠢⣤⠀⠒⠊⠁⢗⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⢁⡉⠠⠉⠁⡙⠀⠇⠀⠀⠀⠀⠀⠀⠀⢿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠏⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⢸⡄⡸⠀⠀⡠⠂⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⡰⡇⠀⠀⠊⠀⠀⠀⢀⡤⠆⠀⡄⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⣀⠀⠀⠀⠀⠁⡀⢀⠄⠀⠀⠀⢀⠔⠁⠃⠀⠂⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⠀⠊⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠈⠀⣀⡀⠄⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠰
⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠙⠉⠁⠙⡖⠲⢇⣠⠀⠀⠀⠀⠀⠄⠀⠀⣇⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡎⠸⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠳⠶⠀⠤⣔⠉⠀⠀⠀⠀⠀⢀⡷⠀⠈⠳⣀⣀⣠⣤⣀⣤⣄⣼⣦⠴⠶⠃⠿⢸⢒⡤⢄⡀
⠀⠀⠀⡁⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⡠⠀⣀⠠⣀⣸⠁⠀⠀⠰⠃⠤⠾⢸⡒⢦⡀⠘⠉⠝⢀⢁⠀⡀⢀⡏⠐⠴⠒⢞⢦⠄⣀⠑⢪⡑⡄
⠀⠀⠀⢱⢄⡀⠀⠀⠈⠁⠒⠶⠤⣈⣤⡀⠁⠀⠄⠈⢆⠈⠐⠒⢈⡠⡔⠒⠃⠀⢱⠘⢢⢀⠅⢉⡩⠋⠨⠂⢀⣘⡱⠦⠄⠒⠈⠉⠁⠀⡇
⠀⠀⠀⠈⡄⠈⠑⠂⠤⢀⡀⠀⠀⠀⠀⠉⠉⠑⠒⠂⠈⠇⠰⠾⠯⠤⠄⠤⠤⠤⠷⠶⠾⠗⠐⠚⠒⠈⠉⠁⠀⠀⠀⠀⠀⣀⡠⠤⠒⡋
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠐⠒⠒⠉⠁⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠑⣆⢇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠄⣲⠎⠛⢢⠀⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠄⠤⠘⠀⡸⠀⣔⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠋⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠤⠤⠄⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⣤⠶⠞⠛⠛⠉⠉⠉⠙⠻⣶⠟⠉⠙⣧
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣤⣧⣀⠀⠀⠀⠀⣀⣀⣠⣤⣿⣀⣀⡀⠀⠀⠀⠀⠉⢙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠉⠻⢶⣶⠛⠉⠉⠀⠀⠀⠉⠉⠛⠳⢦⣄⠀⣰⠏⠁⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⣽⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣽⣷⣿⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣾⠋⠀⠀⠈⠹⣧⡠⠤⠒⠊⠉⠁⠀⠀⠀⢠⡟⠀⢹⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⣧⠀⠀⠀⢀⠀⢿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⠷⢦⣶⠋⠀⢸⣇⣀⣤⠶⠞⠛⠋⠉⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢹⡆⠀⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢸⡇⠀⢀⣠⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠷⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⠀⢠⡆⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣟⠁⠀⢹⡇⠘⣷⣾⣷⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡏⠀⠈⠉⣉⣿⣿⡶⠿⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢩⡿⠀⣀⠀⢸⡏⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣴⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡇⣠⡟⠁⠀⠉⠀⠀⠙⠷⠶⠶⠶⠛⠋⠁⣀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢰⡟⢉⣿⣾⠋⢀⣄⠀⠀⠶⠀⠀⠠⡦⠀⠀⢀⡄⠀⠉⠀⠺⠂⠸⣧⣀⣀
⠀⠀⠀⠀⠀⠠⣿⣁⣾⡟⣃⣀⣀⣁⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣁⣀⣀⣤⣤⡶⠾⠛⣩⣽⠇
⠀⠀⠀⠀⠀⠀⠉⣿⣛⣛⡛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣁⣀⣀⣀⣀⣉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⣻⣷⠄⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣿⡏⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣶⣤⣴⡶⠶⠟⠋⣩⣤⣤⣤⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⢤⡎⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠚⠉⠁⠀⠀⠀⠀⠀⠸⡆⠀⠲⣤⣈⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠱⣌⣉⣲⣤⠄⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣠⣴⣶⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣄⠀⠀⣀⣠⠼⠳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠴⠟⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢉⡷⢀⣾⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡄⠿⣤⣀⣤⡿⠁⡼⠀⡇⢀⣤⡦⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠙⠁⡼⠁⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠾⠤⠤⠭⠿⠿⠿⠿⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⠶⣄⡀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣦⣤⣄⣠⣤⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣋⣭⣥⡀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⡄⠀⠉⠉⢹⡇⠀⠺⣿⠋⣿⠁⠐⢿⡇⢰⡏⠀⠺⣿⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠈⠛⠶⠞⠁⠀⠘⠳⠶⠛⠁⠀⠙⠶⠶⠋⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡴⠊⠁⠀⠀⠈⢦⣀⠄⠒⠒⠒⢄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⢀⣀⡀⣤⠤⠞⠁
⠀⠀⠀⠀⠀⡠⢛⣆⠀⠀⠀⢀⡄⠀⠀⠀⠀⠉⠀⡇⠈⢱⡀⠈⡆
⠀⠀⠀⢠⠞⡐⣁⠀⡀⠀⠀⠀⠈⠢⠀⣀⣀⡤⠞⠁⠀⡸⠁⡐
⠀⠀⣰⠃⠀⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠜⠁⠘⣄
⠀⠀⢇⠀⠀⠀⠀⠒⠖⠋⠉⠓⠠⢄⣀⣀⠤⠴⠚⢡⡄⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠱
⠀⠀⠈⠐⢠⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⡀⠀⠀⠉⠒⠠⠄⣀⢀⣠⠴⠋⡠⠀⠀⠀⠀⡐
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⣀⡤⠟⠒⠢⢤⣀⣀⣠⠴⠞⠁⣠⠎⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠒⠒⠠⢄⡈⢆⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠔⠒⠉⠉⠉⠉⠉⠲⣄
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⢲⠂⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡦⠤⢄⣀⣀⣀⣠⣤⣄⠀⠀⠀⠀⢸⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⡁⠀⠀⢸⠀⠀⠀⠀⢸⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠉⠉⠉⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⢤⣄⣀⣀⣀⣠⡤⠴⠒⠚⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⡀⠀⠀⢀⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣯⣬⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣒⣒⣦⣤⣀⣠⡤⢄⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠑⠒⠮⠥⣌⢻⡗⢦⢡⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⠀⠀⠀⢰⣖⡒⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠡⠇⡸⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⡢⢄⡀⠀⠀⡀⢴⡩⢉⢹⢎⠢⡀⠀⠀⠈⠢⣀⠀⠀⠀⢀⡰⠂⠈⣩⡶⠾⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡙⠒⠤⣄⡧⠞⠋⠀⠑⢌⡑⠸⠤⠤⠜⠁⢸⡉⢁⣀⣴⠞⡡⢊⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠈⠑⠒⠤⣈⠑⠢⣠⠀⠀⠈⢑⡶⠀⠐⠀⢠⣌⣙⠛⣓⣫⠴⢃⡀
⠀⠀⠀⠀⠀⠐⠤⣀⣤⣤⢴⣴⡒⣢⣀⣠⣄⣎⣩⣉⣳⣄⣈⣒⣂⡰⢙⣱⣋⣣⣳⣿⣏⣀⣉⣄⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠭⠵⣆⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠽⠈⠉⠀⠀⣠⠐⠀⠀⠀⢀⢴⣙⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣠⡺⠋⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠙⢴⡀⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⣶⣶⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠚⠉⠉⠀⠀⢠⣿⣿⢻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣻⠿⠽⠟⠗⠒⠒⠋⠉⡏⠨⠀⠌⠓⠢⡇
⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠈⠀⠌⠀⠀⠀⢨⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠂⠀⠀⣿
⠀⠀⠀⠀⢀⠔⠁⠀⡠⠁⠀⡜⢀⠂⠀⠀⣿⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠅⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡇⠐⢚⡇⠠⢀⣀⣣⣓⣤⣤⣤⣶⣤⣴⠀⠸⠇⠠⠀⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠾⠿⠀⣘⣛⣛⣋⣭⣭⣭⣥⣶⣶⣶⣶⣿⣿⣿⣿⣶⣤⠛
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⡠⠖⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠈⠃⠀⠀⠀⠃⢀⣙⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠁⠀⡨⠇⡠⠠⠔⠐⠲⠤⣄⠘⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣀⡀⠉⠋⠁⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣤⣀⣀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠼⠋⠀⠀⠀⠈⠷⢀⡀⠀⠀⠀⠀⠀⠈⠉⠓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢠⠞⡕⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⡆⠀⠉⠉⣱⠟⠂⠀⠀⠀⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢢⠑⠀⠀⠀⠀⢰⠏⠀⠣⣀⠀⠀⠻⠲⣀⠀⠀⠀⠀⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢠⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠜⠀⡀⢀⠀⠀⡏⠀⢠⠄⠬⡙⠒⠒⠈⠋⠁⢀⣀⣜⠀⠀⠀⠀⣯⠀⣀⡀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⡩⠭⣉⠙⡦⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡠⠖⠢⣀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⣈⠉⢈⣉⡼⠁
⠀⢀⠠⠤⠀⠀⠠⠠⠀⠀⠀⡀⣠⣲⠉⠙⣏⠉⠑⠔⠒⠒⠉⠙⠒⠀⠤⠤⠀⠀⠠⠤⠤⠴⠒⢾⠭⡀⢏⣉⢉⠉⠁⢸⠂⠁⠈⠒⠀⠀⠀⠀⠀⠀⣀⡀
⠰⡁⢰⣖⠆⠐⠀⠀⠑⠢⠠⡙⢁⡠⢤⣠⠬⡄⠢⣠⠔⠲⠄⠀⡄⠀⠒⠀⠀⠰⠖⠆⠀⢂⠙⡋⠙⢆⣠⠷⠈⠙⠒⠙⠲⠀⠀⠀⠀⠀⠀⠠⠄⢤⣲⠝
⠀⠙⢦⣍⣙⡒⠀⠤⠀⣀⣀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠉⣠
⠀⠀⠀⢻⡈⠉⠙⠒⠒⠀⠤⠄⢈⣉⡀⠐⠒⠂⠀⠤⠤⠤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠠⠤⠄⠐⠒⠀⢁⣀⡤⠤⠖⠒⣽⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠀⠤⠤⢤⣬⣉⣉⣉⣉⣉⠛⣉⣉⣉⣉⣉⠀⠠⠄⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⣤⠘⠙⠁⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⠋⠷⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣇⡔⠂⢀⢀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⢦⣘⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⠈⠉⠛⠀⠲⠶⠀⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⠴⠶⠒⠚⡇⠀⣨
⠀⠀⠀⠀⠀⠀⢠⠖⠊⠁⠀⠛⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠃⠀⠙⠒⢦⡀
⠀⠀⠀⠀⠴⢶⣿⣶⣧⣀⣀⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣀⣠⣷⣶⣷⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣠⠖⠉⠉⠀⠉⠙⠲⡄
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠻⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠼⠆
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢤⣀⣠⣀⠀⠀⠀⠀⢀⣠⡤⣄⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠀⠀⠀⣀⡀⠀⢀⡈⠛⠋⠛⠶⠋⠀⠀⠀⠉⢦⣤⣄⡀⣀⣀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠖⠒⠲⠤⠖⣒⠃⠀⠀⣴⡄⢀⡀⠙⠁⠀⠘⠋⠀⠀⠰⣶⠀⠀⠠⣶⠄⠀⠀⠀⠛⠁⠀⠈⠙⢦
⠀⠀⠀⢸⠀⠀⣀⡤⠞⠀⢰⡦⠀⠀⢈⡛⠀⠀⠀⠈⠀⠘⠋⠀⠀⣠⣄⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠘⠟⠀⠀⢀⣀⠀⠀⠚⠓⠒⢦⡀
⠀⠀⠀⢸⠀⡼⠁⠀⠀⠀⠀⠀⣀⠀⠙⠋⢀⠀⠐⠿⠀⡀⠐⠿⠂⠈⠁⣠⡀⠈⠛⢀⣀⠈⠛⠁⣀⡀⠀⢶⠆⠈⠉⢀⣄⠐⠿⠂⠀⢽⣤⣀⡀
⠀⠀⠀⣸⣀⣇⣀⣀⣀⣀⣀⣀⣛⣁⣀⣀⣛⣃⣀⣀⣘⣟⣀⣀⣀⣀⣀⣉⣁⣀⣀⣈⣋⣀⣀⣀⣙⣃⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣙⣆⣀
⠀⢰⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡆
⠀⠈⠳⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠞⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠛⠙⢻⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠋⡿⠛⠛⢏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⣶⠒⠒⣶⠶⡶⠶⡶⠶⡶⠶⡶⠶⠶⡶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⢶⡶⣶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠛⠉⠁⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣤⣴⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠊⠁⠀⠑⠤⠒⠢⣄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠒⠋⠀⠀⣀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⠚⠒⠒⠒⠚⠒⠒⠒⠒⠒⠤⠴⢄⠀⢀⠤⠤⠴⢄⣀⡠⠤⠔⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢀⠞⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠙⢆⠘⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿