Botanical Emojis & Symbols

⡀⠛⠀⠀⠀⠀⠀⠀⡀⠀⠀⣜⣿⡛⡁⠀⢐⣇⣤⠾⠃⢤⠀⣀⢀⠠⡌⠀⠀⠀⠉⠀⠀⠈⠛⠛⠃⠀⠇⠐⠘⡤⠄⢀⡄⣀⠁
⠁⠠⣄⠐⠂⠀⠀⠀⢿⣦⢸⣾⣿⡟⠃⠀⠸⠅⠀⠀⠀⠈⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠄⠀⠀⠀⠀⠻⠀⢁⠀⡈
⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⢸⡿⠏⠁⣀⣠⠄⠀⢸⣷⡄⠀⣀⣀⠀⠀⠰⠌⣰⠀⠀⠀⠙⠀⠆⢰⠀⠠⣀⠀⠁⢘⠀⠁⠀⠰⠆
⠀⢤⠀⡤⠀⠀⠀⠀⠘⣿⡝⡆⢠⠞⠋⠁⠀⠀⣶⣿⠿⣿⣿⠏⠀⠀⢈⠓⣙⠃⠀⢠⠄⠹⡆⠺⠆⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⣷⣤⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠉⠀⠶⢀⠾⠀⠙⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉
⠀⠀⠀⠛⠃⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⡀⠀⠈⢆⣠⠀⠀⠄⢁⠐⡄⡶⠘⢀⠘⠳⠄⠀⠀⠀⠠⠀⠀⡀⠀⡀
⠀⠀⢄⡀⠀⠀⠈⠰⠀⠀⠀⠰⠆⠀⠀⠀⡀⠀⣙⢀⣤⠀⠀⠈⠀⣄⠈⠃⡀⣸⠀⠙⠃⠀⠀⠦⠈⠙⠀⠀⠀⠀⠀⠀⡀⠀⠅⠠⠄
⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣘⡁⠌⠀⠄⠀⠀⠉⠉⠸⠟⣧⠐⢻⣅⠁⠀⡀⠄⠀⠀⢀⠀⠀⠀⠀⠰⠀⣤⢠
⠀⠈⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡴⠶⣶⠀⠀⠛⠃⠉⠀⠀⠉⠈⠀⣀⠀⠀⡀⠀⠀⠀⠲⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠻⣿⠧⣦⠀⠘⠀⠀⠀⠀⠀⠀⣈⠀⠈⠝⠂
⠀⠀⡀⠈⠇⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠐⢀⡄⠀⠀⣀⠀⠀⠀⠀⠀⢹⡼⠃⠀⠀⠐⠀⠁⠀⢁⠀⠀⠀⠀⠤
⠀⠀⠙⠀⠀⠀⡀⠀⠴⠛⣧⠀⠐⠢⢀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡆⡘⠀⠈⠠⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⡀
⣀⣀⣀⠀⠀⠀⠀⠀⢀⡘⣼⠆⢀⡀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠈⠀⠀⢸⠀⢸⠟⣠⣷⠇⠀⠄⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠁⠀⠘⠃
⣻⣽⣿⡇⠀⣴⠀⠐⠀⠀⠀⡐⠉⣅⠀⠀⠀⠁⠰⠄⠀⣤⠄⠀⠀⠀⠘⡇⡇⢀⢸⡏⢰⠁⢀⠀⠀⠀⠩⠱⠀⠀⠰⣿⣽⠂⣸⡆
⠉⠉⠉⠀⡼⠃⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⢰⡿⣄⡹⣡⠞⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⡈⠻⠀⢩⣷⡀
⣀⠀⠀⡾⠃⠀⠀⠀⠁⠰⠀⠀⠁⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⢹⡀⣧⢹⣤⡥⢀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠹⣄⠡⠈⣿⠄
⠟⠀⡾⠃⠀⠀⠀⠀⠀⡀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠀⠁⠀⢸⡀⠘⢺⠃⢠⠞⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠐⠻⣦⡑⢄⢘
⢀⠞⠀⠀⠀⠀⠘⠁⡈⠇⠘⠂⠀⠄⠀⠀⠠⠀⠀⠀⠀⣁⠁⠂⠀⠀⠀⠱⣄⣟⠴⠋⠀⠀⢀⠱⡆⠀⠀⠀⠀⠀⠀⣠⣄⡈⠛⢶⡙
⠀⠀⠀⠀⠀⠈⣐⠀⠈⠄⠁⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠈⠰⡠⠀⠀⠐⢲⣿⡥⠤⠄⠀⠀⠈⢇⠁⠀⠀⠀⠀⠀⠀⠙⠋⢀⡤⣤⣌
⠀⢠⣶⠀⠀⠀⢀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⣠⣄⡀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠘
⣀⣾⣿⣄⠀⠀⠐⠉⠀⠀⠀⠀⠂⠀⠈⠀⠐⠀⠀⠂⠀⠀⠐⠀⠀⢀⣤⣴⠄⠀⠀⠘⢯⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣿⠛⠙⠋⠀⠀⢀⡀⠀⠀⠀⠠⠄⠀⠀⡄⡀⠠⠄⠀⠀⠀⠀⡀⠀⠈⠁⠃⠀⠀⢀⣈⣉⠠⡀⠾⡮⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛
⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠈⠴⠉⡱⠛⠁⠀⠀⠀⠀⡄⠀⠁⣀⠃⠀⠠⡀
⡐⠀⠰⠀⠒⠀⠀⠐⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠠⠀⠐⠋⠀⢀⣡⡇⠀⢠⡄⠀⠂⠀⠰⡎⠱⠂⠀⣸⡄⣠⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣴⡀⠀⠀⠀⠀⠒⠄⠀⠠⠀⠀⠂⠀⠀⠀⠜⠙⡿⠧⣄⣻⣿⣆⠀⠀⠐⡀⠐⠦⢀⡤⢀⡤⠀⠆

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡄⠻⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣀⣰⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦
⠀⠀⠢⡀⠁⠀⠰⠀⠀⠀⠀⠀⣀⠸⠆⡀⠀⠀⠀⢨⢋⣽⣶⡛⠲⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠾⠄⡆⠘⠿⠞⠀⠀⠀⠀⠀⢀⣶⣾⣿⡄⠀⠀⠀⢀⣤
⠀⠀⠀⢹⠀⠀⠀⢠⠄⠀⠀⠀⣠⣌⢨⡂⠀⠀⠀⢨⡁⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠘⠛⡀⢠⣤⣤⠀⠀⠀⠀⢸⣿⣾⣿⣧⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠉⠀⠨⢍⠆⠀⠀⠀⢳⡀⠸⡇⠀⢀⠀⠀⠀⠀⢾⡧⠀⠀⠀⠀⠀⠠⣿⡞⠋⠉⠀⠀⠀⢀⣿⡏⢻⢁⣿⣷⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠒⡶⠀⠀⠀⠀⠈⢷⠀⠀⢠⠎⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠘⠢⣈⠙⠁⢸⡀⠙⠃⢠⠏
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡂⣿⠄⡇⣐⣔⠄⠀⠀⠀⠸⣷⣤⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡼⠑⠄⠀⠀⠀⠀⠙⣢⠀⢸⡏⠀⢀⡟
⠀⠀⢀⡀⠀⢳⢼⠃⠀⠀⠀⠁⣈⢭⣀⠀⠈⠇⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠐⡇⡘
⠀⠀⠀⠃⡐⢘⠛⠀⠀⠀⠀⠀⠀⠠⠈⢒⣀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣴⣾⡿⣯⡉⠛⠂⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠐⠯⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠋⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠃⠀⠀⠀⠀⠀⠀⢹⡇⣦⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣢⢄⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠤⠳⠂
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢶⣾⢢⠤⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⣶⣶⣤⡀⠀⠀⠀⠀⠸⡟⢿⡿⠂⠀⠈⣿⡏⠀⠀⠀⠀⠀⠂
⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠠⠈⠃⢫⡀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠟⢋⣤⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠠⠀⠘
⠀⠄⠀⠀⠘⣿⣟⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠛⣀⠀⠀⠀⠀⠐⠆⠀⠆⠀⠀⠘⠁⠀⠈⠈⠋⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠠⡄⠀⠀⠋
⠀⡀⠀⣠⣀⣁⡀⠉⠀⠀⠀⠾⠄⡀⠀⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠠⣿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠉⠉⠀⠀⠀⠈⠏⠿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐
⠀⠄⠀⠻⠟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠂

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠆⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠘⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⢁⠈
⠀⠀⠀⠀⠀⠀⠀⢺⡇⣰⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠘⠃⠛⣃⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣸⣧⡆⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠘⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣠⡟⢠⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠜⢁⠂⠤⢂⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⢷⣾⡿⠿⠋⠀⣠⠉⠾⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⢀⠀⣸⣧⣩⣤⡌⠉⠃⠀⢽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⣴⢫⣟⠰⢆⣿⡟⠋⣩⡀⠗⠂⠀⠃⠀⠐⣰⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⡿⠃⠂⠀⠁⢻⣈⢉⠉⠀⢠⣽⣀⠾⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣃⢲⣀⡀⠀⠸⡿⠇⠰⠀⠀⣰⣥⡆⠁⣶⣄⣈⣹⠀⠀⢠⠉⠉⠀⠀⠀⠀⠀⠀⣼⠏⢘⠁⠀⠀⠀⢶⣟⠛⡉⠁⠡⢀⡿⠟⠛⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⡴⠻⣇⡙⠀⠀⠄⠀⡀⢠⡌⢻⠁⠶⠄⢀⡉⢻⠆⠀⡜⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⢠⡄⢀⡾⡇⣾⣧⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⣴⠾⠧⠀⣤⣄⣾⣧⡈⠀⢸⠀⠀⠀⠨⠑⠼⠀⠀⠁⠀⠀⠀⠰⡋⢙⡄⢀⡤⠀⠀⠀⢊⣱⡁⠀⠑⡶⠚⢁⡾⠉⢳⣿⣧⣶⣄
⠀⠄⠠⣄⢀⣀⡀⠀⣶⠃⠀⢴⣟⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⢠⠃⡀⠀⠀⠆⠀⠀⠀⠀⢀⠏⠀⢰⣴⡆⣾⣾⣧⣜⣿⡇⠿⣙⡆⡈⠀⠀⡾⠁⣰⣶⣶⡯⣿⣥
⠀⠀⠀⢨⠛⠻⣇⡀⠁⠀⣡⣶⠒⣻⣶⢀⣺⣿⡿⠀⠂⠀⢰⡇⠀⠹⣦⠀⡄⠀⠃⠀⠀⠸⠆⠀⢘⣿⣧⣾⡿⣿⣿⣷⣄⠀⠼⠏⠿⢀⡞⠀⣠⣬⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠻⠄⣠⣶⠟⢸⠏⠈⢻⣾⣿⡟⠧⠀⢲⡀⢼⠃⠀⠀⠨⣧⠀⣀⣀⠀⠀⠒⠀⠀⠋⢹⣿⣿⣿⡟⢹⣿⣿⣷⡄⠀⢀⡼⢶⣰⠿⠇⠀⠁⣿⡀⠔
⡀⠶⠀⣀⠀⠀⠀⣹⣿⠁⢀⡿⠀⠀⠋⢦⠽⠀⠀⠆⢀⣁⣾⠀⠀⢀⣤⣌⡠⣿⣇⣴⡄⠀⠙⢀⣰⣿⣿⣿⣿⡇⠛⢹⣿⡟⢻⣀⣾⣻⠿⠁⠀⠶⠠⠀⣩⣴⡇
⠀⠃⣘⣡⡄⠀⠠⠙⢻⣆⡠⣄⠀⠀⣠⣴⣶⣶⣤⣾⣝⣿⣿⠓⠀⠘⠛⢻⣅⢘⡘⣿⡇⠐⠶⢾⣻⠻⠿⣿⡿⢯⣤⣿⢘⠁⢘⣿⢿⣿⠶⣀⣴⣧⣴⣾⡿⠛⣷
⠀⠀⢸⡿⡉⠶⠦⣤⣾⣧⠀⣼⣿⠁⠀⣾⡇⠈⠙⠻⡿⢿⣿⠀⠀⠀⠀⠺⡿⢚⢠⣿⣷⣄⠀⠀⠟⠓⠘⠋⠀⠘⣿⠋⠀⣰⢟⣵⣾⣞⣳⣿⣿⣿⣿⣿⡿⢿⡿
⠀⠀⠀⠘⠀⡇⠈⢢⣿⡟⠸⣿⣿⠀⣾⣿⠁⠀⠀⠀⢱⠀⣿⠀⠀⠀⠀⠀⡶⠋⣡⠆⠹⠋⠀⢸⠀⠀⠀⠀⡀⠈⠁⠀⠀⢡⡾⠛⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣧

⠀⢀⣀⣤⣀
⠀⢹⣟⣿⠿⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠉⣠⣭⣿⣿⠿⣖⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠀⠔⠈⣩⣈⢿⣿⣀⣿⡥⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠳⣀⣄⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡾⠻⢩⠟⠀⠩⠛⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⣷⡁⠉⠀⠀⣠⡄⠐⠀⠀⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⡎⠒⠋⠀⠀⢠⣄⣤⠀⠀⣀⠀⠀⠀⠀⠛⠀⠀⠀⣀⠅⣤⠄⠀⢐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⢀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠦⢻⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣅⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠓⠉⣁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⣴⣦⣴⡆⠀⠀⠀⠀⠀⠈⠁⠉⠙⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⡍⠢⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣍⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠈⠁⢤⠽⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⠏⠀⠀⠉⠘⠂
⠀⠀⠀⠀⠨⢁⠀⠀⠀⠨⢳⡌⢂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠧⠀⠀⠀⠚⠁⢀⠀⢀⡤⠀⠀⠀⠋⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⣘⠃⠰⣂⠀⠀⠀⠈⠶⡀⠈⠉⠀⠀⠀⠛⠁⠀⠀⠂⠠⣀⠀⠀⠀⠀⢉⡤
⠀⠀⠀⠀⠛⡓⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠈⠛⠁⠰⠄⠀⠀⠀⠀⠃⠉⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⢤⡄
⠀⠀⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠠⡀⣶⣿⣿⣷⡴
⠀⠀⠀⠀⢰⠀⠀⠀⠀⢿⡆⠈⢁⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠹⣀⠀⠀⠀⠻⠀⠀⠐⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⠴⠶⠷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠲⣤⣤⣄⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⡀⡀
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠙⣋⠈⠛⠙⢶⣄⡀
⠀⠀⠀⠈⠐⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢦⡄⠀⠀⠀⠀⠀⠐⢂⠺⠄⠈⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠄⠀⠀⢀⠀⡠⡾⠎⠙⢷⣧⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠂⠻⠀⠀⠀⠀⣸⣼⣗⠀⠀⠀⠀⠈⠃⠀⢀⠀⠀⢄⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠄⠉⠉⡆⢠⠇⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠻⢷⡾⣿⣿⣿⣷⣶⢀⠀⡀⠀⠿⡟⠀⠀⠀⠀⠀⣼⣿⣴⡶⠴⠞⠀⠂
⠀⠀⠀⠀⠐⢤⡀⠛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡌⠀⠀⠉⠙⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⣿⠟⣻⣟⠀⠀⠀⠀⠁⠀⠋⠻⣷⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠙⡧⠀⠀⠐⠀⢰⣿⢛⣿⣿⡦⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡀⠀⠀⠀⢺⣿⣿⣿⣿⣷⣾⣄
⠀⠀⠀⠀⠀⠀⠈⠵⢷⣄⣀⣀⠀⠀⣀⣀⡑⡀⠀⠀⠀⠀⠀⢀⡀⠑⠀⠐⠀⠄⠈⠁⠨⣽⠿⡿⢳⣯⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠤⣿⣿⠉⢯⡄⠈⢻⣷⣦⡄⠀⠀⢀⠤⠛⠓⣸⠓⠀⣀⠴⠂⠀⢄⣁⢈⡗⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠁⠈⠁⠀⠈⠁⠙⣿⡌⠂⠀⠈⠀⣀⣉⠄⠀⠉⠓⠀⠀⠀⠀⠀⠉⠓⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⢹⣟⠂⠀⠐⠋⠉⠛⢻⡆⢀⣀⣤⡄⠸⢤⣴⣤⣤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⠛⣦⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣛⣙⣻⣉⡟⢻⡟⣹⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠘⠛⠀⠀⠀⠀⢀⣺⣿⠄⠀⠀⠀⠀⢀⡦⣶⣦⠀⠀⠀⠀⢨⣅⣀⠀⠀⠀⠀⠀⠘⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡬⠄⠂⠀⠀⠀⠀⠉⠉⠀⠀⢰⢂⡀⠀⠳⠞⠻⠄⠀⠀⠠⣼⣿⣷⠆⠀⠀⠈⠀⠀⠀⡄
⠀⠀⠀⠐⠀⡀⠀⠐⠦⡜⣻⡄⠀⠀⠀⠀⠀⠀⠀⠲⣷⣮⠦⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡂
⠀⠀⠀⡀⠠⠁⠀⠀⠈⠁⠈⣤⣦⠀⢀⡀⠀⠀⣄⠀⠉⠙⠀⠀⠀⠀⢀⠀⠘⠷⣴⠁⠀⠖⠀⠀⠀⡀⠀⠀⢸⡳
⠀⠀⠀⠨⠀⠈⠀⠀⠒⠴⠂⡈⠁⠀⠈⠁⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠈⠃⠀⠀⡄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡤⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠤⠈⠀⢀⠤⠀⡀
⠀⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠴⠷⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠰⠀⠸⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⡀⠛⠀⠀⠀⡀⠀⠊⠁⠂
⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢬⠔⠀⠀⠀⠀⠀⢤⠀⠀⠀⠒⠀⠱⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⣳⢜⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⡀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠙⠒⣄⠀⠀⠀⠀⢠⡬⣷⠂
⠀⢘⠀⠀⠀⠤⢹⡈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⡘⠀⠀⠀⠂⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⡃⣠⠀⠀⠀⠀⠀⠐
⠀⠸⠀⠀⠀⠀⠀⠁⡄⡀⣘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⡁⢰⠁⡄
⠀⠀⠄⠀⠈⠂⠀⡌⠀⣷⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡈⠁⢰⠇⢀
⠀⠀⠀⠀⠀⢀⢀⡈⠙⢁⠀⠰⢧⠄⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠈⠑⠉⢀⡜
⠀⡀⠀⠀⠀⠐⠝⠈⠀⠘⢁⠘⣀⢀⢎⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢁⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠠⠋⢀⣀⠄
⠀⠀⠠⠀⠀⢁⣠⢀⠑⢦⠊⠀⠟⠣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⠠⡀⠂⠀⠐⠀⠀⠀⠀⡀⠀⠈⠉⠑⡐⡠⢀⡐⠉
⠀⠀⠀⠈⠀⠢⡅⠁⠀⢸⠀⠀⢰⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢧⠂⠀⠀⡐⠂⠁⠀⠣⠐⠙⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠐⢺⣤⡄⠀⠀⡄⠀⠀⢙⢁⠖⢢⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⣷⡤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⣡⠤⠀⠀⠀⡀⠚⠀⢠⡆⣈⠀⠛⠋⠠⠈⠀⠀⠠⠁⡄⠀⠒⠛⠢⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠤⣤⢡⠤⠖⠀⠀⠀⠀⠀⠀⢣⡄⢠⢁⠀⡴⠐⣆⠀⣰⠤⠘⠀⢀⠀⠀⠀⠀⠀⠀⣄⠱⠵⠄⠀⠀⠀⠀⠂
⠀⠀⠀⢸⠇⠀⠀⠀⠀⢢⡭⠥⠀⠀⠀⠀⡀⡀⠁⠀⠠⡤⠀⠀⠀⠠⠶⠦⠄⣁⢤⡴⠃⠐⠃⠌⡏⠀⠁⠀⡀⠀⠀⠀⠀⢀⡄⠈⠳⠒⠂
⠀⠀⠀⣸⠂⠀⠀⠠⣄⠻⢚⣁⣀⠀⠀⠈⠉⠉⠃⠀⠁⠀⡀⠀⠀⠀⠀⠀⢵⠆⢚⠀⠰⢶⡈⢤⣤⣅⡀⠁⠂⠀⠀⠀⢀⠈⠀⠁⠠⠐⠐
⠀⠀⠀⡿⠀⠀⠠⣀⠈⠛⣉⣅⡤⠂⠐⠀⠀⠀⠀⠀⢰⠐⠁⠀⠀⠀⠀⠂⠀⡘⠙⠛⣤⠌⠤⠊⡇⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⢆⡰⠿⠓⠤
⠀⠀⢰⠃⠀⠀⣀⡘⠷⠿⠗⣀⣀⣀⡀⠈⠙⡢⡠⡀⠂⠒⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⡉⢂⠀⠃⠀⠷⡈⡈⠁⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠙⢲⣷⡾⢙⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠑⠀⠀⠠⠈⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡩⡿⠟⠿⠿⠿⠿⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⡀⠀⡀
⠀⠀⠀⠀⠀⡀⡴⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢹⠤⠃
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠦
⠀⠀⠀⠀⠀⠿⠀⠀⢰⠂⠀⠀⠀⠀⠀⢴⣆⣀⣀⡀⠛⠂⢄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⡀⣀⡜⠀⠀⠀⠀⠀⠀⣀⠟⠋⠈⠛⣦⡀⠘⠇⢸⠙⠁⠀⠀⠀⠀⠀⠈⠉⢁⡄
⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠀⠈⠟⠃⢀⡴⠆⠈⠃⠀⠰⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠃⢉⣄⣀⣀⣤⣤⣄⠙⠁⠀⠀⠀⠀⠀⠀⣄⠒⡟
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⣴⠦⠂

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠷
⠀⠀⠀⠀⠀⠀⢠⣾⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠌⢓
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⢨⣿⣿⣷⡆⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣴⣾⣿⡆⡠⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⡻⠛⡛⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⢀⢦⡀⢀⠀⠀⠀⠀⠀⠀⠤⣾⣿⣿⡿⠆⠀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠐⠦⣤⡀⠀⠀⠀⠈⠂⠸⠃⣀⣀⠄⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⡴⠖⠒⠂⠀⢠⡄⠈⠁⠀⠀⣀⣀⣀⡀⠀⠀⣤⣴⣶⣤⡀⠀⠘⠋
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠿⢿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣂⡴⠆
⠀⠀⠀⣴⠞⠏⠉⠉⠀⢀⠠⠖⠒⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠀⠀⠀⠀⠀⢀⣠⣬⣇⠿⠁
⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠋⠁⠀⠀⣠⣀⡀⡊⠁⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⣾⣷⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣄⣠⣴⡞
⠀⠀⠀⣠⢰⡔⢃⠛⣷⠄⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠤⣀⠀⠀⠀⠄⠀⠀⠀⠸⡟⢯⣀⠄⠀⠘⣹⠟⠉
⠀⠀⠀⠉⣈⠁⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⢠⢓⣿⣿⢀⣾⠃
⠀⠀⠀⠡⠜⠁⠂⠘⠃⠀⠀⠀⠀⠀⠀⢀⡀⢲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠘⠿⢿⣿⡿⠷⠒⠳⢦⢤⡀
⠀⠀⠀⠀⠚⠻⡿⢤⡆⠀⠀⠀⠀⣀⡆⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠙⠉⢢⡀⣄⠀⢀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢫⡉⠀⠀⠀⠀⠀⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠰⣤⣶⣤⡀⠀⠀⠀⠀⣰⠋⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠐⠉⠀⠉⠈⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠛⠀⠀⠒⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢀⡄⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣴⢧⠀⣶⡆
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⣸⡃⠀⠀⡠⠤⢄⡀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠺⣧⡘⡰⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣲⣾⣿⣃⣈⣿⣯⣷⣄⡎⠀⠀⠀⠙⣷⣤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⡀⢰⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⢻⣿⠟⠂⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀⢰⠞⢃⠀⠀⠾⠋⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⠟⠁⣿⡿⠇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠏⠀⠀⠀⠠⠈⠻⠆⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠺⣿⡴⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣠⡤⢄⣴⡶⠰⠟⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠃⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⠉⢠⣄⣡
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⠃⡠⠘⠿⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⡄⠀⠀⠀⠈⡇⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠰⣶⠆⡀⠂⠒
⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⢿⡇⠀⠀⠀⠀⠀⠀⢀⡘⠃⠀⠁⠀⠀⡄⠀⡇⠀⠀⠀⢺⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⣤⣤
⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠋⠠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠓⠟⢋⣈⡀⣄
⠀⠀⠀⠀⢘⠂⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠰⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣼⠿⠛⠁
⠀⠀⠀⠀⠞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⢰⡄⠀⠀⠀⢀⡟⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣄⡀⢰⠀⠀⠀⠃⠰⠖
⠀⠀⠀⢐⡋⠁⠀⠀⠀⡀⠰⢷⡇⡀⢀⠀⠀⠀⠿⠀⢱⠀⠀⠀⣼⠃⠀⠀⢀⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡃⠀⠀⠀⠢⢀⣠⠿⠁
⠀⠀⠀⠨⠧⠀⠀⠀⠀⢱⣠⣿⣇⠃⡈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠿⠀⠀⠀⣸⠃⠀⠀⠀⢸⣿⣻⣻⠀⢀⠀⠀⠀⠘⠫⠁⠀⠀⠀⠀⠘⢃⠰
⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢳⡿⢷⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁
⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠲⣀⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢠⠤⣬⣄⠀⠀⠀⠄⠀⠀⢠⠈⠀⠀⢠⠀⠀⠀⣀⠀⠈⠀⠈⡄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⡏⠀⠀⢀⣀⢠⣶⡋⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣏⢰⣿⣷⣔⣤⠀⠀⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣜⢣⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⠈⠻⠛⠻⠿⣧⠄⡀⠀⠀⢸⡇⡈⠀⠀⠀⠀⢠⠀⢹⠶⠬⠆⠀⠀⡀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡀⠀⠀⠘⢋⠀⣷⠀⣾⠷⠐⢏⣴⡁⠀⠀⢸⣇⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⡄⢰⣿⠐⣁⣀⡒⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢛⡶⠚⠋⢁⡁⠀⠀⠀⣿⠀⠀⠀⡀⠀⣄⣠⣀⡀⠀⠀⡄⠀⠉⠉⠁⠈⠙⠓⠄
⠀⠀⠀⠠⠴⠶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢣⢶⣦⠀⣠⠀⠀⠀⡿⠀⠀⢠⣾⡿⢿⡿⠀⠜⣶⣴⡇
⠀⠀⠰⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⣾⠉⠀⠀⠀⠇⠀⠀⢠⢉⣿⣿⠳⠀⠖⠁⠈⢈⡃⠀⠀⠀⠀⢀⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠂⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢠⢽⣿⠈⠈⠀⠀⠀⠀⠀⠁⠀⡀⠄⠀⠈⠈⡄
⠀⠀⠀⠀⠀⠈⠀⠀⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢑⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠠⠖⢁⡤⡄⠆

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀
⠀⠀⠀⣰⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⡀⠀⠀⠀⢰⡇⠀⠀⠀⠠⡀⠄⠈⠄⠀⠀⠀⠀⢠⣾⣿⠄
⠀⠀⠠⣛⣻⣿⠯⠄⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠨⠀⣀⠐⠁⠀⠀⢸⣿⣿⣷⢆⣀
⠀⠀⠨⣶⣻⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⢈⠉⠠⢀⡀⠀⠠⢬⣭⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠶⣿⣿⢷⣛⣋⠩⠤
⠀⠀⠈⣹⣿⡯⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⢹⠀⠠⠀⠀⠀⠀⠂⠀⠀⠐⠮⢭⣻⣷⣛⣭⠤⠖⠚⠁
⠀⠀⣐⢿⡿⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⣾⣭⡽⣓⣞⣭⠭⠁
⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⣈⣹⣷⡹⠶⠶⢒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⢷⠖⠀⠀⠀⠠⣬⣭⣅⣛⣉⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠤⠤
⠀⠀⠀⠀⠀⣰⣧⠀⠀⢠⣇⠀⠀⠀⠀⠸⢧⠄⠀⠀⠀⢸⠀⠀⠀⣠⠀⠀⠀⠈⢢⠀⠀⠀⡇⠀⢰⣿⡷
⠀⡀⠀⠀⠀⣽⣟⠀⠀⠈⡏⠀⠀⠀⠀⠘⠐⠀⣠⠀⠀⣸⠀⠀⠀⢹⡄⠀⠀⠀⢸⠆⠀⠀⠇⠀⠀⠘⢆⠀⠀⠀⢸
⠀⠄⡂⠀⠀⠛⡯⠀⠀⢸⠇⠀⢠⡄⠀⠈⠀⠁⠀⠀⢀⣿⣆⠀⠀⢸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣁⣭⣿⣿⣾⣿⣿⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣉⢻⣿⣿⣿⡿⠟⠉⣙⡛⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡆⠻⠞⢛⣋⢠⣴⣾⣿⣿⣿⣷⣜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢀⠛⢻⡿⠟⠋⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠑⠽⠿⠿⠖⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠙⠲⠀⠀⠀⠀⠤⠖⠢⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣤⣤⡲⠀⠀⡴⣠⣤⣀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠛⠁⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣁⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⣹⣷⡆⠀⠀⠰⣞⠛⠛⢳⣦⠀⠀⠀⣷⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡄⠀⠀⠉⠛⠛⠋⠁⠀⠀⣰⣿⣿⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣟⠻⣿⣶⣬⣝⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠙⣿⣧⠀⠀⠀⠉⠉⠉⠙⠋⠻⣿⣿⣷⣞⠙⢿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣿⣿⣏⣸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡻⢿⣇⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠉⠺⢿⣿⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⣲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢟⠿⠟⠋⢡⣴⣞⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠠⡑⡄⢈⠿⠋⠙⣷⣄⠀⠀⠀⠀⠀⠌⠀⠀⠖⠀⠐⢛⣻⢯⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠀⠀⠀⢀⣾⠿⠆⠀⠀⠀⠀⣀⡀⠀⠀⠐⣤⣀⢈⠉⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠸⢫⠉⠀⠀⠀⠛⠋⠐⡄⢸⣿⣿⣿⣿⡏⡇
⠀⠀⠀⠀⠀⢘⠁⠨⡽⡆⠀⣠⣤⣄⣸⣿⣿⡟⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣹⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⡋⠑⠚⢿⣿⣿⡆⠀⠀⠀⢈⣀⠔⢀⡀⠀⠀⠀⠀⢠⡝⠛⠉⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢀⠀⠘⠀⠠⣯⡇⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠈⠠⢤⠄⠀⠀⠀⠀⣼⠇⠀⠀⣿⣿⣿⠿⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⣄⠋⠄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⣿⡏⠀⠀⠀⣿⠿⠋⣰⡿⠿⠦
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠐⠿⡿⢱⣦⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⠾⠿⢿⠁⠀⠀⠘⠃⠀⣰⡿⠁
⠀⠀⠀⠀⣀⣤⠀⡎⠏⠀⠔⠺⠛⠁⢸⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠑⢤⠀⠀⠀⣰⡿⠁
⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡸⣼⠆⠀⣰⡿⠁
⠀⠀⠀⣯⣿⣇⠀⠀⠀⠂⠠⠀⡠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣷⣷⠀⣰⡿⠁
⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⢀⣾⣣⣿⠷⣿⢯⠯⢭⣵⣿⢿⣫⣿⣿⣿⠟⠋⠀⣼⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣾⢝⣾⡟⣸⣇⠃⠠⠿⠟⠖⠋⢱⣟⠟⠁⢀⠀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢆⠑⠀⢀⣶⠛⣯⣿⣿⠃⢹⡽⡣⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣸⢻⣻⡿
⠀⠀⠀⠀⠀⠢⡀⠸⣏⣾⣿⣇⢟⣴⡷⠉⠈⠁⠀⠀⠀⠀⡄⢀⠀⡐⠀⠀⡏⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⠈⠉⠿⢿⢶⠫⠿⠁⠀⠀⠀⠤⠊⡀⠂⠈⡆⠀⠀⠀⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠉⢳⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡤⠀⠀⠀⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⢤⡀⡀⠀⠀⣀⡀
⣀⣾⡞⣧⣀⠀⠀⢀⠀⣠⢹⡆⠀⢸⡄⠀⠀⠀⣶⠹⡦⣤⢀⣠⣧⡄⠄⣾⣆⣀⣷⢸⡇⠀⡄⣿⠉⠙⣿⠄
⠙⣿⡧⠿⠟⠶⠿⣾⣷⣿⣿⠃⣴⣾⣇⠀⣠⣼⢿⣾⡿⡋⠅⠀⠀⠀⠀⠀⠀⠉⠛⢾⣿⣷⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⣿⡿⣋⠔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣍⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⡇⠀⣀⣠⠴⠶⠤⠤⡀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⢉⠛⠋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡢⣄⢀⡀⠇⡼⠉⢀⠃⣃⡝⡲⡙⢦⠒⣀⣀⣼⠏⠀⡠⣤⣤⡄⠁⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣖⠍⡂⢶⣿⠀⠛⡰⣯⣷⡒⣦⢸⠿⠿⢿⡇⠀⢘⠉⣟⣷⡘⠀⢸⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠺⠤⠼⢿⣆⠐⢆⣸⣈⡴⠏⡈⠀⣀⣈⣧⡀⠘⢄⢘⡉⠌⢠⠈⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠲⠤⠄⠐⠛⠛⠿⠿⠟⠛⠛⠢⠤⠤⡤⢴⠾⠾⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠀⠀⠒⠂⠠⠌⠋⠙⠫⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠋⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢶⣶⣤⣴⣄⣄
⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⠀⠀⠐⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣇⠀⠤⠸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⣿⣿⣿⣿⡀⠀⠀⠿⡿⠇⢠⣤⣶⠀⠀⠀⠀⠀⠀⢀⣀⡺⣿⣿⣿⠯⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⠙⠙⠿⠃⢀⣀⢤⣤⣤⣾⣿⠿⠁⠀⠀⠀⣠⣰⠋⢙⣿⣽⣿⠟⣀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣾⠛⠉⣽⣿⣿⠁⠀⠀⠀⠀⣠⣌⣻⡟⠲⠆⠉⠈⠻⠟⢯⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠈⣹⣿⡇⠀⠀⠀⠀⣉⣙⠋⠳⠀⠀⢠⠀⠀⠀⡉⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠀⠀⠀⠀⠙⠛⡠⠦⠀⠀⠈⢳⡄⢾⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣤⣄⢁⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⢾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡆⠀⠀⠀⠀⠀⠈⠐⣶⡄⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣿⣿⣷⠀⠀⢀⡀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡧⣿⣿⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⢻⣿⣧⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢹⣿⣿⡆⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠶⡰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⡑⢿⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢧⣼⠟⣻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣆⢹⠆⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡡⢚⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠛

⠁⠀⢀⠈⢀⠈⠀⠀⡀⠁⡀⠀⠀⢐⠈⢐⠀⠀⠀⡀⠁⡀⠀⠈⢐⠈⢀⠀⠀⠁⡀⠁⡀⠀⠨⢀⠈⢀⠀⣀⣁⣠⣤⣦⣤⣬⣀⣨⣀⣥⣀⠁⡀⠁⠈⠀⠨⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢈
⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠠⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠀⢀⢠⣼⣿⠿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣯⢻⣆⠀⢐
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠀⠀⢀⣾⡿⣣⣾⣿⣿⠟⠋⠉⠉⠙⠛⠛⠛⢿⣿⣝⢿⣰⣿⠀⠐
⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡠⠤⡀⠀⣼⢻⣳⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢾⣿⣿⡇⠠
⠄⠀⢐⠠⢐⠠⠀⠄⠀⠄⠀⠀⠀⢐⠠⢐⠀⠀⠀⠂⠄⠀⠀⠠⢐⣀⣐⠀⠀⠸⣄⣀⡸⢀⣿⣼⡿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⠃⠠⠀⠠
⠀⠀⠐⠠⠐⠀⠀⠀⠀⠀⣀⡴⠶⠒⠛⠛⠛⠒⠂⠂⠄⡠⠖⠉⠉⠉⠉⠉⠒⢄⡂⠁⠀⠰⣿⣿⢧⣿⣿⠠⠦⣄⡀⠀⠀⣠⠴⠛⠃⠀⠀⢿⣿⢿⣿
⠀⠀⠠⠀⠀⠐⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢨⣿⣿⣼⣿⡷⠖⣾⡟⠣⠀⠈⠑⠺⣿⠟⠗⠀⠈⡅⠉⡟
⠀⠀⠈⠀⠈⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣷⠀⠐⠀⠐
⠀⠀⠀⢀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣵⣿⡆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⣿⣆
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⣾⣷⣿⣿⣿⠨
⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⢿⢿⠟⠁⠀⠀⣠⣾⣿⣿⣿⣇⠛⠈⠀⠈
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⢾⣿⣿⣿⣿⣿⣿⣦⢈
⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⢰⣝⣯⣻⣿⠟⠻⡎⢳⠒⠒⠋⠀⢸⣿⣯⢿⣿⣹⣿⣿⣷⣨⣀
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠁⠀⠀⠀⠀⠉⠉⠛⠻⠟⠃⠀⡴⠁⠀⠁⠀⠀⠀⠀⠙⠻⣧⣿⣷⣿⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠒⠒⠒⠒⠒⠒⠈⠁⠁⠀⠘⠟⠀⠀⠀⠀⠀⠀⣈⣿⢹⣿⣧⠟⣿⣷
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡀⢀⣀⠀⠤⠤⠔⠒⠒⠈⡅⠀⠀⠀⠀⠀⠀⣠⡴⢁⡼⢿⡏⠀⠛⣿
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣀⣀⠄⠴⠈⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⢾⣿
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⣀⠠⠠⣶⣷⠀⠀⠀⠘⠄⢔⡈⠒⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠉⠉⠀⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷
⠀⠀⢀⠈⢙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⠛⠢⣀⠀⠀⠀⠀⡄⢀⠞⣿⣿⠋⠙⣿
⠄⠀⢐⠠⢀⠠⠀⠍⡉⠍⡃⠘⠊⢐⠠⢘⠢⣄⡀⠀⠀⠀⠀⢀⣠⠠⢀⠤⠤⠤⡤⠶⣷⠀⠀⢸⠀⠀⠀⠀⠀⢳⣿⣿⣷⣶⣿⣷⣄⢣⣸⢠⣷⣾⣿⣿⣷⣾⣿
⠀⠀⠐⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠉⠛⠛⠛⠙⠉⠐⠀⠐⠀⠀⠀⠀⠀⠘⡀⠀⢸⠀⠀⠀⠀⠀⠈⡋⠉⣿⣿⠋⠉⣿⣦⣿⠉⣿⣿⠋⠙⣿⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡄⠀⠀⡎⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠰⠆⢀⣄⠀⡀
⠀⠀⠀⠈⠁⢲⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⡀⠈⠉
⠀⠀⠀⠀⣶⢈⠀⠀⠀⣀⠀⠀⠀⡡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⠀⠀⠀⠙⠁⠀⢂
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠠⠀⠔
⠀⠀⠀⠀⠺⠒⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢴⡄⠀⠀⠀⢄⠀⠐⡃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⢂⠈⣡⢊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⢀⠄⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠊⠉⠀⠀⠀⠀⠀⠀⢐⠀⡀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⢾⠢⡒⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⡏⠀⠐⠀⠀⠄⠀⠀⢀⡔⡉⢙⠒⠃⠈⠀⠀⠀⠘⠿⠧
⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢃⡀
⠀⠀⠀⢤⡀⠂⠀⠀⠂⠁⢄⣳⣤⠀⠀⠀⢀⣼⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠟⠀⠀⠀⠀⠺⠓⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢬⠶⠘⠀⠀⠀⠙
⠀⠂
⠀⠄

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⣿⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⣠⢶⡿⠇⣠⡔⠶⣖⠀⠀⠀⠀⠀⢀⣤⣶⡶⠆⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠈⣁⠉⠚⢠⣦⠈⠀⠉⠀⣶⣿⣿⡻⠆⠀⠙⠃⠀⣶⠟⠋⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⢠⠈⠉⠠⡿⠀⠀⠀⠠⠀⠉⠉⠁⠰⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠈⠄⠀⠈⡧⡀⠀⠀⢀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠈⠃⠰⠃⠈⡀⢀⣬⠀⠀⠠⡄⠀⠁⠀⠰⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⠁⢁⣤⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣴⣾⣿⢟⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠛⠁⠚⠟⠋⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⢠⡄⠤⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠗⠈⠛⠘⠇⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢨⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠐⢠⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠠⣤⠉⠙⠋⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⣤⣤⣼⡇⠀⢠⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠀⠀⢁⣼⣿⡶⢾⣯⠟⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠞⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⠴⠦⠶⠶⠾⠿⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⣣⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠋⠀⢁⡄⠀⣷⠀⠀⠀⢠⡤⠘⠉⣀⣭⢴⠀⠀⠀⢰⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢷⣄⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠄⠀⠀⢺⡇⠀⣿⠀⠀⠀⢀⠀⢠⣾⣿⣦⡇⠀⠀⠀⢸⡟⠀⠀⠀⣠⣄⠈⠛⠛⠃⣤⣶⣤⣤⣄⠘⡃⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠠⣄⠸⠣⠀⣿⣶⣄⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠛⠉⠁⠀⢀⠀⠀⠛⠛⠉⠻⡧⡇⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡄⠀⢠⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠁
⠀⢸⣿⠀⠀⠀⠀⣤⠀⠀⠸⠧⠀⠰⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣬⣍⣄⣀⣉⣧⡀⠀⠀⢸⣠⣤⣀⣤⣀⣶⣦⣼⣿⣿⣿⣿⣦⡀⠙⢷⣆⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠟⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠏⠀⠠⠐⢂⡀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠲⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡆⠀⠀⠀⠈⠀⠈⡀⢠⣈⠻⣶⣤⣤⣤⣤⣦⣴⣤⣴⣾⠏⠁⠀⠈⠃⠀⠀⣿⠄
⠀⢸⣿⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠀⢰⣷⠀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠇
⠀⠘⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⢻⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⣼⡿⠋⠀⣾⣿⠿⠎⣹⣿⣿⡇⠘⡿⣿⣟⠈⠻⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢠⣾⠿⠁⠀⣴⣿⠃⠀⢀⣿⣿⡏⠉⢹⣿⣿⣿⠀⠀⢻⣿⣿⡁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣶⣿⠟⠀⢀⣼⣿⡏⠀⠀⣾⣿⣿⠁⠀⢠⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠂⢾⣿⡟⠀⠠⣾⣿⡿⠀⠀⢸⣿⣿⡟⠀⠀⢸⣿⣿⣿⡄⠀⠈⣿⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢠⣿⣿⠁⠀⢲⠋⣻⠗⠀⠀⣼⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⣿⣿⡆⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡗⠀⣿⣿⡇⠀⢠⣿⣤⣿⠀⠀⠀⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣾⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⢠⣿⣿⠇⠀⣸⣿⣾⣏⠀⠀⢈⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠨⣯⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢈⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢐⣿⣿⠄⢸⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢼⣿⣿⣿⡗⠀⠀⢰⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠘⣿⣿⠀⠀⢿⣿⣿⣇⠀⠀⢘⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡗⠀⣿⣿⡄⠀⢸⣿⣿⣧⠀⠀⠀⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣾⣿⣷⠦⠨⣿⣿⣿⡀⠀⠀⢸⣿⣿⡆⠀⠀⠸⣿⣿⣿⡇⠀⢀⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡶⢿⣿⣿⣿⠀⠀⠈⣿⣿⣿⠀⠀⠐⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠚⣿⣿⣿⣧⢀⣀⣾⣿⣿⣦⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⣃⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢦⡈⡄⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⣿⡟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠸⣿⡇⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⣥⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠄⠀⠀⡄⢀⡄⣠⣠⣤⣄⣀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡄⠀⠀⣿⣿⣧⣽⣿⣿⣿⡿⣆⠈⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠈⠻⠿⠿⠿⠿⠏⠀⠈⠀⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠆
⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢀⢰⢳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢂
⠀⠀⠀⠀⠀⡸⣿⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠬⠐⠄
⠀⠀⢀⡴⠊⠁⣀⡀⠦⠡⢧⣶⠄⠈⢷⡀⠀⠀⠀⠀⣤⡄⠐⠒⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⡷⢦⡄
⠀⠀⠈⠀⠺⠟⠛⠋⠁⠂⠹⠟⣇⣀⣨⣷⣀⣠⣤⣖⠿⢟⣄⣀⣀⣀⠀⠀⠀⠀⣐⣀⠀⠀⣄⣤⣤⣄⣀⡀⣀⣠⣿⣥⣤⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠲⠶⠴⣶⣤⣄⣀⣀⠀⠛⣯⠉⠉⠉⠓⠦⠀⠀⣉⠀⠀⠀⣀⣨⠿⠇⠀⠀⠀⠀⠀⡀⡤⠤⠋⠉⠀⠒⠉⠁⠀⢀⡀⡐⠃
⠀⠀⠀⠀⠀⠀⣐⡀⠐⠞⢣⡉⠻⢦⠉⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⣊⣉⡉⣁⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢿⣿⡶⠓⠀⠙⠲⣤⢌⣉⣒⠲⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠺⢿⣿⣿⣍⣩⡤⣤⣽⠛⢛⣓⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡇⣰⣷⣤⠄⢉⠬⠟⣛⡛⠹⠟⢦⡀⠀⠀⠀⢀⡴⡏⠀⠀⢠⡄⠀⠉⠁⠀⠈⠀⠀⠀⠀⢀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠥⠀⠠⠄⠖⠀⠀⠚⠀⠀⠙⠄⠀⣴⣉⠁⠀⠀⠀⠀⠙⢴⡀⠈⠠⠀⣏⡤⢤⠠⠟⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⢀⢐⠊⠙⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⢀⠀⠂⠀⡀⢚⠋⡀⠰⣦⡇⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣯⡷⣰⡾⠁⢀⡈⠁⢲⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠻⢗⠏⡀⠰⣿⣆⠄⠉⣉⣿⣷⡶⠃⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⡇⠀⠀⠀⣹⠀⠈⠘⢁⡒⠿⠛⠉⠀⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡢⡝⢼⡲⡠⢞⡵⠖⢲⡟⣷⣀⠀⡴⠁⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣗⡠⢳⡸⠸⣵⡇⢿⠃⠈⠻⣙⠇⢹⠉⣠⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡓⢉⣠⠷⢹⣿⡜⢦⣤⣄⣈⡼⣴⠈⠛⠤⡤⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠞⠘⠁⠨⣼⣧⡀⠂⢈⣉⠙⢈⡉⢀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⢠⠀⠈⠠⠖⢍⠒⠿⠙⠉⠀⠀⠀⠀⠠⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⡀⢡⡴⠬⣾⠦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣞⢔⣫⣽⡓⣮⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣍⠨⣿⣟⡵⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠏⠸⣥⣴⣄⣀⣀⣀⠀⡄⡀⣺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢀⣼⣿⣥⣾⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⢿⣿⠿⠛⠁


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⢽⠙⠫⡍⢙⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⢺⢐⡆⡈⣇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠶⠛⠀⢀⣂⣩⣜⠈⣰⡇⡈⠡⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢧⣀⢀⣀⣀⣠⣤⣿⠟⣿⣰⣿⣇⣸⠖⡴⢡⣾⠳⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣈⣂⡀⠉⠁⠈⠉⠉⠈⠛⠀⠉⣿⣿⣿⣾⡿⣡⣾⣯⠂⡁
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠙⠙⠙⠻⠿⡿⣷⣶⣶⠤⣤⢄⣠⣤⢰⣿⣿⣿⡟⣼⢿⣿⠄⠀⢸
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣠⣤⣶⣿⣿⣿⣽⣿⣿⣿⠟⠁⠈⣿⣧⡀⠈⠓⢄⣀
⠀⠀⠀⢠⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⠏⠁⠀⠀⠀⠘⠿⣧⣇⡄⣀⣈⠑⡦⠄
⠀⠀⣠⣀⣀⡁⠀⠀⠀⠙⠻⠿⠛⠛⣻⣿⣿⣿⣿⡏⢿⠫⣿⣿⣿⣿⣧⣀⠀⢂⡦⣄⡀⠀⠀⠉⠛⠿⠇⠎⣑⣷⠶⣄⡀
⠀⢰⣿⡟⡁⠀⠀⠤⢤⡀⠀⠀⣠⠞⡿⠉⠁⠔⠋⣠⣶⠾⡛⠿⣿⣿⣽⣇⣀⡀⠀⡈⠻⠶⡄⠀⠀⠀⠀⢸⣏⡥⢲⠯⠴⢻⡏⠀⠆⣠
⢠⣿⣿⠿⠷⠂⢀⡀⡀⠀⢠⣾⣡⠀⠀⢶⣶⣶⡿⢋⠀⣀⣶⡟⠉⠉⠉⠛⠛⢓⣦⠀⠀⠀⡀⠀⠀⠀⠀⢉⠁⣀⣀⡀⢠⣿⣿⣀⣄⣯⠇
⣾⣽⠏⠀⠀⠀⠘⢷⣿⣦⣌⣙⡙⣗⣿⡿⠛⠁⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠉⠈⢥⠻⣿⠿⠟⠋
⢻⠟⠀⠀⠀⠰⣄⡀⠈⠙⠻⢿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⠀⠀⠀⠀⠀⠀⢀⡼⠷⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡟⠻⣿⣦⡀⠀⡀⢤⣤⣤⣠⣤⣀⣴⠦⡀⠀⠀⠀⠀⢀⣼⡇⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣤⣀⣀⠉⠀⣀⣺⡿⣿⠾⣿⠢⡝⣯⠰⣿⣷⡧⢘⣃⠀⠀⠀⢀⣾⣽⠃⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡁
⠀⠀⠈⠉⠀⠘⠃⠉⠛⠙⠒⠂⢹⣷⣿⠾⣥⣟⠛⠜⠏⠋⠀⠀⠀⠾⣏⣐⣷⠞⠁⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⣍⡛⠛⠒⠦⠄⠀⠀⢸⣿⣿⣿⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠖⠛⠁⠁⠀⠄⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠐⣢⠋
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢀⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠸⢋⣛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀
⠀⠀⢧⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⣀⠀⠀⠰⠆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⡀⠉⠃⣤
⠀⠀⢦⠀⠀⡀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣷⡿⢿⠿⠻⣷⣦⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠂⠀⠒⠐
⣆⠀⠴⠀⠀⡁⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠙⠃⢀⣄⣀⠆⠀⠛⠋⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈
⣿⠙⠲⣆⢀⠃⠀⢰⠄⠀⠂⠀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⠟⠆⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠌⢀⠆
⠻⣀⠀⠀⡈⠀⠀⢸⡅⢰⠀⠀⠀⠀⠀⠀⠀⢽⣾⣿⠁⠀⠀⠀⠀⢀⡠⠀⠀⠐⠀⠱⠀⣀⠀⠀⠀⠠⠀⠀⢲⠊⠬⢀⡀
⡀⡷⠶⡄⠀⠀⠀⠸⡇⢀⡰⠄⠀⠀⠀⠀⠀⠀⢹⣟⢁⠴⡿⢄⠈⠘⠁⠀⣀⠰⠀⠰⣤⡿⠄⠀⠀⠀⠲⢄⠘⣤⠴⠈⠁
⠀⢀⣤⡘⠀⠛⠀⢸⡧⣼⡄⠀⠀⠀⠀⠀⠀⢲⡄⠹⢚⢘⡁⢈⡤⠀⠀⣼⢁⡆⠉⠀⢴⡕⠀⠀⠀⠀⠀⠈⠳⢆⡀⢀⠘
⠀⠞⠁⢹⡀⢘⡀⢾⠀⣹⢿⡠⠆⠀⠀⠀⢀⣤⠀⡆⠀⠉⠠⠼⣄⡿⠳⠭⢰⡇⠸⣌⠿⡁⠈⢢⡀⠀⠀⠀⠀⠀⠠⢀⡀
⢀⠀⠰⣜⣣⢞⡋⢻⢆⡛⢼⣷⣄⠀⠀⠘⢸⡏⠘⢥⡀⡀⠙⠰⠀⠀⠙⠓⢀⣝⣧⡈⠁⠀⢀⠀⢙⢐⣀⢰⠂⠐⠄⠀⠁
⠋⣡⢀⠀⠀⣨⣤⣾⣄⠴⢠⢿⠈⣇⠈⣠⣾⣀⠀⢀⡙⣳⡮⣤⠆⠤⠀⡀⠈⣟⣿⠋⢛⠀⠀⠟⠉⣽⡹⠦⠉⠁⠀⢀
⡀⠸⣋⠉⠽⢾⡄⢼⡇⠠⢌⡛⠀⠹⣠⣉⡝⠁⡼⢤⠍⠁⠃⣼⠂⢀⠴⣡⡄⣘⠿⠷⢊⡄⠺⠿⠈⠿⠠⢤⣢⣄⢀⣈⠱
⢶⠔⣿⡟⣠⣟⡛⢿⡷⠂⠀⢱⠈⣦⣤⣿⣷⣶⣥⣄⠀⠀⣤⡾⣩⢿⢰⡶⣏⡱⠀⠗⣺⢑⡃⢀⠀⢀⠀⢈⡛⢐⡏⠯⣶
⡤⢹⣟⡿⠿⢛⣻⡚⠁⠀⣠⡄⢸⣏⣯⡿⠿⣿⡋⠐⠤⡀⠐⣿⡷⠂⠙⣿⡿⡿⠙⢀⠖⠊⢹⠱⢆⣿⡿⣧⣤⣞⡷⣆
⠁⢴⣿⣠⣦⡀⣨⡴⣿⣿⡶⣲⢻⣇⠨⣴⡞⢻⣂⣠⡖⢠⣦⣏⣗⡁⣀⠃⢿⠑⠠⠘⡃⠸⢺⠈⠻⡽⢣⣹⡾⡿⣞⠿⠂

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣄
⠀⠀⠀⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡟
⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⢀⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⢠⡀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣧⣤⣄⡀
⠀⣸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡿⠁⠀⠀⠁⣰⠀⠀⢀⣤⡤⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣇
⠀⣿⠁⢻⣿⣿⣿⣿⠀⠀⠀⠀⣰⡟⠁⠀⠀⡀⠐⠻⣇⣰⠟⠀⠀⠀⠀⣿⡟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢰⡿⠉⣿⣿⣿⡏⠈⣿
⠀⢿⡄⠈⠟⣛⣿⣿⡆⠀⠀⠀⠘⣷⠀⠀⠁⠙⢰⡖⠻⠁⠀⠀⠀⠀⠀⣿⡁⢹⣿⣿⣧⣀⠀⠀⠀⠀⠀⢸⣷⠀⣹⣿⡟⢃⡀⣿⠇
⠀⠈⣿⠀⢼⣿⣿⣿⡧⠀⠀⠀⠀⠈⢧⣀⠀⠀⠸⡇⢠⠀⠀⠀⠀⠀⠀⢹⣷⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠹⣯⠀⠋⠉⠠⡐⡟
⠀⠀⣿⡆⠈⣽⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣁⡀⠁⠀⠀⠁
⠀⠀⠈⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠨⣀⡀⠘⠒⢠⠀⢢
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠂⠉
⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢰⡟⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⢀⡾⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⣿⠃⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠰⣿⠃⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣾⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⣻⣿⣿⡿⣟⣿⣿⣿⢋⣉⣻⠟⠉⠛⢛⡟⠉⠙⢛⠛⠻⣟⠛⠿⢿⣟⠛⠻⣷⣄⡀
⠀⠀⠀⠀⠀⢾⠿⡿⠿⣿⠿⠿⢿⣿⣷⡿⠿⣿⣷⣶⣷⣿⣶⣶⣶⣿⣽⣶⣶⣬⣦⣤⣤⣵⣤⣤⣽⣦⣤⣤⣬⣿⣦
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⣄⢀⠀⠹⣄⠀⠀⠹⡅⠈⠈⠀⠀⡇⢸⢹⠀⠠⢀⠋⠀⢀⡼⣋⠵⣊⠝⠋⠁⠀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠠⡉⠻⠿⣆⠀⠀⢱⠄⠀⠂⠀⡇⠀⡈⠀⠀⡰⠢⢐⣟⡪⠕⠊⠁⢀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢄⠀⠈⠛⢦⡌⠂⠀⡃⠀⣧⠀⡆⣠⣾⢱⢾⠟⠉⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣿⢤⣿⣾⡿⠟⠋⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⢨⡝⡿⣍⠀⠀⢀⠂⠀⣠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⡀⡾⢲⠷⣿⡀⠠⠁⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣿⣾⣳⣎⣿⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣖⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⢠⣾⣷⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⠖
⠀⠀⠀⠀⢀⣥⠼⢻⡿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡄⠀⠀⠀⠐⢻⣿⠟⠉⠉
⠀⠀⠀⠘⠆⠟⢠⣾⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡀⠀⠀⠄⠀⠀⠀⢹⡫⢿⣿⡇⢀⣴⠏⠀⠀⠁
⠀⠀⠀⠰⡐⡦⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⢃⣾⣿⣷⣼⣿⣄⣠⣄⣀⠠
⠀⠀⠀⠀⢋⣀⣤⣤⠀⡀⠀⠀⠀⠀⠀⢀⠀⠶⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⡿⢏⡉⠉⠉⠉⠚⠛⠀⢠
⠀⠀⠀⠀⠆⠈⢳⠉⠶⠃⠀⠀⠀⠄⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢤⡀⠀⠀⠀⠀⠃⣤⣹⣤⣠⡄⠰⠆⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⢲⡀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣶⡀⠀⠀⠀⠀⢀⡞⠁⠀⠸⠀⠂⠀⣀⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠁⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠉⣿⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠘⠃⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⢠⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣦⠀⣰⣶
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⢸⡇⠀⠀⢀⣠⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠆⠈⢡⡶⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠀⠸⣿⣿⣷⡄⡀⠃⠀⠀⠘⢿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠹⢿⣦⡀⠀⠀⠀⠀⣠⡴⠃⠀⠀⣸⡶⠃⠙⠇
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣿⣿⢹⣿⣿⡇⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⠄⠀⠀⠀⠉⠐⢦⡄⡀⢈⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢠⣼⡿⢹⠀⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠂⠁⢀⠈⢁⡀⢉⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⢿⡇⠀⠀⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⣵⠿⠂⠤⠿⠟⠉⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣷⠀⠀⣶⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⠈⠠⠖⠈⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠰⢾⡷⠀⡈⠁⠛
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⠘⠀⠀⠀⡄⠀⣾⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠄⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠎⢹⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⡇⠀⢹⠀⢀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠲⠶⠛⣉⠁⢀⡀
⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠘⠀⠼⠄⣸⠆⠈⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣸⠀⠀⠘⠄⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡚⢛⣿⣿⠟
⠀⠀⠀⠀⢠⡯⠙⠁⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⠀⠈⠉⠿⠉⣠⡤
⠀⠀⠀⠀⠼⠖⠂⠀⠀⠀⠀⢠⣠⡄⢸⠀⢸⠀⠀⠀⣷⠈⢳⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⣲⠆⠘⠀⠀⢀⡀⠀⣩⣴
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢾⠀⣿⣧⣸⠀⡆⠀⠀⠀⢩⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⢘⡇⠀⠀⠀⠀⣶⣶⣤⣄⠀⠀⠀⠀⠀⠈⣿⠿⠆⠀⠀⠀⠀⠙⣾⠟⡁
⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡿⣿⣷⢂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢹⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢣⡘⠁⠀⠀⠀⠀⠀⢸⠟⠻⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠇⠀⠀⠀⡀⠸⠇⡀⠀⠀⠀⠀⠀⠀⠛⠖⡉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠠⠄⠷⣤⠀⡀⠀⠰⠀⠀⠀⢸⠀⠀⠁⠀⡄⠀⠀⠀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⢠⣶⣏⠉⠃⠀⠀⠀⠀⠀⢨⡇⢰⠀⠈⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢾⠿⡏⢰⣷⣷⣔⣀⠀⠀⠀⠀⠀⢺⡇⠘⠀⠀⠀⠀⠀⠀⢀⡛⢗⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠛⠾⠟⢻⣿⣯⣀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⣀⠈⢱⣎⣹⣇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡟⠉⡄⠉⣶⣦⡀⡿⠁⠜⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⣹⡆⠰⢃⠀⠠⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠘⠂⠀⠀⠀⠀⠃⠀⠁⠸⢿⣈⣄⣷⠞⠛⠀⠀⠀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠷⠒⠞⠳⠶⣦⡀
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣄⣀⣏⢈⣀⠀⠚⠀⠀⠀⠀⣿⠀⠀⠀⣀⢠⣴⣾⣷⠒⢠⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠉⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙⣏⠛⠃⣴⠆⠀⠀⠀⡟⠀⠀⠀⢫⣶⣯⣽⡏⠐⢀⡽⠻⡇⣸⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠃⠀⠀⠀⠀⠀⠄⠀⢀⠀⠄⠀⣀⠄⠀⠀⠀⠀⠀⠘⢶⡸⠇⠀⠀⠀⠀⠃⠀⠀⠀⢣⣾⡿⡏⢙⠀⠹⠀⠀⠀⢉⠀⠀⠀⠀⠀⠠⠿⡿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⣴⠃⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⡰
⠀⠀⠀⠀⠀⠀⠉⠀⠐⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠜⠓⠠⠰⠇⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⡀⣀⣀⡀⢀⣀⣀⣀⡀⣀⠀⢀⡀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⣀⠀⢀⣀⢀⣀⢀⣀⣀⣀⣀⡀⢀⣀⠀⣀
⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣜⣋⣻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣴⠖⢀⠉⢀⠀⣀⢀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣄⠀⠨⣿⣿⣧⣙⣱⣶⡆⢾⣿⠀⡵⠀⠀⠀⠛⠀⠀⢀⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⢁⡄⠀⠿⠷⠀⠽⣿⠃⢀⣴⣿⠏⢀⠀⠈⠀⢀⣮⡄⢀⣼⠔⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠂⢀⡺⠛⠉⠀⠀⠈⠔⠞⢉⠁⠰⠿⢣⣤⠀⢚⣭⣵⣿⣟⣵⣶⡿⢋⠀⠸⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠟⢟⠻⠿⢻⡾⠆⣠⣿⣿⠿⠀⠀⠏⠰⠾⢿⣿⣯⣿⣿⠟⠀⡼⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡤⠀⠀⠈⠁⠀⠀⠀⠀⠐⣄⣠⡟⣿⡗⠓⠨⠄⠀⠀⠂⠀⠙⠿⣻⣿⠀⠚⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⣙⠇⠀⠀⠙⢈⢛⣻⡗⠀⣀⣉⣯⣷⣤⢡⡶⢴⡷⠢⠆⠀⠀⠀⠀⢐⡿⠁⣰⣦⢦⣤⢄⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠌⠁⠀⣀⠿⠀⣯⠽⡿⢩⠋⠀⢶⠉⣤⣽⣋⠀⣀⡀⠀⠀⠀⣺⣯⣤⠀⢣⠈⠲⣷⡿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡀⠢⠣⠰⡜⡫⠉⠦⡴⠁⣰⣧⣿⣿⡦⠸⣷⡄⠀⠀⠙⢿⣿⣆⠼⡆⠰⣿⡘⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⣀⠀⣀⡀⣰⣧⠈⠐⠢⢞⣿⢿⣿⣾⣧⣤⣭⣴⠶⠀⠀⢠⣞⣉⣀⣳⣴⣤⠉⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠻⠀⠂⠀⠁⣈⡠⡄⠀⠀⣙⣴⣿⠿⠷⢿⣷⢛⣉⠶⠊⠈⣿⣿⣿⣿⠷⣿⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠈⠂⡘⠃⢈⣱⠎⠐⠂⢁⠈⣠⣴⣴⣷⣡⣿⣿⣟⣣⠀⠀⣤⣤⠀⠀⠀⢰⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠁⡴⠄⠁⢀⣘⠋⢀⠀⢦⡤⣿⠛⠛⠻⠻⠿⢿⣾⡛⠃⠀⢠⣿⣿⡧⠰⠄⠘⠵⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠔⠋⠀⠀⠀⠀⠐⢤⣥⠌⣿⡏⠀⠀⣄⣀⣀⠀⠛⠁⠰⡶⠀⠠⡄⢹⣿⣿⡄⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠅⠙⠶⠦⠶⠂⠀⠀⢨⡟⠀⠀⠐⢿⣿⣿⣷⣎⣩⣿⣄⠀⢢⡀⠈⠙⠿⡃⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣧⠀⠀⠀⢁⡀⠘⠢⠀⠉⠻⣿⡿⡟⢤⣾⡷⡘⠀⢀⣱⡄⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠀⠀⠈⠂⠀⣬⠘⠛⣀⡄⠀⡀⠈⡁⠀⠀⠀⣿⠀⠑⠀⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡤⠀⠘⠃⣀⠓⢶⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢠⡄⠀⠂⠢⢰⠀⠀⡁⡀⠒⠀⡀⠀⠒⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠂⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠀⣸⣟⠀⡟⠀⢀⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠃⠒
⠀⠀⠀⠀⠀⠀⠀⢠⣟⠂⠀⡿⠡⢸⡏⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠜⠀⠀⡀⠀⣾⣧⣰⠟⡖⠀⣤⠀⠚⠉⢘⣤⢠⢀⣀⠀⡆⠀⠀⠀⠀⣤⣼⡏⠀⠀⠒⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠐⠏⢰⡀⣾⠋⢰⠇⣹⡟⡹⣯⠀⠀⠀⠀⣄⠈⠃⠉⣠⠴⡿⠧⡀⠀⠀⠈⠘⣿⠀⠀⠠⣤⣴⣶⡛⠋⠉⠙⢣⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣷⡟⠀⠙⢷⠀⢷⠈⣶⡶⠷⠐⠶⠂⢮⡁⠖⠛⠞⠋⠀⠐⠂⢀⡿⢰⠁⡀⢀⣀⠀⠙⣦⠀⠀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠃⣿⡈⢻⡀⠐⠄⠈⣇⠘⠇⢈⠀⠀⠀⠀⠀⠀⠘⡦⠁⠀⠀⠂⢀⠀⣀⣄⣈⢀⣿⣾⣿⡶⠶⠿⠶⠦⠶⠤
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠘⢃⠚⠧⢀⣠⠜⠻⠹⠶⢮⢠⣶⣶⣄⣀⠀⠈⢰⡆⠀⣠⠤⠚⠋⠉⠉⠁⠀⠀⠀⠀⣀⣀⣤⡴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠈⠃⠀⢀⡀⠀⡀⠀⠀⠀⠉⠙⢣⣂⡵⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣉⣿⣤⣼⣳⣿⢏⡿⢗⣶⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢫⠄⣹⣇⣸⣦⠋⣁⣴⢁⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠒⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠘⣿⢿⡯⣿⣹⣶⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣀⣙⣶⣯⣼⣽⣟⣤⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⠁⠀⠀⠀⠙⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣤⢀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢰⠎⠉⠛⠀⠹⠛⠿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧
⠀⠀⠀⠀⠀⠀⣤⡟⢦⣄⠀⣴⠐⠂⠀⣀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣝⢀⠀⠋⡀⡁⠀⠀⢀⣜⠀⣻⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠓⠛⠚⠿⠿⠛⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁
⠀⠀⠀⠀⠀⠀⢈⠀⢱⡀⢲⡆⠠⣤⠀⢠⣄⣠⡶⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⡗⠀⠇⠀⠘⠋⠎⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠄⣀⣀⡀⣠⠔⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠤⠄⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣿⣿⣷⣦⣤⣀⠀⠀⠀⣀⣠⡤⣤⣄⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⣤⣤⣭⣻⣿⣿⣿⣾⢝⣧⣶⣿⣷⡜⢿⣿⣿⣿⠁⣹⡿⠟⢿⣿⣷⣶⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⣛⣿⣿⣿⡟⢋⣤⣾⣿⣿⣿⣿⡇⣼⣻⣿⣿⠀⢿⠸⠯⢸⠟⠉⢁⢹⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠐⣒⣛⣛⣿⣿⠟⢉⣼⣿⣿⣿⣿⣿⣿⡿⠥⣛⡿⠉⠸⢀⠈⠛⠚⠁⠀⠀⠞⠧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠭⠛⠛⣫⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⢠⡈⠀⠀⠀⠑⢢⠀⠀⠀⣠⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠤⠖⣺⣿⣿⠏⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⠀⠈⣄⠀⠀⠡⣠⠔⠁
⠀⠀⠀⠀⠀⣀⣤⣴⣿⢃⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⠀⠀⠠⠴⠐⠦⣌⣙⡲⠞⠁
⠀⠀⠀⠀⠈⠁⠘⣽⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠿⠳⢤⡀⡈⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠴⣿⡟⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣧⣀⣀⠀⠁
⠀⠀⠀⠀⠀⣠⣾⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠈⢙⣯⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣀⣴⣿⣿⠋
⠀⠀⠀⠀⠠⢻⣿⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⢾⣿⣻⠿⡫⠃⣰⣿⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⢠⢿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠭⣛⡈⢯⣳⣉⣑⢶⡿⠏⠉
⠀⠀⠀⠀⢀⠁⢸⡆⢿⣿⣿⣿⣿⣿⣿⣿⡓⠄⡁⠀⠉⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡄⠙⢣⠸⣿⣿⣿⣿⣿⣿⣿⢃⠢⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣳⢾⡶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠡⣀⠙⣁⢻⣿⣿⣿⣿⣿⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠁⠀⠀⠈⠉⠙⢳⣝⢮⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⢿⣤⠑⣤⢿⣿⣿⣿⣿⣿⣟⡰⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠃⠙⡞⡶⡄⠀⠀⠀⠀⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣌⣿⣿⣿⣿⣿⣿⣽⢳⡂⠀⠀⢀⣴⣶⡶⠦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠃⣳⣧⠀⠀⠀⠀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡡⣿⡆⣙⢿⣿⣿⣿⣿⣿⣽⣄⠘⠿⣯⠭⠴⢦⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⣿⠀⠀⣠⣀⣴⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢄⢻⣆⠛⣿⣿⣿⣿⣷⣯⣦⠀⠀⠂⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣮⣿⣿⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢘⠏⡛⢶⣼⡻⢿⣿⣿⣿⣯⣴⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠙⠺⣏⢀⡀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣴⣭⣤⣄⣴⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠦⢭⣭⣭⣽⣿⣿⣿⣽⡿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⡞⣻⣏⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⢠⠀⠀⠰⣴⣶⡴⠀⠀⢰⣶⡦⠀⠀⠀⠀⠀⠐⢛⡴
⠀⠀⠀⠀⠉⠙⣿⠂⠉⠀⠀⢀⣾⣶⣿⣤⠀⠀⠀⠘⠓⠛⠀⠀⠀⠀⠻⠟⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⢧⠘⡀
⠀⠀⠀⠀⠀⠀⡜⢰⠀⠀⠀⠀⣿⣿⣿⢽⠄⠀⠀⠀⡤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠀⠀⠀⠀⠀⠀⢿⠈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠩⠛⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⡄⠀⣲⣬⠃⠀⠠⢠⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣴⡇⠀⢀⢸⠀⡄⢀⡀⠀⠀⠄⠀⠀⠀⠉⠕⠃⠀⠁⠀⠀⠀⠀⠈⠁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠏⠉⠁⠀⠀⠈⠀⣘⠿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⠤⠀⠀⢀⣠⡀⠀⠀⡄⠠⣤⠆⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠃⠀⠀⠀⠈⠃⠲⠆⠀⠘⠛⠁⠀⢄⣷⠠⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠠⣤⣄
⠀⠀⠀⠀⠀⠘⢠⡧⠖⠀⠀⣾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⠃⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⣦⠠
⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡶⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⢸⣿⡿⠛⣿⡀⢻⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠘⣧⠀⠀⠸⠟⠁⢀⣻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⣿⠀⢠⡄⠀⣠⡘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⠀⠀⢸⣿⣿⣿⠇⢀⡛⣤⣽⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⣿⣿⣿⠆⣿⠛⠉⠉⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠀⢹⣿⣿⡄⠀⣠⠞⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⢿⣿⢳⠛⣬⣹⣷⣾⠛⣿⣶⣿⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡾⢷⣾⣟⣿⠉⣀⣤⠘⠋⠙⠁⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⠳⣾⣭⡉⣿⠠⠉⠁⠀⢀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠹⣿⣿⠿⠦⠶⠌⠃⣈⣡⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⣠⣿⣁⣤⣠⠀⣴⠂⣠⣿⣿⣿⣿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠁⠉⠉⠛⠶⠿⠿⠿⠿⠛⠋⠉⠁
⠀⢲⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⢰⡆⢀⣼⠃
⠀⣄⠀⠀⢾⣷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⢸⣧⣸⡿⠃⠀⠀⠀⢠⠄
⠀⠈⣿⡇⢾⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠈⣻⡏⣀⣤⠞⢁⣴⡟
⠀⠀⠛⠃⣀⠻⠂⠀⠘⠃⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠟⠉⢀⡤⣉⠎⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⢄⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣆⠙⢿⣿⡿⢦⣐⣴⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠲⠾⢧⡼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠈⣿⡆⠈⠿⣿⡿⠟⠋⠉⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠺⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣿⣿⣧⡸⣧⠀⣿⠀⠀⢀⣄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣸⣾⠃⣰⡆⠛⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠈⠁⠀⠀⠀⣄⡀⠀⢸⣿⣿⠛⢿⣿⣟⠸⠿⣄⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣍⠻⣷⣌⣿⡏⠀⠈⠹⠉⢀⣶⢟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣅⣴⠀⠀⢸⡆⠹⣿⣿⠀⠶⠀⠀⣠⣟⣵⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣀⠀⣤⡄⢹⣿⡀⢸⡆⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠸⣿⡎⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⢋⠉⠉⠉⠀⠘⢿⣮⣿⣧⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⣶⣤⣬⡀⠀⠁⢨⣿⣦⣿⠇⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⡎⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠙⢿⣿⣿⣦⣄⠀⠙⣿⠇⢀⡄⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣾⠀⣿⠛⢿⣿⣿⠸⠀⣿⢠⡌⢡⣾⠋⠀⠀⠀⠀⠀⢠⣄⠀⠀⣀⠀⠀⢻⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠆⠁⠀⠀⠻⠇⠸⡆⠈⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⣷⣆⠁⠀⢰⡄⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⠀⢀⡆⠀⠀⣴⡆⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠙⣄⠀⣧⣼⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣸⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣷⣿⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢻⡏⠀⠀⠀⠘⣿⣧⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⢸⠿⣿⣤⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠀⢰⡄⠀⣼⡆⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⣿⢧⣈⣴⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠙⢷⣎⣡⠀⣿⡇⠸⣿⠂⠀⠀⠀⣠⡄⠀⠘⠋⠀⠀⣘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠰⣌⡹⠁⠈⠁⢠⣯⠀⠀⠀⠈⠉⡀⠔⢀⣤⠀⢀⠋⢀⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣍⣳⣷⠀⠀⢀⡏⠀⠀⠀⠀⢀⣤⣤⠸⣿⣆⣨⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⠻⣿⣿⣿⣿⡇⠀⡇⠀⡀⠀⣸⡿⢿⣿⠀⠹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠈⠙⢿⣿⡁⠐⡇⠘⢃⡼⠋⣀⣰⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠙⢿⣿⡇⠰⠟⠁⢰⣿⠛⠛⠆⢀⣠⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠆⠀⢹⠁⠀⣼⡇⢰⣿⡇⠰⢼⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⣇⢰⣿⡇⠸⣿⡿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⡀⠀⠀⣿⠀⢹⡇⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⠀⣿⠀⠈⠁⠀⣱⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢿⣿⣟⠛⢰⣿⠀⢠⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢻⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣹⣿⡄⢹⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣟⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⡠⣶⣶⣿⣍⠉⠐⠒⠂⠤⣄
⠀⠀⠀⠀⠀⡀⠀⠈⠙⢿⣿⣿⣶⣦⣐⢀⡤⣠⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⡒⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠒⠒⠒⠒⠆⠀⡀
⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠈⠩⠐⣂⡲⠆
⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣠⣤⢾⣿⡿⠃
⠀⠀⠀⠸⡀⠀⠀⠀⠐⠐⠒⠂⠀⢽⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⣄⠂⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠈⢦⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣼⣻⡅⡮⣀⢘⢏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣛⡾⣿⡽⡒⡋⠀⡃⠀⠀⠀⠀⠀⡠⠞⠉⠈
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣀⣠⣄⣀⠉⠓⢾⢿⣿⣜⠧⢶⡠⠓⢠⠟⠀⠀⠄⣀⣀⣠⠄⠀⠂
⠀⠀⠀⠀⠀⠉⠉⠉⠻⠿⢿⣿⣿⣿⣿⠿⠛⠒⣾⣿⣿⣿⣿⣛⣁⣤⠟
⠀⠀⣰⡇⠀⠁⠂⢀⣤⣴⣾⣿⣿⡟⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⢸⣆
⠀⢰⣿⣃⣠⣴⣾⣿⣿⣿⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⢸⣿⣿⣿⣿⡿⠟⠋⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠱⡀⠈⠙⠲⠀⠀⠀⢀⣀⡀⠤⠤⠀⠚
⠀⠘⠟⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠂⣬⡶⠿⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡄⠀⠀⠀⠐⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⢶⠆⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢄⠈⣵⠀⠈⡉⣀⣀⡀⠀⢀⣠⠀⠀⠀⠀⢀⡀⠂
⠀⠀⠀⠀⠐⠛⢀⡄⢀⠀⣂⠠⠀⠤⠂⠀⠛⢿⣶⣾⣿⣿⣿⣷⣿⡿⠁⡤⠀⠀⣀⠘⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⣬⡿⢀⡴⢝⡅⠋⣀⡛⢿⣿⣿⢽⣿⣿⣧⣧⣰⢶⣎⠁⣰⣄⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠙⢁⢏⣓⣾⣿⣈⠛⠁⠀⠙⠁⠀⠈⠻⣟⣾⣷⣾⣏⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⢠⡄⣳⡏⣻⣿⣿⡷⠀⠀⣴⣾⣶⣦⡀⠉⢹⣿⣿⣿⠅⠐⠒⠀⠀⠉⠁⡀
⠀⠀⠀⠀⢀⣀⣠⠀⡨⢻⠷⠀⠀⠾⢛⢛⣛⡋⠠⣀⣿⣿⣿⡟⠁⠀⢨⣿⣇⠱⠄⠋⠀⠀⠄⢀⠘⠓
⠀⠀⠀⠀⠈⠋⠀⠀⠁⠀⠐⠛⢀⡀⣤⣿⠹⣿⣶⡀⠀⠈⢀⠀⠐⢠⣟⡛⣿⣧⣤⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⡭⠀⡈⢙⣷⠐⣠⣬⠁⠀⠈⠛⠀⠘⠍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣬⡄⠙⠟⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠰⢄⣀⡀⠀⠀⠂⠸⡆⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠇⠀⢿⡑⡈⠁⢒⢨⣿⠃⠀⠘⠫⣼⣭⣭⡻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣶⡾⠇⠀⠀⠁⠙⢻⠋⠋⠀⠀⠀⢠⣶⣯⣿⣿⡄
⠀⠀⠀⠀⠀⢺⠤⢄⡀⠈⠈⠀⠂⠀⠀⠀⠀⢰⡆⠀⢰⣧⡀⠀⠉⠙⡏⠛⠁⠀⡤⠓⠀⠀⠀⠀⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠐⠀⣜⡳⣶⣤⢀⠀⠀⠀⠀⠀⠀⡇⢀⣺⣾⣧⡄⠀⠠⠀⠀⢤⠒⠻⣀⣀⣻⠿⢟⠟⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢥⠈⠙⠿⣧⠀⣄⠀⠀⠆⢳⠀⠈⠇⣷⣆⠀⣈⠰⡖⠻⢇⣴⠌⣋⡵⣂⠱⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠐⡮⣷⣝⠿⠁⠀⢻⣦⡄⠈⠿⣗⣠⡟⠉⣡⣾⣿⣿⠯⠅⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠔⠀⠛⠀⠿⢿⣦⢻⡧⠀⢚⣿⣿⣴⠿⠿⡙⣭⣿⡶⣯⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⡀⠀⠠⢂⣀⣶⣮⣝⣿⡂⢨⡿⢟⣾⣭⡎⠄⠩⠜⠙⠀⠙⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣈⣍⠉⣲⣿⣿⡏⠃⠀⣿⣿⣿⣿⣿⠾⠶⠶⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠙⠛⠓⠛⠛⠋⠙⠛⠃⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠠⠀⠀⠠⠀⠐⠄⠀⠰⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢀⠆⠰⠂⠄⠀⡴⠀⠲⣄⠀⠀⢀⣰⣶⡆⠀⠀⡿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠘⠲⢶⡐⢠⡄⢀⢚⠁⠹⣵⣾⡍⢯⠀⢤⡀⠳⠛⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠊⠀⠀⢠⠀⠂⠀⠀⠀⠀⠐⢄⡾⢧⠀⠀⠈⠛⢧⠀⠀⠀⠹⠇⠻⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠒⠆⠀⠈⠁⠀⡄⣃⢉⣤⣄⡀⢀⡤⠓⢁⠀⢠⡄⠀⠀⢀⠀⠘⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⣻⠰⣷⣴⣤⠀⠨⠰⠀⢸⡿⠉⠉⠙⡆⠀⠀⡀⠛⠎⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠛⠛⠃⠀⠀⠀⠀⡨⠁⠄⠂⠀⠁⡀⠀⠈⢻⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠑⠀⠁⠀⠀⠀⠀⢠⡀⠀⠐⠲⠀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠻⠦⡄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣶⣶⣴⣄⡻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⡿⣜⠻⢯⣷⣶⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢛⡟⢻⡇⠈⢀⣀⡟⣡⣤⣙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢯⣄⢀⣷⣤⣿⣯⡁⠈⠉⠛⠿⣧⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⢻⣿⣿⡿⠛⣏⢻⢿⠾⢶⠆⣉⠀⣰⠈⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣴⣼⡟⣿⣷⣧⣿⡾⠃⠈⠋⠻⣿⠁⠇⠀⠀⠀⠀⡵⢦⡀
⠀⠀⢀⣤⡿⣦⣉⢻⡄⢠⡟⣡⣿⡿⣻⠉⡐⠀⠀⠈⠀⢴⣿⡆⠆⠃⢀⡄⢠⠇⠀⠐
⠀⢀⣀⡙⠳⠈⠩⣽⡋⣤⣴⣎⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⣣⢗⣚⠲⡄⠔⠁
⠀⠈⢀⣿⠶⠤⠴⣲⣽⣿⣿⣿⢿⣏⣉⡙⠃⠀⠀⠀⢠⣤⣿⣿⣿⣷⣴⠠⠀⠀⠀⠴
⠀⠀⢂⡰⠿⠛⢉⠜⣫⠋⢿⣯⠓⣌⠙⢁⢀⠀⠀⠀⠀⠲⢮⣿⢿⣿⢦⠃
⠀⠀⠈⠻⠷⠏⣰⣋⣥⣾⣆⠻⠗⢀⣤⣴⣮⢳⣴⡀⠀⠠⠾⢋⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠻⠫⣽⠻⠹⣿⠃⠘⠁⢸⡇⠘⠿⣷⣶⡦⢤⣬⣭⣭⣉⣦⡔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⢷⡄⣀⣘⡀⠀⠐⠁⠋⢙⣫⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢳⣬⣿⣹⢷⣍⣦⠀⠀⠀⠾⣿⣿⣿⣦⣹⣦⡙⢿⡛⢻⣿⠷⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⣨⣽⣿⣿⣷⣿⣤⠀⠀⠀⠙⠛⢿⣿⣿⣿⣳⣾⣥⣼⡽⠿⠿⢧⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢉⠛⠛⢧⠉⠛⠀⠀⠀⠀⣠⣼⣿⣿⣷⣶⣾⣿⣧⣾⣟⣻⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⢤⣈⢱⣦⣤⠀⠀⠀⠏⠈⢩⡟⣷⣿⣷⡿⢿⣿⠋⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡙⠁⠀⠀⠀⠀⢀⠎⠀⠛⠋⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢘⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠸⢀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣀⣀⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢴⡻⣏⢹⡿⣿⢿⠉⢉⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣶⢲⣿⣿⣦⣄⠙⠋⢀⣼⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⠛⠂⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⢿⣿⣿⣿⡿⣿⣳⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠙⣿⣿⣦⣤⣴⡀⣩⣽⡇⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠡⣾⣻⣿⣿⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⢨⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⣘⡀⠴⠟⠁⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡈⣸⣿⡶⢶⣿⣷⠠⣄⡀⠀⠀⠀⠹⣿⠃
⠀⠀⠀⠀⠀⠐⠃⠐⠂⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣶⣶⣿⣿⣿⣿⢷⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢻⠛⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡛⢻⡟⠛⠉⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣀⡈⡀⠀⠀⠀⠀⣀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣾⣿⣟⣉⠉⠀⠉⢙⡖⠁⠀⢩⣿⣾⣿⡄⠢⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠰⣾⣦⣀⠀⠀⠀⣀⠛⠛⠛⠿⠻⠷⠦⠀⠀⠼⠦⠿⠿⠿⢿⣿⣆⢦⡀⠀⠀⠀⢘⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⠀⢠⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢈⡏⢀⣤⣤⣤⡀⠀⠰⣄⠀⠀⠛⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇⠺⣿⣿⠏⠀⠀⠀⡿⠀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠘⠿⠀⠀⠀⡄⠀⢆⡜⠀⣀⣀⡁⡼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣦⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠘⠉⠉⠓⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣶⡀⠀⠀⠀⠀⠀⠀⢠⣧⣴⡄⠀⠙⠻⡿⠷⢄⠀⢠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣓⡀⠀⢀⣾⡿⢛⣉⣏⠀⠁⠿⠿⣦⢀⡀⠀⠒⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠻⠗⠊⠁⣾⡋⣽⣿⣤⠄⠀⠀⢈⠀⠀⠁⠀⠒⠉⠓⠈
⠀⠀⠀⠠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠈⠉⢉⣿⣿⡏⠀⣀⣠⢴⡄⠀⠐⠀⢠⡄
⠀⠀⠀⠀⠙⠳⢤⣆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣨⠗⠩⣤⢾⢯⣤⠈⠁⠀⠂⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡼⠀⠀⠚⠈⠄⣻⠁⠀⠋⢹⣷⡆⢠⣀⣲⡔⠛⠛⠻⢦
⠀⠀⠀⠀⠀⠐⠶⠛⠉⠁⠀⠀⠉⠁⠀⠀⢀⢘⣶⡆⡍⠀⠀⠀⠈⠻⡇⠀⠉⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⢀⣰⣾⣯⡉⢰⡇⠀⣴⣤⣄⣤⠀⠀⢀⡀
⠀⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠹⣿⣿⡍⢿⣷⡻⡇⡞⢻⡄⠂⠈⣿⠿⠀⢸⠛⠏⣡⣴⡶⣦⡴⠤⠄
⠀⠀⠀⠚⠉⠁⠀⠈⠠⠿⠛⠛⠛⣻⣧⠤⠈⢄⠀⡇⠈⣿⡠⢀⡭⣤⣤⣤⣤⣄⠀⠉⠛⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠂⠀⠀⠀⠰⠀⠈⡅⢀⣀⣤⣗⡏⡟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠒⠆⡘⠀⠈⠉⠛⠛⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶

⠀⠁⠀⠀⠀⠈⠧⠀⠀⠀⢠⡀⠀⠀⠀⡀⠐⣿⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠰⠓⢂⠀⠉⠀⠀⠀⠀⢀⠀⠈
⠠⠀⠀⠀⠴⡀⣆⠀⠀⠀⠸⠏⠀⠀⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠂⠘⡀⠁⠀⢁⠀⠀⠀⠀⠀⡄
⠁⠀⠀⠀⢠⠁⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⡀⡀⡀⠀⠀⠀⣄⠀⠀⠈⠀⡿⢀⡀⢤⠀⠂⠀⠀⣀
⠂⠀⠀⠀⠁⠀⠑⠁⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠈⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⡤⠀⠀⠀⠀⠀⠘⠫⠖⡀
⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⡞⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢈⣹
⠀⠀⠛⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⢨⠇⠁⠘⠂⠀⢠⠄⠀⠀⠀⠀⠒⣀⠄
⠀⠀⠀⠛⣆⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣈⡄⠀⠀⠀⠠⡆⠉
⠀⠀⠀⠐⠻⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⡌⠀⣴⠀⠀⠀⠀⠀⢶⣇⡞⠁⠀⣠⣠⡅⠀⢀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢤⠖⠀⡀⢠⠀⡀⠉⠁⠀⠀⠀⠀⠈⢿⠃⠀⡄⠀⠙⡇⠠⠀⠀⠀⠀⠀⠐
⠘⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠐
⠁⠀⠠⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠊⠠⣦⠀⠀⠡⠐⢀⡀⠀⠀⠀⠈⠀⠐⣢⣸⡆⠈⠠⠀⠀⠀⠀⢄
⠀⠀⢀⣠⠀⠀⠀⠀⠀⡉⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠐⠘⠽⡃⢰⠉⢀⠀⠀⠀⠀⠐⠸⠷⡀⠄⠀⠀⠀⠉
⠀⠀⠉⢠⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⡽⠯⠀⠀⠀⠀⢐⣆⠀⠀⣀⠁⢠
⠡⢠⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⢲⣤⠩⢉⣇⠀⢀⠀⠀⢮⣈⠉⠒⠻⠬⣆⠀⠄
⠀⠀⠉⠀⣰⠇⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡆⠀⠘⣿⣿⣾⣁⠿⠃⠀⠀⠉⠁⠀⠀⠀⢢⣅⠀⠀⠀⠀⡀
⠀⠀⠔⣫⠘⠬⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⡴⠀⠁⢀⠀⠉⠉⠙⠚⠀⠀⠀⠀⠀⠀⠐⠂⠀⠬⣈⠀⠂⠀⢸⡇
⠀⠠⢴⠻⡅⠀⠀⠀⠀⠀⢀⡈⠲⠀⣄⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠰⡏⠀⠀⠀⢠⡁⠌⠶⢸⣷
⡤⠀⠀⣀⣤⠤⠖⠂⠀⠀⠀⠋⠅⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⢠⠀⣼⡇
⢀⠔⡋⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⣀⠔⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠑⠂⠘⣇⡏⠀⢸⡇
⠲⠎⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⠁⠀⠀⠀⡈⠀⠠⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠚⠀⠀⢸⠁
⠀⠀⠂⠀⠀⠠⠓⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡵⢋⣥⣄⡀⠀⠀⠀⢄⠀⠀⠠⠁⠠⠀⢀⠀⠀⠀⠀⠀⠈⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣛⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢄⡙⢀⢲⡾⠁⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣆⠀⠀⠀⠆
⠀⠀⠀⠐⠆⠈⣀⠏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠐⠀⠀⢘⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠏⠀⠀⢠⡇
⠀⠀⠀⠀⠔⠶⠉⡴⠁⠀⠀⠀⠐⣼⣆⡠⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠈⠰⣠⡴⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢹⣴⢃⡀
⠀⠀⠀⠀⠑⢪⡏⢠⠄⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡈⢋⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⢸⢀⡊
⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠈⠁⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠇⠀⠀⠀⢷⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠽⣷⠋
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢂⡀⠀⠀⠀⠀⡀⠀⠈⠛⠀⠀⠀⠿⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⠿⣂⠀⠀⠀⠀⠠
⠀⠄⠂⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣀⢴⠈⠠⡄⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠰⠂⠀⠀⣀
⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠰⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠄⠠⠀⠀⠀⠀⠀⠀⠂⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁
⠀⠂⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⡂
⠀⡀
⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⢃⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢴⠂⡀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢱⡀⠀⠀⡀⠆⠀⠀⠀⠀⠒⢶⣄⠸⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠌⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⡲⡆⠀⣠⠄⠀⢁⠄⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠀⠀⠀⠈⠁⡀⢁⣦⡛⠀⠀⢲⣿⢴⠁⢐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠄⠊⠲⠰⠈⡃⠺⠻⣐⠛⡓⠖⢀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣄⠀⠀⠀⠿⣷⡍⢿⠿⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⣾⣿⣿⣶⡆⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠠⠊⢹⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⢌⡀⠀⠿⠀⠀⠀⠀⠛⠛⠋⢩⠀⠀⠙⡧⠀⠀⠀⠀⠀⠀⠀⢷⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⢁⠿⡄⠀⣴⣴⣇⠀⠘⠂⠈⠀⠀⠀⠛⡅⢄⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⣰⠟⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⡀⣀⢀⣀⣀⡀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⡀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⠿⠂⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⡛⠛⣈⣉⣷⣹⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⡀⠀⣴⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣷⣽⡿⠿⠿⣿⣿⣿⣿⣶⣦⣦⡰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡚
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢻⡏⠝⢿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡷⡾⣿⠿⠓⢶⣧⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣶⣴⣿⡿⢦⣄⣤⠈⣤⣬⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⡜⢃⣤⠿⠉⠀⠈⠉⠒⢦⢁⣤⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⡾⣧⡞⠁⠀⠀⠀⢠⣤⡀⠛⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣽⢿⣏⠀⠾⠋⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⢿⣾⢿⣆⠀⠀⠀⡄⠀⠀⡸⠋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣠⢟⣭⣿⣦⠀⠀⠀⠀⠰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠙⢶⡿⠇⠀⠀⠀⠀⠀⠛⣫⠀⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠀⢀⡀⠾⠶⠉⠠⡀⠀⠀⠀⠀⢯⠂⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠀⠐⠂⢠⣠⡶⠀⠁⠈⠀⠀⠀⠀⠈⢟⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⠀⠁⠲⣤⠐⢶⣆⡀⠀⠐⢧⡄⠀⠀⢘⡇⢈⡂⢋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣠⡀⠑⠦⢈⠓⠀⠀⠹⣷⣄⠂⣨⣷⣿⣧⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⡀⠉⢶⡀⠀⠀⢿⡟⢳⣉⣿⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⡆⠀⠘⡅⣸⣿⡿⣿⣿⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠏⠀⠖⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⠟⠀⠈⣷⣾⣭⣿⣧⣴⣶⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠘⢓⣤⣤⣵⡟⡛⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⢺⣿⠿⠁⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡾⠋⣠⣭⣿⣶⣿⣾⣿⣇⣬⣿⡿⢿⣿⣿⣟⢁⠀⠀⠀⠀⠀⠈⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠻⣿⣿⣶⣄⣀⣤⡤⠤⠶⠲⡿⢶⠒⠀⢀
⠀⠀⠀⢠⠀⠀⠀⢀⣾⣿⣿⡇⣴⣿⣿⣿⢿⡿⣿⣇⡀⠀⢶⡄⠀⠙⠫⣍⣉⣉⣤⣤⣶⣟⡾⣿⡇⠀⠀⠑
⠀⠀⠀⡌⠀⠀⢠⡜⣿⣿⣿⣼⣿⣿⢻⣿⡀⣤⣿⣿⣿⣶⣌⣱⠶⠦⠀⠈⠙⢦⣀⡒⡩⠋⢀⣾⠂⠀⠀⢀
⠀⠀⠀⠆⠀⠀⣾⣷⣿⣿⣿⣿⣿⣥⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠈⠙⠃⠴⡾⣆⠃⣀⢡⡞
⠀⠀⠀⠠⠀⢼⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢉⡅
⠀⠀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢱⣶⣿⣆⣾⡿⠓⢾⡄
⠀⢰⠟⠉⡻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆⠀⡀⠸⣿⣿⠙⣻⡇⠀⠀⢶⠶⠲⠶
⠀⣶⣶⣾⣿⣿⣿⣿⣿⢳⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⠀⠀⣿⡿⠀⣿⡇⠀⣠⣂⡀⣀⣀⡀
⠀⠹⢿⣿⣿⣿⠻⢻⣿⣈⣛⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⢹⡇⠀⠈⣿⣿⣿⣿⡍
⠀⠀⢰⣿⣿⣯⠀⢨⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣯⠀⢸⣷⠀⠀⣿⣿⣿⣿⣿⣷
⠀⢠⣾⡿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡄⠹⡄⠰⣿⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠘⣿⣿⣿⣏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣴⠀⣼⠀⠰⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⡿⠦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⢻⡇⠘⠀⠀⢻⣿⣻⣿⣿⣏⠇
⠀⠀⢴⠿⣿⡇⠀⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡄⢁⡀⣸⣿⣿⣿⣿⠏⡆
⠀⠀⢠⣀⣽⡇⠀⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣷⣿⠃⢹⣿⣿⡏⠑⢾⡟
⠀⠀⣸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣉⣤⣯⣥⠀⡄⢸⣿⣿⣿⣿⡿
⠀⠀⢹⡿⢿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠦⠀⠀⣴⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠃⠀⣽⡟⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠶⠂⠀⢸⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣭⡿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠛⢿⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡿⣿⣿⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠸⠃⠠⢿⠹⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⠛⠛⠛⠛⠻⠿⣿⢿⣯⡴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀⠀⠀⠀⣠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠲⠂⠠⡰⠄⠆⢀⢀⡉⠀⠀⣿⡋⠁⠾⠢⢄⣈⠀⡖⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠶⣠⣦⡀⠆⣠⠀⠄⡔⠎⠘⠀⠞⣷⣛⣧⡄⣡⠄⠊⣉⡿⣣⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⣄⡀⢠⣍⠁⠐⠉⠈⢂⡰⠒⢶⣮⢐⣿⣯⢏⣿⣷⣷⡦⢠⣆⡼⡆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠼⠂⣀⡘⢠⢻⣍⠨⣤⣴⣮⣇⡈⠀⠉⠠⣜⢿⡁⡉⢿⣦⡿⠿⣱⣤⣁⠶
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢀⡠⢀⣿⠋⠈⢀⡈⢩⣦⣿⣧⡁⠈⡿⠊⢏⠀⡈⢻⣇⠓⠈⠈⠙⠁⠻⠟⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐⣃⡄⠀⠀⢰⣟⣻⣿⠿⠇⢀⠐⣤⠀⠘⡄⠈⡀⣿⠁⠙⠶⡀⢀⣤⠁⠈⡄⣀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠸⢦⠀⠠⠌⢩⣿⣿⣦⣄⠚⢰⣆⡇⣀⠂⠐⡖⢿⡦⠒⠀⣸⠄⢀⣀⠓⠆⢨⠁⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠛⡀⠒⢡⠠⠚⢥⣛⣿⡁⠰⠈⠉⠄⡘⢂⡈⠷⠈⠀⠃⠠⡬⡤⠼⣩⡧⡀⠉⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠙⡁⠀⢀⠀⠁⡫⠈⣦⡤⠀⣶⠋⠀⠛⠛⠉⣰⣷⣶⠖⠘⡁⠠⠬⣅⠠⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣄⢹⡦⠴⠦⢄⣿⡀⠿⢆⣀⡜⠨⢠⡀⠀⡗⠛⢻⣿⣀⣀⡷⠖⠈⠉⢤⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⡾⢣⡀⠀⣼⢻⣷⠀⠈⠀⣿⠶⣎⠁⡈⢄⡠⣾⣗⣟⡉⠢⣷⣤⡔⠶⠍⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢎⡀⢸⠙⠁⡠⠋⠠⠘⠋⠂⡃⢐⡟⠀⠳⠀⢀⠈⣿⣿⡁⠀⠘⠏⢑⣶⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⢌⠀⣤⢟⣠⠾⠧⢤⣤⠏⠘⢳⡞⠠⠔⡦⠜⣤⡿⠓⠀⣤⠀⠂⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣦⣬⡞⢳⡄⣤⢋⢋⠄⠀⢸⣧⣀⡀⣃⡘⠋⠐⠄⡄⠀⠀⠒⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠛⠃⠁⠴⠀⣿⣻⡾⣾⣠⣿⡛⠗⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡈⠻⣧⢿⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⢆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣯⡈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣟⢉⠂⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠌⡿⠄⣿⡐⣧⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠘⠓⢘⠃⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠂⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠀⠐⠋⠋
⠀⠂⠀⠀⠀⢣⢀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠤⡉⡰⢀
⠀⠀⠀⠈⠀⠀⠸⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⠞⢠
⠀⠀⠀⠀⢤⠂⠀⠆⠨⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠰⠃⢀
⠀⠀⢀⠀⣦⠁⠃⡌⠐⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠠⠄⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⡂⠀⠐⢊⠤
⠀⠀⢳⠂⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠐⠀⠀⠈⠁⢰⠠⠀⠉⠀⠀⠀⠀⠀⡀⠐⠑⠂⠀⠀⠀⡀⠃
⠀⠀⢸⡀⠀⠀⠀⣸⡃⠀⠀⠀⠐⠒⠈⡀⠀⠀⢀⣀⡓⠘⢀⡄⠀⠂⠾⠃⠀⠀⠀⠀⠀⠀⠐⢌⠍
⠀⠀⢸⠀⠀⠠⡐⢕⣀⠀⠀⠐⠛⠆⠂⠀⡀⠀⠀⠀⠠⠄⠋⠀⢦⡀⣤⣄⡀⠈⠀⠀⢀⠈⠀⠤⠂
⠀⠀⡞⠀⠀⢤⣈⣩⠢⠂⠀⠢⣀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠉⠱⡆⢢⠀⡀⠀⠀⠀⠀⠀⠁⠲⠘⠋
⠀⠀⠀⠀⠀⠢⣭⣠⠶⠖⠂⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⢀⣧⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠟⠛⠿⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⢀⢤⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠃⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠛⠀⠀⠘⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⣿⣿⣷⠀⠀⠀⠀⢻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢀⡼⡇⠀⠛⠁⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠯⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢠⣤⣶⠾⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠉⣁⣀⣤⡞⠓⢤⣀⠀⠀⢀⠴⠖⠘⣿
⠀⠀⠀⠀⢠⡀⡀⡠⠤⢈⡀⢉⠉⠻⠘⠿⠋⠁⠀⠀⠀⢹⣟⠷⠋⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⢶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠚⣁⣘⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡜⠁⠀⠀⠀⠀⠀⣿⣹⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠀⠉⠉⣉⣉⡀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⣸⣟⠉⣤⠀⠀⣰⠊⡱⠆⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠐⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣇⠀⢿⣀⠶⠙⠦⣽⠀⠀⠀⠘⢫⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣰⡿⣻⣿⠋⠐⠀⠀⠀⠀⠀⠀⣎⣻⢷⣾⣇⣠⣤⣿⠁⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⠀⠀⠀⣼⣿⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠺⠝⠛⠋⠉⠀⠀⠀⠳⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⢻⣿⢿⡟⠀⠀⠀⣸⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠠⣄⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⢨⣿⣿⡀⠀⠀⢀⣹⡟⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠀⠀⢀⠀⠘⣇
⠀⠂⠀⠀⠀⠀⣾⣿⡟⢡⡀⣀⣿⣉⢰⣿⢤⠀⡤⠀⠀⢘⣃⠀⣰⠄⢐⢿⠙⣧⡤⡄⠀⢀⣆⠀⢃⠀⢱⡀⠀⢀⡸⢆⠀⢹⣧⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⣿⣿⠁⠀⣸⡿⠁⠀⣿⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⢳⠀⠀⠁⠀⠃⠀⢹⡆
⠀⠀⠀⠀⠀⢸⣿⡿⠂⢠⡿⠁⠀⢰⠏⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⣼⣿⠇⢀⣾⡟⡾⢠⡿⢠⠇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠈⣿⣿⠀⣼⡿⢹⠃⣿⡁⠊⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⢠⣿⣿⣶⣿⠃⡎⣰⡟⠳⡇⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⠀⠀⢸⣇⠀⠀⠀⢠⡀⠀⠤
⠀⠀⠀⠀⠀⣿⣿⣿⡿⣼⠃⣿⠀⠀⠇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠻⢛⣻⣛⠋⢸⡇⠀⠀⠀⣼⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⡇⠀⠀⢰⣦⣀⠀⠀⢘⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢢⣾⡿⣿⡿⠀⣾⣁⠀⠀⢠⡟⠁⠀⢀⣮⣄⠀⠀⠀⠀⠀⠀⣼⡇⠉⡶⣦⣀⡀⠀⠀⣤⠹⡀⠁⠒⠀⣀⡄⢀⡠⣄⠀⠙
⠀⠀⠀⣼⠨⣿⣏⠻⣿⣿⣟⣿⣆⡀⠈⢗⣤⠴⣿⠁⢸⠗⢤⣄⣀⠀⢀⣿⣿⠀⢣⠈⣏⠻⣿⡂⢻⡄⢳⡀⠀⠀⠈⡿⠇⠀⠀⠀⠀⠀⢻
⠀⠀⠀⣼⣧⡙⣿⣷⣿⣿⣿⣿⡟⢡⣴⣿⡏⢰⡿⠀⢸⠆⠀⣿⠉⠙⠛⢻⣿⠀⢸⡄⢹⠀⢏⠹⣌⣷⠈⣧⠀⠀⠀⢐⠂
⠀⠀⠀⢿⣿⣷⣦⣉⣙⣛⣋⣥⢀⣿⡇⣿⠃⢸⣇⠀⢸⠀⠀⣾⠀⠀⠀⢹⢹⡇⠈⣇⠀⠀⠘⠆⠉⢻⣇⠸⡄⢀⠀⢈
⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⢻⡟⢸⣿⢰⣿⠀⢸⡟⠂⢸⠄⠀⢸⡀⠀⡀⢸⠀⣇⠀⢻⡄⢰⡀⠑⠀⢻⣿⠀⢳⠀⡆⠸⡆⠀⠇
⠀⠀⠀⣿⣿⣿⠿⢱⡟⠀⣿⠁⢸⡟⢸⡿⠀⣿⡃⠀⢀⡇⠀⢸⣇⠀⠀⠀⠀⣿⠄⢿⣿⠈⡇⠀⠀⠀⢿⡁⠈⠀⠙
⠀⠀⠸⣿⣿⣤⠀⠀⠀⢸⠃⢀⡞⠀⡾⠃⠀⣿⣶⠀⠸⠿⠀⠀⠉⠀⢸⠀⠠⣧⠄⠸⠅⠀⢃⠀⠀⣀⣸⣧⣀⣤⣄⣠⣤⣤⣠⣤⣶⣶⡶⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⣴⣦⣤⣤⣀⣠⣾⣁⣀⣀⣦⣀⣀⣴⣶⣶⣆⣠⣴⣧⣤⣴⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡉⠁
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠻⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠈⠂⣠⡄⠀⠈⢉⡤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠉⠊⠢⡰⠓⠐⠴⠈⠀⠘⡦⠒⠃⠀⠀⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠑⡄⠀⠠⠄⠀⢀⠚⠉⠲⣀⣀⠁⠄⠀⢦⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢠⡄⡉⠉⠣⠀⠀⠀⠀⢠⠔⠀⢀⠑⠀⠀⠊⣀⠀⠀⡞⠁⢀⠅⢀⡜⢀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢘⡒⠂⢖⣁⠀⠠⡀⠀⠀⠀⠀⠄⢀⡘⡴⢮⠔⣤⣃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠖⠸⠒⢀⠀⠨⠣⠖⠾⣠⡇⠀⠁⠊⡘⠀⠓⡡⠼⠀⠁⠀⠀⠀⠘⢓⠀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸⢇⠀⠀⢈⡀⠹⡧⠄⢰⠲⠉⠊⠤⡎⠀⠀⠀⠀⠈⠀⠀⠈⡢⢀⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⢆⡀⠈⠌⢉⠈⠘⢴⡌⠁⠠⠠⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⢬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠠⡀⢠⡀⢐⠐⢳⣠⠀⡀⢤⠍⠓⢦⠀⠀⠈⠀⢠⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⣀⠊⠋⠉⠁⢄⡀⠏⠈⠱⠘⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⠂⢲⠤⡦⠀⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢠⢴⢻⢨⠑⠢⠤⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠁⠁⣇⠐⡀⠀⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠸⡔⠘⡌⣗⠀⠈⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢶⢳⠠⡱⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⠤⠀⠐⠒⠲⠋⠀⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠾⠤⣤⡄⠀⠀⠀⠀⠀⠇⠀⠁⣀⣀⣀⡀⣠⠤⠠⠤⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠋⠀⠀⢀⣬⣷⣶⠀⠀⠀⢠⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣦⣄⣀⣀⣀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⣙⡖⠁⠙⡷⡄⠀⠀⠰⠁⠤⠈⡿⡁⢀⣀⠬⠶⠯⣤⣀⠀⠀⠀⠀⠀⠐⠀⠈⣶⣮⣍⠉⠛⠒⠒⠞⠷⢾⡄
⠀⠀⠀⠀⣀⣴⣶⣽⣿⣇⠠⢀⣷⣧⠀⠀⠰⡀⠀⣠⣿⣿⣷⣾⣿⣾⣿⣼⣿⣿⣦⣀⠀⢰⠃⠀⢲⣽⣿⡘⡆⠀⠀⠀⡰⠋⢺⣿⡄
⠀⠀⠀⣾⣿⡛⣿⣿⡍⢿⡿⢿⣿⣿⠀⠀⢀⣽⣿⣻⣿⠟⠉⣠⡿⠿⠛⠛⠿⣿⣿⣿⣷⣽⡀⢠⣼⣿⣿⠆⡇⠐⠀⢰⣇⠀⣾⣿⣷
⠀⠀⠀⠉⠠⠞⣿⣿⣧⣾⣿⣿⣿⣿⠀⢠⣌⣷⣿⣿⣿⣾⣿⠋⠀⠀⣰⢮⣑⠊⢻⣿⣿⣿⣧⢸⣿⡙⠃⢀⣧⣴⣦⣶⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣤⣌⣻⣿⣿⣿⣿⣿⠁⠀⠀⢎⣤⡶⣻⢥⠀⣿⣿⣿⣿⣷⣿⢧⣄⣽⣿⡿⠿⠛⢛⣻⣿⣹
⠀⠀⠀⡄⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣟⣽⣶⣵⢸⢠⡽⠋⠉⠉⠙⠛⠿⣿⣯⠤⠖⠊⠉⠀⢿⣿⡿
⠀⠀⠀⢁⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠃⠀⠀⢨⣽⣿⣏⣼⠃⠈⡆
⠀⠀⠀⠈⢄⠀⠈⠻⢟⣻⣿⣿⡿⠛⠻⠿⠿⠿⠿⠿⠿⡄⠀⠀⠈⡖⡻⡟⠛⠀⠈⠃
⠀⠀⠀⠀⠀⠑⠠⠅⠠⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡳⡧⠤⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⠑⢌⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠟⠀⠀⠀⣤⡀⠰⠀⠀⠐⣐⠞⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡄⢀⡀⠀⠠⠀⠈⢀⠄⠐⠷⠌⠋⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⠄⠀⠐⠀⠀⢠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠿⠇⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠀⢁⡀⠀⠀⠀⠀⠘⠃⡜⠀⠀⢀⣤⣤⣄⣄⢨⠖⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠀⠀⠀⠀⠀⠀⡄⠀⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⢹⠰⠆⠀⠀⠀⢠⣤⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣀⡤⢀⠀⠻⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⢹⠀⠀⠻⢿⢿⣿⣿⣿⣿⠃⢸⣿⠟⠃⠈⣶⣷⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣷⡐⠀⠀⣠⣖⣸⣦⡄⠀⠀⠀⠘⠛⡿⢸⠀⠘⠉⠀⠀⠀⠀⢹⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠁⣠⡄⢴⣯⢹⠉⠁⠀⠀⠀⠀⠀⢠⣼⡃⠁⠀⠀⠰⡖⠀⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠀⠀⠙⡁⠈⠁⠀⢐⣶⣾⠤⠀⠈⠙⢿⣿⠇⢠⠀⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠛⠛⢩⣦⠀⠀⣤⣴⣛⡆⠀⡶⠒⠀⢰⣟⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⢧⡀⠈⠀⠀⠀⠤⠀⠀⢀⠀⠀⠀⣴⣄⢠⡸⣷⣶⣼⣿⠿⡇⠰⠟⠚⣿⡾⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢳⣤⣹⠀⠐⡄⠂⣀⡼⠲⠀⠀⠈⠁⠀⠙⣿⣿⣿⠛⠀⣿⡀⠺⠿⠛⠋⠀⠑⠀⠀⠀⢠⠀⡸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠄⠸⡿⠧⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠀⣀⢸⡆⢀⣤⣀⡆⠀⢟⡅⢀⣤⣾⣞⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡀⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠘⠋⠀⠛⢪⠁⣾⣿⣿⡇⠀⠘⠁⣸⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⣸⢃⡴⠀⢀⠀⣀⣠⡟⠃⠀⠀⠀⠀⢀⣸⣾⣷⣾⣿⣧⣤⠇⠀⠀⠀⠘⠀⠈⠉⠛⠃⠀⠀⠀⠙⢚⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⢹⣷⡬⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⢠⣠⣄⣀⣐⣷⣦⡼⠟⠀⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠄⠀⣶⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠠⠬⠛⠀⢲⣤⣤⣽⣿⡿⢿⣿⡛⠛⠉⠀⠀⡆⠀⢤⣹⣿⣥⣿⠿⠟⠋⠁⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣟⣀⠀⣠⠞⠋⠀⠀⠘⠀⠁⢀⠀⠀⡔⠁⠀⣼⢿⣿⠋⠙⠀⣀⣴⠂⠀⢀⡠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠷⠛⠀⢀⡀⠑⣀⠉⠠⠰⠞⢉⣡⠶⠚⠉⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣴⣾⣶⣤⣄⣤⣶⠶⣿⣷⣶⣶⣿⣧⠀⠉⠙⣤⣠⠶⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣿⣦⡿⡿⠛⠃⢀⠀⠿⠿⣶⠟⠋⠀⠀⢀⡀⠐⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⣿⣿⣟⠛⣿⣏⣾⡿⢿⢿⣿⣀⣀⠘⠃⣀⢀⣿⣤⠀⠰⠂⠀⢄⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣿⠯⠟⠉⢿⣿⠋⠙⢷⣼⡈⠛⣿⣇⣀⣠⣿⣿⣿⣿⡤⢀⡄⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⢄⣠⣀⠀⠘⢿⡇⠀⢸⣿⠿⢸⣿⡟⠋⠉⡀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⣷⣤⣄⢻⣿⡚⢳⡆⢸⣿⠁⠀⣴⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⣉⣼⡿⠿⢿⣿⠁⢸⡇⠈⣿⢀⠸⣿⣬⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⠀⠀⠀⣿⠀⠘⠓⠀⣿⠁⠀⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⡰⠁⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⡈⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠁⠠⣴⠀⠂
⠀⠀⢀⠀⠈⣁⠻⣿⠏⠀⠠⠀⠈
⠀⠀⠈⣹⠀⠁⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡤⡶⠈⡝⢿⠀⠀⠀⠀⠀⠀⠻⡄⠩⠉⢻⣿⠇
⠀⠀⠀⠀⠘⠗⡀⠀⠀⠀⣀⠤⣀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡏⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠆
⠀⠀⠀⠀⠀⠀⠁⡶⠀⠆⣸⠖⢋⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠎⠀⣆⠀⠀⠀⢀⠺⡡⣄⢀⠀⠀⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡱⠈⢽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣤⣀⣀⢶⣾⣥⡾⠀⠀⠀⠀⠀⠐⠁⠛⠀⠀⠠⣶⡜⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢘⡃⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠹⡿⢻⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠈⢿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⠄⠰⠆⠈⣀⣤⣤⣤⡘⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠴⠚⢋⢿⡟⣿⣿⡇⠀⠀⠉⠅⠓⠆⢀⠀⠀⠀⢀⠈⠀⠀⠉⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠟⠀⣼⠁⢠⡎⠀⡿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠐⠏⠀⣿⡇⠀⣷⡟⠀⠀⠀⠐⠀⠀⠆⠀⠀⡄⠱⣤⠀⠀⠀⠚⡥⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⣰⣿⠇⣸⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⣿⡗⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⢻⣿⣿⡾⣹⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⢋⡇⠀⠀⠀⢠⠄⡠
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠢⠀⠂⠀⠀⠀⠽⣃⠠⠀⠀⢞⡆
⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣿⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡗⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⡿⠀⠀⠠⢿⣶⠀⠀⣽⠇⠀⠀⠀⠀⢈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠾⣿⣼⠃⠀⢀⡤⠚⠁⠤⠀⠍⣤⣆⠠⠘⠦⠈⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡿⢲⣿⠀⠐⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⠸⣷⣦⣤⠀⢔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠹⠟⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠉⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠐⠘⡇⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⡀⣸⣿⡜⠰⣆⠀⠀⠀⠀⠄⠀⠀⠀⢠⣯⠙⣩⡃⢶⣴⡄⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⢤⢰⡶⠔⢤⡝⠛⠉⠀⣆⠈⠀⠀⠀⢀⢠⡄⠀⠂⣿⠷⠿⢈⢥⢸⡿⠵⣏
⠀⠀⠀⠀⠀⠐⠛⢦⡀⡀⠿⠛⠀⢨⣧⠈⣦⣐⡇⠀⡘⠋⠀⠀⠀⠠⡾⢘⠁⠀⢠⣾⠓⠲⠆⣿⠿⠆⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠎⣣⡁⠐⢀⡀⠆⠉⠐⠀⡌⡗⠀⠃⠀⠀⡀⡄⠀⠀⠀⢀⣀⠀⠉⢨⡄⣸⣗⣶⠦⠀⣿
⡀⠀⠀⣀⠀⣠⠀⣹⠋⠁⢻⣿⣏⠁⠀⠀⠀⠁⠃⠀⠀⠀⠄⢁⣗⣰⣄⣠⣤⣼⡄⠘⠋⣠⢁⣙⣿⣿⠆⣿
⠁⠀⠝⢻⡇⠁⢠⣟⣶⡆⣸⣿⠉⠁⢸⠀⢳⡀⠀⠀⠀⢰⠀⢸⣿⣽⣿⣿⣏⠈⡗⣶⣰⠃⣘⠛⣿⣿⡿⣿
⢀⡀⠀⠀⢁⣴⠏⡜⠀⡿⢿⠛⠀⠢⣽⠀⠀⢷⢀⣄⠀⠐⡀⢉⣽⣿⣿⣹⣿⣷⡀⢠⣷⡔⠟⠀⢻⡉⠃⣿
⠃⢐⣃⠀⡸⢿⣀⡁⠀⣈⣭⣄⣠⣶⣿⠀⢰⢶⠚⢳⣿⢀⣁⣾⣿⣿⣿⢉⡿⡏⣧⣿⣟⠁⠘⠀⣸⣾⡆⣿
⠀⠈⠏⠲⠤⣾⠅⣼⠎⢩⡏⠙⢿⡿⡇⠀⠀⢸⠷⢣⣿⣄⠉⡿⠎⠟⠁⣿⠃⢠⣿⣽⣯⣿⣿⣿⣯⣭⣧⣿
⠀⠀⠀⠀⢰⣿⡈⣿⠀⣿⠁⠀⠀⣆⡇⠀⠀⢠⠞⡱⠘⠋⠀⠀⠀⠀⠀⠁⠀⢡⠟⢻⡿⣿⣿⣿⣷⣿⡇⣿
⠀⠀⠈⠉⠉⠁⠉⠈⠉⠉⠁⠀⠀⠉⠉⠂⠒⠊⠒⠙⠒⠒⠒⠓⠐⠒⠂⠐⠐⠋⠐⠃⠖⠚⠟⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⣂⡀⠄⠂⣠⣶⣦⣤⣅⠛⡦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡋⢠⣿⡛⣫⣖⣘⣿⣿⣿⣿⣿⣯⣀⣾⠟⣁⡿⣾⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢻⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣾⣿⣟⣷⣦⣀
⠀⠀⠀⠀⠀⢠⣾⡿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣄⣀
⠀⠀⠀⠀⢀⠛⣿⣷⠈⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣦⣄
⠀⠀⠀⠀⢸⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀
⠀⠀⠀⢸⣿⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷
⠀⠀⠀⣨⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⡾⠛⣻⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⢤⡀
⢀⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣧⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣨⢃
⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢤⣤⣤⣾⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣤⣀⣀⠀⠀⠀⠀⠀⣉⣭⡴⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣬⡝⢻⡆⠀⠀⠀⠀⣩⣷⣤⣄⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣏⣹⣿⡟⢢⠻⡆⠀⠀⢨⡎⣹⣿⣏⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣘
⠘⢿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡏⡛
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠐⢄⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢾⣤⢿⡆⠴⠤⠀⠀⠀⠀⠀⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡻⡾
⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠠⠶⢿⡶⣶⣦⡤⠦⡄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣶⡱
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠰⣶⣦⣀⢀⣠⠶⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠙⠉
⠀⠀⠀⠀⠀⠀⠻⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠉⠉⠉⠁⠀⠀⢀⡔⣻⣿⣿⣿⣿⣿⣿⡻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠿⠛⠋⠙⢻⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣤⡾⠋⠀⣿⢋⠉⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠐⠀⠀⠀⣿⠜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠁⢹⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⡟⡄⠸⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⠀⠘⡀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣷⠀⣷⠨⡙⠒⠤⢄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣀⣾⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⢀⣸⠁⠠⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⢠⠀⠀⡟⠋⢀⠁⢲⡤⠀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢦⣄⡉⠡⢀⠊⢀⠀⢷⣁⣰⠃⠐⡠⢠⠄⠀⠀⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠊⠁⠂⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠩⡓⣸⢀⠢⠀⣠⠛⠨⢀⠌⢀⠈⠠⠐⠂⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⢤⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠤⠠⢍⡼⠚⠁⠒⢬⣤⡾⠇⠲⢿⠀⠰⣶⠊⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⡄⠀⠀⠠⠀⡠⠀⠀⣁⡴⠋⠀⠀⠀⠀⡜⠁⠀⠀⠀⠘⣦⠜⠀⢈⠁⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠀⢌⣀⠴⠖⠀⠀⡀⡎⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡦⠈⢭⠀⠐⠂⢀⠐⣒⡀⠀⠘⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡽⠊⠀⠀⠀⢀⡼⠓⠉⠉⠒⢤⡀⠀⢸⣀⣄⣀⣀⣆⡴⠊⠀⠀⠀⠘⡄⢠⣽⠚⠃⠋⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠣⡀⠦⠄⢠⠏⠀⠀⠀⠀⠀⢤⡴⣻⠟⠉⠉⠹⢭⡑⢆⡠⠄⠀⠀⠀⢳⠈⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠉⢠⠀⡄⠀⠀⠊⣙⠀⠀⢀⠤⠀⠀⣿⡜⠀⡠⠀⠀⢀⠀⠐⡈⢧⠀⢀⣀⣤⠾⡤⠄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢉⠀⠀⠠⠆⠽⠤⠖⠁⠀⠀⢠⡏⡄⠘⠠⠆⡩⠂⠆⢀⣼⡼⠖⠋⠀⠀⢀⡇⠄⠪⠈⠲⠶⣅⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠠⠤⣄⡄⠀⠀⠀⢠⠿⣷⣀⣀⠀⠀⣁⢠⣾⠟⠉⠂⠤⠤⠤⡞⢠⠈⠢⠀⠤⠀⠠⡉⠛⢶⠖⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⢈⡠⠚⠁⠐⠄⣀⠠⠉⠈⠙⠛⢦⡿⣯⠟⡟⠀⠀⠐⣦⣤⡠⢜⠯⣜⢣⢂⣬⠢⠐⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠿⢧⡗⢊⣇⠀⠀⡰⠟⠻⡀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⢸⡄⠠⢀⡋⠝⢶⠟⡠⡶⢈⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢤⠀⠘⢛⠉⢈⡙⠅⠀⠀⠀⠀⠑⠤⣀⢤⠖⠁⠀⠀⠀⢂⣄⡤⡴⣿⠉⢿⣷⣄⣀⡐⠃⠀⠘⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡀⠈⠄⠀⠂⠐⠁⣜⠀⠒⠀⠈⠁⠀⠀⠀⡀⠀⢰⣗⢋⡉⡇⠀⣷⠀⡉⠁⡼⡛⢄⠂⠁⠛⠀⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⢖⠀⠀⢠⠄⠁⠀⢀⢋⣌⣱⠃⣠⠴⡀⡠⡀⠀⠉⢺⣶⠆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠁⠀⠙⠻⡇⠀⠀⠈⠀⠧⠜⠀⠠⠀⣧⠂⢀⠀⠀⠀⠀⠰⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠁⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⡀⠀⠳⠦⠀⠀⠀⠀⡠⠀⠀⠀⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡁⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣶⣷⡄⠀⠀⠀⠠⠙⠀⠀⠀⠀⢀⣶⣿⣿⣶⡄
⠀⠀⠀⠀⠴⣗⠀⠀⠀⠀⠀⠈⠛⠗⠢⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠻⡿⠁⠀⠀⠀⠐⠃⣤⠀⠀⠀⠸⣿⣿⣿⣿⠇
⠀⠀⢀⢜⣼⡯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠐⠁⠀⠀⣁⢀⠲⠆⠀⠀⠀⢩⡙⠉⠁
⠀⠀⠀⣟⠟⢵⡜⡄⠀⠈⠀⠀⢰⠋⠀⠀⢵⡇⠀⠀⠜⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠠⡆⠀⠀⠰⣄⠈⠘⣩⣄⡀
⠀⠀⠀⠉⠐⠈⠉⠀⠀⠀⠀⠀⠂⠀⠐⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠐⠯⡓⠄⠁⠀⠀⠀⠛⠃⡸⣿⠋
⠀⠀⠀⢖⡀⠖⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠰⢾⡟⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⣴⠀⠀⠀⠡⣙⠉⠀⠀⠀⠀⠀⠀⠠⣀⣀
⠀⠀⠀⡆⠀⠐⣟⠦⠀⠀⠹⢿⡿⠇⠀⠀⠰⣀⠀⠀⠀⣶⡆⠀⠀⠀⠙⠉⠁⠀⢰⣺⣿⣿⠆⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠁⠀⣰⣿⠂⠀⠀⠀⣦⡀⠀⠀⠀⡀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣴⠌⠠⠀⠀⣀⡀⠀⠀⠁⢤
⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠢⢹⣧⡞⠀⠀⠈⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣶⣄⠀⠀⠈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠻⣮⣱⣿⠏⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣴⢶⣦⡄⠀⢠⡆⠈⠁⢬⣿⠏⠀⢠⡏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠀⠀⠀⠙⢿⢿⣿⡋⠀⠙⠗⢤⢦⣄⡀⠀⣼⡁⠀⣠⠏⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⢀⣤⡀⠈⢏⣛⣹⡆⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣐⠀⠀⠄⣀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠹⢾⣇⠀⠈⠛⠻⣽⣶⡦⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⢅⠀⠙⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣠⣿⠀⠀⠀⢢⣹⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠢⡀⠀⠀⠀⠀⢀⣟⣿⣿⡇⣿⣿⣧⢀⣒⣸⣿⡯⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠀⠀⠀⠀⠀⣻⢻⣿⣇⣽⣿⣿⣇⢉⣿⣿⡋⡄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠛⠧⠀⠀⣀⠀⠉⠀⣿⠁⠋⠏⣿⢹⣷⣿⣿⡇
⠀⠀⠀⠀⠀⣠⡀⠀⢠⣤⣤⣤⣤⡤⡀⢰⡷⡟⣾⣻⡄⠀⠀⢠⢿⣷⣦⣄⣈⠀⠀⠀⢸⡎⢻⣿⣿⣇
⢀⣤⢶⡀⣰⣿⠘⢆⢟⣷⣇⣞⣻⣄⡈⣨⣯⣹⣿⡟⠁⣤⣶⢟⡛⠉⡸⠃⢹⣿⣶⣶⣦⣤⣀⣿⣿⣿⠀⢠⠀⢀⡿
⠨⣿⣿⣿⠋⢋⢠⢞⣬⡿⣍⡽⢛⣯⠞⠣⠊⢹⣇⣠⣶⣿⣿⡌⠑⣤⠈⠀⠘⠋⢿⣿⣻⣿⣿⡿⠿⠛⠁⠸⠟⠛⠀⠀⢂
⠀⠉⢛⣏⣴⣦⢟⣼⣻⣝⣊⣼⣦⡥⣾⣽⣿⣿⡟⠻⣶⣭⣸⣇⠙⠋⠀⠀⢀⡀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⣧⣽⡟⠳⢦⡾⣿⣧⣦⢛⣹⢷⣿⣽⣏⣼⣴⣧⣌⡛⣿⢹⡗⢠⠀⠀⠀⠀⠨⡇⠀⠀⡀⠀⢤⣤⣄⣂⣻⣄⣤⠄
⠀⠀⠙⠿⢛⣻⣖⠛⣪⣇⣹⣾⠣⣤⣿⢿⡿⠿⠯⢛⣿⠹⢡⡀⠿⠿⠀⠀⠀⡀⠀⠀⠀⠾⠀⠀⠈⠛⠥⠔⣫⣈⡅
⠀⠀⠀⠀⢠⣾⣿⠃⡿⢀⣾⣩⠒⣾⣾⢿⣿⡶⢒⡐⠋⢶⢻⡍⠁⡀⠀⢀⣀⢙⣶⡤⠦⣄⠀⣀⡒⠀⢀⡈⠹⢿⠿⡷
⠀⠤⠄⠀⠹⠿⠿⠿⠧⣨⢿⣛⣿⣧⣿⣮⡯⣑⡿⠿⠷⠞⠓⠀⠀⠀⠀⠛⠛⠛⣿⣦⡴⠿⠾⠿⠗⠒⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢦⣄⣀⣠⣄⠚⠁⡀⣊⠀⠀⡆⣀⠠⠀⠀⢠⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣄⣐⡀⢀⠰⣤⢀⣦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⡹⣷⣞⠛⢋⣡⣼⣯⠴⣠⣀⣴⣷⣾⠥⣤⡴⣶⣶⣋⠀⠀⠀⠀⠀⠸⡀⠉⢙⠿⢿⣼⡥⠟⡟⠀⠀⢀⡀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢌⠣⠈⠻⣟⠺⡿⢿⣿⡿⠃⠙⢿⣟⠛⠲⠦⠑⢄⠈⠀⠉⠀⠀⠀⠀⠀⠈⠙⠋⠀⠩⣭⣥⣤⡘⠛⢉⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠈⠐⠀⠀⠈⠻⡎⠀⠀⠹⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠶⣤⣇⠈⠙⢢⠀⠠
⠀⠀⠀⠀⠀⠀⠛⠄⠠⠀⠐⠀⠠⠄⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⠘⣗⠒⠒⠴⠚⠉⡩⠖⡎⢹⠻⣄⣀⢀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠘⣧⣀⠁⢀⡜⠁⣸⠇⢠⣿⠅⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠈⢻⢀⣿⣆⣴⣿⣝⣿⣷⣶⡽⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⡾⠋⢠⠗⡄⠀⠀⠀⠀⠂⠂⠒⠆⠁⠒⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⢻⣿⠟⠉⠀⠀⠈⠱⠆⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠈⡉⠹⣧⣀⣈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⢧⣀⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠇⢀⠀⠁⢄
⠀⠀⠀⠀⠀⠉⣀⢀⠴⠒⠬⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠂⠀⠀⣀⣙⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠈⠑⠉⠁⠀⠠⠀⠀⣴⣇⡀⠀⠀⠀⣠⡆⠀⡷⠀⠀⣸⣿⢛⠈⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⢐⠀⠀⠹⣦⣀⠉⠄
⠀⠀⠀⠀⠀⠚⠃⠈⣬⡀⠀⠀⠁⠀⣹⠇⡀⠀⠀⠀⢻⡑⢾⣥⠄⠀⣉⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠓⠾⡆
⠀⠀⠀⠀⠐⠻⠛⡹⠿⢿⡀⠀⠏⠛⠁⠀⠀⠀⠀⠀⠙⣍⡀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠂⡴⠉⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠆⢲⡶⠶⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⣿⡀⠀⠀⠀⡀⠀⠀⡔⡄⢠⡀⣠⠤⠂⠔⠂⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠈⠀⠠⠤⠀⠀⢠⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠙⠃⠀⠀⠈⢇⠀⣴⠏⡇⢸⡾⠋⠐⠀⠄⠀⠀⠀⠀⠨⠆⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣤⠀⠀⠀⠁⠀⠀⠀⢰⠄⠀⡆⣻⠏⢸⡇⣸⣅⠈⢀⠀⠀⠀⠀⠀⠀⠂⠀⠲⠓⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠔⠋⠙⠀⡁⠀⠀⠀⠀⠀⠀⣬⡄⠀⠀⡿⢀⣾⡧⢿⢁⣀⣤⣀⠶⠋⠁⠀⠢⠈⠀⢢⡀
⠀⠀⠀⢰⡆⢄⣀⠀⠀⠀⠀⠀⠀⢀⡆⡄⢠⠄⠀⠐⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⡇⢺⣿⡷⠛⠁⢁⡠⠜⠀⠀⠀⠐⢀⡄⡀⢀⢠⣴⡲
⠀⠀⠀⢐⠀⠢⠀⠉⠐⣄⠀⠀⣄⣸⡧⢠⡞⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⣿⡄⠁⢹⣿⢋⣠⠴⠚⠋⠀⠀⠀⠀⠐⡶⠟⠛⡠⠛⣈⠉⠶⠂
⠀⠀⠀⠀⢦⠀⠁⡆⣀⢸⡆⢸⣢⡈⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠘⣇⣠⣼⣿⠛⢁⠀⠀⣂⡐⠞⠀⠀⠀⣀⡞⠀⠁⠞⢁⠀⡀
⠀⠀⠀⠀⠈⠻⢶⣿⣿⣿⣿⡀⢻⡷⣿⣿⣤⣦⣤⣤⣄⡀⠀⠀⠈⢧⡁⠄⠈⢿⣏⣷⣿⡷⢞⡿⠀⠀⠀⠀⠀⠐⠈⡉⠈⡸⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⣻⣿⣿⣿⣿⣿⡟⠙⠛⠯⡉⠖⠀⠀⠳⣿⡄⠀⡸⠛⠛⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠏⣁⢌⣉
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣉⢘⣉⢸⣻⡿⢋⣝⠶⠄⠊⠀⠀⠀⠀⠀⠘⢿⣦⡃⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠐⠁⠒⠂
⠀⠀⠀⢀⣾⡿⠛⠛⠉⠉⢙⠛⠋⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⠀⢠⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠀⢈⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠠⢄⠄⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠠⢀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢣⡼⠋⢂⣄⡤⠄⠒⠀⡤⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣋⡀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡖⣰⡆⣩⣀⢇⡄⣘⠐⠄⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠤⠆⠉⡅⢀⡦⠈⢠⠀⠀⢀⣶⡂⣀⠀⠀⠀⠀⠀⠀⠁⢩⡄⠸⠸⠗⠘⠉
⠀⠀⢀⡀⣀⠀⢀⠠⢄⠀⠈⠉⢺⡅⠀⢸⡄⢡⠍⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡀⠐⠒
⠀⠀⠀⠀⠉⠊⠀⠱⣦⡁⠀⢠⡀⡟⠀⠘⠃⣈⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠚
⠀⠀⠀⢀⢀⠀⣀⠀⢸⠇⠀⠀⢘⣧⢰⣤⡅⠸⠋⡀⠀⠀⠀⠀⠀⠀⠐⠛⠷⠉
⠀⠀⠀⠈⠉⠀⢍⡀⣴⡄⢀⠀⠈⡟⠉⠙⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢈⠙⠉⠙⠂⠠⠓⠴⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠀⠰⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⣌⢥⣄⠐⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⡐⠒⢸⣗⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡘⠀⡽⠋⠠⣘⠁⣅⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣼⠟⡀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡐⣝⣴⣶⠟⣟⡷⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢠⠿⡌⠒⠘⠁⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠲⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠚⠃⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⡆
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⢠⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢋⡗⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⣀⡤⡁
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡁⠎⡀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⠛⢙⠊⣓⠄
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣀⢀⣀⠔⠁⠀⠀⠀⠸⠉
⠀⠀⠠⣀⣄⡰⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⠀⢦⠶⢆⣤⡀⢄⣠⣤⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠒⠚⠋⠁⠉⠉⠉

⠀⠀⠒⠀⠁⡂⠁⠀⣸⡄⠀⠹⠄⠑⠀⠈⢖⡈⢉⡄⠴⠀⣄⠀⠀⡜⡇⠄⠀⣼⠀⠀⠀⠀⠸⣟⠷⠖⣰
⠀⢀⠀⠀⡈⠛⡀⠀⠙⠃⠀⡀⢰⠆⠀⠈⠑⢁⠀⡿⠐⠠⠀⣠⠞⠀⠁⠁⠀⠉⠃⠀⠀⢀⠀⠙⠀⠀⣰
⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⣰⠓⠘⢷⡇⠀⠐⠊⣴⠁⠠⣦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠥
⠀⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠁⠀⠀⠘⠁⠀⠘⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⡠⠈
⠀⠀⡀⠀⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢳⠀⠀⣠⢃⣤
⠀⠀⢀⣀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠟⠿⡿⠃
⠀⠐⢛⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠴
⠧⠈⠁⠄⣱⣦⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠈
⡇⢰⠛⠃⠈⡠⠿⣏⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠘
⠁⠎⠐⡖⠋⠀⠠⡟⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⣠⡤⡄⠀⠀⠡⢢⠄⠀⣷⡄⠀⣤⠀⠐⡤⠀⠀⠸⡿⢦
⠈⠀⢈⠁⠤⡶⠊⠁⢀⢀⠀⠀⠀⠀⠀⠀⡼⠘⠇⡀⡿⠃⠀⣋⣁⠐⣄⠘⠟⢀⠃⠀⠁⠓⠀⠀⠀⢀⡄
⣀⡀⢠⡄⠸⠃⠀⢖⠀⡄⠀⢀⡤⠀⠀⢸⡟⠀⠐⡿⠀⠀⠀⣉⠉⠀⢻⠁⠀⡜⠘⢤⡆⠂⠀⠀⠀⠉⠁
⠻⠷⠞⠥⠃⠀⠀⡀⢤⣤⢀⠤⠀⠀⣐⣮⣽⠀⠠⡀⠀⠀⠀⠘⡛⠿⢰⣀⣾⠉⠀⢀⠠⡄⠁⠸⠷
⣾⣟⡷⠶⠶⠶⠶⠷⢾⣿⣿⣶⣾⣿⣷⣿⣶⣶⣶⣿⣶⣶⣾⣷⣷⣾⣿⣿⣶⣾⣷⣶⣷⣷⣶⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⣀⠱⢤⠒⢀⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⠒⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⣤⡈⠙⠓⠀⠀⡀⠀⠀⠀⠀⠂⠁⠀⣘⠃⢤⠒⣬⣷⡆⠳⢲⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⠿⠃
⠀⠀⠀⠀⠠⣾⠷⠙⣢⣇⠀⠀⠀⢙⠀⠀⠀⣀⣂⠦⠤⣽⠁⢮⣛⣽⣋⣟⣯⣉⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠁⣴⣿⣦
⠀⠀⠀⣠⡏⢁⡴⠋⣃⠴⠤⠂⠐⠀⠀⠀⠠⣼⠟⢲⠤⠿⠢⣟⣿⣽⣏⣁⣠⣉⡸⡁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠐⠈⠛⠛⠃
⠀⠀⢐⡏⠀⢸⣃⣠⡟⠒⠒⢢⠀⠀⠣⠀⠀⢸⣟⣛⣶⣀⡙⣉⣿⣿⣿⢿⠟⠛⠂⠓⠀⠀⠀⠀⠀⠀⣼⣿⣧⣶⣾⣶⣆⣀⡀
⠀⠀⡜⢁⣼⠃⣸⡟⣀⡜⠀⠈⠣⠔⠁⠀⠀⠀⢻⣻⣦⣤⣀⣼⢁⣨⠇⠛⠢⠠⠀⢀⠀⠠⠄⠀⠀⣤⣿⣿⣿⣿⣿⣿⡿⠸⠇⣶⡀
⠀⠀⣿⣾⣭⣿⠋⣶⡏⠁⠀⠀⠰⠷⣄⠀⠀⠀⠀⠙⠻⣿⣷⣿⣁⣥⣤⠳⣀⣰⣤⡼⠁⠁⠀⢠⣶⣿⣿⣿⣿⣟⡟⣨⠋⠀⠀⢋⣴⠂
⠀⠀⣿⣯⣵⣯⡟⣧⣨⠐⢁⡄⠁⠀⠀⠑⠄⠀⠀⢀⠄⠈⠁⠻⠹⣿⣇⠀⣿⠈⠓⠀⣠⣄⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⠀⠀⠀⠛⠉⡠
⠀⠀⠸⣿⣿⣿⡿⢟⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁⡀⢠⣴⠀⠀⣀⠀⠀⣿⠀⠀⡄⠘⣿⣿⣿⣿⣿⣿⠟⠡⠤⢼⣟⡤⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠉⠈⠁⠀⠀⣀⣀⠀⠀⠀⢀⡀⠀⢹⣿⣿⣦⣿⠟⠀⠀⣿⡆⠀⢸⠀⣴⠁⠀⢹⣽⣿⣟⣿⣾⣿⣿⣿⣯⡯⠠⡀⠤⢤⣄⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣜⣛⣦⣄⡈⠙⡏⠙⡆⢧⣼⣿⣷⣤⠈⣴⠃⠈⢧⠈⣽⣿⡿⢿⣿⠛⡟⢿⡃⠀⠀⠹⢷⣤⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣇⢈⡀⢾⡄⢻⣸⣿⣿⣿⣿⢸⡇⠀⢀⡼⠋⠀⣿⣾⡷⢃⠄⢀⡎⡧⢈⣰⡄⣶⡿⠉
⠀⠀⠀⠀⣧⣤⠀⠀⣀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣾⣷⣠⣕⣼⢿⣿⣿⣿⣿⢸⡄⢠⡞⠠⠀⢰⠁⠈⠛⠟⠡⠾⡷⢿⠎⠓⠙⠈
⠀⠀⠀⠀⠽⢿⣆⣀⡌⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡆⢹⣿⣿⡇⣿⣡⡏⠀⠀⢸⡇⣶⣭⡇⠀⠀⡀
⠀⠀⠀⠀⢰⣤⣴⠿⣷⡖⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⣼⣿⣿⣷⡵⠋⠀⣰⡀⢘⢃⡼⠋⢁⢀⣴⡄
⠀⠀⠀⠀⠉⠛⠁⣴⣇⠀⠀⡤⠀⠀⠿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⢹⣥⣼⣼⣯⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣾⠟⢈⣉⣁⣤⣄⣀⣁⣤⣴⣿⣿⣿⣿⣿⣏⠔⢀⣡⣴⣿⡟⣿⣿⣿⣿⣷⣴⡶⠖
⠀⠀⠀⠀⠀⠀⠼⠶⠏⠐⠟⢀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠛⠃⢰⣿⣿⣿⡿⣵⢃⠾⠋⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⢿⣿⣿⣿⣿⣿⣿⠿⠻⣷⣬⡿⠉⢀⣴⣶⣌⠷⣿⣿⢁⡟⣠⣶⣷⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠋⠁⣠⣾⣿⡿⠤⠂⢈⣉⢛⠿⣇⢸⣇⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⠀⠀⢹⣿⣿⣿⠀⣾⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣿⣿⣿⣿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠙⠲⣄⠀⠀⢀⡤⠖⠋⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣠⣼⡛⠛⠻⣤⡀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⡔⠉⠁⠠⠌⠉⣓⠢⣤⣀⠀⠀⠀⠀⠀⠈⢿⠀⣿⣦⡈⣬⣡⣾⡇⠀⣿⠇⠀⠀⠀⠀⢀⣠⠤⠂⢈⠀⠉⠒⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠡⠀⠒⠄⠁⠀⠈⠙⠲⢄⣀⠀⠀⠘⢴⣾⢛⣿⣿⢿⣿⣶⡮⠋⠀⢀⣠⠴⠚⠉⢀⠀⢀⠀⠠⠔⠂⠒⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠄⠀⠐⠀⠀⠀⠀⠂⠀⠉⠒⠦⡼⣯⣿⡇⡛⠛⠐⡿⠤⠖⢚⡉⠀⠀⠒⠁⠘⠀⠀⡠⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⡤⢒⡀⠠⠅⠄⢀⠤⡄⠚⣷⣿⣿⣿⣴⣤⣤⣞⠀⠛⠂⠠⠤⠤⢈⣁⣀⠘⣀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠄⣠⣀⠤⢤⣤⠖⠛⠭⣿⣿⣿⡶⣶⣿⣻⠍⢶⣿⠤⣀⡐⠀⢐⡂⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢠⣶⣾⣿⣿⣿⣿⢻⣿⣿⡶⣤⠻⣦⣄⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⢠⣿⠀⣿⣿⣏⣿⣿⡿⠽⢿⡇⢸⢧⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⣯⡿⠀⣿⣿⣿⣗⣶⣆⣾⣾⡇⠈⢶⣇⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠇⠀⢹⣿⣷⡟⣿⣞⣼⣿⠃⠀⠈⢯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠈⢿⣿⡯⡭⣿⣿⠏⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⣏⠒⠀⠀⠀⠀⠀⢠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣶⣼⣵⣮⡀⢠⣿⡄⣀⠝⢀⣶⡎⠀⠀⠀⣰⠄⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠛⠉⢡⡸⡌⠻⣟⠧⣺⠋⠉⢦⡄⢰⠀⠀⡹⢿⡝
⠀⠀⠀⠀⠀⠀⠀⢹⣟⠃⡐⠊⠸⣥⡴⠛⠿⣇⠀⠀⠾⠁⠀⣠⡀⣠⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣯⣿⣥⡀⠀⣯⣕⡟⣛⣏⠀⠁⠀⢀⡴⣿⣿⣧⣡⡀⠀⠀⠀⠀⠀⠀⣌⡀⠁
⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣷⡀⣷⡨⠃⠀⠀⣠⡖⠚⣿⡤⠿⣟⣩⣷⡙⠦⡀⠀⠀⠀⠀⢏⣤
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢇⠀⠀⢸⣿⣿⣿⠛⣷⣶⣿⣏⣹⣷⡀⢀⠲⠀⠀⢠⡾⣴⠿⡀
⠀⢰⣿⣿⣼⣿⠿⢶⣿⣿⣿⣯⣿⡟⠈⠀⣴⣿⣿⣿⣿⣿⢛⣿⣶⣿⣿⣿⣷⢿⡀⠀⠀⣿⡆⠁
⢀⣾⣿⣿⠛⢿⣿⣥⣿⣿⣿⣿⣿⡁⠀⣼⣿⣿⣿⣿⣿⣿⣿⢟⣿⣾⣿⣿⣿⡿⠉⡇⠀⢿⣄
⣜⠛⠑⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣷⣿⣿⣿⣫⣿⣿⢛⣿⣿⣿⣿⣷⠀⡍⠰⣶⣽⣷⡄⠀⠉
⢻⣷⣶⠀⠀⠀⢠⣿⣿⣿⣿⣿⣯⣷⠀⢸⣿⣿⣿⣴⣿⣿⣿⣿⣟⣻⣿⡿⣿⣏⠀⠇⣀⣴⡝⠛⠻⢃⡰
⠀⠙⢿⣿⣦⣀⣿⣿⣿⣿⢇⣿⣿⣮⡄⠀⠈⣿⣿⣿⣾⣿⣿⣴⣿⣿⣿⣿⣟⣷⡞⠸⣽⣿⣉⠃⡁⢸⣿
⠀⠀⠀⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣅⠉⣁⣼⠻⣿⣮⣿⣿⡾⣿⣽⣧⠀⣽⠏⠉⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠸⣸⣿⣿⣿⣿⣿⣿⠀⠀⠸⣯⣿⣿⠏⣿⣶⣿⠿⠳⣿⣷⣿⣷⡿⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣁⢸⣷⣬⠿⠿⠚⠉⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⡬⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡀⠀⠀⠀⢳⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠻⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡯⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣃
⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡏⣿⠀⠀⠀⠀⠀⠀⢀⡾⢸⣿⣿⣯⠀⠈⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠘⠂⠀⠀⠀⠀⠀⡼⠁⠀⣿⣿⣿⣆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠂⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠙⠻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠈⢳⡖⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣷⣶⣾⣷⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣱⣻⣿⠋⠉⠙⠟⣿⡏⠉⠉⠻⡍⠉⠻⣿⡉⠹⠟⣿⣟⠛⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣶⣿⣿⣿⣴⣶⣿⣯⣯⣷⣴⣤⣤⣽⣄⣤⣬⣽⣆⣩⣬⣽⣷⣄⣄⣙⣋⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢄⠈⠓⢮⡀⠀⡙⠩⣯⠀⠀⠈⠻⣿⠋⠙⠁⢿⠉⠉⣿⠉⡟⣟⡙⠉⡙⢹⠟⠉⠉⢙⣿⠟⢉⡽⠛⡿⠛⠋⠉⡹⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡑⢄⠈⠳⡑⠢⣀⣌⣷⡀⠐⢀⠘⣆⠀⠀⣼⠀⠀⣿⠸⠃⡟⠀⠈⡠⣊⠀⢀⣴⣋⡴⢚⡥⠶⠋⠀⢀⡤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠐⢄⠘⢦⠀⠙⠻⢷⣄⠠⠑⢬⠃⠀⣸⡀⠀⣿⠀⢰⠁⠀⠈⣴⡧⣚⣵⣋⠴⠚⠁⠀⠀⢀⠔⠝⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠑⢄⠀⠀⠙⡻⢶⣀⣓⠀⢜⡅⠀⣿⡀⢸⣁⣴⣾⣧⡾⡷⠋⠁⠀⠀⠀⢀⢴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠉⠻⡤⢘⣷⣤⣿⣵⣿⣿⠿⠛⠁⡰⠁⠀⠀⠀⣠⡸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢌⢂⠀⠀⠀⠀⠀⠈⠛⣿⣿⡟⡋⠀⠀⠀⡰⠁⠀⠂⡠⡦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡑⠀⠈⠀⠀⣆⣿⣁⣯⣻⡆⠀⠀⡔⠀⢀⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠈⢦⢸⡇⢻⣙⢿⣷⡄⡜⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣿⣿⣿⣽⣷⣼⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣩⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠿⣻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⣛⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢋⠉⠋⡉⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠛⠃⢀⠶⠔⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠾⠃⠺⢧⠾⠾⣿⣤⣄⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⢠⡜⠀⢀⡀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣶⣇⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀⡐⣾⣧⠘⢻⣿⡿⠋⠁⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⣿⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⡟⠋⠀⣤⣽⣶⡇⢿⡀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⠋⢰⣿⣀⠀⡂⢰⣯⢽⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠁⠀⠾⣿⡇⣺⣿⢄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠆⠘⠹⣃⣰⠃⠲⣾⠟⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠲⣿⣷⡎⣻⣿⣿⣷⣄⣠⣶⠀⠀⣀⡀⠀⢨⡿⠂⠘⢻⣷⣾⠰⠾⠾⠛⠒⠂⣀⠀⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠈⠿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣿⠟⠊⠀⣀⠃⠠⣼⡖⠢⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠁⠰⢮⡿⠂⠀⠐⢻⣿⣦⣋⡹⠿⣿⣿⣿⣿⡿⢿⡹⡟⠋⠀⢀⡴⠟⠀⠀⠙⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉⠉⢉⣛⠲⠿⡄⢳⣷⣄⠀⠉⠉⡿⢿⣷⣤⣤⣝⡁⣈⣀⡀⠛⢿⣶⣾⣿⠅⠀⠀⠀⣠⡈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣉⡴⠒⠛⠛⢄⢻⡿⠀⢀⣀⠀⠀⠘⠃⣉⣹⣿⣿⡟⠁⠀⠐⣿⣿⡿⠆⠀⠀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠋⠁⠀⠀⠀⣤⡀⠙⡁⠀⢸⡏⠀⠀⠀⠀⠻⣿⠿⠟⠁⠀⠀⣴⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⢉⡠⠀⠀⠑⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣤⠎⠀⠀⠀⠀⠈⢸⣤⠔⠂⠉⠛⠦⣀⣉⠓⠛⠻⢿⣿⣛⣖⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣈⣤⡠⠟⠁⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⢻⣷⣤⠀⠀⠈⠙⠻⠿⠦⠽⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠘⠀⠀⠙⢮⣧⠙⠲⠤⣶⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠺⢷⠦⣍⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠐⠀⠠⠐⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⢀⣤⣦⢴⡀⠠⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⢻⣿⣿⣷⠀⠙⠿⢓⣴⣿⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠇⢀⡀⠘⣽⢁⠘⢷⣀⣤⣤⣄⣀
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣀⣀⣄⣀
⠀⠀⠀⠘⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢨⣤⠰⠟⣿⣿⣍⡍⢿⡩⠹⣿⡻⠿⠆⠀⠀⢀⡙⢿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⢦⠀⠈⠻⢿⣿⣿⣷⡄⠀⠀⠀⡼⠀⠀⢀⡰⠙⠛⠷⣶⣽⡶⠤⠒⠀⠀⠀⠀⠈⠹⣶⡙⢿⣿⣿⣿⡄⠠⣶⣤⣤
⠀⠀⠀⠀⠀⠃⡀⠀⠐⡙⢻⣿⣿⡆⠀⠀⡇⠀⠀⡰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢎⡻⣿⣿⡇⠀⡘⠻⣯⣼⠁⡦⡄
⠀⠀⠀⠀⠀⣄⣈⠓⠀⠉⠙⣛⣿⣷⠀⠀⠃⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠃⣰⠃⠀⠙⠙⢿⣿⣤⡆
⠀⠀⠀⠀⠀⢹⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠄⠀⠀⠈⢹⣧⢾
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⡀⠀⠀⠹⣆⠀⠀⠀⠀⢀⣀⣤⣤⣤⣠⣇⠐⠁⠀⠀⠀⣠⡄⢀⡄⠀⢀⣀⠀⠈⡶⠁⠀⠀⠀⠀⠘⡻
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣄⠀⠀⠏⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠻⣷⣿⣧⣴⣿⣿⣷⡀⠇⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡀⢀⠀⠀⠀⢠⣀⠀⠈⠉⠻⣿⣿⣷⡛⣝⠆⠀⠀⠈⠀⠹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠸⣧⡑⣄⡀⠈⠀⠉⠻⣷⣹⣸⡆⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠿⠋⠈⠓⠆⡠⠀⣀⣠⡛⢧⡿⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣠⡤⢄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢨⣽⢾⡇⠀⠀⠀⠀⠀⡶⡤⠖⠂⠌⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠰⠿⠿⠿⠾⠿⠶⣿⣿⣷⣤⣁⡆⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡀⠀⣦⣀⢀⢄⡀⠀⠒
⠀⠀⠀⠀⠀⠠⢄⡀⡀⠀⠀⢀⣀⡉⡽⠛⠿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⢆⣶⣴⣤⣾⡿⠛⠋
⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣉⡉⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⢰⠴⣿⣿⣟⡿⠟⠏⠁
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⠀⠀⠀⢻⣆⠀⠁⢰⣎⣸⣿⠿⣉⣀⣀
⠐⢿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣰⡆⠘⣿⡿⠂⣠⠀⢴⣟⣿⣷⣴⠏⢁⠟⠟⠓⢂⣤⣬⣀⡀
⠀⠈⣿⣿⡅⢀⡀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣦⡉⠻⠃⢹⡄⠀⠛⠓⢈⠋⢀⣿⣷⠞⠁⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠈⠻⢟⡄⠀⠀⠀⠀⠒⠋⠀⠀⣙⣛⣻⢿⣿⣷⡀⠤⣌⢳⣆⠀⣤⠀⣠⠞⣁⢹⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠙⠛⠿⠛⠿⠛⠻⠛⠛⠛⠛⠛⠋⠁⠀⠀⠲⣤⣌⣻⣾⣠⣿⡃⠘⠀⠀⠙⠀⠰⠂⠐⢿⡟⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⡛⣿⡹⢾⣷⠀⠀⠀⠀⠀⠀⢠⡴⣾⣿⣟⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡧⣬⣿⣿⣶⣶⣶⣤⣀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠈⢰⡆⠘⣆⠉⠻⣿⣿⣿⣿⣿⣧⡀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⡄⠀⠀⠀⢀⡀⣧⠀⠈⡄⠀⡇⠉⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⣀⣩⣻⣿⣄⠀⢰⡿⠁⢸⣶⣦⠀⡄⠙⡀⠀⠋⠙⣿⣿⡿⠉⠀⠁⠈⠙⠛⢁⠀⠀⠚⠀⡌⢉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⠘⠣⡄⠀⢠⣼⣟⠛⠳⣄⠀⠑⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣖⣺⣿⣿⣾⡯⢿⣦⠀⠈⠀⠀⢻⣿⣿⣦⣈⢻⣿⣾⣷⣶⣾⣶⣄
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠉⠀⡀⢁⠀⠀⠀⠀⠈⠛⡀⢸⡏⠈⠉⠁⠈⢿⣿⣿⡟⢻⣿⣿⡀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢰⣼⠃⠀⠀⠀⠀⠈⠻⢿⣧⠀⠻⣿⠇
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠀⠀⠀⠀⠀⠘⠀⢀⣤⠰⢏⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠨⣴⡎⠼⡙⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠠⢀⠀⠐⡏⠀⢀⡄⠈⣻⡴⢦⢤⣬⡟⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⢍⠀⠀⠀⠐⢂⡀⠀⠙⠛⠁⠀⠀⡌⡟⢘⠧⠁⠀⠀⠀⠁
⠀⠀⠀⠈⠑⠂⢠⡄⠀⠀⠀⠀⠀⠀⠀⡀⠉⡆⠠⢝⠂⠤⠀⠙⠀⠠⣄⠀⠀⠀⢰⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢄⠀⠀⠌⠉⢱⣈⢿⣛⣶⡞⣖⠀⠀⢐⠀⠄⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⣁⠈⠀⠐⠛⢈⠋⠉⢫⠈⠀⢁⣶⡖⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣐⡟⠖⢠⣳⡀⠀⠰⠀⠐⡠⠀⣿⣿⡿⣡⡀⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠕⣀⠛⣑⠂⠀⠀⠀⠇⠢⢎⢳⠋⠉⠁⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⢇⡀⢸⢦⠄⡲⣏⣡⣠⡆⠸⠄⢴⡏⡀⠄⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⢀⡼⣯⠍⢻⣥⠈⠸⠎⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⣝⠃⠘⠿⠀⣉⡤⠟⠐⠀⠁⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠃⠀⠀⠀⢀⣀⠀⣹⠀⠀⢠⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⢾⡐⠀⡿⠧⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡽⣤⣤⡀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⢀⣴⡿⠂⠀⠈⣿⣿⣶⡀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⠃⠀⢀⣲⣿⡟⢸⣧⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠓⠲⡉⢻⣿⡇⣼⣿⣗⢀⠀⡀⡀
⠀⠀⠈⠀⠉⠀⠀⠀⠁⠀⠀⠀⠉⢀⠄⠈⠉⠁⠡⡀⠀⠀⢂⡟⢰⡙⠛⠫⣵⣄⠁⡅
⠀⠀⠰⠀⠉⡙⢫⠑⠒⠛⢩⡯⠀⢀⣳⡭⣍⣛⣻⣟⡾⠋⠈⠀⢸⡷⡄⠀⢿⢿⣿⣷⡶⠤⠤⠄⠶⠆
⠀⠀⢸⠂⠐⠀⠘⠂⢀⠕⠃⠀⠀⢹⢛⣧⣮⣿⣿⠿⡘⠀⠀⠀⠜⠁⢸⡀⠈⢰⣿⣿⡥⠄
⠀⠀⠺⠒⠒⠒⠲⠶⠃⠀⠀⠀⢀⡿⢿⡿⣿⠿⠁⠀⠀⠀⠰⣦⠀⠀⠙⠗⠀⠘⣿⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡀⠄⣮⠁⠀⠀⠀⣀⣤⣾⡿⣆⠀⠀⠀⠀⠘⢻⣿⣐⢂
⠀⠀⢠⣀⣀⣤⣄⣀⣀⣀⣀⣿⣷⣽⣷⣿⣶⣤⣶⣾⣿⣿⣿⣟⣦⣁⠀⣄⣀⣀⣼⣿⡿⣧⢀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣽⣿⣿⣿⣿⣦⣤⡉⠳⡆
⠀⠀⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠣⣡⠜⠈⠀⠛⠀⡏⣿⣿⣷⣾⣿⣣⡅
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⢉⣡⠤⡞⠋⠁⠊⠀⠀⠀⠀⠀⠀⠀⠠⠇⣹⡻⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣯⡽⢿⣿⣿⣿⣿⣟⣿⣯⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣿⣿⣿⡇
⠀⠀⢻⣿⣯⣶⣾⣿⡿⠋⠀⡈⠀⢀⣽⡗⠐⠀⢀⠀⠐⠠⠄⣀⠀⠀⠀⡄⠀⠀⢀⡸⢙⣟⣿⣿⣿⡇
⠀⠀⣨⣶⣿⡿⣿⣾⡋⣴⠊⠀⠀⣨⣇⠁⠀⠀⠀⠀⠀⠀⠘⠁⣿⠛⠁⠀⣀⣴⢿⣧⣤⣧⣿⣿⣿⡇
⠀⠀⣿⣿⡿⠓⣎⠉⠻⣦⣽⣾⣛⣶⢿⣴⣀⣀⢤⣠⣀⢀⣰⠚⠛⠨⠀⣲⣿⣟⣿⣟⣿⣁⣻⣿⠀⡄
⠀⠀⣿⢹⡇⠀⠈⡃⠀⠙⢿⠿⡿⣿⣿⣿⣶⣫⣿⡾⢶⣶⣾⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣿⡟⣿
⠀⠀⣾⠋⢠⣀⣴⣷⠖⠒⢺⠞⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠋⠙⣇⣿⣿⡇
⠀⠀⢀⣴⣶⣿⠿⠷⠶⠴⠾⠟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄