Age Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣷⣶⣦⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠁⣀⣈⡙⢄⣈⢙⣿⠙⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⣰⣾⣿⣿⠿⠂⠙⢿⣿⣇⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣟⢣⣿⠟⠋⣩⣭⣷⣤⠀⢻⡿⠇⣪⣽⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡦⣙⣻⡿⠛⠙⠻⠿⣽⡩⢥⣿⣧⣤⣛⣫⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⣙⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣿⣯⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠀⣠⠶⠦⢤⠀⠀⠀⠰⠖⠛⠲⢼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⢿⡟⠀⣀⣴⣿⡶⠔⠀⢰⢴⠿⠿⠗⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣾⣧⠀⠀⠀⠈⠀⠃⠀⢸⠀⠀⠀⠀⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣽⡄⠀⢀⢀⠄⠐⠶⠾⠛⠠⠀⠄⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠀⠀⠺⠥⠭⢿⠉⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡷⢤⣄⠀⠈⠐⠊⠁⢀⣴⡏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣇⢷⣄⠈⠓⢦⣤⣤⣴⢿⣿⠃⢸⣿⣶⡶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⢿⠙⣧⠈⠈⠀⠙⠷⣤⣀⠀⠀⣠⠞⠁⠀⠈⠛⢹⡇⢸⢻⡏⣷⣶⡤⣄⡀
⠀⠀⠀⢀⣠⡴⢖⣻⡇⢹⡸⡇⢹⣆⠀⠀⠀⠀⠀⢹⢫⠛⡝⣄⠀⠀⠀⠀⢸⡇⠈⡟⣷⣿⣿⣿⣾⣙⣦⡀
⠀⠀⣰⠟⡇⣾⣿⣿⢰⠈⠇⢳⠀⢻⣦⡀⣀⣤⣶⣿⣾⣷⣾⣿⣿⣶⣄⣀⣾⠀⠀⡇⣿⢿⣿⣿⡿⣿⡏⣿⣄
⠀⣸⣿⣆⢳⢻⣿⣿⡟⡆⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⢸⣿⣿⣧⣿⢳⣿⣿
⠀⢿⣿⣿⡼⡞⣿⣿⣿⢱⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⣿⣿⡇⡿⣿⣿⣿⣿⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⢸⣿⣽
⠀⣸⣿⣿⣷⢻⢻⣿⣿⡞⡆⠀⠀⠀⠀⠀⠙⢿⣿⡸⣿⣿⡇⣇⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿
⢰⡿⠸⢿⣿⡏⣇⣿⣿⣿⡸⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⢱⡿⣻
⢸⡿⠷⢶⣽⣿⢿⢸⣿⣿⣧⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣸⡏⠟⠐⢿
⣿⣷⣬⣳⣿⣿⡞⡜⣿⣿⣿⣷⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣾⣿⣿⣿⣿⣇⢀⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠈⠁⠉⠁⠈⠉⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠀⠀⠐⠀⠐⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⢼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⠔⠂⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡀⠀⢉⣀⣠⣴⡿⠃⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠹⣿⡿⠛⠉⡉⠃⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⠀⠀⠈⠁⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⠤⠤⣶⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⡄⠒⠂⠁⠀⠀⠀⠚⠓⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⠀⠒⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠛⣄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⡇⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⢣⡀⠀⠀⠀⡀⠃⢠⡤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠰⢄⣀⣼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡑⠀⠀⣀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⠐⠒⠋⠀⠀⠶⠁⢀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⠀⠀⣆⡘⠀⠀⣘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠀⠀⠉⠁⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡖⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣴⠀⠀⡈⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠘⢶⠄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣼
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠹⡏⠀⠀⠀⠉⠁⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⠀⠀⠀⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡃
⠀⢰⠇⢀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣠⣤⣤⣠⣄⠃⠐⣧⣀⣀⣀⣀⣤⣄⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⢹⡍⠀⠀⠀⠀⠀⠙⠁⠀⣩⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠄⠀⢸⡇⠀⠀⠀⠀⢰⡆⠠⠴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢼⡇⠀⠀⠀⠀⠀⢸⡆⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⡸⠁⠀⠀⠀⠀⠀⢸⡅⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⢠⣮⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠃⠘⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣎⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠁⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⠘⠻⣦⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⡀⠀⠀⢀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠈⢿⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠉⣤⠖⠉⠉⠉⠉⠉⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⠀⠀⠀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⠉⠀⠀⠀⠀⠀⠀⠀⢸
⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⡿⠿⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⢀⡀⠀⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠹⡄⠀⠀⠀⠀⣀⢤⡀
⠀⠀⠀⠀⢀⡤⠖⠤⣄⠀⠀⠀⠀⣠⠴⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣷⠶⢦⡀⠞⠀⠀⣿⠛⠛⠲⢦⡀
⠀⠀⠀⠀⡎⠀⠀⠀⠈⠑⠶⠶⠊⠁⠀⠀⠀⠉⠳⠦⡤⠴⠖⠤⠀⠹⣤⡴⠞⢇⡀⣸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⣤⣤⡤⠶⣤⡀⠉⠁⠡⡀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣇
⢀⠔⠁⠀⣀⡤⠴⠖⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⠀⠀⢀⠀⠀⠀⠈⣷⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⢀⠀⠀⡏
⡌⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠟⠀⠐⠉⠀⠀⠉⠇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠁
⢹⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⡀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⢦⣀⣀⣀
⠀⣧⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡔⠀⠱⣄⡀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⡈⠉⠉⠛
⣰⠃⠀⡰⠃⠀⠀⠀⠀⠀⢀⠞⠀⠀⣠⠏⠀⠀⠀⠈⠙⠓⠒⠒⠛⠋⠁⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⢇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣠
⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣋⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠖⠋⠁
⠀⠀⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠳⠦⢤⣤⣤⣤⣤⡤⠖⠋⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⡼⢃⡴⠒⠂⢠⡖⢲⠒⡤⠋⠀⠈⠒⢰⡏⢹⣄⡀⠀⣀⣤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠖⠋⠀⠈⠀⠀⢒⣭⠁⠘⠀⠰⣄⣀⣀⣠⠎⠁⠰⠆⠉⠉⠉⠄⠀⠀⠀⠐⠦⣤⣤⣤⣤⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠔⠀⠀⠀⠀⠈⠁⠉⠀⢀⡂⠐⠈⢄⠑⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠌⠴⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠲⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⢐⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⠤⠼⡇⠀⠀⣀⣀⣀⣀⣀⡀⠀⣧⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠉⠉⠉⠉⠉⠉⠉⠉⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢰⠁⢆⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢠⠃⠀⠈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡄⣼⠀⠀⠀⣇⣀⣠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⠀⠀⠀⠀⡇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⢀⠇⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠈⣅⠀⡀⠀⠈⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠑⠦⠐⣂⡼⠋⠁⠀⠀⠀⠀⠀⠈⠙⠦⢥⣀⢈⠀⡠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠈⠉⠉⠉⠉⠉⠉⠁⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⠒⠂⠐⠲⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡄
⠀⠀⠀⠀⠀⠀⢠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀
⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆
⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠉⠙⢶⡄⠀⠀⠀⠲⠀⠀⠀⠀⠀⠰⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⡀⢠⠀⠀⠀⢰⡆⠀⠄⠀⠀⠀⠀⠀⢸⠃⠀⠠⡀
⠀⢡⡄⠀⠀⠀⢰⠄⠀⡠⠔⢉⣿⠛⠀⠀⠀⠀⠀⢠⣿⠃⡦⠀⠀⠀⠀⠁⡘⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢠⡌⠀⠉⠀⠀⢀
⠀⠀⢡⠀⠀⠀⡄⠀⠀⢠⣤⠈⠻⠿⠀⠀⠀⠀⠠⢤⠿⠿⠃⠀⠀⠀⠀⠀⠁⣴⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠆⠀⠀⠀⠀⡀⠸
⠀⠀⢀⠰⠦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣼⠄⢀⠀⠀⢠⠋⠀⠀⠀⢀⣀⠁
⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⡀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⣠⠜⢀⣾⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⡁⡁
⠀⢀⡄⠀⢰⡎⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠃⢀⠀⠂
⠀⡌⠀⢠⠈⠇⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⢳⡞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⡄⠀⢀⠈⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠈⢇⠀⣠⠂⣄⠀⠀⠀⠀⠀⠀⠀⠎
⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⢈⠛⠲⣤⣄⣀⣀⣀⠀⢀⣀⣀⣀⣤⣶⠞⠋⠀⢀⡐⠀⣦⠀⠀⠹⠀⠘⢇
⣷⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠉⠉⠛⠋⢻⠋⡉⠀⠀⠀⠀⢠⡎⠀⢤⠘⠇⠀⠀⠀⠀⢸⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⡄⠀⠀⠀⠀⡆⠀⢰⡄⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠁⠄⠀⠀⠀⠀⣾⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡜
⠀⢡⡄⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠠⠆⠀⠀⡀
⠀⠀⢱⡄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠆⠲⠄⠀⢀⣀⣀⠗
⠀⠀⠀⠙⢦⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠘⠆
⠀⠀⠀⠀⠀⠈⢡⡌⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⠃⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠆⠀⢀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠾⣦⣀⠈⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⠀⠀⠀⠀⢰⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢘⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠶⠖⠒⠋⠉⠉⣠⣤⣤⣄⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠃⠳⠤⠤⣤⡤⠀⠀⠀⠀⠠⠇⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠤⠄⠀⠀⠀⠀⠀⠀⠶⠄⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⢰⠈⠉⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠶⠆⠀⠒⠶⠶⡀
⠀⠀⠀⠹⣀⠀⠀⠀⠛⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⠲⢆⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠀⣀⠀⠀⠶⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠈⠋⠉⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢙⣤⡀⠤⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠚⠛⢳⣤⡌⠁⠠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣸⠟⠀⠀⠀⠀⠈⠛⠿⣧⣤⣴⣶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢼⡇⢀⣼⠏⠀⢀⣤⡴⢶⣦⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠉⣧⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⡇⢀⡀
⠀⠀⠀⠀⢴⠄⠹⠇⠀⠀⠀⠀⠙⢿⣿⣋⣤⡀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⣿⡀⠀⣼⡏⠀⢸⣷
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⣿⠀⠀⠀⠀⢀⡜⠃⢸⣿⣟⣉⣿⣤⠀⠀⠀⠀⠙⠁⠚⠉⠀⠀⢸⡿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠸⣷⣤⡄⠙⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠻⣧⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠰⣿⠀⠀⠀⢀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠈⠁⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⣠⡿⠋⠻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⡀⠀⠀⠀⢀⣀⣴⣾⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠻⣷⣶⣿⠟⠛⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠔⠛⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠓⠂⠀⠀⠀⠀⠀⠐⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠉⠹⠿⣤⣄
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠑⢀⣀⣀⣀⣀⠴⠟⠀⡠⠆⠀⠀⠀⠀⠀⠈⠉⠿⢦⡀
⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠉⠉⣁⣀⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡀
⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠈⠉⣶⣶⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⢠⡀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⢸⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⡄⢀⣤⣤⣤⠀⢠⣾⠛
⠀⠀⠀⠀⢸⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⠟⢿⣏⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠘⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠋
⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢠⡶⠏⠉
⠀⠀⠀⣿⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⢻⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟⠁⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠛⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠌⠀⠀⠀⠀⣠⣾⠛⠁
⠀⠀⢠⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⣤⡔⠛⠁
⠀⠀⢸⠀⠀⠀⠀⠘⠻⠿⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠃
⠀⠀⠀⠀⠀⠀⢸⠃⢠⡆⠀⠈⠉⠙⠿⠷⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠
⠀⠀⠀⠀⠀⢠⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠷⠶⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠰⠀⠀⠀⠈⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠲⠶⢶⣾⠏⠀⠀⠀⠺⠷⢤⡀
⣦⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠄⠀⠠⠤⠄⠈⠁
⣇⠀⠀⠀⠀⠹⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠉⢦⡀⠀⠀⢠⣦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠙⠓⢶⡦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⠶⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠉⠉⣿⠟⠶⠶⠶⣤⣄⣀⣀⡀⠀⠀⢀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣄⠀⠀⠀⢸⡟⠉⠉⠁⠀⠲⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠇⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⣀⣀⣿⠄⠀⠀⠀⠀⢸⡏⠀⠲⠶⠶⢾⡏
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠉⢉⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴
⠀⢴⠊⠉⠉⠰⢄⠀⠀⠠⠤⠀⠈⠁⠀⠀⠀⢘⣿⡀⠀⠀⠀⠀⠸⣇⣀⡀⠀⢠⣿
⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⢰⡟⠙⠛⠉⢻⣯
⣿⣄⣀⠀⠀⠀⠀⠈⠋⠉⠋⠈⠉⠙⠋⠉⠛⠺⠿⠃⠀⠀⠀⢠⡼⠁⠀⠀⡄⠘⣿
⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣤⣄⡀⠀⠀⠛⠋⠀⠀⠀⠀⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠛⢁⠀⠀⠀⠀⠀⠀⢀⣤⡀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭
⣀⣤⣀⣀⣀⣠⣀⣀⣀⣀⣀⣼⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠉⠁⠈⠋⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡄⠀⠀⢀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣟⠃⠀⠀⠀⠸⢿⣿⠟⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⢠⣦⣤⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⢠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠈⣹⣿⣿⢿⡗⠀⠀⠀⢸⣽⣿⣿⣿⠀⠀⠀⠸⣿⣿⣟⡇
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣾⣿⣇⠀⠀⠀⣸⣿⣯⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⢀⣿⣿⡿
⠀⠀⢰⣿⣿⡇⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⢹⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⠹⣿⠀⠀⠀⣼⡟⢿⣿
⠀⠀⢀⣿⣿⡅⠀⠀⠀⢨⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⠄⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⡇⢰⣟⡀⠀⠀⢹⡇⢸⣿
⠀⠀⠀⣿⣿⣿⠒⠀⠒⢿⣿⣿⠆⠀⠀⠀⠀⣹⡅⣿⡀⠀⢀⣽⢹⣏⠀⠀⠀⠀⠀⠀⢸⣇⠸⣿⡿⠀⠀⠀⠇⣸⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⣀⣀⠀⠀⠀⢀⣤⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢠⡴⣾⠛⢃⠢⠂⠁⠀⠈⠀⠀⠀⣼⣿⣧⣀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢿⡿⣟⠷⢄⠈⠁⠀⠀⠀⠀⠀⢸⢡⣿⡅⠉⠀⠘⠓⣙⠛⠛⠷⠂⠀⢠⣿⣿⣿⣿⣿⣽⠿⠿⠿⠿⠿⠿⠿⠧
⠀⠀⠀⠟⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣧⣤⣅⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⣀⣶⡆⣠⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⢻⠉⠉⠉⠉⢹⡟⠉⢻⠁
⠀⠀⠀⢸⣿⠭⠿⠶⠀⠀⢺⣿⣟⠧⢄⠈⠀⠀⠀⠀⢀⣤⡟⢁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣹⠛⣆⠀⠀⠀⠀⠀⣹⠁⠠⣾⣶⣆⠀⠀⠐⣿⣿⡮⣽⣷⢠⣦⣦⡀
⠀⠀⠀⠃⠀⠙⠀⠀⠀⠀⠀⠈⠀⠘⠋⠉⠙⠁⠀⠀⠉⠉⠁⠉⠉⠈⠉⠉⠁⠀⢶⣶⠿⢿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣧⣠⣄⣿⡟⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⢠⣿⣿⣮⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⣿⡇⣿⣿⡇⣿⡇⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠀⠀⠀⠘⣻⡿⠡⣦⣄⠀⠀⠀⣠⣴⣶⣾⣿⣿⣷⣾⣿⣷⣿⣿⣧⣿⣷⣿⣤⣄
⠀⠀⠀⠀⠀⠀⢀⡺⡷⠀⢀⡈⣿⠆⠀⠀⠀⠀⢙⠃⠰⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⢾⣿⢷⡀⠸⠁⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣍⣀
⠀⠀⠺⢶⣦⣤⣼⣿⣦⣬⣥⣤⣤⣤⣤⣶⡖⠀⠂⣴⣦⡀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⣺⣿⣗⣂⣀⣀⣀⣀⣤⡤
⠀⠀⠀⠈⣿⠉⣽⠋⢹⡟⠛⠉⠉⠉⢹⡏⠀⠀⢼⣧⣼⣧⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣻⠟⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⠿⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢀⣀⣀⣀⣀⣀⣀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠿⠂⠉⠉⠙⠉⠉⠉⠋⠉⠑⠚⠿⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠁⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⣤⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠔⠀⠀⠀⠀⠀⣴⠟⠀⠀⠘⢧⡈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡠⠃⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠈⠳⣄⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡜⠁⠀⣀⡰⢎⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠓⠒⠂⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣄⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠟⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠶⢤⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡸⠃⠀⠀⠀⡀⢠⣤⡄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⠘⣇⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⡿⠃⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⣴⠆⠀⠀⠐⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠘⣿⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣤⡄⠀⠀⠷⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⣤⣄⣀⠀⠀⣀⣤⣤⣀⠀⠀⢠⣤⣶⡟⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⢹⡟⠛⣉⠉⠉⠋⠉⠉⡁⠴⢉⣴⡇⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠺⡏⠀⠀⠀⠀⠈⣿⠧⣤⡀⠒⠒⠀⢀⣠⡴⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⡇⠀⠀⠀⠀⠀⢿⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢰⣴⡇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣆⠀⣷⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⢀⡇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢦⡀⢀⣾⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢤⡿⠋⣹⠀⠀⠀⠀⠀⠒⠺⡿⠂⠀⠀⢀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⣆⠀⠀⠀⢀⣀⣀⣀⣸⡿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢹⡄⢀⣤⣄⣒⣻⡇⠀⣿⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢴⡯⠁⠈⠙⢻⠟⡋⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠻⣯⡴⠊⠉⠉⠙⣦⡽⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣷⠈⣀⠀⠀⣴⠟⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⠀⠀⢀⣾⠅⣦⢤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢧⣤⠛⣫⢰⡟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡟⠁⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢉⣴⠇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣧⣠⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⠔⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⣠⠞⠁⠀⣀⣀⣤⡶⠞⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣤⣴⣴⣿⢤⠶⠶⠞⠉⠉⠀⠀⢀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣏⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⣠⡄⠀⠀⠀⢀⣠⣤⠴⠒⠉⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡶⠴⠦⣀⣀⣀⣀⣀⣀⣀⣤⣶⡟⠣⠴⠶⠲⡟⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠉⠉⠈⣿⠉⠉⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠴⠤⠶⢴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣤⢄⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡴⠛⠶⣦⣄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠙⠳⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠐⠚⠋

⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡄⠀⣤⡄⣤⡀⠀⡠⠀⢀⠀⠀⢀⡀⠄⠀⠀⠀⠀⡄⢀⠀⢀⣠
⣿⡀⢸⣿⣤⣀⣠⡀⠀⠀⠀⢀⢀⡀⠢⡀⠀⢢⠀⠰⠀⠈⠸⠋⠀⢰⠃⢠⠃⠀⣠⠆⠀⢀⠤⠈⠘⠀⣥⣄⣤⣼⣿
⣿⡿⠂⠹⠿⠟⠁⠀⠀⠄⣀⠀⠹⠷⠀⠈⠂⠀⠃⠀⠁⠀⠀⠀⠀⠃⠀⢃⠠⠞⢁⠼⠆⠁⠘⡤⠐⠂⠀⠙⠿⢿⠏
⣿⠀⣀⣀⠀⠀⠸⠇⠀⠀⢉⣈⣰⢤⠤⣲⣴⣷⠀⠀⠀⣥⣀⢀⡀⠀⢸⣿⡗⢐⣧⠤⢴⣊⣀⠀⠂⡐⢿⠆⠀⢀⣠
⣿⠀⠚⠃⠀⢐⡀⠀⠀⣦⣦⢿⣘⠻⠿⡿⢒⣧⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠒⠚⠿⠤⠿⠇⢰⣿⡄⠀⢀⣴⡆⠛⠛
⣿⠀⠀⠐⠀⢉⡄⠀⠀⠹⠿⠀⠉⠘⠂⠈⠈⢁⠀⠈⠀⠈⠀⠈⠀⠀⠀⠉⠀⢁⠀⠀⠀⠀⣈⠉⠉⠉⠀⠉⠁⢐
⣿⣀⠀⠀⠀⠸⠟⠀⣀⠀⠀⠀⠀⢶⣦⡄⠀⠈⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣿⡇⠀⠀⡀⠀⠉⠀⣣⠀⠀⠄
⣿⠟⠁⢠⡤⠄⠀⠤⢭⡤⡤⡤⠤⢬⢽⢤⠤⡤⡄⠀⠡⠤⢠⠤⠤⠔⠨⡤⡤⣤⢬⢭⢥⠤⡤⡤⡤⡤⢴⡁⢸⣶
⣿⢰⡆⠠⠀⠄⠀⠄⠀⡀⠀⠀⡀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⣀⠀⣀⠀⠊⠁⠋⠠⢠
⣿⠀⠀⠀⠠⠄⠀⠠⢈⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠀⢉⠀⠀⠀⠀⠘⠈
⣿⠀⠃⠈⡀⠀⡀⠀⡾⣷⠀⠀⠈⠀⠀⠀⠀⠈⠐⠚⠶⣶⣳⣰⡶⠖⠒⠀⠀⠀⠁⠈⠳⠀⠀⢡⡿⡇⠀⡀⠁⡉
⣿⣦⡀⠈⠛⠐⠀⣼⡿⢿⣆⠀⠁⢀⠀⠀⠀⠀⠀⢰⡆⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢀⣾⡿⣿⡄⡇⠘⠛
⣿⠉⠌⠉⠢⠀⣹⠿⣷⣾⠿⣆⠀⢀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠥⠌⠩⠀⢀⠀⠈⠳⣾⢿⣶⡿⢿⡇⠠⠊⡉
⣿⠀⠀⠀⠀⡁⣿⣶⡟⢻⣶⣿⠈⠉⠀⠀⠀⠀⠀⠀⢻⡆⠀⣨⡶⠛⠲⠀⠀⠀⠉⣀⡀⡸⢷⣾⠛⣿⣾⣧⡇⢀⣈
⣿⠀⠀⠀⢀⡀⣿⣹⣿⣿⣉⡿⠀⠄⢀⠀⠒⠀⠀⠀⠈⣥⣭⡋⣀⣀⠀⠠⠀⠀⡦⠉⠙⠲⣏⣹⣿⣿⣹⡇⣱
⣿⠀⠈⠐⠜⣠⡈⢩⠞⣩⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠛⠛⣀⣛⠊⠲⢂⣄⢫⡆⠀⠀⠈⡡⢞⡭⠉⣄⠉⡖⠊
⣿⣷⠄⢠⠁⠈⠁⠰⢞⡵⠀⠐⢦⡀⠀⠀⠀⠀⣤⠀⢠⣄⣢⠘⠷⣋⢿⡞⢶⡗⣹⠇⠠⠀⠀⠴⣫⡴⠀⠉⠀⢡
⣿⢁⠀⠇⠠⠰⣶⠖⢋⠶⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠿⠏⣿⠀⠀⠙⠘⠛⠛⠋⠁⠀⠀⠀⠀⠜⣡⠞⣾⡦⠡⠀⡆
⣿⠀⢸⢀⠀⠀⠀⠜⣉⠌⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⣴⠃⣛⠁⠀⠀⠀⠀⠀⠀⠶⠈⠐⠤⡀⢚⡵⢛⠀⠠⠀⠁⠩
⣿⠀⢸⠀⠀⠲⠂⢠⡡⢀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⡸⣇⢶⡶⣻⣏⡴⣋⠀⠶⠀⡀⣰
⣿⡰⠆⡂⠀⠠⠀⡞⠱⣫⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⣿⣵⣾⠟⣩⠞⣹⠀⠄⠐⢀⠂
⣿⠟⠃⠈⢆⠛⠀⠁⢘⣩⣀⣀⡀⠀⠈⠀⠀⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠟⣿⣾⡧⢞⡥⢠⡜⢃⠎
⣿⠀⡀⢠⠀⠱⠤⠞⠛⠛⢻⣏⢟⡙⠛⠶⢂⣀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠉⠻⢿⣿⠛⠛⠿⡆⠖⠁⢤⢀
⣿⢰⣿⠄⢀⣖⡿⢀⠀⠀⣘⣯⡛⢦⠴⣷⣯⡿⣇⣤⠺⠳⠠⠰⠻⢦⣄⠿⢷⣦⠨⣤⡸⣿⣿⡀⠀⣤⠸⡷⣆⠀⣼
⣿⠀⠉⠀⠸⡟⢠⠀⡆⠀⠙⣾⣧⡼⠷⠤⣹⡶⣮⠅⠂⠋⢓⢉⠒⠆⣩⣶⣿⠯⡄⢳⣦⢙⣽⠃⠉⡄⣤⢙⡷⠀⠈
⣿⣜⡿⢆⢀⣷⣦⠀⠈⣤⢤⡈⠲⠙⡜⢷⣦⣶⣙⣲⣖⡀⠀⠘⢢⣞⣾⣭⣭⡶⠃⢿⠃⣈⣵⢴⡧⠄⢠⣶⡆⣀⠾
⣿⠛⠁⣻⣤⡙⠁⠰⠀⣸⡿⠝⣿⠀⠘⣃⠈⢳⡿⣿⣤⣭⣛⣋⣽⣿⣷⣴⢉⣀⠏⠀⢸⡿⢆⣿⡀⠴⠈⠛⣡⣼⡃
⣿⠀⠀⠻⠉⣷⣿⣶⣴⣭⠙⢖⠈⢳⠶⠆⠀⠰⠄⠀⢄⣥⣼⣥⣅⣤⠀⠤⠀⠈⠴⡾⠑⠒⠞⣩⣴⣴⣾⣾⡟⠿⠇
⣿⠀⠀⡄⢿⠇⣿⠀⢛⠃⠀⠘⢱⠼⠷⠀⠀⡄⠠⢀⠀⢠⠨⠄⣤⠠⠀⠠⠀⠄⠰⠷⢰⠋⠀⠈⣺⠉⢸⡇⢿⠇⣄
⣿⠀⠀⠀⠀⠀⠸⠃⠸⠆⠀⠀⠄⢤⠀⠠⠀⠄⠀⠀⣄⢀⡀⠀⠀⣄⢀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠞⠀⠼⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠘⠛⠛⠛⠃⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢠⡍⠀⣀⣀⣀⡀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂
⠀⠀⠀⡸⠁⠈⡛⠉⠉⠉⠛⢋⡙⠷⠶⠾⠒⠛⠚⠛⠶⠶⠶⠷⠶⠾⠶⠾⠟⠷⠚⠛⠛⠛⠛⣿⠉⠀⠀⣷
⠀⠀⢠⡇⠀⠀⢳⠀⠀⠀⠼⢷⠐⣶⣶⡦⢺⡀⠀⠀⠀⠀⣤⡀⣴⣶⣶⡆⠒⢦⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻
⠀⠀⢸⡇⠀⠀⠸⡀⠀⠀⠀⠋⠛⠿⠟⢁⡴⠁⢀⣀⠀⠀⠻⠷⢾⡿⠿⠁⢀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸
⠀⠀⢠⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠳⠀⠀⠐⠀⠤⠄⠐⠃⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⣿
⠀⠀⠀⢧⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠈⢷⣄⡀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣠⠏⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠾⠿⢶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣤⠾⢧⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡶⠦⣤⣀⣀⡀⠀⠀⢀⣀⣠⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠈⠰⡆⠀⠉⠉⢻⠋⠙⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢐⡇⠀⠠⣀⡿⢄⡐⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡴⣦⣦⠠⣤⡐⠋⠓⠈⠓⠊⠉⠰⠖⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠁⠀⠀⠈⠻⠖⠀⡄⠀⠒⠂⠁⠀⠀⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⢀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀⣀⡀⠀⠒⠒⠂⠠⠤⠤⠄⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠉⠉⠉⠛⠳⠶⠶⠤⣤⣤⣤⣤⠴⠶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠲⢶⣤⣄⣀⡁⠀⠀⢀⠀⠀⣀⡀⣠⣤⣤⠴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠈⠉⠛⡟⠓⠛⠛⠋⢻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡇⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠧⢸⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠚⠁⠀⢸⠇⠒⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠀⠀⠀⢀⣠⣼⡇⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠶⠋⠉⠀⠙⢇⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣄⣠⡤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⠉⠉⠀⠀⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠁⢀⡀⠀⠉⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠘⠻⠁⠘⠷⠋⠀⢀⣋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠑⢀⠀⠀⣰⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠛⢃⣅⣠⡊⠀⠀⠀⠈⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢩⡉⠋⢈⢉⡄⡀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠁⢠⠂⠚⢐⠀⠀⠀⡇⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠀⠀⠀⠀⠀⠀⢌⢇⣀⠀⢱⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠢⠀⠑⠀⠀⡏⠀⠀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠈⠳⣄⠀⢠⠧⠤⠴⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣀⣀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⢀⢠⡀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠤⠚⠁⠀⠹⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⢀⠇⠀⠀⠀⠀⠀⠱⡀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⡁⠈⠑⢤⣀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠹⡍⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠊⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⡤⠴⠚⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⠀⠤⠒⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠒⠀⠒⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣢⣿⣤⣞⢻⣷⠃⣿⢩⠋⢳⢸⣿⣴⡟⣿⣾⣷⣶⣦⣶⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠙⠙⠉⠃⠻⠿⠿⠋⠈⠋⠉⠉⠙⠘⠋⠉⠁⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢠⣿⢿⣿⣿⣷⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠟⠁⠀⠀⠉⢿⣿⣿⠟⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀⠀⠀⢠⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠘⢻⣿⣿⣶⣶⠀⠀⠀⢰⡟⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⡁⠀⠀⠀⢹⣿⣟⠁⠉⠀⠀⠀⠈⢳⣿⣿⣟⠁⠀⠀⠀⢘⣿⣿⡼
⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⣾⣿⣶⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠟⣿⡆⠀⠀⠀⣾⡟⣿⡇
⠀⠀⠈⣻⣿⡟⠀⠀⠀⠀⣻⣿⣟⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⠇⠀⠀⠘⣿⠀⣿⡇
⠀⠀⠀⣿⣿⣿⣤⡄⢠⣤⣿⣿⣟⠀⠀⠀⠀⠘⢿⠛⡏⠀⠀⠈⢻⠛⡟⠀⠀⠀⠀⠀⠀⠘⡿⠀⣿⣶⡆⠀⠀⢹⡃⢸⠇
⠀⠀⠀⠉⠋⠛⠀⠀⠀⠈⠋⠙⠁⠀⠀⠀⠀⠐⠛⠀⠛⠂⠀⠘⠛⠘⠓⠀⠀⠀⠀⠀⠀⠀⠙⠂⠉⠋⠁⠀⠀⠈⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣠⡾⠋⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢀⣤⠞⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣴⡟⠁⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⣿⡟⠀⠀⠀⢰⡇⡆⣀⣀⣤⣶⣶⣤⢤⣄⠀⠀⣠⣴⡾⠟⠉⠀⠀⠀⠘⢿⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣶⣤⣤⣶⣶⣿⣿⠿⠛⢋⣽⣿⣿⢿⣧⣷⣿⠛⠁⠀⠀⠀⠀⠀⢻⣶⢸⢺⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣹⣿⣿⣿⣿⡏⣴⣶⣶⣤⣹⣿⢯⡀⠀⠻⣿⠋⠠⠘⣧⡀⢹⠀⠀⠀⠀⠀⠀⠀⢈⡿⢈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣿⣿⣿⣿⣿⡇⠉⠉⠀⢀⢸⡇⠈⢳⡀⠀⠈⠉⠀⠊⠉⣇⡸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠛⠋⠉⣼⡇⠀⠀⠙⠲⢤⣤⣄⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣧⣀⣀⣀⣴⡏⠀⠀⠀⠀⢀⣤⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠘⢧⣄⣀⡀⡖⠀⠀⠀⠀⠈⠙⢳⣤⡀⠀⠀⠀⠀⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣠⠆⠀⢀⣀⣁⣠⡤⠤⢀⣨⠟⠛⣯⠀⣄⠀⠀⠀⣿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡻⣤⣶⠿⣿⣧⠷⠞⠋⠁⠀⠀⠀⢻⡀⢸⡇⠀⠀⣿⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢱⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢸⠇⠀⡰⠃⠀⠀⠀⠈⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠜⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣷⠞⠒⠁⠟⠛⢿⡆⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣷⣄⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠰⠀⡃⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣒⣠⣼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣭⣶⣿⣿⡿⠿⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠉⣲⡀⠀⠀⠀⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠃⠀⠛⠁⢐⠺⠏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣠⠄⣈⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣈⠛⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠴⠲⡎⠀⢀⠀⠉⠉⡋⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣄⠀⠀⠀⠘⢀⣀⠈⠄⣀⠀⠇⢀⢙⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⠀⠀⠈⠛⢋⡉⠢⡀⠀⠈⡀⠞⣠⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢾⡆⠀⠀⠀⠀⠙⢶⣄⡷⣈⡴⠞⠁⠀⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠⡞⣸⠇⡀⠀⠀⠀⠀⠀⣹⡿⣉⣴⣶⣦⣸⡷⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡖⠀⣿⠀⠛⢶⣦⣤⠤⠀⠈⣶⠉⠉⠉⢩⡏⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠟⠀⠲⢸⡀⠀⠀⠀⠀⢀⣀⠸⠆⠀⢀⣴⠟⡷⠀⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣀⡸⠇⠘⣧⠀⠀⠀⠀⠀⢉⠆⠀⣠⠞⠁⠀⢸⡆⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠧⢌⠋⠀⢀⣿⣠⡤⠤⣄⣠⠟⠀⣰⠏⠀⠀⠀⠀⣷⠤⢤⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡘⠀⣴⠛⠉⠉⠛⠂⠈⡙⠀⠀⢻⡄⠀⠀⠀⠀⠈⡄⠐⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠁⡾⠁⠀⠀⠀⠀⠀⠀⢽⠀⣀⣌⣷⣄⡀⠀⠀⠀⢱⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡛⣸⣶⣶⣾⣿⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣷⠀⠀⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⡌⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣆⣠⣾⣧
⠀⠀⠀⠀⠀⣀⣀⣠⢿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠹⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⠆
⠀⠀⠀⢠⡟⣡⣄⡀⢠⠼⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿⣧⢤⡤⢤⠤⠽⠋⣄⠀⢀⣀⡉⠜⢢
⠀⠀⠀⠘⠧⠚⠊⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⡟⠀⠀⠀⠀⠀⠆⢀⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⡘⢠⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⠞⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠏⠀⢀⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣐⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡼⡇⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠘⠀⣷⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢹⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠆⠔⠉⢳⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠃⠀⠀⠀⠀⠀⣤⠠⠄⠠⠀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⢠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠠⠤⠄⢀⣄
⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣀⣀⠀⡀⠀⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠤⢔⠒⠊⠀⠀⠀⠀⠀⠀⠡⠈⠉⠀⢀⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣨⡵⢿⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠄⠊⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢣⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢀⠶⠉⠀⠈⠀⠘⢄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⡁⠣⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢠⠞⠀⠂⠀⠀⠀⠀⠐⠀⠀⠈⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠘⢄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⢄⡀⣀⣀⣀⠴⣇
⠀⠀⠀⢨⡓⣦⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢴⠆⠀⠀⠈⢳⡀
⠀⠀⠀⢸⣀⡟⠙⡿⠒⠒⠀⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⢹
⠀⠀⠀⡞⢰⠀⢰⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠦⣄⣀⣀⣀⣠⣮⠀⠀⠀⠀⠈⣡⠈⠀⡀⠀⠀⠠⡄
⠀⠀⣸⠁⠨⠀⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⣾⣄⠀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⣿⠀⠇⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠁
⢀⠤⢇⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢳
⠌⠓⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡡⠄⠊⠁⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢾
⠀⠀⠈⠉⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠐⠀⢀⡠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⣿⠒⠒⠢⠐⠤⠤⠤⠠⠤⠤⣤⣶⣤⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣠⠴⠂⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀
⠀⣠⠖⠉⠁⢀⠀⠄⠂⠁⢀⣠⠞⠁⠀⠀⠀⠀⠈⠢⣄⡀⠈⠐⠂⠤⠀⠈⠈⠳⣄
⣞⠁⠀⠀⢀⣀⣠⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⣄⣀⣀⣀⣈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣴⡖⣿⢉⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⢀⡴⠿⠿⠗⠈⢠⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣷⣾⡇⠀⠀⠀⢠⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠀⠀⡀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣧⠀⠰⠁⠀⣰⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⡾⢿⣷⠀⣹⣷⠂⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⣼⠀⠈⣀⣬⣧⢸⣿⠃⠹⣿⡑⢈⠁⢤⠀⣦
⠀⠀⠀⠀⠀⡩⠃⢒⣲⣶⣦⠜⡈⠀⢰⣤⠗⠂⢈⣿⠀⠈⢿⣧⣾⣎⢢⣄⢘⣧⣀
⠀⠀⠤⣶⡶⠁⠬⠂⠙⣃⣁⡁⠉⠀⠈⠉⢀⣤⣾⣿⣄⣷⣤⣿⣼⣷⣶⣼⣶⣶⣿⣅⣩⠵⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡿⠁⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣀⣀⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠷⠀⠀⠀⠀⢸⡿⢻⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡧⠀⠀⠀⣀⣠⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣶⣿⣿⠿⠿⠷⢤⣾⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠙⠛⠛⢿⡿⠟⠛⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠃⠒⠚⠒⠒⠐⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇
⠀⠀⠀⢠⠀⢀⠀⠄⠀⠀⠈⠁⠀⠀⠈⠀⠈⣧⠀⠀⠀⠠⠤⠄⠤⠤⠤⠤⠔⢀⡀⢿⣿⡇⠀⠀⣀⠔⠁
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⢈⡤⣤⣓⣎⣴⣮⣼⢇⠴⠋
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢠⡶⠒⠂⠐⠒⠀⠊⠈⠉⠈⠿⠁⠿⠥⠤⠼⠀⠂⠐⠀⠐⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢠⠀⠰⠀⢠⡀⠀⠀⠀⠀⠀⣏⡆⣿⣿⣿⣿⣿⣾⣷⢸
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣿⣄⡀⠀⠐⡱⡀⠀⠀⢻⡄⠀⠀⢰⠀⣩⡆⠋⡿⠿⠿⢻⢸⢿
⠀⠀⠀⠀⢸⡄⠐⠀⠂⢀⣩⣭⡛⡟⣟⡿⣿⠿⠿⣿⣿⠦⡀⠐⡙⡄⠀⠀⠹⣄⠀⢸⡀⣀⣀⣠⡤⠤⠤⠼⠤⡼⢀
⠀⠀⠀⠀⠈⠄⡈⠄⠀⠈⠘⡎⠃⠁⠁⠡⠀⠈⠀⠀⠀⠀⠉⠢⡈⢾⣆⣲⣿⣽⡅⡀⠉⢁⣈⣉⣀⢀⡀⠲⠾⠿⠟⠟⠟⠛⠃
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⠄⡀⢀⣐⣤⣤⡤⠶⠶⠛⠋⠀⡉⠛⠛⢚⣡⣄⢀⡥⣌⣭⡭⣭⣍⢅⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠪⢠⣄⣤⡴⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⡤⠀⡀⠀⠨⠐⠀⠈⠀⠉⢓⢈⠂⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣐⠚⢉⠄⠀⠀⢠⣼⠅⠠⠀⢀⠠⣠⣴⡽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⣄⠠⠉⠀⢀⠐⣻⣯⣵⢾⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⠀⣀⣀⢉⣥⠴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠉⠉⠀⠁⠐⠠⢄
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠤⡀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢀⠊⢀⠤⢄⠀⠀⠈⢂
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⡈⠀⢁⡀⠀⠡⣴⡀⠀⢂
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠐⠀⣴⢥⠶⡤⡤⠦⡵⠦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⡀⣀⠀⠀⠀⠈⢂⠙⡀⠘⢄⡠⠀⢠⢃⠎
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠽⣊⠋⠄⠀⠀⠀⠀⠈⠚⡒⠒⠂⢖⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⣁⣸⡄⠀⢀⣴⣾⡟⠬⠐⠂⠅⢻⣷⢦⡀
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⣿⣷⣿⢀⣾⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣳⡀
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢿⢿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⠄⠠⠤⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠿⠿⠇⠀⠀⠀⠀⢸⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣿⠇⢠⣿⠿⣷⡄⠀⠀⠀⠀⢠⣾⠿⣿⡄⠸⣿⠋⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢠⣿⠁⣸⡟⠀⣾⡏⢀⣿⠃⠀⠀⠀⠀⠘⣿⡀⢹⣧⠀⢻⡇⠈⣿⡄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠻⣧⠀⣼⡇⢀⣿⠇⢰⣿⠀⣼⡟⢻⣦⠀⠀⣴⡟⢻⣧⠀⣿⡆⠘⣿⡀⢸⣧⠀⣼⠟⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⣧⣿⠀⣼⡟⠀⣾⠇⢠⡿⠀⣼⡏⠀⠀⢹⣧⠀⢿⡄⠸⣷⠀⢻⣇⠀⣿⣼⡟⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠈⠻⠃⠀⠿⠁⢸⡿⠀⣾⠇⢠⣿⠀⠀⠀⠀⣿⡄⠸⣧⠀⢿⡇⠈⠿⠀⠘⠟⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠾⠀⠀⠗⠀⢀⣀⠀⠀⠛⠀⣼⡇⠀⠀⠀⠀⢸⣇⠀⠛⠀⠀⣀⡀⠀⠺⠀⠀⠶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣠⡀⠀⢀⠀⠉⠀⡀⠀⣰⡿⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠉⠀⡀⠀⢀⣄⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⠀⠀⠛⠀⠀⠘⠃⠐⠿⠁⠀⠀⠀⠀⠀⠀⠈⠿⠂⠘⠃⠀⠀⠛⠀⠀⠁⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⠐⠖⠀⠀⠠⡦⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⢴⠄⠀⠀⠲⠂⢴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢴⣦⠄⢠⡿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢿⡆⠠⣴⡦⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢀⡀⢿⣇⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⡿⢀⡀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠁⣠⣆⠀⠀⠀⠀⣠⡆⠈⠉⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⡿⢻⣆⠀⠀⣰⡟⢿⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⣷⣾⠟⠀⠀⠻⣷⣾⠇⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉






⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⠶⣶⡶⠶⠶⡶⠶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠇⠀⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠙⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣿⣿⠈⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠁⠀⠀⠀⢈⣿⣿⠇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣰⣿⡟⠁⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⢀⣿⡟⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣾⣿⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢀⣿⡟⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣾⣿⠏⠀⠀⠀⠀⢀⣴⣿⡟⠋
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣼⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⢰⣿⡟⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠜⠛⠛⠃⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣼⣿⠇⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⢀⣤⣴⣾⡿⠋
⠀⠀⠀⠀⣸⣿⠇⠀⠀⢸⣿⡿⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡄⠀⣴⣿⡿⠟⠉
⠀⠀⠀⢠⣿⣿⠀⠀⠀⣼⣿⠃⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⢸⣿⡇⠀⠀⢰⣿⡿⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⣾⣿⠀⠀⠀⣾⣿⠁⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⢸⣿⡟⠀⠀⢰⣿⡿⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⣿⣿⡇⠀⠀⣿⣿⠃⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⣾⣿⠏⠀⠀⠐⣿⣿⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⣴⣿⣿⣄⣀⣀⣤⣿⣿⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⢿⣿⣿⣿⣇⣸⣿⡿⠋⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠘⢿⣿⣿⣿⣿⡟⠁⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠙⠛⠋⠉⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣷⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠘⣿⡇⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⡏⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠠⣿⡇⠘⣿⣇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⢠⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⡏⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠐⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⣀⣠⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣤⣀⡀⠀⢀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡿⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣤⣤⣤⣴⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢸⡇⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣀⣀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠘⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⡈⠻⢿⣿⣿⠿⠛⣡⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣿⣶⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢀⣠⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣷⣌⠛⠛⠛⠛⠛⠛⠛⠋⣡⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⣬⣉⠻⣿⣿⣿⣇⢹⣿⣿⣿⣿⡇⣼⣿⣿⣿⠟⣉⣥⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡘⠿⠿⢋⣼⣿⣿⣿⣿⣧⡙⠿⠿⢃⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠙⠛⠻⠿⠿⢿⡿⠿⠿⠟⠛⠋⢹⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣾⣿⣻⣽⡛⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤
⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿⣿⣏⠙⠛⠃⣠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠉⠛⠒⠛⠻⠿⠧⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠦⠬⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠉⠀⠠⠴⠶⡶⣤⣄⠀⠀⠀⠈⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⢹⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠉⣠⡀⠢⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣄⣤⣤⣤⣤⡀⡘⠢⡀⢀⡙⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣝⡻⣿⣷⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠊⠁⢬⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠋⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣷⣭⣫⣿⣿⣿⣷⣿⣿⠛⠳⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣨⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣭⣿⣗⡀⠀⠀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣿⠿⠟⠛⠁⠀⠈⢙⡻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀⣠⠴⠒⠛⠁⠀⠁⠀⠀⢀⣠⣰⠾⠛⠁⠀⠈⠙⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡌⠀⢈⠉⠁⠀⠀⠀⠀⡀⢠⣤⡶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠆⠀⠀⠘⠀⠀⡠⠒⠀⠀⠀⠀⢢⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠰⠰⠁⠀⠀⠀⠀⢂⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠊⠉⠁⠘⠛⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣀⣀⣀⣀⣀⣀⣀⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠛⠃⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⠛⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⢠⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢶⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⠐⠁⠀⠀⠀⢀⣴⠏⠀⠀⠀⢳⣄⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⠂⠀⠀⠀⡀⣰⡟⠁⠀⠀⠀⠀⠀⠙⢧⡀⠉⠲⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣴⣀⣀⡠⠔⣃⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠉⣉⣤⠞⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠳⢦⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠶⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠁⠀⠀⡀⠀⠀⣿⠇⠀⠀⢀⡈⠀⠀⠀⠀⠀⠘⡿⠗⠀⠀⠀⠀⠈⢷⣼⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⢷⡀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡼⠛⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠊⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢹⡷⠶⠒⠚⠛⠛⠛⠒⠒⠉⠛⣹⠇⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⠋⠀⠀⠀⠀⢿⢦⣈⠀⠠⠀⠀⠈⣉⡤⠾⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢾⠀⠀⠀⠀⠀⢻⠀⠉⠙⠛⠛⠛⠛⠉⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣦⣾⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠰⠀⢰⡆⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢻⣄⠆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡉⠀⠀⠀⠀⠰⣄⠀⣰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠟⢹⡇⠀⠀⠀⠀⠚⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣹⠀⢸⡇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣠⣤⣤⣀⣿⣁⡀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⢿⣀⣀⠴⣄⣉⣿⡀⢸⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠠⣾⡇⡀⠀⠙⠿⢋⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠻⣧⠞⠉⠉⠉⠱⣾⠃⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣆⢁⡄⠀⣰⡏⢀⣀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⢀⣴⠇⣼⠶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣎⣩⡄⡿⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠴⠟⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣴⠀⠀⠀⠀⠻⠿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡴⠎⠀⠀⠀⢀⣀⣤⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣣⣴⠛⣤⣀⠴⠶⠞⠋⠉⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢹⠛⠛⠓⠒⠒⠶⠶⠶⠖⠲⠶⠛⠛⠛⠋⠉⠀⠁⠀⠀⢀⣤⠴⠖⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣊⣁⣀⢠⡶⠖⠋⠉⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⠀⠈⠉⠙⠛⠛⠛⢿⠛⠛⠋⠀⠈⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⣀⣠⡄⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⣀⡅⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⡿⢦⣤⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢰⡄⠀⠀⠙⠷⣤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠀⠚⠋⠁

⠀⠀⠀⡄⠡⣞⠉⢃⣀⣀
⠀⠀⠘⠇⠀⡇⠀⡞⠁⠙
⠀⡇⠀⠀⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣠⣴⣿⣿⣯⣭⣙⣛⠻⢿⣷⣦⡀
⠀⠀⣤⡄⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡷⣦⣭⡙⢿⣦⡝⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣫⣾⣫⣾⣿⣿⣷⣮⡙⢷⣼⣿⡿⣷⣿⣝⢣⣻⣿⡀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⢰⣿⣿⢟⣿⡿⠋⠙⢿⣿⡄⣿⣿⣿⣿⣿⣿⡆⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣸⡟⣠⣿⡿⠃⠀⠀⠀⢻⣷⣼⣿⣿⡿⠻⣿⡇⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⣧⣿⠋⠀⠀⠀⠀⠀⢸⣿⠃⠻⠟⠁⠀⢻⣿⣿⣿⡇
⠁⡀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⠁⠀⠠⠀⠀⠀⠈⣿⣿⣋⡀
⠀⠑⢠⡄⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⣿⠇⠀⠀⢀⠀⠐⣀⠀⠀⠀⢠⣤⡄⠀⠀⠹⣯⠈
⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠸⠿⠧⠀⠈⡆⠀⠀⠘⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠂⠀⠀⠀⠀⢶⣦⠶⠶⢦⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿⣏⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠾⠁⠀⣿⣿⣷⡀⢹⣿⡶⢿⣷⡀⠀⠠⢀⣀⠀⠀⠀⣀⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠐⠓⠒⠂⠀⠀⢸⣿⣿⣿⣷⣤⣽⣿⣮⠻⣿⣄⠀⠀⠉⠉⠈⠉⠉⠀⠀⣠⣿⡿⢹⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣦⣄⣀⡀⠀⣀⣠⣴⣿⣿⣿⣿⣹⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⠿⣿⣿⡿⠟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣀⠀⣠⣿⣿⠟⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⠧⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡋⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠟⢋⣥⡾⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣭⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣽⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠘⢧⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣧⠀⠰⠀⠀⠰⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⠀⠀⢴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠀⠀⠸⣥⡀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⢼⣿⣿⣿⣶⠆
⠀⠀⠀⠀⠀⣀⣴⣾⣿⡗⠀⠠⠒⣿⣿⣷⣦⡀⠀⠀⠀⠉⣿⣿⣯⡽⠀⠀⠀⠀⠀⠀⠈⢯⣿⣿⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⠀⣸⣿⣿⣿⣿⡇⠀⢀⡀⠀⠙⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⠀⠁⠀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣷⠀⠘⠀⠀⠀⠀⢸⡀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣾⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢰⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠸⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣧
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠙⣿⡏⠠⠚⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⠄
⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣤⣴⣾⣿⣿⣿

⠀⠀⠀⠀⠀⣰⣶⣄⡀⠀⠀⢀⣀⣴⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⢀⣶⣷⡄
⠀⠀⠀⠀⣾⠏⠉⠻⣷⠀⣼⣿⣿⣯⡛⣿⣿⣿⣷⠀⢠⠀⠁⠀⢆⠀⠀⠀⣿⢿⠿⡿⡇⠀⠀⡟⠛⠋⠹
⠀⠀⠀⢠⣧⠀⠀⠀⣿⡄⠈⠻⠿⠀⣁⠀⠿⠟⠉⠀⠈⠀⠀⠈⠘⠂⠀⠀⠈⠀⣀
⠀⠀⠀⣾⣿⣧⠤⣾⣿⣧⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⢠⡇⠤⠄⢲⡁⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠻⠃⠁⠀⠀⢘⠃⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠎⠀⠀⠀⠀⠡⠃⠀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⢀⡀⠠⠄⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢌⡑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠉⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢄⡈⠑⢌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢠⠊⠀⡠⠈⠀⠀⠀⠀⡀⠀⢈⠐⠠⠄⣀⠈⠑⠠⡑⠱
⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⡀⠀⡠⠂⡠⠊⠈⠂⢄⠈⠒⠠⢀⡈⠁⠁⠈⠂⠃
⠀⠀⢔⢴⡘⠆⢢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣩⠔⢊⠤⠊⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⢈⣉⣁⣀⡄
⠀⠀⠰⡓⠀⠀⠀⢀⠦⡀⠀⠀⠀⠀⠰⡀⡠⠅⠐⠈⠁⠠⡦⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⡥⡸⢠
⠀⠀⠀⠈⠒⠤⠒⠁⠀⠈⠢⡀⠀⠀⠁⠪⢘⡀⠀⠀⡀⡀⠀⠀⢀⠈⢁⠀⠀⠀⡀⠀⠀⠀⠠⠋⠀⡞
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠢⣀⠎⠀⢄⢐⡄⠈⠀⠂⠀⠀⠀⠉⠉⠀⠀⠀⠂⠊⠀⡠⠇⡀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠑⠠⢎⡁⠀⢰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠱⡖⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⠈⠁⠐⠂⠀⠀⠐⠂⠈⠀⡘⠢⡀⠀⠀⠠⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠤⠀⠒⠠⠤⠤⠀⠊⠀⠀⠈⠢⠀⠀⠱⣨⣴⣖⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠃⠟⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⠹⠸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠐⡀
⠀⠀⠀⠐⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⢦⠀⠀⢀⠠⠔⠀⠤⠂⠀⠂⠐⠈⠀⠀⠀⠀⢐
⠀⠀⠀⢀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣀⣎⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⡟⢛⠻⣿⠟⠚⠿⠿⢿⠚⠛⠻⡾⠛⠿⣾⠟⠿⣿⣿⡿⠿⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣬⣽⣿⣿⣟⣀⣻⣻⣱⣀⣀⣤⣆⡿⣆⣀⣀⣘⡆⢀⣉⡳⡄⠀⡘⢿⣄⠀⠈⠛⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠙⢌⠙⢍⠙⠻⣍⠉⠉⠛⢻⡟⠉⠉⠛⢿⡻⠛⠏⢻⠛⠛⡟⠛⡟⡟⠛⠛⠛⣿⠟⠙⠛⡿⡿⠛⣻⠿⣿⠿⠛⠛⡿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠑⢄⠈⢧⠂⢄⣠⣙⣄⠀⠀⠈⢇⠀⠀⢈⠀⠀⡇⠸⠁⡏⠀⠊⡰⠁⠀⣠⡜⣫⠔⣋⠴⠊⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠐⢄⠉⠚⠻⣦⡀⠀⢨⡃⠀⠘⡀⠀⣇⠀⠠⠀⠀⢪⣞⠅⣪⣝⡩⠔⠋⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡑⢄⠠⡀⠀⠈⠛⠲⣄⢱⠀⠐⡁⠀⣿⡀⣸⢀⣴⣿⢑⢯⠞⠁⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢀⣷⣀⣿⣴⣿⡿⠛⠋⠀⠊⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⢙⡻⣿⡟⠁⠀⠀⢀⠎⠀⠀⡠⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡁⠀⠀⡀⢀⣼⣠⣧⣿⡄⠀⢠⠃⠄⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠱⣸⣇⣸⣬⡻⣷⣤⣣⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣿⣿⣾⣷⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣶⡿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡭⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠶⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠀⠀⠀⠀⠠⢀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠎⠀⠀⢠⠄⠀⠀⠀⠣⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠠⡀⠒⠁⠈⠢⢄⣀⣀⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡌⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠑⣢⣤⣀⣀⣀⣀⣠⡴⠞⠉⠀⢀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠌⡉⢻⣄⠀⣨⡿⠀⢄⠀⢠⠊⠉⠁⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣠⠎⠀⠁⣸⠀⠉⠀⢢⡀⠸⡀⢈⠀⠀⠀⠠⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⠣⢤⣤⣞⠁⠀⡄⠀⠀⠉⠓⠛⢀⣀⠀⠀⠀⢇⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢠⢞⡳⠁⠀⠠⠖⠲⣍⠁⠈⠁⠀⠀⡸⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠖⠤⣀⠯⠼⠁⠀⣤⣀⠀⠀⣸⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠇⠠⠒⡂⠒⠛⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⣠⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣈⡑⠲⠤⣀⣀⠀⢀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠔⠒⣩⣀⣠⠾⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⢦⣤⣤⠀⢨⠈⣉⡁⣀⠤⢄⠠⡴⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡁⠀⢨⢀⠐⠰⣿⡶⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠛⠒⢻⠙⠶⠖⢻⡃⠀⠤⠂⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠟⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠻⣿⠛⠛⠛⣿⠛⠛⠛⣿⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠶⠾⠿⠶⠶⠾⠿⠶⠶⠾⠿⠶⠶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠁⠀⠈⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣔⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠼⣿⣿⣿⣿⣏⡿⣿⣯⡛⢷⣄⠙⢢⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣏⣀⠄⠚⠋⠉⠀⠀⠀⠈⠛⠺⣿⣇⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⣰⣿⠿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⢋⣀⣤⣴⣶⣤⣄⠙⢿⡁⠀⠀⠀⠐⡿⠿⠟⠛⠛⠛⠿⣿⡆⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠀⠸⣿⣿⣿⡏⠈⢻⡇⠈⠃⠀⠀⠀⠀⠀⣴⣿⣿⠛⢷⣦⠈⢿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣥⣿⣿⣿⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠏⠀⠼⠿⠁⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⣤⡀⢀⣀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣾⣿⣧⡛⠳⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣿⡷⠿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⢿⡈⢿⣦⡀⢉⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠈⢳⣀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠠⣿⣿⣟⣻⣿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣏⢻⣿⣧⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣤⡤⠿⠛⠋⠁⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣹⠟⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢂⣾⣿⣿⣿⣿⣿⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢿⣦⣹⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠙⣿⡿⣿⣿⣿⣿⣶⣄⣀⡀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣿⣷⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣽⣿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⢯⣦⣿⣿⣿⡟⡍⠻⢮⣍⠀⠀⠀⢹⣿⣿⡟⠛⠉⠀⠀⣼⡿⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠈⠀⠉⠘⠋⠻⠄⠀⠈⠉⠀⠀⠀⢺⣿⣿⡇⠀⠀⢀⡾⢹⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⢻⣿⣇⠀⠀⢸⠃⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⡏⢻⡄⠀⠘⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣦⡀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠃⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢸⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠘⡆⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡇⠀⢀⣀⣼⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠅⠛⠉⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣀⣀⣠⠤⠔⠒⠊⠉⠉⠉⠉⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠘⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⡖⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⣶⡄⢸⣷⡀⢻⡇⠀⠀⠀⠀⢱⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⡇⠀⠀⣰⣶⣦⡀⠘⣿⡀⠀⢸⣷⠀⢿⣇⠸⣿⣀⣀⣀⠀⠀⣇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢣⠀⠀⣿⡇⠙⠃⠀⢿⡇⠀⠀⣿⡄⠸⣿⡀⢻⣿⠛⠉⠀⠀⢸⡄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⡄⠀⢸⣧⠀⠀⠀⢸⣿⠀⠀⠸⣧⠀⢻⣇⠈⣿⠀⠀⣀⡀⠀⣧⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢱⠀⠈⣿⡀⣶⣾⡄⣿⣇⣠⣄⢻⣧⣾⡿⠀⠻⠿⠿⠛⠃⠀⠸⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⡆⠀⠸⣧⣀⣿⡇⠘⠿⠟⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢡⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠴⠶⠒⠒⠚⠛⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢦⡤⠔⠊⠉⠀⠀⣀⣠⡤⠴⠒⠚⠉⠉⠉⠁⠀⠠⠄⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⢚⣡⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣤⣀⣀⣀⣀⣀⡉⠤⠤⠔⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡶⠔⠒⠛⠛⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⣉⠀⣈⡉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠥⣆⠡⠉⣆⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡅⢀⣾⠿⣿⣿⠿⣿⣻⣶⣦⣄⣀⠀⠀⠀⡇⠀⠀⠀⠈⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⠛⣶⣿⠋⠀⠉⠛⢿⣬⠿⣿⡀⠀⠀⢃⢀⠀⢠⡖⠀⠃⠀⠀⠇⣤⠀⠀⠀⠀⠀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣾⣿⣥⣀⠀⠀⠀⠚⢻⣧⣿⠁⠀⠀⠈⡈⠄⠰⣧⠈⣦⣴⢆⠛⠒⠀⠀⠀⠀⢰⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⣨⠂⠀⠲⠾⠛⣿⣿⠀⠀⠀⠀⢡⠀⡀⠈⠲⢬⡵⠊⠀⠀⠀⠀⠀⢠⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠛⠋⠀⡆⠀⠀⠀⡿⣿⣡⠀⠀⠀⠀⠳⡈⢠⣀⢈⡁⠀⠀⠀⠀⠀⡠⣏⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠉⠻⢿⣄⡀⠀⠀⢹⣥⠄⢠⠁⠟⣧⢳⡀⠀⠀⠀⠈⠠⣉⡙⣉⠐⠒⣀⣤⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣽⣦⣄⡀⠀⢀⣠⡃⠀⠘⣝⠃⢳⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢼⣏⠙⢀⣠⣿⣽⣿⠯⣍⣉⣀⠜⢡⡷⢀⣿⣦⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠢⡌⢄⠀⠀⢠⡟⠈⢻⡟⠻⠛⠛⣿⠂⢾⣾⣷⣴⣟⣁⠌⠙⠻⢿⡀⠂
⠀⠀⠀⠀⠀⠀⠘⢦⣌⣧⠀⠀⣸⣿⣴⠃⠀⠀⠀⢠⠿⠦⠼⠛⢻⠛⠿⣿⣤⣁⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⣍⡿⣧⡞⠀⢿⣿⣇⠀⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠈⠙⠋⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⣙⣻⣾⣿⣿⡿⠀⠀⠀⢽⣿⠀⢀⡄⠀⠀⠀⠄⠀⠀⣿⠀⠀⡀⠀⠀⡀⢀⡀⠀⠀⢱⣿⣦
⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⡇⠀⠀⠀⠈⣿⡄⢰⠁⠀⠀⠀⠠⠀⢠⣿⡇⠀⠄⠀⠀⡇⠸⣧⠀⠀⠀⢻⡻⣿⣆
⠀⠀⠀⠀⠶⣯⣿⣿⡷⣿⠂⠀⠀⠀⢀⣿⡇⠈⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠂⠀⢀⠈⢰⣿⠃⠀⠀⠀⢻⣏⠻⣿⡆
⠀⠀⠀⠀⠶⣮⣿⣿⣿⠟⠀⠀⠀⠀⢿⣿⡇⠀⠀⠰⠀⠀⠀⠀⠘⣼⡗⠀⠀⠀⠀⡀⣸⣿⣤⣤⠔⠀⠀⠻⢳⣮⡳⢀
⠀⠀⠀⠀⠐⣧⣿⣿⣻⡆⠀⡀⠀⠀⢸⣿⡿⡀⠀⢢⠀⠀⠀⠄⢀⣿⡇⠀⠀⢀⣻⣿⣿⣿⣿⣡⣴⠗⠀⠀⢸⣿⣉⠎⣀
⠀⠀⠀⠀⡟⡷⣿⣿⣹⡇⠀⠀⠀⠀⢸⣿⡏⠱⠂⠁⠀⠀⠀⠀⢸⣿⠃⠂⠀⢈⣿⣿⣿⠛⡋⠁⠐⠀⠀⠀⠀⡛⠟⠓⠋
⠀⠀⠀⢠⣯⣷⣿⣿⡿⠛⢄⠐⣦⠀⣾⣿⣇⡀⠀⠀⠨⠀⠀⠀⣾⡿⠀⠀⢰⣿⢿⣿⡉⠀⠉⢷⣄⠀⠑⠀⠀⢸⣧
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠈⠆⠀⠀⢴⣿⣿⣿⡅⠈⠀⠤⠀⠐⢲⣿⢇⣠⡴⠋⠉⠉⠀⣿⣏⠀⠀⢉⢇⡀⠀⣠⣾⡿⠁
⠀⠀⠀⣨⠿⡿⠉⠸⣧⡴⠆⠀⢀⠂⠻⢿⣿⡇⠀⠀⠀⠀⠀⠈⢋⣍⣙⣥⢤⠄⠀⠀⣨⣿⡆⠀⢸⡏⢀⣧⣀⣿
⠀⠀⠀⠉⡘⠫⣟⢿⡿⠆⠀⠠⡄⣀⠀⠀⠙⣷⡄⢀⢀⡤⠋⠁⠿⢛⣭⣖⣁⣠⠴⠛⠉⠉⠻⠦⠼⠷⠚⠁⠀⢀
⠀⠀⠀⠀⠀⠐⢮⠔⢱⡀⣰⠃⣾⠁⠀⠀⣠⠻⣿⠖⠋⠀⠀⠀⠐⢛⣫⣵⠾⠃⠀⠀⠀⠐⠦⡀⠀⠀⢠⡔⡁
⠀⠀⠀⠀⠀⡴⠳⡁⠀⠹⣧⡀⠘⡄⠀⠀⢻⠈⣿⣀⣀⣤⣴⡶⠘⠋⠉⠀⠀⠀⠠⡀⠀⣀⡀⠀⠀⠁⠘⡇⠀⣀⠠⠄⠲⠶
⠀⠀⠀⠀⠐⠀⠢⡁⠀⠀⠘⡍⢄⠹⣄⠀⠀⠛⠉⡹⠋⠉⠙⠛⠁⡀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠛⠒⠤⣤⡅⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠚⠁⠙⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡠⢶⣶⣶⣶⣤⡀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣲⣬⣿⣿⠛⠋⠉⠉⠉⠉⠙⠛⠛⠻⠷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣫⡵⣾⣿⡟⣿⣿⡇⠀⠀⠀⠠⣤⣴⣒⣤⣔⣲⣤⣌⡙⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣔⣛⣭⣶⠟⢁⠀⠸⡌⠀⣿⠃⠀⠀⠀⠀⠀⠳⢾⣽⣿⣿⣿⣿⣿⣿⣷⣮⣙⢿⣷⣄
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⢀⡄⠹⣆⠘⠃⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡍⠻⣿⣆⠙⢿⣷⣿⣿⣷⣄
⠀⠀⠀⠀⣴⠟⣽⠟⢋⣥⣿⣿⣿⣿⢿⣿⠀⠀⠸⣸⣇⠀⠈⠛⢦⣸⣦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠘⢿⣆⠀⠙⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠘⠁⣾⠁⣰⣿⠟⠹⠛⠉⣡⣿⣿⡇⠀⠀⠀⢿⣴⣀⢇⠀⡀⠙⠻⢷⣤⡀⢦⡐⣄⠀⠈⢻⣿⣆⠀⠻⡆⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡇⢀⣿⢃⠀⣀⣴⠟⠉⣿⢹⣿⣄⢣⡀⠀⠙⠿⣾⣷⣧⡀⢶⣄⠈⠻⣮⣷⡈⢷⡀⠀⢻⣿⡄⠀⠙⠀⠀⠀⠹⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢋⠘⣿⣧⣷⠏⠁⠀⠀⠘⢷⣿⡿⣯⣷⣄⡀⠀⠈⠙⠻⣷⣄⡻⣷⣄⡈⢻⣷⡈⣷⡀⠀⣿⣷⠀⢀⠀⠀⢢⡀⢻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠙⠷⠈⠛⢿⣿⣶⣤⣀⡀⠀⠉⠛⠿⣿⣷⣆⢻⣷⢸⣷⠀⠸⣿⡆⠘⣧⠀⠘⣷⠈⣿⣹⣿⡏⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣻⣿⣿⣷⣶⣤⣀⠈⠙⢿⣾⣿⣎⣿⡇⠀⣿⣷⠀⣿⣇⠀⢿⣇⢹⡇⣿⣿⡌⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣄⠀⠀⠀⠀⠀⣴⠾⠛⣋⣉⡉⠀⠀⠀⠉⠙⠿⣷⣄⠀⠹⣿⣿⣿⣷⠀⢸⣿⠀⣿⣿⡀⢸⣿⣸⣇⣿⣿⣷⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣥⡀⠀⠀⠀⠀⠀⢰⡿⢻⣿⣿⢻⣿⡿⠟⠀⠀⠈⢻⣦⠀⠹⣿⣿⣿⠀⢸⣿⣇⣿⣿⡇⢸⣿⣿⣿⢹⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠟⠀⠀⠀⠀⠀⠈⠀⠈⠛⠉⠈⠁⠀⠀⠀⠀⠀⠈⣿⣇⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⣾⠉⣿⡏⣼⣿⣿⡋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⣿⣿⡏⠀⢸⡟⢸⡿⠹⣿⡿⠀⢸⡇⣿⣿⣿⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢹⣿⢠⣿⣿⠇⠀⣾⠇⠸⠃⠀⣿⠇⡀⠀⢰⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⣼⣿⣾⣿⡿⠀⢸⡿⠀⠀⠀⠀⠏⢰⡇⢀⣿⣿⣿⣿⠇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣸⣴⣿⣿⣿⣿⠇⢠⣿⠇⠀⠀⢀⠀⠀⣾⢃⣾⢯⣿⣿⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⢸⡟⣾⣿⡟⠀⣾⡟⠀⡆⠀⣸⡇⣰⣿⡾⢃⣾⣿⣿⣇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⡦⠀⠀⠀⢠⡿⠀⣾⡇⠈⣸⣿⣿⠀⣼⣿⠁⣼⠇⣠⣿⣷⣿⡟⢡⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠁⠀⠀⠀⠀⣼⡇⠀⣿⡇⢠⣿⣿⠇⣼⣿⠇⣸⡏⣠⣿⣿⡿⠋⣴⣿⢋⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡁⢸⣿⡿⣰⣿⡟⣴⡿⣰⣿⡿⠋⢀⣾⠟⠀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⢻⡇⣿⣿⣥⣿⣏⣼⣿⣿⡿⠋⢀⣴⠟⠁⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⠘⣷⣿⣿⣿⣿⣾⣿⠟⠋⠀⠐⠋⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⢻⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠙⣾⣿⣿⠁⠀⠀⠀⠀⠀⢀⡴⢁⣼⢟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠈⢿⡆⢶⢹⣿⡟⢀⣴⠞⡠⢀⣴⠋⣠⡾⢣⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⢀⡿⣿⡄⢧⣿⣷⣿⣧⢞⣵⠟⢁⣴⠟⣠⡟⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⣎⣿⣻⣿⣿⠟⢁⣴⡟⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣈⢿⣿⣿⣿⣇⣠⡿⠋⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⢀⡟⡀⠙⢿⣿⣿⡏⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣧⣿⣰⠟⢿⣿⣿⢃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣷⣿⣿⡇⢰⣿⣿⠇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⣿⣿⣇⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⢻⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠸⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠄⠤⠄⠠⠀⠤⠀⠂⠠⠠⠆⠠⠀⠄⠠⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣶⣤⣤⠤⣄⣀⣀⣀
⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⣿⣿⣷
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣟⣭⣿⠿⢿⣿⣿⠿⠏⠙⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣛⣻⣿⣿⠯⢒⡶⣟⣛⠛⠀⠀⠆
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⡃⠀⠀⠀⠸⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣾⣭⣶⠋⠀⠀⣠⠶⢶⠇
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⡉⢿⡿⠀⠀⠀⠀⠔
⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⢆⢀⡀⠀⠀⠀⠀⠀⠀⠃⠀⡄
⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡸⠂
⠀⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠛⠦⠂⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠈⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠚⣢⠄
⠀⠀⠀⠁⠠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢧
⠀⠀⢀⡀⠀⠈⠑⢦⡀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠴⠃
⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⠀⠀⣰⠉
⠀⠀⠀⠀⠀⠈⠳⡄⠀⡄⠑⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⢰⣧⣤⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣿⡷⣿⠁⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⠀⢀⢔⡿⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣅⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢐⡵⠋⠠⢀⡀
⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡠⠒⠢⢄⣀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⢀⡴⡡⠋⠀⠀⠀⠀⠈⠑⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠈⢳⡄⢀⡤⠂⠀⠚⢆⠀⠀⠀⣄⠀⠀⠀⠀⠈⠁⠒⠤⢀⡀⠀⠀⠀⢀⠒⢤⣠⡞⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡼⠁⠀⠀⠀⠀⠀⡄⠀⠀⠙⠒⠤⣀⠀⠀⠀⠀⠀⠈⠑⠢⢀⡌⠁⣾⠀⢁⠀⠀⠀⠉⠐⠒⠤⣄⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠴⣫⠏⠰⣤⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠉⡲⠆⠀⠀⠀⠀⠀⡟⠀⢸⡇⠀⣾⡀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⣰⠏⢈⡆⠀⠈⠻⢦⡀⠀⠀⠸⡇⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⡔⢁⠞⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠊⢁⠄⢸⡄⠀⠀⠀⠀⠈⠁⠀⠀⢞⠀⠀⠀⠰⢅⡀⠀⠀⣠⠊⢀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠈⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⢀⡔⠁⠀⠀⢿⡇⠀⠀⠀⢀⣴⠊⠀⠛⠀⠀⠀⠀⠀⠈⠑⠒⠁⠀⢸⠀⠀⠀⠀⠀⠄⣠⠊⠀⠀⡰⠁⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠈⠀⠈⠉⠐⢿⡀⠀⠀⠀⠚⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠞⠁⠀⠀⠜⠁⠀⠀⠀⠀⠰⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⢈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠐⠤⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠞⠀⠀⡠⠂⠀⠀⠀⠀⠀⠐⠄⡀⠀⠉⠑⠢⢄⡈⠢⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠋⠀⡰⠋⠀⠀⠠⠀⢀⡤⡀⠐⠠⣀⠁⠒⠠⢄⣀⣈⠒⢌⠘⡄
⠀⠀⠀⢀⣄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠊⠀⠘⣀⠔⢀⠔⠁⡠⠊⠀⠈⠒⠄⡀⠁⠒⠠⢄⣀⠀⠀⠀⠀⢠
⠀⠀⢰⡢⣧⠹⠄⢢⠎⡆⠀⠀⠀⠀⠀⠀⡇⠀⠄⠒⣉⡤⠒⢁⠔⠊⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠤⠀⢈⣉⠀⢀⡌
⠀⠀⠠⡴⠎⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⣡⡀⣀⠩⠤⠐⠊⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠡⢼⢠
⠀⠀⠀⠈⠂⢄⣀⠔⠊⠀⠈⢦⡀⠀⠀⠀⡉⠂⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠁⣼
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠑⠤⠀⠀⡎⠄⠈⠙⡄⠀⠐⠁⠀⠀⠀⠀⠓⠖⠂⠀⠀⠀⢄⠨⠀⠀⢠⢃⠢⠂⢇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠲⢅⠀⡱⠖⠋⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠙⣄⢄⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⣀⡌⠒⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⠤⢲⡁⠀⠀⠀⠈⠃⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⡸⠈⠢⡀⠀⠀⠘⡄⢀⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠒⠘⠒⠂⠀⠀⠒⠈⠀⠀⠀⠈⢢⠀⠀⠸⣥⣶⠿⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠸⠋⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠰⠹⠈⢇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⢤⣄⠀⠀⠀⠀⣀⡄⠀⡠⠤⠤⠤⠤⠤⠃⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠂⡠⠒⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠓⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⢿⣿⣿⡍⠛⠛⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣶⣬⣽⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡻⣿⡏⠁⠠⣶⡔⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⡇⠉⠡⠀⠀⠑⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡄⠀⠀⠀⠾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠌⠙⠲⠦⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⣿⠛⠛⢲⡶⠶⢦⣄⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠈⠳⠂⠀⠐⠒⠶⠁⠊⠀⠀⠰⣤⡀⠈⢻⣦
⠀⠀⠀⠀⣼⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠙⣦⠀⢿⣷⡄
⠀⠀⠀⠀⣿⠀⠙⣷⣤⠄⠀⢀⣀⠀⠀⠀⠀⠀⠹⣇⠰⣦⡿⠀⠀⠈⠙⠛⠛⠛⠷⣦⣀
⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⢰⡟⠑⠶⣤⣤⣤⣤⠄⠀⢀⠘⣿⡶⠂⢠⢸⡆⠀⠈⠙⠾⠛⠷⡄⣀⣠⣤⢶⣟⣷⣆
⠀⠀⢸⡗⣿⠀⠀⠀⢠⡆⣸⠇⠀⠀⠀⣤⣤⣄⣀⠀⢸⡇⢸⣷⣤⣼⣆⠻⣤⡴⠶⢀⣀⣤⣴⡾⠟⠛⢻⡟⢛⣿
⠀⠀⢸⡇⠀⠴⠴⠖⢋⣰⠏⠀⠀⡐⠶⠶⠤⠉⠀⣠⡟⣠⡿⠁⠀⠀⢙⣷⣶⣶⡾⠿⠛⠉⠀⠂⠀⠀⣽⡇⢸⣿
⠀⠀⣼⠃⠀⠲⠶⠒⠻⠷⣤⣄⠀⠉⠉⠀⠀⠰⠚⢉⣰⣟⣀⣤⣶⣾⣿⡿⠏⢷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣥⡿⠃
⠀⢸⡏⢀⣤⣄⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⡶⠚⢻⣿⣽⣿⠿⠟⠟⠉⠀⠀⠀⠀⠁⠀⠀⠀⣠⣴⣶⠶⠛⠋⠁
⠀⠈⢷⣤⣬⡻⠷⣦⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢉⣩⡅⣀⢠⡄⠠⡄⡀⠀⠠⢠⣴⠴⠟⠋⠁
⠀⠀⠀⠀⠈⠛⠛⠳⠶⠖⠚⠻⠶⢶⣤⣄⠀⠀⠀⠀⢼⡇⠉⠈⠀⠀⣀⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⣄⣀⣸⣿⣁⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠿⠛⠉

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠄⠒⠂⠀⠉⠉⠉⠉⠉⠙⠓⠲⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠃⢃⠀⠀⠀⠀⠀⠀⠀⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢬⡀⠀⠀⡄⠀⠀⠰⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠘⢂⡄⠀⢠⡠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡻⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡐⡐⠀⠀⠘⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠅⠀⡄⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠀⠀⢸⠀⠀⠀⠐⣲⣦⣤⣄⠀⠀⠀⠀⠀⠰⠶⣟⣉⢠⣀⠀⠀⠀⢦⠞⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⠀⢸⠀⠀⠠⠚⣯⣯⠟⠘⠁⠀⠀⠀⠀⠀⠚⠋⡭⠛⠋⠀⠀⠀⢰⠞⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⢃⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣠⡾⠋⢉⣭⡉⠙⣶⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠳⡄⠀⠀⠀⠀⠀⠠⠟⠛⠻⠆⠀⠀⠀⠀⢀⡞⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣾⠃
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢹⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠻⢿⡿⣶⣤⣀⠀⠀⣂⢀⣠⣾⠾⠻⠏⠀⢰⠒⠆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠁⠛⠻⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠚⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠷⣀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠋⠉⠀⠀⠀⠀⢀⡠⠀⠀⢀⡴⣾⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣄⣀⠀⠀⠉⠉⠋⠓⠒⠂⠲⠂⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠷⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣾⣿⡿⠿⠿⠿⠛⠉⠁
⣶⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠙⢿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡀⠸⡅⠘⠀⠀⠀⠀⠀⠀⠀⡼⠀⠿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠉⢡⠀⢙⡄⠀⠀⠀⠀⠀⠰⣧⠀⣾⡇⢰⠀⠀⠀⠰⠆⠠⠏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠀⠈⠀⠈⠁⠐⠃⠀⠰⠀⠚⠁⢠⣽⠀⡈⠀⢀⠀⠄⢀⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣦⣰⣿⣿⣤⡀⠘⠇⠀⠁⠀⠀⠐⠀⡎⠀⠀⠀⠀⠠⠋⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠆⠓⠀⠀⠐⡀⠀⠀⣼⣿⣿⣿⣿⠟⠈⢹⣿⡆⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢁⡞⡥⠀⠹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠃⠀⠀⠀⠡⣠⣿⣿⣿⣿⣿⣿⣷⡖⠛⠉⠁⠀⠀⢀⣀⣀⣜⠟⠀⠀⠀⠀⡀⠏⠎⠁⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣿⣿⣬⠉⠀⠀⠀⠀⡀⢠⡜⠃⡀⢀⡜⣹⢿⣿⣿
⣿⣿⣿⡿⠓⢀⠀⠘⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⢿⣿⠛⠛⠛⠉⠀⠀⠀⠀⡀⢈⡀⣀⠺⠀⢉⠜⠁⠀⢻⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠢⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⠻⠷⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡡⠉⠀⡰⠂⡰⠉⡀⢸⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠈⢀⣠⠚⠤⢋⣤⠊⠀⣿⣿
⣿⣿⣿⠇⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣟⠁⣀⠀⢀⣠⣴⡤⠀⠀⠀⠀⠀⠀⠀⠠⢿⡽⠋⠀⠈⠀⡰⠞⠀⣿
⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⠐⠢⠃⣀⠺⣿
⣿⣿⣿⠃⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣹⢞⣔⠦⠂⠀⣼
⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⣿⡿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢋⡄⠀⢈⣴⣿
⣿⣿⣿⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠉⣠⠖⠉⣹⣿
⣿⣿⣿⣿⡄⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡊⠁⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣤⠀⠀⠀⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⠳⠞⠁⢀⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣏⠠⣼⠏⠁⣠⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁⠀⠀⠂⠀⠀⠀⠊⠱⠚⠉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣄⣀⣈⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠁⠐⠀⠐⡄⠉⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠆⠶⠶⠦⠶⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠠⢤⠀⠠⠤⠤⠀⠀⠄⡤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠃⣀⣀⠀⣀⣀⠀⢀⣀⡀⠁⠀⠘⢚⢺⠀⢰⠚⠒⠀⠀⠒⡗⡇⠀⠁⣈⣁⠈⢀⣀⡀⠀⣀⡀⠉
⠀⠀⠀⠀⡷⢾⠀⡷⡷⡇⢸⢾⠇⠀⠀⠼⠬⠼⠀⠸⠬⠬⠆⠠⠧⠥⠇⠀⠀⡷⠶⠀⢰⡷⡇⠘⢾⠶
⠀⠀⠀⠐⠛⠛⠀⠚⠛⠃⠘⠛⠓⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠛⠛⠂⠘⠛⠃⠘⠛⠓
⠀⠀⠀⡂⡤⡤⠀⠠⡤⡄⢠⢦⢤⠀⠀⢈⣩⣹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤⢤⠀⢠⡴⡄⢠⢤⠆
⠀⠀⠀⠀⣯⣿⠀⢨⣯⡇⢸⣽⣽⠀⠀⣠⠴⢘⠀⠀⠀⠀⠰⠰⠀⠀⠀⠃⠀⣏⣹⠀⢸⣏⡇⢸⣹⡅
⠀⠀⠀⡀⠉⠉⠀⠉⠉⠁⠈⠉⠉⡀⠀⠉⠉⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⡂⡀⠉⠉⠀⠉⠉⠁⠈⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠹⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠈⣏⡀⠀⠀⠀⠀⣾⣿⣶⢸⠀⡀⢠⣤⣄⠀⠀⠀⠀⠀⠀⣧⡆⣾⣇⣀⣀⣀⣿⢿⣿⣺⣿
⠀⠀⠀⠀⠀⠀⣿⡟⡽⣇⠀⠀⠀⠀⠛⣉⣿⣾⣿⣵⣦⡄⠇⠀⠀⠀⠀⠀⠀⠿⠧⢹⡿⣿⣿⣿⣿⣼⡇⢸⣿⣠⠄
⠀⠀⠀⠀⠀⠀⢸⢃⣗⡟⠀⠈⣉⢠⣤⣿⣿⣧⣼⡟⢻⣿⣷⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣷⣿⣾⡿⣿⣇⣿⣿⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⣿⠷⠾⠿⠿⠇⣤⣄⠀⠀⢀⣀⣀⢸⣿⣿⣿⣿⠃⠛⠛⠛⢻⣿⣿⣿⠅
⢠⣖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠸⣭⠀⠀⢺⣽⠿⠘⠛⠛⠛⠛⠀⠀⠀⠀⠘⠿⠟⢇⢤
⠀⣿⡿⣧⣠⠀⠀⠀⠀⠀⠀⠂⠢⢸⣿⡿⠿⣻⣿⠀⠀⠈⠀⢀⣤⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢳⡀⠘
⠠⣿⣿⣿⣻⣀⣀⣀⣀⣰⠿⣄⡀⡘⠛⠛⣻⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⡆⠀⠀⠀⠀⢀⣂⣩⣭⣍⠂⠈⣟⡱
⠠⡿⣿⢿⣿⣿⣿⣿⣿⣿⣔⠹⠾⣿⠀⠀⢽⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⠉⠀⣷
⠀⠖⠸⢿⢸⣿⣿⣿⣿⡿⠿⠿⠶⠶⠀⠀⢾⣿⣿⣀⣀⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠉
⠀⣿⣿⣾⣼⣿⣿⣿⣿⡏⠐⠎⠂⠀⠀⠀⠸⠿⠿⢼⣿⣿⣁⠙⢿⡿⠋⣀⠛⢛⣻⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢤⠀⠀⠰⣿⣾⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡛⣛⠃
⠈⡿⠛⠛⢿⡇⢰⠀⠈⠐⢄⠉⠀⠘⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢠⣷⣦⣀⠀⠀⢲⣷⢠⣶⣿⣷⣾⣿⣿⣿⣟⣤⣤⣤⣤
⠀⣧⣤⡀⠀⡇⠠⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⣿⣿⣷⣾⡇⠾⠿⠿⠟⠀⢀⣾⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣇⣀⠀⠀⣀⣿⣿⣿⣿⣦⣤⣤⣠⣤⣿⣿⣿⣿⡇⠀⠈⠀⣶⣶⣾⣿⣿⢿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠿⠿⠿⢠⣴⣿⣿⣿⣿⣿⣿⡿⠛⠛⠷⠜⠛⠛⠛⠛⠃⠀⠀⡀⣿⣿⣦⣽⣿⣈⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣾⡿⠉⣿⡛⠋⠋⢋⡋⠠⣾⠿⢿⣷⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠘⣧⡀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣶⣾⣿⢀⣀⠀⢘⠛⢀⡀⠀⣼⣿⠀⠐⠂⠀⠘⠳⣤⠂⡿⠛⠛⠛⠛⡄⢠⡍⠉⠃⠠
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢿⠀⣙⠁⢀⠀⢀⣄⠀⠀⠀⠀⠀⢰⣶⣿⣶⡞⠋⠀⠀⢀⣴⡆⢻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣯⣤⣾⣯⣿⣻⠄⠀⠀⠀⠀⣿⣿⣿⣿⣇⣥⠆⠀⠀⠉⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⣾⣿⣧⠀⠀⠀⠀⠉⠙⠛⠛⢳⡖⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠋⠀⠀⠀⠀⠉⠛⠓⠶⣄⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠋⠉⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣀⠐⢇⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠀⠐⠋⢠
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠳⣀⣀⣀⣴⠀⠼⣄
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠌⠋⢁⠀⣶⡀⠈⣦
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⢳⡀⠘⣧
⠀⠀⠀⢀⡿⠀⠀⠀⠀⣀⣀⢀⣠⣀⣀⣀⣀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠈⣧⠀⠘⣄
⠀⠀⠀⣼⠷⠶⠺⠏⢻⠉⠉⠉⠋⠉⣻⣿⡿⠛⣿⠉⠉⠉⡙⠋⢱⣶⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⣿⠀⠀⢿
⠀⠀⢠⡿⠀⠀⠀⣤⡌⠀⠀⠀⠱⡀⠻⣿⣿⣿⡟⠀⠀⠀⡇⠀⣿⣿⣿⣄⣼⡿⠀⠀⢹⠋⢻⠶⠶⣿⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠁⠈⠛⠁⢀⣀⠀⠀⠈⠢⢈⣿⣿⡿⠟⠀⠀⠀⢸⡤⠎⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢀⡠⢶⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡰⠀⣀⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠂⠐⠛⢉⣠⡾⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⠀⠠⠀⢀⠌⢠⡊⠄⠀⣀⡝
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⠿⠛⣹⠇⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠰⠀⢷⡀⠀⠈⠁⠔⠛⣉⡀⠦
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢊⣡⣴⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠙⢆⠀⠀⠒⠠⠍⡁
⠀⠀⢻⡆⠀⠀⠀⢀⣀⣠⣤⣤⠴⠖⠛⠛⠒⠲⢤⣤⣤⣤⡤⣤⡴⠒⠉⠉⠉⠉⠉⠉⠉⠁⠓⠒⠒⢦⣤⣄⡀⠠⡇⠀⠀⢘⡀⠀⠀⠀⠀⢀⠖⠒⠀⠉
⠀⠀⠸⡷⠶⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠆⠀⠀⠌⠁⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠔⠲⠒⠂⠉⠀⠀⠉⠲⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢨⠉⠉⠉⠉⠉⠀⢰⠄⢀⣠⣀⣀⣠⠋⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠁⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⢄⠀⠀⠀⡄⠀⠀⠀⠁⠀⠃⠀⡀⠀⠒⠀⠈⠀⠀⠀⠳⢄⠀⠀⠸⠓⠶⠶⠤⣤⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡷⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⠆
⠀⠀⠀⠀⠀⠔⠁⠀⢀⡔⠋⠀⠀⠉
⠀⠀⠀⠀⠐⠦⣄⡀⠈⠐⠢⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⠀⠑⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢀⣀⣀⣀⣀⣤⢠⣄⣀⣀⡤⠦⣄⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⣠⠋⠀⠈⠏⠀⠀⠀⠀⠙⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡝⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡧⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣇⠀⠀⠔⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⡀⠠⠀⠀⠉⠀⠀⠀⣀⠤⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠦⢀⣀⣀⠀⠤⠄⠒⣃⡡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⣄⠀⠀⢀⣀⠞⢱⡄
⠀⠀⣦⠀⣀⣈⣉⣡⣤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠐⠓⠈⠉⢀⣰⠇
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠒⠲⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⣠⣤⣤⣾⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠟⠉⠁⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣨⣤⠒⠀⠈⠄⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠉⠛⠃⣼⡦⠟⢠⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⡀⠴⠿⣤⣼⣶⠾⣧⣴⣄⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⢱⣿⣿⣧⡀⢠⣿⢿⣿⠇⢸⣿⣿⠈⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣿⢡⣾⣧⣿⣿⣧⣼⣧⣼⠃⣤⠈⠙⣋⢘⡃⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⣿⣿⡟⢹⣿⣿⣿⠛⠃⣤⠙⠖⠀⢈⡸⠃⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⣿⣻⠇⠏⠹⣿⡟⠀⣼⠏⠀⠀⣘⠋⠁⢰⠁⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⠀⣠⠀⢈⣿⠇⠀⡾⠋⠀⠀⠈⠀⠀⡏⣿⡀
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⠼⣬⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⢻⠀⠀⣦⡀⠀⠀⠀⢡⡄⠹⣦
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡦⠀⠀⠀⠋⠀⠂⠀⠀⠉⠸⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠂⢀⡸⡇⠀⠀⠀⠀⠃⠀⠱⠦⠀⠀⠨⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⡄⢃⠀⡇⠀⠀⠀⠀⠀⢨⣦⡀⢒⠀⡀⣈
⠀⠀⢠⡀⠛⠁⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋
⠀⠀⢸⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠁⠀⠀⢯⡀⢀⣇
⠀⠀⢸⠀⣷⠀⠀⠈⣦⢜⠀⠀⠀⠀⠀⠀⠀⣼⢀⣷⠶⠶⠶⠶⠟⢸⡇⢸⣿
⠀⠀⢸⠀⠉⠀⠀⠀⠁⣾⡄⠀⠀⠀⠀⠀⠀⣉⢀⣿⠀⠀⠀⠀⠀⣾⠁⢸⡟
⠀⠀⢸⠀⡷⠀⠀⡀⢃⣙⡇⠀⠀⠀⢀⠀⠀⡿⢈⣿⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇
⠀⠀⢸⠀⡇⠀⢀⠋⢸⡏⣀⠀⠀⡀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⠀⡇
⠀⠀⢸⠀⠷⠀⠊⠀⢾⡏⠙⠀⠀⠗⠀⠆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⠈⡁⠀⠀⠃
⠀⠀⠾⣀⠠⠤⠈⡁⢻⡇⠙⠂⠀⠳⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢾⠃⢰⡇⠀⠀⠇
⠀⠀⠃⠉⣤⠲⢈⣱⣾⡿⡅⢠⡀⢀⠈⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠀⠘⡇
⠀⠀⠀⡀⠛⠀⠛⠁⠚⢷⡄⠄⠀⠈⢠⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⠀⠀⡇⠀⠂
⠀⠀⡖⠃⠀⣶⠟⣀⣐⠶⠀⢀⠀⠤⠈⣧⠀⢠⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣷
⠀⠀⡇⠀⠀⣇⠀⠉⠁⣰⢏⣿⠁⢀⠀⡇⠀⢠⠀⢻⠀⠀⠀⠀⠀⢷⠀⠀⠇⠀⣿
⠀⠀⠁⠀⠀⠀⣦⢀⣛⢙⣾⡏⠀⠈⣴⡷⡀⠀⠀⣿⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡔⠀⠉⡞⠋⡙⠛⣁⠀⠀⣿⠀⣿⠀⠀⣼⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⡏
⠀⠀⠀⠀⡇⠀⠘⠁⠄⢿⠀⠛⠀⠀⣿⠆⣿⠀⠀⣽⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠇⠀⠀⠄⠀⠈⠀⠀⠀⠀⢻⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠃⠀⠀⠸⠃⣿⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⢰⡀⠀⡀⡿
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⠂⢸⢃⡄⢿⠀⢀⣸⠀⠀⠀⠀⢻⠆⠀⢸⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡄⠀⢸⠀⠈⠋⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠖⠀⠻⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣷⠀⠀⠂⠀⣿⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠹⡆⠀⠀⢀⣿⠀⠀⠀⠀⢈⡇⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠷⠀⠀⠈⣿⠀⠀⠀⠀⠘⠇⠀⢸⠀⢠⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠰⠆⠀⠀⡛⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢘⠀⠁⠀⢸⠃⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠀⠀⠀⠘⠈⠀⠀⢹⣇⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⠀⠀⣾⢹⡆⠀⢡
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢦⠄⠀⠠⣿⠀⠀⠀⢰⠀⠀⠀⡿⢸⡇⠀⢸
⠀⠀⠀⠀⠘⠁⠰⠆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣿⠀⠀⠀⢸⡇⠀⠀⣧⣼⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠄⢠⡄⠀⢀⡄⢀⣀⠤⠃⠀⠀⠀⠈⣿⠀⠀⠀⣼⡇⠀⠀⣿⣽⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⣠⡘⠛⣴⠃⠀⠀⠀⢠⣿⠀⠀⠀⣿⣇⠀⠀⣟⣹⡄⠀⠘⠃
⠀⠀⠀⠀⠀⢀⣘⣇⠠⡾⣉⠰⢞⡟⠀⠀⠀⠀⠸⠿⠆⠀⠀⠈⠛⢀⣤⣿⡿⢿⣿⣿⠷⠀⠤
⠀⠀⠀⠀⠐⠿⢿⣿⣧⡄⢉⣓⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣧⡤⠀⠀⠀⠛⠀⢠⣤⡀
⠀⠀⠠⠶⠛⠶⠒⠻⠾⠿⠾⠛⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠟⠛⠛⠃⠰⠶⠶⠂⣈⣛⡶⠾⠁
⠀⠀⠀⠀⠐⠀⠐⠶⠖⠲⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠟⡁⡶⢂⣠⡀⠀⣹⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⠎⣰⠠⠁⠈⠘⠖⠘⠉⠈⠋⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⣵⣾⣿⠻⢿⣿⣷⣶⡀⠀⠀⣤⣴⠀⣦⡉⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡁⠈⣹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢷⣾⣿⡿⠀⠀⢀⣀⠀⢠⠀⣀⣀⡀⠀⠀⠈⣿⠀⠀⣼⡁
⠀⠀⠀⢠⠆⡀⠀⢠⠒⡆⠀⠀⠀⠀⠘⡷⠾⣿⣿⣧⠀⣩⣽⣿⡀⠀⣾⣿⣿⡷⣄⠀⠀⡟⣷⡀⠐⣻
⠀⠀⠀⢸⠀⡅⠀⠨⠀⠇⠀⠀⠀⠀⠈⢳⠄⢙⣿⣟⠉⠀⠀⣹⠇⠀⠻⠉⠀⠀⠀⠀⠁⡏⢁⣿⡶⠋
⠀⢇⠠⠘⠀⢤⠀⡀⢸⠀⠀⣀⠀⠀⠀⠈⠳⢿⣿⡇⠀⠀⣠⣇⣀⠀⣀⠀⠀⠀⠀⠀⠀⣧⢾⡟⠁
⠀⠘⡀⠀⣆⠀⢠⡁⠨⡤⠊⢠⡀⠐⠀⠀⠀⠸⣿⡇⠀⠀⣏⡀⠈⠀⠀⣀⡸⣄⠀⠀⠀⣃⡼⠁
⠀⠀⠐⣄⠈⠀⠀⠀⢀⣀⡖⠁⠀⡱⢺⠀⠀⠀⠙⢧⠀⠐⠃⠙⠷⠶⠞⠋⠀⠏⠀⠀⡰⠋⠁
⠀⠀⠀⢸⡆⠀⠀⠐⢉⠎⠹⡤⠒⠃⡸⠀⠀⠀⠀⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⢷⡀
⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⢀⡼⠁⠀⠀⢀⣼⠙⢻⣿⣦⡑⠠⠄⠠⠒⣠⠶⠋⡿⠁⠌⢧
⠀⠀⠀⠈⢷⡀⠀⠀⠸⠀⠀⢠⠞⢀⣀⡤⢶⡿⠁⡀⠂⣽⣧⡉⠀⠀⠀⠉⠀⣀⣾⠅⠁⠠⠈⢿⢦⣤⣀⣀⣀
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠴⠟⠊⡉⠂⣀⣾⡄⠢⡴⠾⡿⣿⣿⣦⡀⠀⣠⠞⣫⣽⠦⣌⣠⡈⢸⣯⠀⠈⠀⠈⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠂⡀⠂⢀⠂⢀⠀⢀⢈⡿⠻⠻⣞⠡⠈⠨⠿⣄⠈⠀⠍⠁⠌⠁⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠐⢀⠐⢀⠐⣰⣯⣠⠈⠀⠹⡆⠄⠀⣄⣩⣦⠁⠄⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠐⠀⠀⠀⠈⠉⠝⠁⠄⢻⠄⠋⠍⠁⠄⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠁⠄⠱⠿⠉⠆⠁⠀⠀⠀⠈


⣿⣿⠿⢿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠤⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⣦⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⠋⠙⣷
⠀⠀⠀⠀⠀⠀⠀⣠⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡔⢶⡄
⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢳⣄⠀⠀⣦⡄⢀⡾⠛⢦⣤⡀⠀⠀⣤⢀⡏⠛⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠙⠳⣶⡏⠙⠿⠃⠀⠀⠈⠛⠷⢶⣿⠻⣧⠀⠀⠙⠻⠶⣄⣀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣠⣤⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣤⣤⡀⠀⠈⠉⢹⣷⠀⠀⣿
⢿⡀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢸⣿⠀⣸⡇
⠸⣷⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⣠⠶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⣀⠀⠀⠀⢸⡟⢀⡿⠃
⠀⠸⣧⡴⠛⠛⠻⣤⣾⠇⠀⠀⠀⢺⠁⣤⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣤⡄⢈⡆⠀⠀⣼⣁⣸⠇
⠀⢰⡏⠀⠴⠆⠀⠈⠉⠀⠀⠀⠀⠻⣄⡀⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⡜⠃⠀⠀⣿⢿⡇
⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠘⣧⣸⠇
⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⣄⣀⣀⣀⣀⠠⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⣈⣻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠉⠆⣠⠖⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⢦⣤⣤⣤⣤⣀⣠⣤⡠⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠄⣠⡌⠀⣼⠞⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⢾⢿⣀⠀⠀⠀⢈⡿⠛⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠟⠁⠠⠁⢠⡼⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠛⢋⣀⠉⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠆⠀⠀⢀⡠⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⡔⢿⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠻⣦⠀⠀⠀⠀⣠⠾⠋⠁⢀⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⠐⠛⣧⣀⡴⠎⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣤⣀⠁⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⢀⣠⣴⠾⡿⠋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⢟⠁⠀⠀⠀⠀⠀⣠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢧⡀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠰⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠟⠾⡏⢸⣇⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠙⣿⡛⠉⠀⠀⠀⠀⢹⠁⠀⠀⠈⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣴⡏⠻⣄⠸⣷⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⢷⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣤⠄⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠷⠿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⠈⣿⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡇⢹⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠘⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡀⢀⡿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⣸⠃⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢰⣿⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⣀⣀⣀⣀⣼⡆⢿⣄⣀⣀⣀⣀⣸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢻⡟⠉⠉⠉⡉⢙⣣⣾⠉⠋⠉⠉⠉⠻⡟⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⣀⣘⣁⣀⣀⣀⣋⣙⠿⢿⣀⣋⣀⣀⣀⣈⣉⣀⣈⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠛⠙⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣠⣀⣀⣀⣀⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠞⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡢⠂⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⣀⡄
⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⣤⣄⡀⠀⣶⣯⠀⡏⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⠛⠁⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⢀⡀⠀⠀⠀⠀⡤⡀⠀⠀⠀⢠⠶⢦⠀⠀⠀⠀⢸⡇⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢡⣀⠠⠀⠀⠀⠀⠠⠀⠀⣰⢆⠀⠘⢛⣉⠆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⡡⡴⠖⠀⠀⠐⠀⠀⠰⠛⠙⠆⠀⠀⠀⢀⠤⠤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢟⠙⠻⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⡀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠀⢉⠀⠄⠀⡉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢴⣀⣄⣐⣀⣀⣀⡦⠴⢂⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣸⢀⠈
⠀⢀⠀⠴⠀⡄⠀⠀⠀⠀⠀⠠⠁⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠶⠀⣀⠀⠀⢠⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢡⡄⢁⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⡠⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠁⠀⠀⠀⠈⠉⠰⠀⠈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠰⠛⠃⠀⠀⠀⠙⣛⣳⠄⠀⠈⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠂⣀⣰⣆⠀⡜⠁⣀⣀⠂⡀⠀⢀⡀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠀⡁⢸⣿⣥⣿⢀⡁⣾⣿⣉⣼⠃⠀⠘⠃⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠙⠖⠛⠋⠙⠈⠳⠿⠿⠟⠁⠀⠀⢠⡟⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣙⣁⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠡⠍⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠶⠲⢶⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⡰⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⢸⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢦⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠁⣀⣀⠀⠤⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠁⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠀⠃⢠⡀⠙
⠀⢠⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡆⠘⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣦⠀⡞⠀⠆
⠃⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣀⠈⡀⢀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠒⠒⠶⠶⠶⠉⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢂⡀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⢠⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠠⠶⠆⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠉⠀⠛⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢠⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⣠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⠀⠘⠓⢀⠔⠉⠀⠀⡄⠈⠁⠈⠁⣆⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠂⠈⠀⠀⠀⠀⠀⠈⢀⣀⣀⣀⣉⠐⠈
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡛⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡊⡃⣸⠀⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠉⣹⡏⢹⣟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠭⠤⠼⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⡒⢀⡀⠓⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣴⣿⣿⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢻⡞⠑⢿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⠔⠀⠀⠀⠀⠳⠙⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢛⠅⠉⠁⠀⢀⣀⡀⠀⠂⠀⢝⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠕⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠒⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢛⠕⠁⠂⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠈⠀⠤⣤⡙⠝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠵⠁⠀⠀⠀⠀⠀⠠⣠⡾⡛⠿⢧⣄⠀⠀⠀⠠⠤⠄⠀⠐⢝⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠗⠗⠀⠀⠀⠀⠀⠀⣠⡾⣫⠉⠁⠀⠑⡝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠙⢟⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣷⠁⠀⠀⠀⠀⠀⠉⣩⡾⡁⠊⠀⠀⠀⠀⠀⠀⠀⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⡶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⠄⠀⠠⢤⣤⡤⠬⠛⢾⡭⠭⠭⠄⠀⠀⠀⠀⠀⢽⡷⠛⠃⢀⢢⣖⠀⠀⠀⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠐⢺⣿⡗⠀⠀⢸⡏⠀⢠⣀⣀⣠⣖⣀⠀⣿⡇⠀⠀⢚⣯⣽⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠠⠤⢸⣿⡧⠀⠀⢸⡷⠀⢸⡇⢠⡄⠀⠷⠀⢿⡇⠀⠀⠠⣿⣿⠇⠀⠀⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⠂⢀⣸⣿⡗⠒⠂⢸⣟⠀⢐⡇⢺⠆⡅⢖⠀⣻⡇⠀⠀⢒⣿⣿⡃⠒⠒⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢿⣿⡇⠁⢀⢸⡏⠀⠠⡇⠼⠂⡉⠨⠀⣿⡇⠀⠀⢤⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⢀⠀⠛⠻⠛⠀⠀⢸⡷⠀⢰⡇⠒⠀⠂⡶⠀⣿⡇⠀⠀⢘⡉⠉⠓⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⣀⠀⠀⠉⠉⠉⣀⣺⢹⣶⠊⠓⠒⡒⠚⢽⣷⡏⣛⣐⣀⡀⢀⣀⣁⣀⣀⣊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠙⠋⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⢾⣄⣠⠤⠴⠖⠒⠶⠶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠵⠎⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⢄⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡝⠀⠀⠀⢀⣤⣒⣲⠀⠀⠀⠀⠸⢭⣳⡄⠉⡏⠀⠈⠑⠢⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢀⣠⠤⢬⣇⠀⠀⠀⠀⠘⡆⠀⠀⢰⠋⢹⠀⠀⡀⠀⠀⠀⠀⠀⠾⠀⠃⢸⠀⠀⠀⠀⠀⠀⣀⣠⠜
⠀⠀⠀⢀⡔⠉⠀⠀⣤⡼⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡴⠛⠛⠒⠤⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠨⠷⡀
⠀⠀⠀⢈⡧⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⣀⣤⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠧⠷⣄⠀⢀⣏⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣬⣮⢙⣝⡉⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⡅⠀⠀⢿⠉⠉⢹⡧⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⠟⠹⡄⠀⣸⡤⠴⠿⣄⠀⠈⠓⠦⠤⣄⣀⣀⣀⣤⠤⠖⠊⠁
⠀⠀⠀⠀⠈⠓⠢⠤⣤⣤⣤⣤⠤⠴⠒⠋⠁⠀⢠⠏⠀⣴⠷⠚⠁⠀⠀⠀⢸⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢠⠇⠀⠀⢀⡧⠄⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣣⣀⡞⠀⠀⢀⡞⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡼⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣹⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢋⠀⠀⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣶⠀⠀⠰⠆⢸⠅⠚⠂⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠁⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⠀⠀⠀⠀⠀⢀⣤⣭⠐⠒⠂⠒⠀⠀⠀⢤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠛⠛⣃⠀⠀⣴⣇⠀⠀⠀⠂⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠂⠉⣿⣤⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⠠⢾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⢠⣼⣷⡆⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠱⡌⠙⠃⡀⠀⠀⠀⠀⡇⠀⠠⣬⣏⠁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢡⡀⠀⠀⠈⢳⡄⣀⢽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠉⠉⢡⣄⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢣⣤⣤⣄⠊⠁⠀⠀⠀⠀⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣐⠈⠀⠀⡤⠄⠀⠐⠒⠀⠁⡀⠈⠒⠪⠀⠀⠸⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢙⠗⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠘⠂⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠤⡀⡀⡙⠂⢀⠄⣀⡄⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠂⠀⠀⠉⠀⠐⠊⠠⢄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⣤⠀⠀⠀⠀⠀⣠⣤⣶
⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠀⠈⠁⠀⠀⠀⠀⠀⢉⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⣀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡁⠈⠀⡀⠀⠀⠄⠈⠁⠀⠀⠀⠄⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠖⠀⠀⠁⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠢⣤⠀⠀⠀⠀⠀⠀⢀⠄⠠⢄⢀⡀
⠀⠀⠀⠀⢀⠂⠉⠀⠑⠂⡀⠂⠀⢀⠆⠀⡠⠀⠀⠀⣄⠀⠑⡄⠀⢀⠀⠀⠀⠀⠈⠠⠀⠄⠂⡙⡥⠀⠀⠀⠀⠀⠘⢲⠀⠀⠀⠠⠁⠀⠀⠀⠠⡀⠁
⠀⠀⠀⢠⠁⠀⠁⠀⠀⠀⡁⠀⠀⠀⡄⠰⠀⡀⠀⢀⠘⡄⠈⠆⠀⠀⠀⠀⣀⠀⢀⢀⠀⠀⠀⠠⠒⠀⢀⠀⠀⡀⠀⠠⢆⡀⠀⢀⠀⠀⢀⠀⠀⠑
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠱⡀⠀⠀⠄⠀⠀⡠⠊⢀⡄⠀⠀⠀⠀⠀⠀⡈⠠⠂⠀⠑⠁⠀⠀⠀⠀⠀⠐⠢⡌⠁⠀⢠⡈⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠣⠶⠚⣭⡱⢲⠁⠀⠀⠀⠀⡈⠵⠂⠰⠔⡈⠀⠀⠂⣖⠡⢤⠒⠀⠲⠍⠀⠀⠀⠀⠀⢇⣀⣠⠜⠒⠒⠒⠊⠁⠀⠀⠀⠉⡰⠀⠀⠒
⠀⠀⠀⠀⢸⠀⠀⣿⡇⢠⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⠸⠀⢀⣤⠌⠐⠰⠐⠀⠀⠀⢢⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⢸⠀⠀⠈⠂⠀⢃⠀⠀⠜⢀⠃⠀⠀⠀⡂⠠⠀⠀⠀⠀⠂⠀⠀⠁⠀⡄⠸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠨⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⣲⣭⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢠⠁⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⣜
⠀⠀⠀⡠⢦⣜⡠⠤⠠⠀⡜⠀⡈⠁⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠸⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⣴⡤⢼⠀⠑⠀⠀⠀⠇⠀⠑⠤⢀⠀⠀⠀⢀⢇⡘⡀⠀⠀⢀⡇⠀⢰⠀⠀⢁⣀⠀⠀⠀⣠⠀⡈⠀⠀⠀⠀⠀⢂⡑⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⢠⣤⠈⠀⠀⠁⠂⠀⢀⠔⠀⠀⠀⠀⢠⠀⠀⠀⠰⠈⠻⠀⠀⠀⠈⠁⠀⢈⠀⠀⢘⠁⠀⠀⠀⠛⠃⠁⠀⠀⠀⠀⠀⠘⠟⠃⠀⠉⠒⠀⠀⠀⠐⠚⠃
⠸⣿⠀⠀⠀⠀⡜⠀⠘⠀⠀⠀⠀⠀⠀⡆⢠⡀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠸⢨⠀⠸⠀⠀⠀⠀⠀⠘⠁⢐⠒⠦⠤⢤⠀⢊
⢸⣿⠀⠀⠀⠸⠀⡆⢨⠀⠀⠀⠀⠀⠀⡇⠀⠃⡀⢠⠀⠀⠀⠀⠀⠠⠀⢰⠀⢠⠃⠀⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⠈⠄⠈⣄⠀⠀⠀⠀⠀⠀⢀
⠸⣿⠀⠀⠀⡔⠸⠡⡈⠄⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠠⣼⠠⡆⠀⠀⠀⠀⠀⠀⠇⠈⠁⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣿⠀⢀⠌⠰⠀⠀⠃⠐⢄⠀⠀⠀⠀⠸⠀⡀⠠⠁⠸⠀⠀⠀⠀⠀⠈⡄⢠⡘⢢⠀⠀⠀⠀⡰⠃⡜⠀⠀⠀⠀⠀⠀⠀⢂⠀⠤⡀⠀⠊⠀⠐
⢠⣿⠀⠈⠂⠀⠀⠀⠈⠢⠤⠃⠀⠀⠀⠡⠤⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠉⠉⠀⠀⠀⠘⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠜⠂⠤⠄
⠨⡿

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠐⠒⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⢀⢜⡵⠂⡉⠤⠀⠐⠉⠓⠤⡀⠉⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⢠⡳⡟⢠⠋⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⠄⠀⠀⠀⠀⣠⣤⣤⣠⣤⢠⣤⣤⣤⣄⡄⣸⠖⢄
⠀⠀⠀⠀⢲⢁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢠⠀⢠⣿⣿⡿⣿⡿⣿⣿⣾⣿⢿⠇⠏⠀⠀⡇
⠀⠀⠀⠀⡈⠈⠀⠀⠀⠤⠶⠤⠀⠀⠀⠴⠒⠒⠀⠀⠀⠀⠀⠀⢆⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠈⠙⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⣶⣦⠀⠀⠀⠰⣾⡿⠖⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡀

⠀⠀⡜⠈⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠆⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠁⠒⠒⠂⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣐⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢤⠀⠊
⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⢠⡄
⠀⠀⠀⠀⠀⠛⠀⠘⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣀⠀⠄⠒⠀⢀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠄⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠜⠓⠠⠀⠀⠐⠀⠗⠀⢴⡎⢷⠖⠒⡆⠁⠀⠀⠀⠀⠈⠀⢂⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠈⠙⠀⠀⠀⠤⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠀⠀⢤⡂⠶⡆⠂⢰⡄⠀⠀⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠚⠃⡤⡠⠀⠁⠈⡀⠉⠑⠂⠄⢀⠀⠀⠀⠀⠐⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢡⣾⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣰⣶⠄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⣿⣿⣿⡿⣟⣿⣇⠀⠀⠀⠀⠻⣿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣤⣤⣤⡄
⠀⠀⠀⠀⡄⠈⣇⠀⢀⢰⡀⠸⣿⣿⣷⣿⣿⣿⣆⢠⠀⠀⢴⣿⡧⣴⠋⡀⢠⣀⠀⢙⣦⢀⢀⠀⢀⠀⠀⢀⣾⣿⣿⣇⢸⣿⣿⣿⣇⠀⡆⡀
⠀⠀⠀⠱⣷⣤⣧⣷⣿⣆⣱⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣂⣿⣿⣧⣿⣼⣷⣿⣿⣤⣿⣼⣬⣾⣷⣬⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢌⠢⡓⢕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡑⢕⢌⠢⡱⣕⢄⠀⠀⢀⣴⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢌⡢⡑⢕⢌⠪⡳⣕⢄⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡑⢕⢬⡢⡑⢕⢌⠪⡳⣝⢟⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠪⡢⡑⢕⢌⠢⡑⢕⢌⠪⡳⣑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡑⢌⠪⡢⡑⢕⢌⠢⡓⢕⢌⠪⡢⡑⢄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠪⡣⡑⢌⠪⡢⡑⢕⢌⠢⡑⢕⢌⠪⡣⡕⢄⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣻⡛⠛⠛⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠑⣌⠪⡢⡑⢌⠪⡢⡑⢕⢌⠢⡳⣕⢌⠪⡢⡑⠄⠀⠀⠀⠀⡀⠴⠆⠠⠾⢿⠿⠦⠀⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠑⢌⠪⡢⡑⢜⠪⡢⡑⢕⢌⠪⡳⣕⠌⠊⠀⠀⠀⣀⣼⣿⣦⡀⢀⣴⣿⣷⣄⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⢌⠪⡢⡑⢍⢪⡢⡑⢕⠌⠂⠀⠀⠀⠀⠀⠈⣩⣿⣍⠁⠈⣩⣿⣭⠉⠀⢉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣱⢌⠪⡢⡑⢝⠎⠂⠀⠀⠀⢀⡘⠛⠂⠚⢛⣟⠛⠃⠘⠛⣻⡛⠛⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⠞⠁⠀⠑⢌⠪⠂⠀⠀⠀⠠⣴⣿⣿⣦⡀⣴⣿⣿⣷⡄⢠⣾⣿⣿⣦⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡠⠊⠀⠀⠀⣀⡀⠀⣠⣾⣷⣄⠀⣠⣴⣿⣦⡀⢀⣴⣿⣷⣄⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡠⠊⠀⠀⠀⢀⣴⣍⠉⠈⢉⣽⣯⠉⠁⠉⣩⣯⡉⠁⠈⢉⣽⣍⠉⠈⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐⠛⣿⠛⠓⠐⠛⢻⡛⠛⠂⠚⢛⣟⠛⠂⠐⠛⣻⡛⠓⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⣤⡄⣠⣾⣿⣷⣄⢠⣴⣿⣿⣦⡀⣴⣿⣿⣷⡄⢠⣾⣿⣿⣦⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠰⠷⠀⠀⠀⠰⠿⠆⠀⠀⠀⠾⠷⠀⠀⠀⠰⠿⠄⠀⠀⠠⠾⠆⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⠾⠀⠀⠉⠀⠀⠉⠉⠉⠑⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢢⡀⠀⠀⠀⢰⢄⡀⣠⠚⠢⣍⣁⡀⠀⠞⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠙⠢⣄⡀⠘⡀⠀⠀⠀⠀⠀⠈⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⡇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡄⠀⣤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⡇⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⡇⠀⠀⢠⡆⠀⠀⠀⢀⠔⢛⠀⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠀⢀⡰⠋⢀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡄⠋⢀⠴⣿⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⢲⡁⢀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠤⠤⣤⣤⡤⣤⣼⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠓⣄⠀⠀⠀⠀⠀⠀⠀⠅⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡀⠀⠀⠀⠀⢀⠰⠧⣤⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡾⠉⠢⣄⡀⠀⠀⠀⠀⡜⠀⢘⡦⠴⠒⠒⠒⠒⠤
⠀⠀⣀⠄⠐⠂⠀⠀⠈⠃⠀⠀⢳⡄⠤⠐⠊⠁⠀⠀⠀⢉⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢯⡀⠀⠀⠀⠉⠉⠒⠒⠚⠀⠀⠈⠀⣀⠀⠀⠀⠉⠀⢉
⠀⣮⡡⠤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣨
⢦⡠⣤⡴⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣀⡤⠴⠒⠉⠀⠀⢠⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠙⠲⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡠⠞
⠀⡔⢁⣠⡤⠀⠀⠀⢀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠙⠉⢤⣠⠞⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⠤⠤⠴⠧⠤⠼⠤⠤⠤⠐⠒⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠤⠤⠤⠔⠋⠳⠐⢲⠚⠛⠛⠛⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠀⠀⠆⠀⠀⠀⠀⠸⠂⠀⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢳⡤⠄⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⢄⠠⠤⡆⠀⠀⠀⠀⠀⠀⠀⣷⠤⠤⡴⠶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢤⠃⠀⠀⠀⠀⠀⠀⠀⢻⡔⠀⠁⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠐⠧⣤⣀⣀⣀⡤⢻⠁⠀⠀⠀⠀⠀⠀⠀⢸⡳⢤⣀⣀⣠⣤⠴⠂⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠈⠉⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉⠁⠀⠀⠀⣠⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣲⣦⣤⣶⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣦⣤⣴⣖⣚⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠒⠉⠉⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⢀⡌⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢀⠔⠉⠀⠀⠀⠙⠟⡄⠈⡏⠁⠚⠓⠒⡒⠓⠓⠢⠤⠏⢀⠢⠤⣤⠤⠤⠤⠴⢤⠼⢢⡤⠤⠤⠄⣀
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⡔⢳⠀⠀⠀⡴⢣⣶⠶⡉⠇⠀⢸⢉⣶⡟⣍⢳⠀⠀⠀⢸⢤⡞⢷⡄⠀⠀⠀⠙⢦⡀
⠀⡌⠀⠀⠀⠀⠀⠀⡜⠀⢣⣀⡄⠀⠀⢡⠘⠿⡿⠃⡌⠀⠰⡈⠿⠿⠋⡼⠀⠀⠀⢸⢀⠃⠀⢣⠀⠀⠀⠀⠀⢳⡀
⠀⡇⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢡⠀⠀⠀⠑⠒⠒⠈⠘⠉⠃⠈⠐⠒⠉⠀⠀⠀⢠⠟⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣
⢠⠁⢀⡠⠄⠒⠁⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⢧⣀
⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢉⣐⠈⠁⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⢀⣐⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⡤⠤⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⢂⡀⠄⠛⠓⢪⣤⣔⠓⠘⠻⣍⠐⠐⠒⠂⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠰⠩⠁⠀⠄⢰⠋⠁⠀⢱⡄⠀⠀⠙⡄⠀⠀⠀⠈⡟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡄⠀⠀⠀⠀⡮⠀⠀⠀⠦⠈⡄⢰⢀⢀⠀⠀⠀⠀⠃⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠆⠐⠀⠀⠀⠀⠀⠀⠘⠆⠀⢠⡊⠈⠉⢂⠀⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀⠱⠀⠀⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⣸⠀⠀⠀⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⣄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⣀⡠⠛⠀⠀⠀⡎⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣈⠛⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠙⢄⠀⡇⠀⠀⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠉⠀⠀⠀⡇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀⠀⡠⠊⠉⠑⠒⠒⠒⠒⠒⠒⠊⠁⢣⠀⠀⠀⠀⠀⢰⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠶⠶⠮⠥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣉⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠒⠲⢤⡴⣤⣀⣀⣀⣤⠤⡤⠴⠴⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠈⣸⠀⠀⠀⢸⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠘⡠⠀⣹⠃⠀⠀⠀⡎⠀⢆⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡶⠁⠀⠀⠀⢠⡁⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡠⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡞
⠀⠀⠀⣀⠤⠚⠁⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⢀⠴⠊⠁⠀⢀⡠⡢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠑⢄
⡎⠀⠢⢀⡰⢊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡡⡀⠀⠑⢦⡀
⠳⣄⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡑⠀⠀⠊⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⡠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠓⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡒⡲⣷⡀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⣰⣖⣒⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡄⣤⠉⠀⠀⠀⠀⢀⠤⠊⠒⢄⠀⠀⠀⠀⠉⢠⢠⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡷⣿⣀⠀⢀⡠⠒⠁⠀⣠⡀⠀⠙⠢⣀⠀⣀⣺⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠿⠿⢸⡔⠉⠀⠀⣀⢸⢽⣅⠀⠀⠀⠈⢑⡷⠾⠿⠃⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⡁⠉⠉⠉⠡⠉⠉⠉⢣⠀⠈⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠛⠀⢺⠙⠙⠓⠷⠁⠀⠀⠀⠀⠷⠋⢋⠛⢻⠀⠛⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⡒⠁⠀⠰⠀⠀⠐⢿⠃⠁⠹⠶⠆⠀⠀⠀⠐⠦⠟⠈⠀⢿⠂⠂⠠⠴⠀⠀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠸⠶⠀⠀⠶⠀⠸⢀⣀⠀⠀⡀⡀⢲⠀⢀⠀⠀⣀⡀⢸⠀⠶⠀⠀⠸⠾⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢄⡀⠀⠀⡠⡀⠰⢸⣿⡀⠀⠋⣟⠛⢹⠻⠁⠀⣿⡇⢸⠀⠀⠀⠀⢀⢠⠐⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡅⣀⢀⢀⢀⡇⡇⣼⠀⠀⢀⡖⣆⣷⣂⢲⣰⠒⡆⠀⠀⣸⡀⠀⠀⢀⣀⢀⣈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⢑⡒⠦⣄⡀⠤⠤⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣀⣈⣀⣀⠀⠀⠙⢆⠀⠈⢆⠀⢀⠔⢩⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠠⠀⢀⡠⢄⣀⠀⠀⠀⠀⢈⢀⠀⢈⠐⠁⢠⠃⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡇⠰⠀⡦⣀⠉⠡⠌⠉⠳⢦⣄⣘⡧⠶⢏⠀⠀⠀⢀⠄⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠳⡠⠰⠃⣁⡀⢠⠚⡇⠲⠊⠀⢹⣿⡄⠣⡀⠀⠀⢀⣀⡤⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢁⣰⠅⠿⠋⢣⡭⠜⠀⠀⡜⣿⣿⣦⣈⣒⣂⣦⢱⡤⢀⣀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠑⠤⠺⠄⠀⡠⠊⣵⠸⣿⣿⣿⣿⣿⣿⠀⡄⠈⠑⠢⣸⣕⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⣤⣤⠠⠂⠠⠜⠉⢆⠈⠻⣿⣿⣿⠏⡸⡂⢀⠀⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⢿⠀⢢⠀⠀⠀⠀⠃⣀⠀⠀⢀⠔⢁⠌⠁⢤⠀⠀⢠⠔⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢳⣄⡑⢂⠀⠰⡀⠀⢀⣤⠎⠀⢠⠀⠀⠀⠃⢀⠄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⠈⢳⠚⠛⠅⠀⠎⠀⠀⠞⠀⠘⠘⠢⡄⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠠⠀⣀⡐⠀⢀⠄⠓⢤⡾⣀⠔⡀⠀⠀⠣⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠤⠔⣡⠇⠀⠀⠀⢀⠞⠀⠀⡔⠠⠤⢄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⠴⠁⠀⠀⠀⠠⠃⠀⣠⠞⠀⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠄⠀⢀⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠊⠉⠀⢄⠀⠀⠀⠘⠤⠄⠀⢀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠁⠀⠀⢈⠀⠀⠀⠀⣀⠔⠀⠀⠰⡉⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣤⣤⣤⣤⣀⡀⠒⣋⡁⣤⣤⣄⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡞⣿⡟⣳⣦⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⣾⣿⣿⣿⣧⣼⣿⣏⣹⣿⣥⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠐⡬⣼⠀⠈⢻⡏⠉⠉⠉⠁⠀⠈⢻⣷⢾⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠿⠙⠋⠀⠋⠁⠀⠀⢀⣃⣀⠀⣠⣴⠖⠂⠈⢻⣿⣷⣼⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣆⠉⠔⠹⠷⠂⢹⠛⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠃⠀⠀⠀⠀⠀⠀⣨⢴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⣘⣃⠀⠀⠀⠀⢀⣷⣮⣿⠅
⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠇⠀⠀⠀⣀⣴⠟⣿⢇⠿⣿⣢
⠀⠀⠀⠀⠋⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⡿⠋⠀⠀⢷⣸⠷⣟⣿
⠀⠀⠀⢸⡀⠀⠀⠠⠘⠷⠶⠶⠒⠛⠛⠛⠲⢦⣴⠶⢶⠟⠛⠛⣶⣤⣴⣿⡁⠀⠀⠀⠀⠈⠻⣿⣟⠃
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡞⡆⠀⠀⢿⣿⣿⠿⣿⣆⠀⠀⠀⠀⢠⡏⠙⣦⡀
⠀⠀⠀⠙⠳⢶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢀⡿⠀⠀⠀⠙⠋⠀⣠⡘⣆⢀⣠⠴⠋⠀⡼⠁⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣤⣀⣀⡀⢲⣿⣿⠟⠸⠁⣄⠀⠀⠐⠟⠛⠉⣿⣹⣯⠗⢲⡄⢸⡇⠀⢀⠀⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣧⡿⣠⡟⠀⠀⠀⠀⠀⠀⠙⡿⠃⠀⠈⠳⣼⠁⡴⠋⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⢻⡟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⢈⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠰⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠄⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠘⠂⡀⢠⣿⣀⣠⡤⠶⠦⣄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡾⠹⠿⠛⢛⣛⣓⠢⠄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⣆⢹⡇⠀⠀⠀⠀⠀⠀⢠⡿⠠⣷⡶⠶⠿⠿⢶⣯⡒⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠲⣄⠙⡘⡇⠀⠀⠀⠀⠀⠀⣸⠷⠚⠉⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⢀⡘⠦⠙⢣⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⠙⣂⣀⣈⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⠀⠀⠀⢀⢀⣠⡤⠤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠉⠉⠉⡐⠢⢄⡠⠄⠂⠤⢀⡀⠀⠀⡠⠄⠒⠀⠀⠐⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⡀⠀⠀⠠⠄⡀⠑⠄
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠐⢌⡀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠁
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⢠⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⢤⡀⠈⠢⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠉⠒⠠⠬⢱⣄⠑⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠲⠀⠀⠀⢀⠀⠀⠀⠙⠆⠈⠄⠄
⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⠸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⢰⡆
⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢘⠀⠁⠤⢁⡒⠄⠀⠀⠀⠀⠀⠀⡘⠀⢀⠁⠀⠀⠀⠀⠀⢸
⠀⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠉⠁⠀⠀⠰⠄⣀⠠⠊⠀⢀⠌⠀⠀⠀⠀⠀⢀⠇
⠀⠰⢡⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⠞⠁⠈⠑⠤⢄⡀⡀⠠⢤⠴⠆⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⢠⢊⠂
⠀⠀⠡⢂⠀⠀⠀⠀⠑⠤⢀⠀⠴⠃⠀⠀⠀⠀⠰⠌⡀⢀⡀⠀⣡⠌⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣌⠁
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠉⠱⠊⢤⠀⠙⢄⣀⠀⢀⣀⠤⠂⠁⢀⠞⢸
⠀⠀⠀⠐⠀⠳⣀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠰⠋⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠉⠆⠒⠐⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⡁⠀⡠⠐⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠠⠀⠀⠀⠀⠀⢀⠜⠢⠐⢈⠔⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⢄⠑⢄⠀⠀⠀⡀⠀⠀⠈⢠⠙⢄
⠁⠀⠀⠀⠀⠀⢡⣄⠸⠃⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠳⢄⡀⠂⠰⠙⢤⠂⢀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⠂⠾⠀⣤⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠱⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⢀⣀⡠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠉⠀⠒⠂⠀⠤⠀⣄⠀⠠⠤⠤⠄⠀⢀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡆⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢩⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⠀⠀⠀⠀⠀⠀⣼⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠷⠀⠀⠀⠀⢀⣍⠀⣉⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠐⠒⠚⢤⡀⠀⠤⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠑⢠⡄⠀⠀⢀⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠙⢦⣀⣀⠶⠈⡏⠢⠔⢋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⢀⣼⠧⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⢒⠄⡄⠃⠂⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠃⡖⡟⢸⢳⡆⡇⢸⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢰⢰⡏⣇⢸⣿⡇⠇⣰⣾⢷⣄⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠈⡄⣧⢻⡌⣿⣧⢰⣿⣿⣿⣿⣷⣄⢀⠘⠄⢀⠀⠀⠀⠀⠀⠀⠐⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢧⠐⢼⣦⡇⢹⣱⣿⣿⣿⣿⣿⣿⣜⢿⣦⣸⣌⡃⢦⠀⠀⠀⠀⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢶⣿⢹⣦⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣑⣤⣤⡀⣱⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣨⣻⡸⣏⣿⣿⡛⢯⠷⡙⠛⠻⣿⢿⣍⣻⣿⣿⡿⠿⠛⡿⠛⠈⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⣿⣧⡛⢷⡎⠀⠀⢀⠈⠁⠀⠈⠢⠐⠛⠁⠤⠆⣀⣸⣧⢀⣤⠠⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡻⣿⣿⣟⣸⠃⠚⣿⣿⣿⣦⠀⠀⠀⠀⠀⣀⣰⠿⠛⠻⣿⣿⣿⡗⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣻⣿⣿⣿⠏⠀⠀⠻⠟⢻⣿⣷⣦⣠⣶⣶⣿⣛⣈⣁⠀⢻⣟⡹⣿⣿⣿⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠿⣿⣿⡀⠀⠀⠈⠙⠛⢿⡿⣿⠀⢸⣿⣟⡛⠁⠉⠁⢼⣯⢙⡽⠿⣿⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠹⣿⡦⠀⠀⠀⠀⠈⠁⣀⠄⠀⠀⣄⠈⠁⠀⠀⠀⠸⢋⡼⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣾⡇⠀⠀⠀⠞⠉⠛⠶⠟⠛⠣⠀⠀⠀⠀⣴⡟⠻⣦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠚⢹⣿⣧⠀⠀⠀⠀⠠⠄⠐⠆⠀⠀⠀⠀⠀⢀⣿⠛⢢⡈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⣿⠃⠀⢸⡟⠏⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠁⠀⢀⠏⠀⠀⠀⣿⠘⣄⢀⡀⠀⠀⠢⠄⠀⠀⠀⢠⡄⣠⣾⣿⠀⠀⠀⢀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡏⢣⠈⠛⠷⣤⣀⣀⠀⢀⣠⡤⠊⠁⡻⣿⣿⠀⠀⢀⡠⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠣⠀⠀⣠⣼⠉⠉⠉⢹⢧⠠⠊⠀⠸⡿⠀⠀⠈⠡⡀⠀⠀⠀⠀⠉⢢⣀
⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠉⠙⡟⠀⠘⡀⠀⠀⠀⠀⡀⠀⠀⣇⣀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣷⣤
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣾⡇
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⠸⣇
⠀⢸⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹
⠀⡾⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣷⠀⠀⠀⣰⠀⠀⠀⠀⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸
⢸⡇⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⣿⣤⡀⢀⡟⠀⠀⠀⠀⣿⡆⢰⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠘
⣿⣥⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣧⣤⣤⣤⣤⣼⣿⣧⣾⣥⣤⣤⣤⣤⣿⣷⣿⣧⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣿⣿⣧⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠒⠒⠛⠛⠛⠛⠒⠂⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⡤⣤⡀⠀⠠⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⠀⠙⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⢠⠋⠠⠐⠂⣀⡀⠐⢦⣄⠀⢻⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⡰⠃⣠⣤⣶⣿⣉⡏⠀⡸⠋⠀⠈⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠄⠀⢠⠋⠘⢀⠙⠿⠿⠟⣁⠔⠁⢀⡰⠆⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⢠⡘⢀⠀⠈⠑⠒⠒⠊⠠⠤⠚⠉⠀⠀⢸⠇⠀⠀⢸
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠆⠐⠀⠀⡘⠁⠈⠁⠀⣀⠐⠂⠉⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡀⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⢄⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣆⠘⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢹⡆⠀⠠
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⢸⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⢸⠃
⠀⠀⠀⡿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡀⠀⠀⣼⡃⠀⠀⠀⠀⠀⢀⣀⣠⣤⠖⠛⠉⠀⠀⠀⠀⡸
⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠀⠀⡜⠉⠉⠁⠐⠒⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀
⠀⠀⠀⡇⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣄⠀⠀⢰⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠸
⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠏⠀⠀⠘⠃⠀⡀⢤⡄⠊⠀⠀⣠⢤⣀⣀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠉⠀⠁⠀⠐⣄⠀⠤⠁⡄⠉⠉⠑⠶⣄⠀⠀⡧⠀⠀⠀⢸
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠈⠀⡈⠛⢀⠈⠀⠀⠀⠀⠀⠈⢳⡄⠁⠀⠀⠃
⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢻⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠘⣦⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠋⠀⠀⠀⠠⠄⠀⠀⢠⡄⠀⠀⠺⠂⠀⠀⣿⠀⠐
⠀⠀⠀⠀⠀⠀⢹⡄⠀⢃⡘⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠇⣀⣀⠴⠉⠀⠴⠾⠷⠤⠤⠦⠤⢀⣀⡀⢀⣌⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⡇⠸⠀⠀⠀⠀⠀⠀⠁⠀⣿⡦⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠊⢀⠳⠘
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡀⠷⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠻⡀⠇⠀⠀⠀⠀⠀⠀⠘⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢻⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠣⡌⠁⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠐⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⣤⣀⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠀⠀⠀⠀⠴⠖⠒⠶⢶⡶⠶⢶⣶⠶⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⣾⠀⠀⣾⠄⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠀⠀⠀⠈⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠸⠇⠀⠀⠀⡹⠒⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠏⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢰⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣷⠀⠀⢻⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⠀⢸⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠈⣄⡀⠀⠀⠉⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠹⠗⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠒⠒⠂⠀⢀⡽⣧⠐⠂⠀⢈⣡⣤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠛⠋⠀⠀⠀⠙⠛⠋⠉

⠀⠀⠀⠀⢤⣖⠂⡀⠀⠀⠠⠒⠢⢤⡀⠀⠀⠠⢂⡀⠀⠀⠀⠀⠀⠀⣄⠢⠀⠀⠀⡀⠤⠂⠒⠒⠀⠐⠒⠁⠂⡄
⠀⠀⠀⠀⠀⠉⠀⠈⠢⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠠⠀⢀⡀⠰⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢂⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠠⠆⠀⠀⣤⠄⠁⠀⠛⠀⠀⠀⠀⠀⠘⠒⠜⠁⠀⠀⠉⢠⠂⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡈⠀⢀⠀⠀⡀⠀⠁⠀⠀⠈⠐⢲⠆⠤⠀⠀⠀⠀⠀⠠⠄⠖⠐⢈
⠀⢰⠀⢸⠀⢠⡀⠀⠀⠀⠀⠀⠚⢻⢈⡀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠐⡀
⠀⠻⠃⢸⠀⠈⠀⠀⠀⠘⠃⠀⠀⠘⡉⠁⠀⠀⠀⢨⠀⠀⠀⠀⠀⢨⠉⠀⠀⠅⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄
⠀⡀⠀⡰⠄⢠⡄⠀⠀⠀⠀⠀⠀⢼⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢀
⠈⠁⠐⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉
⠀⠀⠀⠀⠀⠋⠀⢀⠂⠈⣃⡭⠛⠟⠶⠶⠞⠢⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠒⢲⠾⠶⠶⡗⠒⠦⣈⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠆⢡⠊⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠵⡄⠀⠀⠀⠄⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢇
⠀⠀⠀⢠⠾⣀⠀⡀⠎⠀⢐⠀⠂⠀⠀⠀⠀⠐⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠲
⠠⠀⠀⠀⠀⠐⠠⠁⠀⠀⡄⠀⠈⣁⣀⣀⣈⠁⠀⠠⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⣀⠀⠀⠀⠈⡀⠀⢸⠀⠀⠄⠠⡀⠀⠁⣀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡃
⠈⠄⠀⠀⠀⠀⠌⠁⠀⢸⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠂⠀⠁⠀⠀⠂⠀⠀⣼⠀⠀⠀⠼⠆⠀⠀⡀⡂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⢀⠀⢀⡀⠀⠀⢀⠃⠀⢰⠀⠀⠀⠀⠙⢣⣄⠀⢬⠀⠀⠄⠠⠧⠈⠀⠁⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠐⠤⠤⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⠐⠤⠴⠀⠀⠀⠀⠀⠘⠹⣬⠼⠱⠈⣦⣥⠃⠫⢴⠀⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠦⠤⠤⠤⠤⠶⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠰⠎⠀⠀⠛⠂⠂⠈