Veggie Emojis & Symbols

⠀⠀⢿⢈⠀⣴⣿⣛⣿⣷⡿⠀⠀⠙⠻⠿⠿⢿⠟⢻⣷⡦⠀⢶⠟⠂⠀⠈⠻⢿⣿⣿⠷⠁⠀⠈⢹⣿⠉⠀⠸⣿⣿⣿⡿⠀⠀⢿⣶⣿⡗⠀⢀
⠀⠐⠋⠀⠀⠈⠛⠛⠋⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢠⡄⠐⢄
⣀⣀⣀⣠⣴⣦⢀⣦⡅⠀⠶⠆⠀⣀⣠⣿⣶⡄⠀⢺⡾⡞⣿⡆⠀⢰⢢⡄⢰⣾⣿⣿⣿⣷⠀⠀⢀⣤⣤⣤⣤⣄⠰⣿⣿⠀⣸⡇⠀⢠⣤⠀⡀
⠹⠿⠿⠿⠛⠁⠘⠿⠟⠀⠘⠂⠸⣿⣿⣿⣿⡿⠀⢻⡇⣇⠟⠃⠀⠇⢸⡇⠸⣿⢿⣿⣿⣿⣷⡄⢿⣿⣿⣿⣾⣿⠀⠙⢻⡶⠛⠁⠀⠻⠟⢀
⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠸⠿⠶⠖⠋
⠀⣠⣾⣿⣿⠁⠀⠀⢠⣶⣠⠃⢰⣦⡀⠀⡴⣦⣠⣄⠀⠀⡤⣀⠀⡰⣧⣄⡀⠀⠀⠀⠀⣠⣵⡄⠀⠀⠀⢾⡷⣤⡄⠀⠀⠀⠀⠀⠀⣀⣀⠠
⣿⣿⠿⠋⠁⠈⢿⠀⢿⣿⣿⣿⣿⣿⠃⢐⣷⠘⡁⠉⠀⣸⠀⣿⠀⡷⢿⣿⡇⠘⢷⣶⣿⣿⣿⠇⠀⠀⢿⣿⢿⣿⡅⣼⣿⣯⣵⡄⠀⣿⣿⣦
⠉⢰⣆⠀⣀⠀⠈⠀⠀⠉⠛⠛⠋⠁⠀⠈⠀⠚⠉⠀⠀⠘⠀⠿⠀⠉⠒⠉⠀⠀⠀⠉⠛⠛⠁⠀⠑⠐⠀⠉⠀⠈⠀⠈⠛⠛⠋⠀⠀⠛⠿⠛
⣿⡿⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⢀⢲
⠀⣰⡀⠈⠀⡶⠂⠰⠶⠆⠠⣤⠀⠀⠙⣿⠿⣿⣿⠃⢀⡀⠀⢩⣾⣻⡟⠛⠁⠀⡿⣽⠟⠛⢸⣾⣷⠀⠺⣷⣄⠀⠀⢠⣶⣾⣿⣿⣦⠀⡎⢼
⢼⣿⣿⠆⢠⣵⣶⢤⣰⡆⠀⢹⡄⠀⢰⣯⠟⠁⠀⠀⠻⠇⠰⠏⠉⠛⠐⠀⠀⠸⠟⠁⠀⠀⠈⠻⠟⠀⠀⠀⠙⠳⠄⠘⠿⠿⠿⠛⠛⠀⠁⠸
⡀⣈⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠁⣄⠀⠀⠀⠀⠀⢀⡤⡶⣤⡀
⣇⠀⢷⡀⠀⢠⣶⣿⣿⣶⣦⢂⠀⠀⠀⠀⢀⣬⣶⠀⠀⢠⡄⠀⢻⣿⣇⣠⡿⠀⢺⣤⣄⠀⣉⡞⣿⢻⣻⠀⢀⣀⠀⠀⢀⣤⣄⠀⢤⣰⡄⠀⢠
⣷⣰⠿⢁⡀⠸⣿⣿⣿⣿⣿⣦⡀⠻⣶⣾⣿⣿⣿⠃⣾⣥⣾⡷⠀⠈⠿⠋⠀⠀⠛⢿⡿⠀⠩⡇⣿⡸⠋⢀⠀⢿⠠⣿⣿⣿⣿⣷⢰⣷⠀⠀⠘
⠙⠁⠀⢸⡇⠀⠀⠀⣉⠉⠙⠛⠃⠀⠈⠙⠛⠛⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣀⡀⠀⠘⡇⠀⠠⠿⣄⡉⢦⠀⠀⣠⠀⠀⠀⣀⠴⣶⣦⡄⠀⠀⣀⢀⡄⣀⡀⠀⠀⣀⣤⣄⣀⡀⠀⠀⢠⣴⡀⠀⠀⢀⡀⠀⠀⠀⡀
⡙⡿⠻⠆⠃⠀⠀⠀⠈⣳⠈⠇⠰⣬⣿⣿⡆⠣⠠⣯⡀⠄⠀⣾⣏⣿⣤⣾⣿⠂⢹⣿⣿⣿⣿⣿⡀⢰⣬⣿⣽⡟⠀⡌⢸⠀⢰⣷⡌⠀⢛⠃
⠉⡴⠂⠀⠀⠀⠂⠀⠀⠼⠁⠀⠀⠤⠩⠟⠁⠀⠀⠿⠇⠀⠀⠻⠿⣿⣿⡿⠟⠀⠘⠛⠛⠿⠿⢿⣿⡆⠙⠋⠙⠃⠀⠃⠸⠃⠘⠛⠋⠠⠉⠐
⠀⢰⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿
⣿⠿⣿⣿⡷⠀⠀⠀⠀⣰⣶⣶⣤⡀⢀⣔⣻⣷⣤⠀⠀⠀⠸⠃⠈⢀⣾⣧⠀⢺⡄⠀⠀⠀⡀⠀⠀⢀⡀⣀⣀⠀⢹⡇⠀⡴⣏⡉⢢⡀⠀⡀⠰
⠀⣴⡀⠀⠀⠀⣰⣶⠀⢙⡿⣿⣿⡏⠨⣿⢸⢺⡯⠀⠀⣄⣶⡄⢀⣈⠻⣿⣤⡿⠃⢰⣿⣿⣭⡆⠀⠏⣀⠈⣉⡀⠸⠇⠀⠀⠈⠛⡄⢹⢠⢱⡇
⢺⣿⡿⠀⠀⣈⠛⠋⡀⣺⡷⠉⠀⠀⠀⠛⠸⠏⠀⠐⠀⠉⠋⠀⠺⠿⠀⠈⠁⠀⠀⠀⠙⠛⠛⠁⠀⠛⠋⠙⠛⠁⠀⠀⠐⢀⡀⣠⠟⠀⠈⠈⠃
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣀⡀
⣤⣤⣀⣀⣀⣀⣀⠂⠀⣀⣤⣶⡶⠀⡄⣤⡀⠀⣤⡄⠀⢠⢃⡆⠀⠘⣴⣗⣛⠟⠛⠀⣺⡟⣟⣿⣳⠀⢀⣀⣾⣷⣍⠋⣴⣄⠀⠀⣘⡙⡷⠻⡇
⠙⠛⠛⠻⠏⢹⣿⠷⠀⣿⣿⣿⡇⠀⣿⣿⣿⠀⠘⣧⠀⠸⠸⡇⠀⡾⠉⠘⠃⠀⠀⠀⠩⡇⣿⡘⠉⡄⣿⣿⣿⣿⣿⠇⠈⠙⠳⣄⠿⠛⣤⠆⠁
⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⣀⣀⣀
⠻⢦⡈⢣⠀⠀⠀⣀⣄⣀⡀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠰⠉⢉⡋⠛⠁⢀⣴⣴⣤⣤⠀⠀⢀⢠⠄

⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠄⠀⠈⠀⠀⠀⠀⠐⠀⡀⢀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠈⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠈⠀⠁⠈⠙⠃⠢⠄⡀⠀⠀⠀⠐⢠⣤⠂⠒⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⡀⠈⠂⠀⠀⠀⠃⠙⠀⠀⠀⡰⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢀⠀⢠⠎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠀⠙⢀⠠⠂⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡠⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠂⠄⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢁⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠆⠀⠉⠀⠀⠀⠀⠶⠷⠠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠆⡀⣀⠤⠀⠀⢠⠀⠀⠀⠀⠀⢂⠀⠐⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡶⣏⠀⠀⠀⠀⠀⠀⢶⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠠
⠀⠀⡀⠐⠀⠀⠀⠀⣀⠤⠐⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠂⡀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠠⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠿⠛⡟⢻⡿⢛⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠆⢠⡖⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠁⠀⡀⢄⡀⠀⠀⠀⠀⠀⢸⠣⢂⣠⠶⡄⠐⠀⠀⣠⠀⠀⠀⠈⠠⣶⠼⢷⡄
⠀⠈⢤⣀⡀⢻⠀⠀⠀⠀⢐⠀⠀⠀⣎⠀⢀⠀⢠⡈⠒⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠁⠈⠁⠀⠉⠀⠀⠀⠀⠰⡬⣗⢷⢾⢾⣆
⠀⠀⠀⠉⠉⠀⠁⠀⠀⠔⠋⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠊⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠂⢸⢃⠀⠒⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⢨⠭⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠡⡀⠀⠠⠀⠆⢠⠖⠂⢄⠀⠀⠀⢰⠈⢃⣠⠷⡇⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡀⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⠡⡠⠄⠀⠀⠀⠈⠲⡖⠃⠀⠙⠄⠀⠀⠈⠀⠀⠀⣄⡀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠐⢷⡄
⠀⢦⣄⠀⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡙⠢⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠒⠶⠤⠀⠀⠠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠚⠦⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠚⠃⠀⠀⠀⠀⠠⠀⠀⠜⠀⠃

⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠂⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠶⠟⠓⠄⠐⠢⢰⣷⡠⠀⠀⠀⢀⡤⠒⠀⠀⠐⠀⠠⠔
⠀⠈⠀⡀⢄⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠸⠸⠁⠀⢀⠐⠉⠀⠀⠛⠀⢀⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠌⣄⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠂⠂⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⢀⡇⠀⣀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠁⡀⢸⠀⠀⠀⡀⠀⣴⡁⠠⠆
⠀⠀⠁⢣⠘⠀⠀⠀⠴⠲⡒⠢⡀⠀⠀⠀⠀⠌⢋⣦⡄⠀⠀⠀⠀⠀⣖⢡⢸⠷⠐⡿⠂⠀⠀⠐
⠀⠀⠀⠘⠀⠀⢰⠀⠀⠀⢸⠀⠱⠀⠀⠀⠑⠀⠹⠁⠀⠀⠀⠀⠀⠀⢼⠐⠂⠐⠀⠇⠀⠀⠀⡜⠂
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⡀⠐⠀⠀⠒⠛⠀⠀⠰
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⠀⡀⢨⠀⠀⠀⢀⠔⠀⠀⠀⠈⠁⠉⠠⠀⠀⠐
⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠀⣷⠀⣾⠠⠇⣠⠇⡀⠀⢐⠀⢠⣣⣄⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⢀⡀⠂
⠀⠀⠀⠠⢆⣁⠀⡉⡄⠀⠀⠈⠛⢼⣟⡼⠃⠀⠀⠀⠀⠀⡈⢼⣧⡄⠓⠀⠀⠀⠐⠤⠀⠤⢰⠂⣤⡀
⠀⠀⠀⠐⠢⠀⢂⢠⠈⠀⠀⠀⠀⠄⠻⠦⠀⠀⠀⠀⠀⣠⣯⠮⢅⢀⡄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠇
⠀⠀⠀⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡹⠀⠘⠁⠀⠀⠀⢀⡿⠊⢄⠀⠀⠀⢀
⠀⠀⠠⠆⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⣤⠄⠂⠀⢀⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠊⠛⠀⠠⠒⠋⠀⠀⠀⢿⣿⠉⠀⠀⠐⠒⠚⠡⠴⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢦⢰⡇⡜⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⣿⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣩⣿⣿⣻⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣍⡿⣾⣽⣼⣧⣷⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⣾⣻⢓⡷⢺⡷⠺⡟⢙⣆⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢺⠧⣿⣉⣟⣻⣗⢒⣟⢉⣼⡀⢀⡼⢃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⡀⠀⠀⣾⣙⡟⢶⣧⣼⡯⣭⣿⣍⣼⣭⡴⣷⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠳⣄⢠⠯⣽⣏⣻⡏⢻⡷⠴⡿⢤⣼⡧⡤⢿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⣿⠳⣾⣍⣹⡇⠀⢻⡶⢿⠦⠼⡷⠤⠞⡆⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠻⡄⠀⣿⡓⡷⢤⢼⡇⠀⠘⡷⣻⠷⠶⣿⠶⢚⣧⣿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠳⣿⠀⡧⢭⣟⠒⣿⠀⠀⠀⣟⣹⡗⠶⢿⡗⢋⣿⡏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠹⣦⡷⠴⣏⣹⠇⠀⠀⠀⣯⣽⣏⡛⣹⣏⣉⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠹⣟⣒⣿⡟⠀⠀⠀⢸⡷⠾⣧⣭⣽⣧⣽⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣍⣿⠇⠀⠀⠀⢸⡓⢚⡷⠤⢴⣷⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⢷⣾⠀⠀⠀⠀⢸⣍⢋⡷⣤⡾⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⢿⠀⠀⠀⠀⢸⣯⣭⡿⠋⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠸⡆⠀⠀⠀⠈⣷⠏⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⢻⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠻⣄⠀⠀⠀⡇⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣬⣷⡦⢴⡷⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⣀⣇⣦⣼⡆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⡀
⠀⠀⢀⣿⣿⣏⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠉⡅
⠀⣾⣿⣿⣿⣟⣛⡆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠻⠿⣿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⡀
⠀⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠚⠁
⠀⢿⣿⣿⣿⣿⣶⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠄
⠀⢸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠢⠖⠈⠀⠀⢀
⠀⠘⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⢽⡏⠙⠋⠙⠋⣻⡯⣿⡇⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠠
⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠙⠿⢿⣿⣿⣿⣯⣻⣦⣄⣠⣾⣟⣿⡿⠃⠀⠀⠀⠀⠀⠠⢀⢸⢀⠠⠈
⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃
⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢿⣿⠇⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠸
⠀⠀⠀⠘⠛⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣤⣀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠰⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃
⢠⣶⣿⣷⣾⣿⣿⣶⣿⣷⣦⠀⠀⠙⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣿⣯⣤⣤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣦⡀⢀⣠⣴⣶⣶⣶⠖⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡏⠉⢹⣿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⢷⠒⡶⠲⣿⠛⢻⣁⢀⣿⣶⣿⣿⣶⣶⡶⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠘⠿⠿⢿⣿⣿⠿⠿⠟⠀⠀⠀⠉⠛⠒⠿⠖⠚⠛⠉⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⢿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⢴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⣀⡄
⠀⠀⠀⠀⠀⢀⣀⡀⡇⢀⡞⠀⠀⠀⠀⢻⣦⢀⣶⡟⠀⠀⣠⠶⠘⢇⡠⠯⠉⠁⠠⡀⠀⠀⠀⢠⣾⢻⠳⡿⢳⡯⠁⠳⠢⡀⠀⢀⡴⡋⢡⠍⠉⣙⢖
⠀⠀⠀⠀⠀⢸⡅⢹⣇⣸⠄⢠⠀⠀⠀⠀⢻⢸⣼⡴⠀⠀⡏⢊⠄⠈⠀⢀⠀⠀⠀⣷⠀⢀⠤⠛⠉⠃⠘⠁⠀⠁⠀⢰⠞⠁⠀⡾⠀⠁⠀⠠⠄⢀⠈⡆
⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⠴⠃⠀⠀⠀⣴⡾⠉⠹⡄⠀⠀⠻⡄⠀⢠⠀⠐⠀⠀⣠⠃⠀⠘⠤⠢⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⣷⠆⠚⠀⠀⡤⠈⡰⠃
⠀⠀⠀⠀⠀⢀⣀⣨⣿⣏⣠⣀⠀⠀⢰⠿⠋⠀⢺⡇⠀⠀⠀⠀⠀⠢⠤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠉⣀⣀⣚⠉⠀⠀⠀⠀⠀⡇⣴⠆⠘⣡⡴⠚⠁
⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠁⠀⢱⠀⢸⢋⡦⠀⡼⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⡄⠀⠀⠀⠀⠀⢠⣶⠟⣿⣹⣿⢿⣦⠀⠀⠀⠀⠈⠐⠞⠊⠁
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⠴⠁⠀⢸⣿⠇⡹⠃⠀⠀⠀⠀⣰⢛⠀⡏⠹⡷⢫⠍⠑⡄⠀⠀⣾⠛⣻⡉⢹⣥⡼⣿⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠳⡔⠁⠀⠀⠀⢸⣧⣴⠁⠀⠀⠀⠀⢰⣷⠃⣎⡄⠀⠁⢹⣦⠀⣰⠀⠀⠣⢑⠙⠧⠈⠋⠀⢣⠀⠀⠀⣀⡴⠒⠛⡿⠃⠐⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⣾⠟⢸⢏⡶⠀⠀⣸⡟⢀⡇⠀⠀⠀⠀⠀⠉⢉⣉⡁⠊⠀⠀⣼⢻⣷⡀⠉⠉⠁⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆⣲⠀⣀⣐⣂⣶⠒⣄⠀⠀⣿⠀⣼⣾⡇⠀⣰⡿⠀⡞⠀⠀⠀⠀⣠⠔⠊⠁⠀⠙⡗⡀⠀⡏⣿⢏⠾⡶⡠⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣀⢾⣉⠡⡾⠃⠈⣧⢾⣏⠋⡻⣁⡅⠀⠘⠧⢿⢿⣷⣶⣿⣷⠞⠀⠀⠀⣠⠏⢠⣞⣥⣶⠀⢸⡇⡇⠀⢻⣃⠖⠌⠘⠑⠁⢀⡀⣠⠟
⠀⠀⠀⠀⠀⢠⠔⣟⠐⡄⠉⠀⠀⠀⠙⡶⢻⣭⣤⡦⡇⠀⠀⠀⠀⠉⠉⠘⠋⠁⠀⠀⠀⠀⣿⠀⠻⣿⣧⠟⢀⡟⢰⠁⠀⠀⠈⠙⠢⢶⣤⡴⠟⠚⠁
⠀⠀⠀⠀⢰⣇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠟⢻⡿⢺⠗⠀⠀⠀⣀⣠⣤⠆⠀⠀⠀⠀⠀⣠⡄⠻⡦⡀⢀⣀⡤⠞⡰⠃⠀⢀⣀⣠⠤⠤⣈⡀
⠀⠀⠀⠀⣼⡿⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⣋⣝⣁⣀⣀⠀⢀⡴⡿⢹⠁⠀⠉⠈⠈⠁⠀⠁⠀⢠⣾⣉⡀⠀⠀⠐⠀⢈⣆⡀
⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⠀⣐⣻⣶⣿⠿⠿⠛⠋⢉⠠⣿⠟⢁⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡾⡶⣀⢀⣀⠔⠂⠁⠀⠀⠁⠂⡀
⠀⠀⢸⡿⣿⢣⡄⠀⠀⠀⠀⢹⠀⠀⠀⣴⠎⢡⠏⠁⠀⠀⠈⠢⡀⠀⠀⢸⢷⡓⠒⠁⠀⠀⠀⠀⠀⠀⢀⢸⡇⢤⡀⠙⠢⠁⢾⡧⣿⠶⡤⢀⠀⢀⠀⢸⡄
⠀⠀⠘⣗⢡⡾⣻⢦⠄⠀⢠⠏⠀⠀⡾⠙⡇⢸⡴⣇⠀⠀⠀⠀⢱⠀⠀⢸⠀⠙⢦⡀⢀⡀⠀⠀⠀⣰⠃⢸⣧⠀⠹⡀⠀⠀⠀⠓⢌⢲⠆⠀⢠⢋⣨⠞
⠀⠀⠀⠈⠛⠷⣧⣯⡾⠚⠁⠀⠀⠸⣇⠞⡁⣿⠁⢁⡀⠀⠀⠀⡼⠀⠀⣸⠀⡀⢠⡟⠗⠀⢱⠀⢀⣿⠀⣿⢯⠀⠀⣇⠀⠀⠀⠀⠀⠈⡉⠉⡉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠱⣐⠥⠻⣄⠊⡐⠀⢀⡴⠃⢠⡆⠐⠂⢸⠘⠿⣿⡿⠋⠀⠀⢿⣃⢹⣾⣄⠀⡇⠀⠀⠻⣗⣢⢼⢿⠺⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠙⠒⠟⠒⠲⠖⠋⠀⠀⠈⠳⠿⠄⠊⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⣧⣫⡾⠀⠀⢤⣄⣿⡿⣴⣿⡴⣏
⠀⠀⠀⠀⠀⠀⣠⢤⣾⣿⣽⠄⠀⠀⠀⠀⠀⢀⡠⣤⠶⠖⠃⣰⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⣻⣤⢶⠒⠁⢀⠋
⠀⠀⠀⠀⠀⢸⡟⣾⣯⡇⢹⡇⠀⠀⠀⢀⡞⠁⠰⢯⡊⠊⣸⠑⢄⠀⠳⣄⡀⠀⠀⢀⣠⢤⡄⣀⠤⢀⠀⠀⠀⠀⠀⠀⢀⣾⡻⡁⠀⡜⠸⢀⡝⢦
⠀⠀⠀⠀⢾⣉⢣⡟⠁⣧⠞⢻⡄⠀⢀⡟⣰⠇⠀⢠⣧⡴⠋⢸⡘⠃⢀⠀⢷⠀⢰⠯⠸⠙⠁⠀⠀⠸⣦⣄⠀⠀⠀⢠⣿⡯⠁⣮⠞⠋⠙⢦⡖⠈⡇
⠀⠀⠀⠀⠻⢽⣿⡿⡆⡧⠀⢠⠇⠀⢸⣤⣿⣰⠄⢀⡟⡀⠀⡀⣱⠀⣼⠀⣼⠀⢸⣴⠂⠀⠀⠀⠀⠀⠑⠎⠁⠀⠀⣼⢿⡷⣿⡯⠐⠤⠜⠘⠇⠀⡵
⠀⠀⠀⠀⠀⠀⢘⢳⡟⠃⠀⠊⠀⠀⠘⣏⢹⣯⠀⣼⠁⡁⢸⠁⠀⣰⠇⣰⠃⠀⠹⠁⠀⢀⠀⣞⡤⣀⠀⡄⠐⠀⠀⢹⡈⣹⣿⣰⡶⣷⠂⡱⣠⠒⡇
⠀⠀⠀⠀⠀⠀⢌⢘⠃⠀⠀⠀⠀⠀⠀⠘⢦⣙⣦⡏⠞⣴⢏⡠⠞⣡⠔⠁⠀⠀⠀⠀⠀⠀⡧⠘⡜⠀⠀⠀⠀⠀⠀⠈⢷⠋⡶⠛⣷⣽⣿⣵⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠞⢽⠿⢼⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠂⠉⠉⣲⢤⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠙⠉⠉⠋⠙⠷⣄⠀⠀⠀⠈⠹⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡺⢃⡥
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⡴⠚⠛⠒⠢⢄⠀⢃⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⡏⠆⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡼⡟⠋⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⣠⣴⣋⠁⢤⣀⣼⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠸⣤⡄⣀⠀⠀⠀⢠⡇
⠀⠀⣠⠞⢛⠷⠛⠳⢶⣌⠉⠁⠀⠀⠉⠲⣌⠂⠑⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠙⠐⠤⣤⣤⡴⠟⠁
⠠⠊⣡⣄⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠱⣄
⡇⢢⡽⢙⠁⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢱⡌⢳⡤⢄⡀
⠀⠴⠓⠚⠀⠀⠀⠀⠀⠐⢿⣆⡀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢻⡶⠚⠳⢼⣽⠖⠛⠲⣄
⠘⡇⠀⠀⠠⢄⣀⠀⠀⣀⣄⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡇⢠⣤⣄⡀⠀⠀⠀⠀⠀⣸⠁⠀⡟⠀⠀⠀⠀⠈⡇⠀⠀⠸
⠀⠙⢦⡀⠀⣀⣀⡴⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠞⣡⣽⣾⣷⢡⠶⠋⠙⠳⣄⠀⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠁⠀⠀⢠
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠀⠞⠙⠚⠁⠀⠀⠀⠀⠸⣇⠀⠀⡟⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣶⢤⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⢀⡴⡿⠋⡷⡦⢄⠘⣄⡈⠙⠶⣄⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⡴⠋⠈⠀⠘⠀⠹⡀⠀⠀⠳⣀⠙⠻⣧⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⣧⠀⠀⠈⠓⠢⠤⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠈⠳⠦⣤⣄⣀⣼⣥⠔⠁
⢸⠇⠹⢲⠀⠀⠀⠀⢀⠴⠠⣞⡁⢦⣄⣀⣼⠎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀
⣾⠀⠀⠹⣤⡀⠀⣰⣗⣐⠉⠀⠀⢠⠆⢸⠉⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⡠⠊
⢻⡀⡤⠀⢢⣈⣙⣍⠀⠀⠀⠀⢠⢟⡴⠊⠀⣧⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠒⠂⢀⣴⠟⢣⠴⠶⠖⠒⠂
⠀⠳⣇⣠⠀⠈⡟⠈⠓⢦⡤⠐⣫⠊⠀⠀⣴⠇⢘⡇⠀⠀⠀⠀⠀⣀⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⢠⡉⢀⠀⠶⠦⢤⣄⡀
⠀⠀⠸⣇⠀⠀⠙⠳⣀⣤⣙⣻⣧⣤⣤⡴⢃⡤⠞⠁⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⢀⣀⣰⣤⣴⡿⠃⠈⠳⠄⠀⠀⠀⠉
⠀⠀⠀⠘⠷⣤⣤⣔⣀⣀⣠⣵⣿⣯⣎⡠⠞⠀⠀⠐⠛⠶⠶⠶⠷⠶⠶⠿⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠢⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠁⠀⠀⢀⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡼⠁⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⠀⠠⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢠⡳⠦⠀⢤⡩⢄⡀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⡾⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⠂⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠈⣀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡆
⠀⠀⠀⠀⠀⣰⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⡇⠐⠂⠀⠀⠀⠀⠀⠰⠄⠀⠀⠒⠋⠻⠧⣤
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠠⠂
⠀⠄⣀⢀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠈⠉⠀⡼⡁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠡⠀⠠⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠈⠉⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣠⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⢀
⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠴⠿⠛⠁⠀⠀⠀⠀⠀⢀⢀⡌⠀⠠⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢧⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠁⠀⠀⠀⠀⡀⠄⠒
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⠋⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚⠵⠘⠗⠘⢤⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⣏⠰⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠰⡀⢀⢀⡠⣀⣀⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠢
⠀⠀⠀⠀⠓⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠠⠀⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄⠤⠐⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡃⠠⠖⠂⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠌⠁⠀⠓⠃⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠠⡄⠀⠋⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢀⡐⠁⠀⠀⠀⠐⠚⠃
⠀⠀⠀⠀⡀⠀⠠⣴⣤⢰⡀⠀⠀⠀⠀⠀⠀⠴⠯⠀⠀⠶⠐⠶⠶⠀⣘⡳⣂⡀
⠀⠀⠀⢀⢺⣤⠴⠨⡏⠉⢳⣿⠆⠀⠀⢀⡀⠀⠠⣧⢀⡐⠁⠲⣄⠀⠈⠡⠙⠻⣤⣄⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢛⠈⠁⠋⠀⠁⠀⠸⡟⠸⣦⣾⡄⠠⠶⡴⢿⡞⠀⠀⠀⠠⣤⡄⣤⠀⢀⠻⠛⠇⠉⠁⠀⠀⠈⠛⠬⡒⠂⢤⣀
⠀⠀⢳⡀⢀⠄⠀⠂⠀⠀⠀⢸⣛⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⣮⢷⣄⠀⠙⠓
⠀⠀⠘⠌⣀⠀⣀⡀⣠⢤⣶⣿⣿⣿⣿⣿⣽⣿⣿⠛⠸⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣤⡄⠳⡈⠣⣽⡷⡆
⠀⠀⠀⠀⠛⠛⠋⢾⠵⠿⠛⠿⠿⣿⣿⣿⣿⠏⠉⠀⢸⣿⣄⠀⠀⠱⣄⡄⢠⡟⠉⠀⠀⠀⠀⠲⠿⠟⠁⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠂⠀⠀⠉⠈⠉⠀⠀⠸⠿⣇⠈⠻⠆⣠⠾⡃⢒⠗⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠈⡄⠀⡀⠀⠀⠰⠉⠀⠀⠄⠠⠞⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠇⠀⠀⠀⠀⠐⠀⠀⠐⠃⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡽⠂⠙⠂⠘⠲⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠷
⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⢀⠐⠀⠂⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⣀⠀⠃⡄⠀⠠⠂⡄⠀⠀⠀⠡
⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠒⢲⡼⠀⠀⠀⠀⠀⠀⠈⣿⠒⠲⡏⠁⠛⠃⠐⠤⠴⠃
⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⢸⠀⠓⠀⢌⡄⡇⠀⠀⠀⢠⣀⣀⣼⣄⡴⠋⠦⠠⠜
⠀⠀⠁⠀⠀⠈⠉⠀⢀⡀⠠⠀⢀⣠⠆⠁⠀⠀⠀⠀⠀⠀⠑⠣⠀⠌⠀⠞⠀⠀⠀⠀⠈⠁
⠰⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⣸⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠳⠖⠛⠊⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠹⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⣰⠯⠘⡒⢲⠤⠄⢁⡠⢄⣀⡀
⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡁⠸⠀⡈⠀⢨⠍⠉⣡⠉
⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⢀⢠⣀⠄⣀⠀⠀⠀⠀⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸⡀⠀⡀⠀⠀⠙⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠙⡂⠉⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣸⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠿⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⡄⡴
⢀⠀⠗⠀⠀⠀⠀⠀⣿⣨⢧⠻⡇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠠⠄⠀⠈
⠉⠀⠌⢀⡀⠀⠀⠀⢨⣾⢡⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⢀⣌⠲⠖
⠀⠀⠀⠈⠀⠀⠀⠀⢸⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⡞⢁⠁⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠑⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣏⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢘⠠⡀⢰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠯⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠓⠀⠀⠀⠀⢤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣓⣖⣅⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣁⣀⣀⣀⣀⣀⣄
⣿⣿⡋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠠⠡⠀⠀⠀⠀⠀⠀⡿⠺⠀⠃
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠸⠋⠀⠄⠀⠀⠀⢀⠀⠚⢿⠀⠀⠞⢀⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠐⠈⠁
⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠖⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣘⠋⡄⠀⠀⠘⢡⠀⠀⠀⠀⠀⢀⡀⣀⢀⠀⠀⠄⠀⠀⠈
⠈⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⢀⡼⡐⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠾⣥⣬⡄
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⠾⠋⠈⠡⠃⠀⠾⠌⠊⠀⠀⠀⠀⠀⠀⠀⠀⠴⣂⣐⡖
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠉⠙⣲⣤⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠛⠉⠓⠚⠳⣯⣀⠁⠀⠈⠉⠙⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⠇⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠉⣿⡆⠀⠀⠀⢀⣠⡤⠶⠤⣄⡀⠀⠰⢀⣴⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠉⠁⢠⣾⠓
⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠏⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠠⢤⣴⡀⠀⠀⢀⣤⣤⠾⢻⠁⠀⠀⠀⠀⠀⠀⠈⡁⠀⡠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡀⠀⢀⠀⠑⠤⣀⣠⡾⠯⢥⣀⠲⢤⠾⣇⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠤⠤⠄⠀⠀⠀⣾
⠀⠀⣠⠞⠋⡹⠟⠛⠛⠿⣦⠀⠀⠀⠀⠀⠈⠓⢄⠁⠈⠲⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠲⢤⣤⡴⠞⠁⠀⠀⢀⡀
⢠⠊⠡⣤⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠹⣄
⡇⢠⣸⡏⠟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⣠⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⡄⢳⣤⣄⡀
⢁⢠⠟⠮⠍⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢿⡥⠾⢧⣨⣟⣦⠽⠷⣤⡀
⠸⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠛⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⡟⠀⠀⠀⠈⠙⢧⠀⠀⠀⢻
⠀⢳⣄⠀⠀⠈⠙⠒⢀⡴⠞⠉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠙⢦⣸⣇⡌⢉⣹⠷⢦⣄⠀⠀⠀⠀⢸⠇⠀⢸⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠙⠲⠤⣴⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠴⠚⣻⣿⣟⡴⠋⠀⠀⠀⠙⢷⡀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣾⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⣠⣤⡖⠒⠒⢾⡓⠦⣄⣀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢀⡴⢿⠟⢉⠿⡖⠤⡀⠳⣄⠀⠙⠳⣄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡟⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⣰⠟⠁⠁⠀⠘⠀⠘⡄⠀⠀⠈⢧⡈⠙⠻⣧⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡾⠁
⠀⡶⢿⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⠦⣬⣷⠀⠀⠀⠉⠰⢤⣄⣀⣀⣀⣤⡴⠿⠋⠀⠀⠀⠀⠈⠻⢶⣤⣤⣀⣀⣰⣇⣤⠟
⢠⡇⠸⣧⡄⠀⠀⠀⠀⠀⣠⠄⣠⠖⠢⣀⡀⠀⣸⡎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉
⣸⠃⠀⠰⣇⡀⠀⠀⢀⣎⠡⠴⠚⠉⠀⢉⡝⢻⠋⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣠⠎
⢿⠀⢀⠀⠈⡏⠶⢴⠚⠒⠒⠀⠀⠀⢀⡾⢀⡸⠁⢳⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣴⡿⢁⣚⣁⣀⣀
⠘⣆⣸⠀⠀⠓⠶⡖⠿⣄⠀⠀⠀⣠⠞⡵⠋⠀⠀⣼⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠁⠀⠈⠁⠴⠟⠉⠐⠋⠉⠉
⠀⠈⢻⣤⠇⠀⠀⣇⡀⠈⠙⢿⣉⣡⠎⠀⠀⠀⡾⠃⢀⣿⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⢤⡉⠉⠙⠛⠲⢦⣀
⠀⠀⠀⢻⡄⠀⠀⠈⠹⠤⠴⢦⣽⣻⣿⣷⣴⠾⢁⡶⠛⠁⠀⣠⠴⠚⠉⠁⠀⠀⠀⡀⢀⣠⣀⣀⣤⣴⣶⣶⠿⠏⠀⠀⠙⠂
⠀⠀⠀⠀⠙⠷⣤⣴⣖⣀⣀⣠⣴⣾⣯⣵⣯⡤⠋⠀⠀⠀⠛⠛⠓⠒⠒⠛⠒⠒⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢦⣶⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡴⢶⣶⣿⠚⠂⠀⠀⠀⠀⢤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠈⠛⠉⢷⠀⠀⠀⠀⠘⠓⣾⣿⡟⠳⣦⡀⠀⠀⠀⠀⠈⠻⣟⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⢀⣠⡾⢤⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⣿⠙⠁⠀⢸⢿⡄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠈⠀⣿⣦⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢀⠻⡄
⠀⠀⠀⠀⠀⠀⠠⡄⡆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠁⢸⠳⣄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⠃⢹⡄
⠀⠀⠀⠀⠀⠶⢤⣷⣿⠋⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣘⢷⡄⠀⠀⠀⣷⠀⠀⠀⠀⠀⢰⠀⣷
⠀⠀⠀⠀⠀⢠⠞⠉⣿⡞⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢸⡄⠀⠀⠀⢠⡟⢀⡟
⠀⠀⠀⠀⠀⣟⠀⠀⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠹⣄⡘⠓⠒⠋⢀⣴⠞⠛⠿⠖⠀⠀⡴⠛⢉⡉⠳⣄⣀⣀⣀⣠⣤⣤⣀⡀⠀⠀⠙⠳⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠋⠀⠀⠀⠀⠀⠀⣼⠁⠀⠋⠀⠀⠈⠉⠉⣠⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢻⡀⠀⠀⢀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⡯⠉⠉⠙⢦⡀⠀⠀⠻⣦⡀⠙⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⡞⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⢾⣿⡙⢧⠉⠁⠀⠸⡎⣷⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⢀⣀⣀⣤⠖⠋⠀⢀⡴⠛⠉⠙⣿
⠀⠀⠀⠀⠀⣼⠁⠸⠇⠁⠀⠀⠀⠀⣠⠆⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⣠⠞⣫⠄⠀⢀⡀⡿
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢫⠶⠋⠁⠀⠐⣫⠞⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⣠⡴⠋⠀⠀⠀⢀⣠⣤⠤⠤⠤⠤⠶⠚⣋⣥⠶⠂⠀⣀⡤⢞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢰⣶⣿⠀⠀⠀⠀⠚⠛⠛⠉⠉⠀⠀⠀⣀⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⣤⣤⣤⣤⠤⠶⠚⠋⠁

⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⣭⣉⠛⣓⠲⢤⡀
⠀⠀⠀⠀⠈⠻⣿⡳⠶⠶⣤⡤⠤⠴⠶⠖⠛⢉⣁⠀⣉⣵⠶⢾⠛⠋⠉⠙⠛⡻⣶⣄⠀⠀⢀⡴⠤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡶⢤⣄⣀⣀⣐⣤⣤⡴⠞⢋⠟⠀⡰⠃⠀⣠⡴⠚⠉⠉⠉⠛⢷⣴⡏⠁⠀⢬⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⡀⠀⠔⠈⠀⠐⠁⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⢶⣻⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣼⣇⣠⡟⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠛⠆⠀⠉⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣧⣼⠇⠀⠀⠀⢀⡴⠋⠉⠙⢷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢛⡿⣿⡿⣿⡀⠀⠀⠀⠀⠀⣀⡤⠚⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣿⢇⣿⢿⠀⠀⠀⠀⣸⠃⣼⠛⢦⣀⣉⣉⡙⢷
⠀⠀⠀⠀⠀⢀⡶⢋⡵⠒⢉⣡⢾⣿⣧⠘⣷⠀⠀⠀⡰⠊⠀⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⡾⡼⣸⡿⢸⡤⠀⠀⣰⠟⡴⠃⠀⠀⠉⠀⠈⡷⢸⡇
⠀⠀⠀⠀⠀⣿⠁⡼⠀⡔⢉⠔⣿⡏⡏⣇⠸⡇⠀⢰⣅⠀⠀⠀⠀⠀⠀⠀⠤⠴⣧⠀⠀⠀⢰⠇⡇⠹⠃⢿⡇⠀⢰⢣⡞⠀⠀⠀⠀⠀⢀⡼⢃⡞
⠀⠀⠀⠀⠀⣿⠀⢿⠘⡇⣿⢰⣳⢃⡇⡿⢀⡇⠀⢸⡀⠀⠐⠤⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⣼⢸⡀⠀⠀⣸⠁⠀⢸⡌⠳⠤⠶⣄⠀⠀⣸⢣⡏
⠀⠀⠀⠀⠀⠹⣧⡈⢧⢱⣿⣾⣫⢞⡴⢃⣼⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢈⡽⠃⠀⠀⠀⡏⠸⠇⠀⢠⠇⠀⠀⠀⠙⠛⠲⡆⠈⠓⠚⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣿⣟⣛⣉⣤⠞⠁⠀⠀⠀⠀⠈⠳⡄⣰⠖⠚⠛⠉⠀⠀⠀⠀⠀⣧⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⡀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⢰⠃⠀⣤⠀⠀⡼⠀⠀⠀⠀⢀⡴⡖⠉⠉⡇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⡴⠋⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⣧⣀⠀⡀⠀⢀⠇⠀⠀⢀⡾⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠁⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢉⣩⣤⡞⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⢹⣄⡴⠃
⠀⠀⠀⠀⠀⡾⠀⠀⢀⠀⢠⣄⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢰⢟⡆⠀⠀⠀⠀⢠⡷⢤⣀⠀⠀⡜⠀⠀⠀⠈⣇⠀⠀⠆⠀⣄⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⢷⠀⠀⣾⠆⠘⠿⠀⠀⠀⣿⣿⠃⠀⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⣼⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⠙⢦⣀⡀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⡿⢿⢸⠀⠀⠀⠀⢠⡇⠀⠠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠹⣄⡀⣀⣤⣤⣴⣾⡿⠟⠀⠀⠀⠀⠀⣿⢸⡏⠀⠀⠀⠀⢸⠋⠂⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⣩⡤⡤⣄⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣀⠀⠀⢸⡀⣠⠏⠀⠀⠀⢀⣤⠶⠒⠶⣄⠀⠀⠀⣼⣳⠏⡁⢸⡵⣀⡹⣆⢹⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡇⠀⠈⢣⡉⢧⡀⠈⠛⠁⠀⠀⠀⡴⢋⡴⠛⠛⢦⢹⡆⠀⠀⣿⣿⢺⡽⣠⣄⠳⠆⣿⢸⡇
⠀⠀⠀⠀⢠⡞⠉⢠⡇⠀⠀⢹⡿⢦⡀⠀⠀⢠⡏⠀⠸⠁⠀⠀⠀⠃⠈⡇⠀⠀⠀⠀⣀⡼⢡⡿⠀⠀⠀⣸⠀⣧⠀⠀⢻⡜⢦⡀⠳⠞⢀⣴⢃⡼⠁
⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⠀⠈⢻⡀⠀⢼⠀⢠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼⠋⡴⠋⠀⢀⡀⠀⠙⣦⠘⡆⠀⠀⠙⠶⣭⣙⣛⣩⡵⠞⠁
⠀⠀⠀⠀⠈⢻⣶⠀⢀⡴⠀⠀⢀⠀⣼⠁⠀⠘⣧⠘⣆⠀⠀⢸⣀⣠⡟⠁⠀⠀⢸⡃⠸⣇⣀⡴⠛⢷⡀⠀⣸⠀⡿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢧⣤⡤⠾⠞⠁⠀⠀⠀⠈⠳⠿⣦⣄⣼⣿⠉⠀⠀⠀⠀⠘⠷⣤⣬⣥⠴⠶⣌⠓⠚⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣍⠛⣛⣭⣶⣾⣿⣿⣷⣶⣭⣛⠛⣩⣾⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢸⣿⣿⡿⣋⣴⢰⣮⡻⢿⣿⣿⣿⣿⡿⢟⣵⡆⣦⣙⢿⣿⣿⡇⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠸⢟⣡⣾⣿⣿⢸⣿⣿⣦⣙⢿⡿⣋⣴⣿⣿⡇⣿⣿⣷⣌⡻⠇⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⡄⢴⣶⣶⣶⣦⠰⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⠆⣴⣶⣶⣶⡆⢠⣶⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠙⣿⣿⣿⣇⢿⣿⣿⣿⠇⠸⣿⣿⣿⡿⣸⣿⣿⣿⠋⢠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡜⣎⢻⣿⣿⡘⣿⣿⣿⢸⡇⣿⣿⣿⢣⣿⣿⡟⣱⢣⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡜⣷⡙⣿⣧⢹⣿⡟⣸⣇⢸⣿⡏⣾⣿⢋⣾⢣⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠘⣿⣎⢻⡆⢿⡇⣿⣿⢸⡿⢰⡟⣱⣿⠃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡙⠸⢡⣿⣿⡌⠃⢋⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⢸⣿⣿⡇⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡎⣿⣿⢱⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠸⠇⠞⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⠀⠀⠺⡀⢀⣷⠄⢠⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠉⠙⠻⢦⡄⠀⢿⢋⢿⠂⠀⡇⠀⠰⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠉⠻⣤⡀⠀⢠⢹⣤⠇⣼⡋⠀⠠⠀⢈⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠈⠻⡀⠀⠀⢻⡄⠹⡧⠂⠀⣶⠉⣠⠿⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⡀⠀⠀⢹⡆⠀⢸⡇⠘⡇⠀⠀⡇⣼⢃⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⣿⡀⠸⣇⢠⡏⠀⠘⢰⡗⠀⠀⠀⠀⠀⠀⠀⠠⠒⡄⠀⣀⠼⠀⠀⢰⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠸⣇⠀⠻⠸⡏⢰⠃⡼⠇⠀⠀⠀⠀⠀⠀⠊⠠⣼⠏⣾⠁⠀⠀⠀⡴⠀⠀⠷⠈⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇⠀⣦⢡⢏⡼⠃⠀⠀⠀⠀⠀⠀⢘⠀⠐⣿⡽⠃⠀⠀⠀⡠⠀⠀⢀⡞⠀⢘
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢹⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣿⡟⠀⠀⠀⣰⠕⠀⠀⢠⡇⠀⣈⡀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣯⠀⠀⢀⡟⡀⠀⠀⣸⠀⢠⡟⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣳⣦⡌⣥⡄⣠⠾⢁⣠⠟⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢙⠋⠉⠡⠔⢳⡖⠛⡁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠐⠁⠐⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣙⡼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣷⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⣀⡀⠈⠁⠀⢨⣳⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⡄⠀⠀⡌⠀⢀⠀⣾⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⠶⠖⣒⣸⠶⢄⠀⠀⠈⢢⣰⡟⠀⢠⣾⣯⠴⠖⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⠙⠻⣦⡰⠙⢶⣄⡘⠘⠛⠓⠞⠋⠁⠀⢀⣠⠄⣒⡭⠟⠲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡀⠀⠀⠙⢻⣄⡂⠈⠻⣯⡑⠯⠠⠤⠛⠷⠧⠚⠈⠁⡠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⣤⣉⣀⣙⣓⣤⣜⡨⣿⢲⠦⣀⣠⣤⣤⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⡀⠤⠟⠋⠀⠉⠻⢊⣁⡀⡀⠀⠀⢀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣲⣤⣤⠤⠀⢃⣠⠀⣶⣦⢠⠰⢂⢤⠤⢀⣤⡄⣤⣠⢴⡂⣄⣦⢄⡠⢠⡀⢀⣠⠤⡆⢀⣂⠃⠀⢤⡤⢾⣂
⠀⠀⠀⠊⠉⠀⠂⠀⠉⠈⠙⠀⠁⠀⠈⠀⠁⠁⠀⠀⠀⠀⠙⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠁⠘⠉⠃⠁⠀⠀⠀⠉⠂
⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⢀⣀⠀⢶⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂
⠀⠀⠄⢠⠈⠀⠔⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⢠⣀⠄⠠⡀⠀⠘⢼⢳⠝⠀⠐⢦⡧⡌⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠄⠠⢰⣀⡼⢉⠀⠈⠀⠀⠀⠄⠀⠀⠠⢙⠁⠀⠀⢀⠀⠀⠺⣿⡆⠀⠀⠲⣧⡤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠂⠈⣿⣦⠀⠐⠀⠀⠀⢀⡀⣤⡆⠀⠙⠀⠀⠠⠂⠀⠀⡀⠯⠀⠀⠀⢀⠿
⠀⠀⠀⠀⠀⠛⠉⢠⠑⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠇⠀⠺⠀⠀⠀⠐⠛⡄⠀⠀⠐⣾⠈⠛⠛⠟⠉
⠀⠀⠘⠂⠀⡀⠀⠁⠈⠀⠀⠀⠂⠄⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⢂⠀⠆⠀⠀⢰⠁⣴⢷⡄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠢⠆⠀⠳⠆⢡⠀⠀⠀⠀⡁⠀⠀⠰⠀⠃⠀⠀⣾⠇⠁⢸⡇⠀⠀⠀⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠰⠀⠀⠄⠂⠢⠘⠁⠀⠸⢈⠁⠀⠀⠠⠀⠁⠀⠀⡏⠀⠘⡀⠇⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⣤⣲⡶⠀⠀⠲⠴⠃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣌⠁⠀⠀⠀⠀⢀⠐⠁⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣤⣀⠠⣄⢁⡀⠀⠀⠀⠀⠀⡰⠀⠀⡰⠁⠀⠀⠀⣀⣠⡐⣄⡄
⠀⠀⠀⠉⠁⠒⠀⠉⠀⢀⣀⣸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠳⠉⠀⠀⠞⣀⠀⠀⠀⠰⠁⠀⠁⠀⢀⠀⠀⠀⠰⡯⠙⠁⠕
⠀⢀⣴⣄⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢁⠀⠀⡤⠒⠀⠀⠀⠐⢄⠀⠀⠀⠀⠁
⠀⠀⠀⣨⡷⠿⠏⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠎⠀⠀⢷⠀⠀⠁⡔⠁⠁⠀⠀⠀⠀⠀⣤
⠀⠀⢈⠉⠁⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠐⠞⠳⠂⠤⠤⠀⠄⠒⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⠓⠶⠠⠄⠀⠀⠀⢰⡇
⠀⠀⠀⠁⡀⢄⠈⣧⢂⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠠⣀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣁⢈⠠⠀⠀⠀⠄⠀⠫⠠⠀⠀⢀⠀⠰⣦⣿⣿⡇⠀⠀⢀⣿⣿⠆⠀⠀⠻⠄⠠⠄⢠⠄⠀⠀⠀⠀⠀⡇⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠡⡀⢀⣗⠈⡠⠀⠀⣀⣾⣿⣿⣷⠀⠀⠀⢻⣿⠀⠀⠀⠀⢢⠀⡄⢨⠂⠄⠀⠀⠀⠀⠁⣀⡎
⠀⠀⠀⠊⡴⠂⣒⣬⣙⢳⡄⠄⠀⠀⢺⠟⠀⠀⠀⠀⠋⡟⣟⣿⣿⡄⠀⠀⠈⡇⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⡌⡇⠀⢍⣁⣨⠀⡇⡤⠄⠀⠘⠂⠀⠀⠀⠀⠀⡇⡷⣿⣿⠀⠀⠀⠰⠷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀
⠀⠀⠈⠃⠨⡀⠠⠀⠤⡰⢁⠇⠀⠈⠻⠟⠀⠀⠀⠀⠀⣟⣿⡿⣿⠀⠀⢆⠀⠀⠀⠀⠀⠰⢃⠀⠀⠀⠠⠀⠀⠀⠉⠀⢀⡍⠈
⠀⠀⠀⠑⢀⢀⣀⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠈⢹⣿⠁⠀⠀⠀⠈⠉⠓⠒⠒⠂⠀⠀⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠋⢡⣴⣶⣷⣾⠿⡿⣿⣄⣬⣭⣓⠲⢤⣀
⠀⠀⠀⠀⢀⡾⢰⣿⣿⣷⣿⣽⣿⣿⣟⣿⣿⣿⣿⣵⣿⣷⣮⡕⠢⣀
⠀⠀⠀⠀⣼⣿⡈⠿⠿⣿⣿⣿⣾⣿⣿⣏⠀⢀⣽⣟⣽⣿⢿⣿⣷⡈⠳⡀
⠀⠀⠀⢠⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⡛⠻⠻⢾⣯⣿⡃⢳
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣬⡙⠛⠹⣿⣿⣿⣿⠍⢁⣺⣿⣆⡅⠀⠈⠙⢧⡼
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣬⣿⣿⠟⠀⠀⡀⠀⢀⣱⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠀⠀⠀⣠⣶⣿⣿⣿⣿⣴⠖⠀⣉⣻⣶⣃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣞⣂⣭⠀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠠⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠙⢊⣙⡛⢿⣿⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠁⠈⠛⣋⠈⠀⡿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⡀⣠⣏⠐⠀⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⡿⠯⠉⠻⢿⣿⣿⣿⣧⠚⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠈⠻⣿⣽⣾⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠋⠉⢉⠉⠙⠛⠙⢿⣿⣗⡀⢀⠀⠀⠻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⠈⠀⡀⡀⠀⠁⣠⣌⢻⣿⣿⣿⢏⡙⢂⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⣿⣅⢶⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠸⡈⠢⢄⣀⣀⣀⣠⠤⠒⠋⠉⠉⠀⠀⠀⠈⠉⠙⠒⠦⢄⣀⣀⣀⣀⠴⠊⡸
⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠁⠀⠀⠈⠀⢀⣀⣀⣀⣀⠀⠀⠀⢐⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⣠⠖⠉⠀⠀⠀⠈⠑⢄⠀⠄⡠⠊⠁⠀⠀⠀⠈⠑⢦⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡸⠁⠀⠀⣠⠤⠤⣤⡀⠀⢣⡼⠁⠀⢀⣠⠤⠤⣄⠀⠀⢳⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃⠀⠀⡾⢡⣶⣶⣦⠹⡄⠈⡇⠀⢠⡏⣰⣶⣶⣌⢳⠀⠀⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⡄⠀⠀⢧⠸⣿⣿⡾⢠⢇⠤⠥⡀⠸⣆⠻⣿⣷⠟⣸⠀⠀⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⡀⠀⠈⠓⠦⠤⠖⠋⣯⣄⣠⢼⠀⠈⠲⠤⠴⠞⠁⠀⡰⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠑⢤⡀⠀⠀⠀⢀⡠⠞⢦⣰⠟⢤⣀⠀⠀⠀⢀⡠⠞⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠋⠀⠀⠈⠉⠉⠉⠁⠀⢀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⢀⡜⠁⠀⢀⣠⠄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣀⡀⠀⠙⣆
⠀⠀⢀⡼⢿⣁⠀⠼⣥⠄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢤⡽⠆⢀⡹⠿⡄
⠀⠀⠾⣴⠞⡉⠀⠀⠓⡶⠀⡼⡸⠀⠀⠀⠸⡀⢀⠀⠀⠀⠀⠠⣀⣀⠞⠀⠀⠘⡜⢄⠙⡖⠃⠀⠨⡛⣶⠿
⠀⠀⣰⠃⣸⣶⠞⠁⢀⢓⡟⢠⠃⠀⠀⠀⠀⠈⠁⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡈⢻⢋⡀⠙⢶⣞⠈⣇
⠀⠀⠿⠚⢱⠇⡅⣠⢾⡞⣰⠇⢀⠀⠀⠣⠤⠂⠀⠘⠦⠔⠁⠀⠀⠢⣄⠜⠀⠀⡰⢹⣄⣻⢧⣄⡇⢯⠙⠛
⠀⠀⠀⠀⢸⣤⠟⣽⠈⢋⣿⢠⢸⢆⠀⠀⠀⠀⣄⣠⠀⠀⠰⣀⣠⠀⠀⠀⣠⡌⢇⢸⣿⣍⠈⣏⠳⡾
⠀⠀⠀⠀⠀⠀⠀⢹⡴⠋⠸⣌⡽⠉⠑⠦⣄⡀⠀⠀⣄⣀⠄⠀⠁⣀⡤⠚⠁⠈⢯⣁⡟⠘⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣇⡪⠛⠒⠒⠒⠒⠒⠻⣕⢼⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⢉⡀⣉⠑⡄⠀⠀⠀⠰⢋⡉⣈⣁⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠟⠉⠊⠀⠀⠀⠀⠘⠚⠈⠞⠉⠘⠃

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡔⡞⠓⣶⡄⠀⠀⠀⠀⠀⢀⠎⠀⢱⠀⠀⠀⠀⠀⠀⠀⡴⠉⠙⡄⠀⠀⠀⠀⠀⢀⣔⣲⠛⠛⣷⡀
⠀⢰⠁⠈⠈⠉⠁⠘⡄⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠱⡀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠀⢱
⠀⠘⡄⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠣⡀⠀⢀⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢸⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡜
⠀⠀⠈⠢⠤⠤⠴⠁⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠈⠚⠙⠚⠉⠁⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⢀⣴⠾⠷⢢⡄⠀⠀⠀⠀⡠⠊⠉⠾⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⡨⠛⢦⡀⠀⠀⠀⠀⣶⣿⣿⣿⡅
⠀⠀⣞⡂⡅⢘⠹⣸⡅⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⠀⠀⠀⣠⡾⡿⣷⣄
⠀⠈⣖⠅⡁⢀⢒⢼⠆⠀⠀⠘⣄⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣀⢀⠤⠊⠀⢀⠇⠀⠀⠀⠀⣟⣝⢾⡳⣿
⠀⠀⠛⡯⣄⣀⡧⠋⠀⠀⠀⠀⠈⠑⠲⠤⠴⠊⠀⠀⠀⠀⠘⣅⣀⣀⣨⠴⠋⠀⠀⠀⠀⠀⠹⣵⣳⣻⠏
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⡰⠋⠙⠉⠉⢆⠀⠀⠀⠀⠀⢀⡠⢤⣀⡀⠀⠀⠀⠀⠀⢀⡠⠦⣧⣤⡀⠀⠀⠀⠀⡴⢋⠁⠈⢉⢙⢦
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⡆⠀⠀⠀⢀⡞⠃⡐⠀⠁⢹⡀⠀⠀⠸⠐⠀⠀⠀⢀⠐⠈⡇
⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⠇⠀⠀⠀⢸⡇⠉⠁⠀⠸⢸⠁⠀⠀⢠⠀⠠⠀⠀⠀⠠⢠⡇
⠀⠀⠀⡇⠀⢀⡰⠃⠀⠀⠀⠀⠀⠈⠓⠒⠒⠁⠀⠀⠀⠀⠈⠻⣴⣀⣀⣠⠎⠀⠀⠀⠈⠢⣁⡀⢀⣀⡴⠏
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠸⠃⢢⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⢴⣶⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀
⠀⠀⠀⠀⠈⡂⠈⠆⠀⠀⠀⠀⡠⠚⢉⠃⣭⠷⣄⠀⠀⠀⣀⡴⠹⠁⠐⢁⠤⡏⠀⠀⠀⠀⢠⣖⣟⣲⣋⡇
⠀⠀⠀⠀⢀⡎⠀⡁⠀⠀⠀⢸⠷⠓⢀⠗⠀⠐⢮⡆⠀⠀⠇⣁⠤⢲⠀⠀⡾⠁⠀⠀⠀⡤⢯⠒⢯⠤⣧⢼
⠀⠀⡠⠒⠁⢀⠔⠁⠀⠀⠀⠈⢄⢛⠨⠆⢠⡉⡴⠀⠀⠀⢇⠀⠀⠎⢒⠞⠋⠀⠀⠀⠀⢳⠞⡶⢻⣲⠏⠁
⠀⠀⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠒⠉⠀⠀⠀⠀⠀⠉⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⢤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠹⢿⣿⣿⢿⣭⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⠉⠙⠛⠻⡿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠐⠛⠛⠛⠉⡛⠛⠛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⣶⣤⣤⡀⠀⠀⠀⢼⣿⣿⣟⠛⠛⠻⣿⣿⣿⡁⠈⠻⣿⡷⢬⡛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡗⠁⠤⣨⣿⣿⣿⠄⠀⢩⣝⠿⣶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⠿⠛⣻⠿⠿⠿⠿⢿⢹⣿⣿⣿⣿⣯⠀⠀⣸⣿⣿⣿⡃⠀⠀⣉⣧⣴
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣤⣴⣿⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⡅⠀⠀⠀⣩⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣶⣿⣿⣿⣿⡿⢻⣿⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢽⣿⣿⣿⡇⠀⠀⠀⢀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⠛⠿⠿⠋⣠⣾⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠘⣿⣿⣿⡇⠀⠀⠀⢠⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣶⣾⠿⠛⠁⢀⣴⣿⣿⣿⣿⣿⡿⢊⣿⣿⣿⠶⠦⢻⣿⣿⡇⠀⠀⠀⢸⣿⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⡟⠉⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡛⠛⢤⣿⣿⡟⠀⠀⢿⣿⣿⠅⠀⠀⠀⢸⣿⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣻⣹⣰⣿⡇⠀⣹⠆⠀⣸⣿⡟⠀⠀⠀⠀⠐⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠠⠀⠀⣿⣿⠃⠀⠀⠀⠀⠨⣿⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣐⣿⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢲⣶⣾⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⠀⢿⢿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⡑⠀⠀⠀⠀⠀⣀⣴⡾⠟⢻⣿⣿⣿⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡀⠀⠀⢰⡾⠋⠀⠀⠀⠘⢻⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣶⣄⠘⠇⠀⠀⠀⠀⠀⢀⣿⣿⡿⠇⠀⠀⠀⠀⠀⢀⣄⣴
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠈⠋⡀⠀⠀⠀⢀⢠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⢀⣤⣶⡿⡛⢛⣩⡄⠀⠀⣀⡀⠀⠀⣾⣿⡿⢟⠻
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣆⠀⠀⠻⠋⢩⣽⡟⣱⣿⣿⠇⠀⢠⣻⣿⣤⣾⣿⡿⠃
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⡽⢿⣿⣿⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣤⣿⣛⣫⠬⠉⠉⢛⠀⠙⠻⠛⠛⠋⠁⠙
⠀⠀⢸⣍⣁⣾⣿⣿⣿⣞⣣⣴⣾⡿⠋⠀⠐⢿⣿⣿⣿⣿⠟⠛⠁⠉⠀⠀⠒⠈⠝⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⢸⣿⣿⡿⣫⣿⣿⣿⡿⠟⠋⠀⠀⠀⢰⣾⣿⠟⠉⠃⠀⠀⣀⡤⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉
⠀⠀⣸⣿⣿⣼⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⣠⣤⣶⠾⠋⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛
⠀⠀⢿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠟⠛⠋⠉⠉⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡘⠻⡆⠀⠀⠀⢥⡀
⠀⠀⠻⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣠⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠀⠀⠀⠀⣸⠸⡀
⠀⡖⠤⣀⣀⠤⠂⢺⠃⠀⠀⠀⠀⢠⠃⠀⢱⠀⠀⠀⠀⢀⣀⣀⣀⡴⡏⠃⡟⠀⠀⠀⢠⠞⠁⠀⠉⠢⡀
⠀⠈⠒⠤⠄⠤⠔⠋⠀⠀⠀⠀⠀⢇⠀⠀⣀⠇⠀⠀⠀⠈⢇⡹⢊⣁⡰⠞⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠊⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⢀⠀⢀⣠⡖⠲
⠀⠀⠀⡠⢤⢾⠤⡀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⠀⠀⢀⡤⠶⠾⠿⠛⢐⢢⠀⠐⠥⠤⡄⣱⣎⡦⠜⠉
⠀⠀⠸⠉⠉⠏⠁⢸⠀⠀⠀⠀⢠⣺⣿⡿⢷⡆⠀⠀⠀⡎⠐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⡤⠿⢄
⠀⠀⠘⢄⣀⣀⡠⠜⠀⠀⠀⠀⠈⢷⣿⣷⡸⣗⠀⠀⠀⢣⠰⡀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠸⡀⠀⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡠⠤⠒⢤⣀
⠀⠀⠀⢀⡔⠉⠙⠁⠀⠀⠀⠀⢀⡴⣿⣿⡦⡀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠈⠆⠀⠀⢀⡏⠁⠠⠀⠀⠈⢦
⠀⠀⠀⡸⠀⢀⠜⠀⠀⠀⠀⢰⡏⠌⢹⡍⣻⠹⡄⠀⠀⠸⣀⣤⣤⠀⢲⡶⠞⠀⠀⠘⠢⡖⠀⠀⠀⣰⠊
⠀⠀⢀⡇⢠⠋⠀⠀⠀⠀⠀⠸⣇⠠⣼⣷⣹⢎⡇⠀⠀⠀⠈⠉⢁⡀⣸⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⡟
⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠢⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⢠⠊⠀⢀⣈⠦⠄⠠⣄⠀⠀⢀⢔⠾⢗⡒⢄⠀⠀⠀⣜⠤⠒⠚⡍⠉⠉⢲⡀⠀⠀⡰⠊⠀⠀⠀⠑⢄
⢠⠃⠀⡔⠁⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⣀⡴⡷⠶⡤⣨⠃⠀⢔⠁⠀⠀⠀⠀⠀⡠
⠘⢆⡈⢆⠀⠀⠀⣀⠠⠊⠀⠀⠀⢳⡀⡀⢀⠎⠀⠀⠀⠈⠉⠙⡅⡀⠰⡃⠀⠀⠀⠀⠑⢄⣀⣀⡠⠜
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⡤⠊⠁⠠⠊⠁⠀⠀⢄⠀⠀⠀⠀⡀⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠔⠋⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⣠⡀⠀⣾⡀⠀⠀⡆⠀⢀⠄⣿⡖⢡⣶⠇⡀⠁⡀⠀⠀⠀⣾⡏⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠹⠗⠀⠉⠁⠀⠀⡀⠀⠀⠀⢉⠙⢊⠛⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠴⠶⠟⠀⠠⠃⠀⠰⡀⠘⠿⠟⠠⠈⠠⢀⠂⠀⠀⠀⠙⠿⠓
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢀⠄⠠⠠⠄⠐⠐⠀⠀⠀⡀⠀⠐⠀⠀⠀⣀⠈⠀⠠
⠀⠀⠀⠐⠀⠀⠀⠘⣤⡄⠘⢻⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢀⣦⡄⢀⣀
⠀⠀⠀⠰⠀⠀⠀⠀⣿⠿⠀⠈⠉⠀⠀⠀⢠⠀⠀⠀⠀⠐⣿⡆⠀⣿⠇⠀⠀⠀⠀⠀⠾⠿⠁⣼⡿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⣶⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠛⠁⠀⠁⠀⠀⡄⢰⠀⠀⣀⣀⣀⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠴⠾⠛⢀⠜⠀⠀⡄⠀⠈⠛⠉⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠁⠀⠀⠀⠈⠂⡀⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣿⣿⣛⣻

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡠⠀⠛⠀⠐⠒⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠇⠀⠀⠀⠀⠀⣠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⢰⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡴⠁⡀⠀⠀⠀⠁⡼⠀⠀⢀⠊⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢠⠃⠀⡠⠁⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠜⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡌⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡘⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⢠
⠁⠂⠠⠀⣀⠀⠀⠀⠀⠀⠐⠉⠀⠀⡆⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⡇⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠠⠤⡀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠎⠀⠀⢠⠢⠀⠀⠈⠂⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⡎⠀⠀⢰⡧⠃
⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣻⡀⠁⣶⠁⣠⠞⡅⢀⡶⠁⣰⠃⢀⡖⣠⠄⣼⠁⢤⢀⡟⠁⢠⡆⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⡟⠀⠐⠇⠈⠣⣸⠃⠘⢅⠀⡏⠀⠘⠂⠹⢐⠟⢠⢯⢸⠁⠀⠻⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⡰⢋⡝⠉⠀⠀⠀⣰⠋⢀⡎⠌⢈⠁
⢃⠀⢠⡇⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠉⠀⡼⠁⠀⡖⣠⠀⡀⢠⠇⠀⡼⠃⢀⠁⡔⣰⠀⡴⠂⢠⡆
⡄⠀⠀⠁⠸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠰⡇⢀⡼⠁⠇⠘⠃⡟⠀⢸⠇⠀⠚⠔⠁⠣⢺⡋⠀⠨⡗
⠀⡀⠀⠀⠈⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠓⠁⠘⠂⣀⣀⣀⣀⣀⣀⣀⡈⠒⠁⠀⢀⠀⢀⣀⣀⣀
⠀⠡⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠐⠂⠐⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡄⠙⠈⠁⠀⠀⢚⣰
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠈⡄⠀⠀⠇⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠁⡠⠔⠒⠀⠄⠂⠀⠀⠒⠀⠤⢄⠀⠀⠉⠉⠐⠒⠂⠤⠤⢀⣀⠀⠤⠊⢁⢀⡀
⠀⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⠄⠀⡄⠴
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⡠⠀⠠⠶⠀⠀⠤⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠌⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠰⠶⠤⢀⣀⡀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠐
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⠀⡠⠶⠖⠀⠄⠀⠀⠀⠀⠀⢨⣥⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠻⡄⠘⠟⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠀⠀⠈⠇⠈⠉⢿⣿⣿⠃
⠀⠐⠚⠿⢛⠻⣤⣀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣿⠢⡀⠀⠀⠀⠀⠀⠈⠀⠀⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣾⡇⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⣿⡄⠘⣆⠀⠀⠀⢀⠄⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢛⣿⣏⠄⠘⡄⠀⠀⠈⢄⠀⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣤⣠⣴⣴⡶⠿⠟⠓⠤⠀⠀⡇⢠⣭⣿⡷⠂⠀⡇⠀⠀⠀⠀⠀⢈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠿⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠠⠬⣿⣟⣁⢀⠇⢀⠀⠀⢠⣆⣀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⡯⢀⠎⠀⠈⠻⣶⡋⠀⠀⣽⣿⣿⠋⡨
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠈⠻⣶⣾⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀⣠⠖⠓⠒⢒⡦⠒⠒⠒⠒⠚⠉⠉⠳⠤⣀
⠀⠀⠀⠀⠀⣀⣠⠊⠁⢠⠞⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣆
⠀⠀⠀⠀⡼⠉⠁⠀⠀⢧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⡔⠒⠚⠉⠉⠛⢤⡀
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⢱⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠓⢢⠀⠀⢰⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠈⡆⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣳⡀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⣀⠀⠀⠘⠦⣄⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⡄⠀⠉⣶⠚⡄⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⠤⠟⠀⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢴⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴
⠀⠀⠀⠀⠀⡴⢋⣀⠄⢀⡞⣷⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡼⠁
⠀⠀⠀⠀⠈⠀⠉⣀⡴⠟⠁⣿⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠤⠒⠋⠉⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢳⣶⠟⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠙⠋⠉⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣸⠃⠀⠀⠀⡔⠘⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠉⠉⠙⢻⡄⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⠇⠘⠢⢤⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠷⢂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣰⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡆⠀⢀⣴⠶⠾⠲⠶⣤⡀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⢀⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⠻⠿⣶⣶⡶⠿⠋
⠀⠀⠀⠀⠀⠀⢠⠖⣦⡰⠀⢤⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠘⢆⠸⣷⢁⣾⣥⣾⣤⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⢴⡚⢲⡤⣄
⠀⠀⠀⠀⣠⠖⠒⠚⢂⣽⠾⠋⠁⠀⠉⠻⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⢘⡥⢤⡿⠛⠦⣤⠷⢤
⠀⠀⠀⠀⠈⠓⣶⡾⠋⠁⡀⠀⠀⠆⠀⠀⢹⣇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣧⣸⠀⢀⣧⡀⠀⠘⠣⠚⢷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠁⠀⠀⡄⠀⠠⠈⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣰⢸⡏⠙⣇⠀⠈⡷⠒⢺⠙⢻⡅
⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠰⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠹⣮⡳⠶⢾⡓⠛⢷⣤⡴⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠠⠀⠰⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⣤⣬⣿⠶⠚⣹⠶⠋
⠀⠀⣀⡀⠀⠀⠀⠀⠉⠲⢤⡁⠀⠠⡀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⠶⠟⠶⠶⠋
⣴⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠘⢆⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⣿⣿⠆⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠐⠶⣤⣄⡀
⠀⠈⠂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠈⢀⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⠀⠉⠻⣦⡀
⠀⠀⠀⢀⠘⠛⠙⠛⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⡟⠁⠀⢀⠀⠀⠀⠀⢀⡟⠲⣄⠈⢻⣆
⠀⠀⠀⣿⡇⠀⢄⡀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⡤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣿⠀⢀⠀⠀⠑⢄⠀⠀⠌⠀⠀⠘⣆⠀⢿
⠀⠀⠀⠸⣷⡀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣾⠏⠀⠀⠀⠀⢸⣿⠀⣼⠀⢀⣀⡤⢽⡿⠂⠐⠒⠒⢻⠀⢸
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠙⠛⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠟⠋⠁⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠘⣿⡀⠸⡏⠉⠀⣠⠏⢠⠈⠢⣄⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠹⣄⡰⠃⠀⠀⣇⠀⠈⣻⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡈⠛⠶⠦⠤⠾⠶⠛⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣤⣤⣶⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠈⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡴⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠉⠄⠛⠉⢉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⠀⠀⠀⠀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣀⠀⢀⡞⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⡀⠀⠘⠀⠙⠿⢷⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠂

⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠀⢰⠂⣈⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠀⠈⢳⡞⢤⡴⠎⠀⠀⠹⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣫⡷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠠⠆⠀⠐⣮⠛⢉⣁⡛⠞⠓⠧⠾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠈⠢⡀⠀⠀⠀⠀⢘⡀⡄⢀⣄⢐⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣤⣼⠁⠀⡈⠛⢿⢠⡎⠀⠀⠀⠀⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣠⡿⢳⡀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠒⠒⢀⡌⠁⠀⠉⠓⡄⡌⠋⠀⠁⠀⠲⠐⠒⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⢀⣀⡥⠞⠋⠉⠓⠋⠀⠀⣀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠼⠃⢄⣀⠀⠐⠻⢀⡇⠀⡀⠀⠀⠀⣀⠀⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡋⠀⠀⡀⠀⠀⡀⠤⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠤⣀⡉⠒⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠌⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠦⢞⠖⣲⣆⠁⡈⠴⠂⢒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⣃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠋⠙⠁⠀⠀⠀⠈⢿⣯⠦⣨⣿⡋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⢿⡂⠀⢠⠶⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⣈⠀⢘⣹⣷⢯⠁⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⣀⣐⡦⢄⠞⠉⠀⡛⢢⣠⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⣤⠀⠀⡙⠉⣲⣉⠹⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠶⡏⠀⠀⠙⡋⠙⣤⡄⠏⠉⠉⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡡⠃⢤⡄⠀⡴⠿⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠲⠀⠀⢠⢤⠄⠞⠁⠀⠈⠉⠈⠀⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣆⠂⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠁⠘⠛⠃⢄⣀⠀⠀⠀⣁⠜⠂⠀⠀⠁⠀⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡽⠛⠒⢄⡖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⢷⡤⠀⣤⠀⠉⠺⠋⠒⢐
⠀⠀⠀⠀⠀⠀⠢⠤⠥⢈⠁⠀⠛⠞⠒⣶⣆⠀⠀⢻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠏⠀⠓⠲⣿
⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠙⠀⠀⢒⠀⠀⠀⠀⠀⢠⢠⠀⣀⡀
⠀⠀⠀⠀⣤⠔⢄⠀⠀⠄⠀⠀⠀⠀⠀⠐⠢⠔⠁⠀⠉⠙⢞⢀⠎⢀⠀⠂⣎⡀⢶⢉⡒⠀⠀⣀⡄
⠀⠀⠀⠀⡇⠀⠘⠳⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡳⠛⠀⣐⢋⡉⠀⠛⠠⢁⡀⠈⠉⣀⠤
⠀⠀⠀⠡⡇⠐⠀⠀⠀⠑⠂⠉⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠘⢀⣈⣩⣥⡉⠠⠀⠀⡀⠀⠀⠀⠠⠄⠶⣴⣤⡄
⠀⠀⠀⠀⠈⠀⢀⡀⡀⠀⠀⠀⠀⠀⢶⣿⠀⠂⠀⠀⠀⠀⢀⡤⢹⠓⠘⠃⠀⣠⣬⣍⠉⠄⠀⠁⠀⠬⢿⣿⣧⣀
⠀⠐⠀⠀⠀⠠⣼⢣⡷⠚⠀⠀⠀⡠⠆⠀⠀⠂⠀⠀⠀⠀⠁⠀⣠⣄⠀⢀⣬⡀⠀⠀⢹⠍⢉⠀⠲⠶⠼⠉⠁
⠀⠀⠀⠀⠀⠀⠙⢉⣁⠹⠉⠀⠞⠁⠀⠀⠀⠀⠀⠄⠀⣣⠀⠀⠉⠁⠀⠈⠀⠀⡀⠀⠀⣴⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠉⠁⠀⠂⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠘⠒⠚⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⢺⣿⡆⠀⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠉⠉⠀⠌⣛⠁⢰⣿⡿⠋⠀⠀⣀⡀⢀⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⢶⣦⡀⠀⠱⣄⠁⠀⠀⠀⠰⠟⠁⣾⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠰⣷⡀⠀⠀⠀⠙⠡⣀⠀⢹⡆⣀⣤⠶⢏⡉⠉⠀⣴⣤⡀⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⢧⣸⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⠀⠀⣼⣷⠀⠀⠀⣸⡿⠁⢰⠿⠃⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢿⡿⠀⠀⢠⣿⠟⠉⠀⠀⠀⠀⠰⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡷⠀⠤⠒⢚⡛⠛⠛⠷⣦⣤⡀⠀⢸⣿⠀⠀⠀⠀⣠⣧⡤⠤⠤⢀⡀⢠⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢾⠇⠀⠀⣠⠞⠛⢻⣦⣸⣿⡄⢀⣴⠟⠉⠀⠀⠀⢿⣶⣄⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢠⣤⣴⠤⠤⢴⠁⠀⠀⠀⠙⣿⣿⣷⣿⠷⠚⠛⢟⠒⠢⠈⠙⠛⠀⠐⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢴⣦⡀⠀⠀⢹⣿⣿⡏⠀⣀⡀⠀⠀⠀⢠⣦⠻⠷⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⠁⠀⠀⢸⣿⣿⡇⠈⠉⢩⣦⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣹⡛⣻⢟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⡀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣀⠀⡀⠀⠀⡀⠄⠀⠠
⠀⢀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠠⢀⠀⠀⡡⡀⡀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠘⡆⠀⠠⠄⠈⠀⠁⠀⠀⠈⢀⠀⠠⠄⠤⢀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⢄⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠱⠀⠀⠈⠠⠄⣀⠀⠃⠀⢀⠀⠐⠀⠄
⠀⠀⠀⢱⠀⠀⢈⠐⠠⠈⠠⠀⠀⠀⠀⠐⠁⠀⠐⠆⠀⡀⠀⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠄⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢁
⠀⠀⠀⠀⠀⢀⣾⠒⠀⠀⠀⠀⠂⠀⠀⠐⢀⠂⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢺⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⡠⠀⢀⠔⠪⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣮⠓⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠉⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡥⠃⢀⠀⠀⠀⢠⠀⠄⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠠⠀⠈⠀⡀⠀⠈⠀⠀⠂⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠈⠀⠄
⠀⠀⠀⡀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⢄⠰⣀⠀⠀⠀⠐⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠰⠄⠘⢀⠀⢐⠦⠈⠀⠀⠅⠀⠀⠀⠀⣿⠀⢤⠄⠀⢰⠄⠀⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠤⠀⠄⠉⠄⠤⠀⠰⠈⡄⠀⠀⠈⢂⠠⠈⠀⣬⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠡
⠀⠠⣈⠂⠸⠀⡠⡈⠂⠹⠀⠀⠀⠀⠀⠙⠀⡄⢀⢸⡁⠐⠉⠀⡀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⣠⠚⠙⠀⠂
⠀⠈⡄⡐⢰⠀⢠⢀⠂⡂⠀⠀⠀⠀⢄⠈⠙⠀⡟⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠁
⠀⠀⠛⠀⠆⠀⠀⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠤⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⡄⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢦⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢂⠀⠀⠀⣄⠀⠀⢠⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⢀⠀⣀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⢆⠂⠀⠀⠀⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⣠⠆⠀⢃⡄⠠⠄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡡⠆⠀⠀⠀⠁⠀⡀⠀⠁⠀⠀⢀⡐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠠⠀⠀⠀⠀⠀⠐⠄⢁⠀⠀⠀⠈⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⡄⠀⠀⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⡄⠀⠀⢁⠀⢉⠀⠐
⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⣿⣿⣿⠿⣿⡿⢿⢿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣮⣶⣾⣴⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⠿⠋⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠬⠋⠐⢂⡀⠀⣀⣠⣆⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣰⠋⠁⠀⠀⣤⣤⣤⣤⣶⣿⣦⠀⠀⠀⠀⢀⡀⠀⠙⢻⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠄⠀⠀⣼⣇⠀⠀⠀⠙⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠊⣿⣶⡾⣿⣿⠿⣿⠽⠯⠅⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣗⣀⣈⣀⡄⠀⠁
⠀⠀⠀⠀⠀⢀⠒⠛⣻⣷⣶⣿⡏⠑⠛⠙⠙⠉⡉⡀⣴⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⠿⣿⣿⣿⡉⣽⣏⣁⣤⡀
⠀⠀⠀⠀⠀⠐⣤⣴⣿⣻⣿⣿⣷⡀⠀⣤⠶⠾⢻⣿⣿⣶⣤⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣸⣿⡙⠗⠿⣿⣿⣯⡗⠂⣀
⠀⠀⠀⠀⠀⠀⠘⢧⠚⢧⣾⠟⢻⣙⣶⣯⢻⣼⣿⣿⣿⣿⢷⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠹⡍⠀⣄⣉⣹⣿⣿⣿⣶⣿⡷⠄
⠀⠀⠀⠀⢨⣵⣾⣾⣶⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⡋⢀⣤⣭⡟⠻⣿⣷⣄⣀⣀⣴⡄⠀⢁⣀⣥⣤⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠿⣿⣿⠿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣾⠿⠿⠛⠛⠛⠛⠛⠒⠻⠿⠿⠿⠟⠻⠛⠛⠛⠉

⠀⠀⡀
⠀⠀⣸⡍⠢⠴⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡳⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡈
⠀⠀⢧⡁⢕⣶⣟⣋⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠁⠈⠉⢢⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣽⣷⣿⣻⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠉⠉⠉⢳⡼⠁
⠀⠀⠀⠉⠙⠛⠛⠻⠶⠀⠀⠀⠀⠀⡈⠃⠀⠀⠀⠀⣠⠏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠷⠀⠀⠀⠀⠀⢸⣻⠁⠴⠶⠖⣢⣞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠋⠓⣂⡡⠋⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣛⣛⣻⠟⠁⡾⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠍⣱⠏⠉⠀⢀⣾⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣻⡟⠉⡕⣀⣼⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣮⣷⣶⣿⡛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣶⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⢀⢦⠠⣀⣀⣈⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡡⣤⣄⣉⣛⣷⣤⡀
⠀⠀⠀⠀⠰⠁⠀⠳⢀⠀⠈⠉⠁⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢻⣦⡈⠉⠉⠉⣉⢿⣄
⠀⠀⠀⠀⠸⡄⠀⢰⠀⠁⢤⡀⠀⠈⢈⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⣸⡇⠉⢦⣔⡚⠋⢣⣻⣷⡀
⠀⠀⠀⠀⠀⠙⠷⣾⢄⣀⡀⠈⢱⣤⣤⢤⣭⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣠⣶⣉⢻⣶⣿⣿⣯⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠫⠏⠤⢿⣽⣿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠿⣿⣿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠒⣒⣀⠀⠀⠀⠀⣐⡒⠂⠤⣀⠀⠀⠀⠀⠀⢠⠠⠠⠀⠀⠒⢳⡈⠒⣴⡄⠀⠀⠐⠒⠂⠠⠄⡀
⠀⠀⠀⠀⡀⠄⢒⡈⠅⠐⠂⢈⣁⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⣁⠤⠳⠂⠀⠀⠠⠀⠐⠒⠀⠉⠁⠀⠙⠶⠀⠀⠀⠀⠀⠀⠉⠐⠂⢄⠑
⠀⡠⢒⡡⠒⠈⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⠄⠂⣁⠤⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⡰
⡌⡔⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⠅⢊⡠⠒⠉⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⠄⠊⡠⣊
⢣⢁⠢⠠⠄⢀⣀⣀⣀⣀⠀⠤⠀⠠⠀⢒⣨⠃⡐⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⠀⡀⠤⠒⢈⠠⠐⠉⠀⢹
⠈⡄⢠⡌⠐⠒⣂⠒⠒⠒⢲⡀⠉⠁⠀⠀⠘⣄⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⢀⣀⠠⠄⠀⠒⣉⡠⠄⢒⣈⠀⠀⠀⠀⠀⠌
⠀⠘⣞⡣⢀⢀⠯⠀⠀⠀⠸⠄⠀⠀⠀⠀⣈⠝⠁⠀⠀⠀⠀⢀⣘⡒⠒⠒⢂⣀⣈⠉⡁⠀⠤⠀⠒⠒⠈⣥⠀⠀⠀⠈⡯⠀⡀⠀⠐⠀⠂
⠀⠀⠈⢄⠡⡐⠀⠢⠀⠀⠂⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⡄⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⢀⠋⠀⡀⠀⠰⠁⠠⡁⠀⠀⢨⡘
⠀⠀⠀⠀⠑⠵⣇⠀⠑⢄⠸⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠨⠃⠀⠀⠀⠀⠈⢆⠀⢠⠀⠀⠄⠀⡐⠀⠠⡀⠀⠀⡇⠀⠑⢄⢀⡞
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣑⣇⡀⠀⠀⡀⠀⠀⠀⠀⠤⠀⢊⠀⠁⠈⢆⠈⠀⠈⠆⠈⢂⠀⠀⠀⠀⠀⠃⠀⠀⠐⢄⠀⠀⠀⠀⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠠⢙⠳⣆⡀⠀⠠⢀⠀⠀⠀⠑⢄⠣⢐⠀⠈⢢⠀⠀⢀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠳⣦⣈⠢⡙⢦⡠⠀⠀⠀⠀⠀⠀⠁⠺⢆⠀⠀⠑⢄⠈⡀⠀⠀⠈⠂⢄⠀⡅⠀⠀⠀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠛⠷⣌⠢⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⠑⢧⣀⣀⣀⣀⠀⠅⠶⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡽⣛⣻⣮⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣽⡷⣿⣿⣿⣧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠻⠿⠿⠿⡄⢠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡎⠙⠶⠾⠿⠟⢣⣤⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⣰⣾⡯⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⡄⣤⣶⣾⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡉⣠⡆⠀⠛⢻⣾⣾⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⡝⠇⠃⠁⠀⠀⠀⠀⠈⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢴⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣮⣠⢀⣠⣀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣛⣛⣛⣛⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠙⠛⠙⠛⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣀⠀⣿⣿⣴⣾⣿⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⣾⡟⣁⣾⠉⠙⠻⢿⣿⣿⠟⠁⣠⣤⣤⣄⡉⠻⢿⣷⣤⡀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠹⠿⣿⣤⡀⠀⢠⣾⡿⠃⠀⠀⠙⠉⠉⠛⢿⣷⡀⠙⠻⣿⣦⡀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠈⢻⣿⣆
⠀⠀⣠⣾⣿⠟⠉⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠙⣿⣷⡄
⠀⣴⣿⠟⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠈⠻⣿⣶⣄
⣸⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠈⠻⣿⣷⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠈⠻⣿⣦⡀
⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠘⢿⣷⣄
⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⣶⣶⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠔⠊⠉⠙⠓⢄⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠻⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠉⠲⢤⣤⡴⠋⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⢠⠗⢄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠈⠓⠶⠤⠶⠋⠀⢈⡇
⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⢀⡼⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠘⢧⡀⢀⡴⠋⠀⠀⠀⠀⠀⢱⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⡛⠀⠀⠀⠀⠀⢺⣄⡈⠻⠿⣟⠉⠈⢷⢦⣀⣀⡤⠚⢁⡴⡃⠢⣄⠀⠀⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⢧⠀⠙⠻⢧⣛⡜⠦⣤⠏⢦⣭⢥⣖⡾⠿⠋⠀⠀⠈⠙⠒⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣬⠿⠶⣄⠀⠈⣙⢷⡀⡤⣶⣟⣉⣠⣴⣶⣦⣤⣀⣀⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⡷⡀⣿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡗⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢙⡌⠈⣢⡈⣛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠹⠤⠏⠉⢯⠟⠙⠪⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢧⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡇⠀⢀⡤⠒⢫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⡇⢰⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢣⠀⠀⠀⢀⣀⠙⣟⠢⣑⣴⢁⠾⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⡆⡴⠋⠉⢸⠀⠀⠉⢉⣿⣡⠔⠊⠉⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉⠐⢾⠀⡁⠀⢀⡜⠀⢀⠔⠁⠈⠑⠦⣀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠉⠉⠉⠑⡄⢳⡧⠔⠋⢠⣖⣁⣠⡴⠒⠉⠉⠢⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠀⠤⠛⢮⡇⢀⠔⢛⠛⠒⢦⡙⠢⠤⠤⠤⠬⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠞⢣⠀⠀⡷⠃⠀⠸⡄⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⢦⠀⠀⠀⠈⢆⢈⢀⣾⠔⠒⠒⡶⠈⠒⠶⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⡇⢀⡴⢣⠀⢻⡿⢇⣀⡠⠞⢁⡤⠤⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠤⣉⠲⡇⡏⠀⢸⠀⡎⠀⢀⠷⣄⠰⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣀⣈⡷⠼⣷⡀⢸⢰⠁⢠⢦⠳⣿⡷⠤⣴⣊⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠳⣿⡷⠃⢸⠀⡇⠈⢣⢸⣠⡞⠁⠀⠀⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠛⠿⣿⣤⣸⠀⢇⠀⢸⣼⠁⠉⣒⣒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣠⠎⠀⠘⡄⠈⢦⣾⢇⡔⠉⠀⠈⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⠄⠂⠤⣀⢳⠀⣸⣿⣋⠀⠀⢀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⡀⣀⣀⠜⡋⠻⡁⠀⠈⠉⢩⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡜⠹⡄⠙⢄⠀⢠⠃⠈⡆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄⡀⢇⠀⢱⠀⡠⢵⣌⡣⣀⣷⠋⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣎⠁⠀⠀⠈⣳⣕⣿⣸⡷⠮⠥⠽⠾⢏⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⣀⠴⣏⠀⠀⠀⡠⠶⠒⠤⢬⠟⠓⠲⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢈⡍⠀⡼⠉⠱⡄⢸⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠋⠀⠀⠣⡀⠀⡇⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢶⠇

⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠋⡀
⠀⠀⠀⠀⣼⣯⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣿⣿⡇⠀⠀⠀⠀⠀⡼⠉⠉⠉⠉⠈⢳
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣥⣾⣿⡿⠁⠀⠀⠀⠀⠀⢳⠀⠐⠂⠂⠀⡸
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠞⠁


⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡇⠀⢀⡀⠀⠀⠀⠀⠀⢰⣦⣀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣤⠂⠁⠀⠀⠀⠀⠀⣴⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠛⣆⣽⡆
⠀⠀⠀⢼⣿⣿⡟⡻⠿⠿⠇⠀⠀⠀⠀⠀⢾⣿⣿⡿⠿⡿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⢋⣁⠐⢢⠀⠀⠀⠀⠀⢐⠻⣤⣺⣾⣿⡿
⠀⠀⠀⠀⠙⠻⠿⢷⡟⣶⠲⣯⠆⠀⠀⠀⠘⢿⣿⣿⣶⠖⡴⣦⣠⠆⠀⠀⠀⠀⠙⠻⠟⢦⣤⣭⣴⡿⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢻⣿⣷⠏⣀⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢼⣿⣿⡿⣟⣿⣿⣀⣤⡀⠀⠀⠀⠀⠀⣾⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣠⣠⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣿⣿⠛⠁⠀⠀⠀⠀⠀⣿⣧⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣙⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⢾⣿⣿⣷⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⣾⢟⣽⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢧
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⣇⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣼⣾⣦
⠀⠀⠀⠀⠀⠀⠻⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⠀⠤
⠀⠀⠈⠀⠀⠀⡀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠘⣥⠐⣢⠀⠤⠤
⣤⡀⠀⠠⠀⠈⠄⠠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⡆⠀⠀⣆⠠⣎
⠘⡖⠀⠀⠀⠀⡄⠀⡀⠀⠀⠆⡁⢠⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠄⠀⠀⠀⠀⢠⠠⡤⠔⡹⠀⠉
⠀⠑⢄⡀⠀⠀⠹⠊⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠖⣢⠀⠢⡀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⡈⢀⡀⠑⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠉⠀⠀⢁⠀⠴⠄⠀⠀⣤⡇⠢⠙⢦⠟⢀⠮⠆⠀⠀⠠⠀⠀⠀⠀⠐⠁⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡄⠀⠀⠉⠢⠈⠃⠀⠀⠁⠁⠀⠢⠄⠰⠘⠀⠀⠀⠀⠘⠠⠄⠀⠀⠀⣀⣀⠇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⠄⢀⠄⠀⢀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠑⢦⡤⠊⠀⠠⢅⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢀⡄⠀⠠⡒⠀⠀⡢⠂⠀⠀⢴⠈⠀⠀⢠⠚⠉⠐⠲⡈⠀⠫⡁⠂⠄⠀⣀⠀⠀⠀⢞⠀⠀⠀⢱
⠀⠀⠀⠀⠠⠤⠷⠄⠴⠥⠄⠤⠵⠦⠀⠠⠾⠤⠀⣀⣬⡷⠀⢠⣾⣤⡌⠉⠁⠀⠀⠀⢤⣇⡀⢠⣀⣱⡄⠀⣾⣀⡀

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⢄⠖⢟⡹⠦⠄⠀⠀⠔⠉⢐⡂⠀⠀⠀⠀⢀⠄⠲⡿⠁⢤⠠⠀⡀⢀⠠⠌⠀⠀⠀⠠⠁⠀⠀⠀⠐⠀⠘⢹⠀⠀⠃⠹⠀⠀⠐⠁
⠀⢉⠓⠉⠡⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠀⠀⠀⠀⡨⠇⠀⠒⠈⠈⠁⢀⠀⠀⠀⠍⠀⡀⠀⠂⠀⡀⠘⠀⠀⡀⢨⠀⠁⠀⠈⠂
⠀⠨⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡠⠀⢀⠑⠀⠄⠀⠄⠀⢀⠀⡀⠀⢰⠠⡖⠈⠀⠐⠈⠁⠖⠘⠁⠀⠈⠀⠀⠠⠂⠑⠈⠈⠀⠀⠄
⠀⠀⠠⠀⠀⠀⠀⡀⠄⠀⠀⠀⣰⠏⠁⠀⠈⠒⠐⣂⠀⠀⠉⠈⠌⠃⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢀⡠⡔⢢⡀⠀⢀
⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⡐⠳⠃⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⢄⠄⠰⠀⠂⠀⠀⠈⠀⠀⠰⠭⠌⠀⠈⠀⣤⢌⣬
⠀⠀⠠⣄⣄⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠁⠀⠀⢤⠰⣋⣥⡠⡀⠀⠀⢀⡄⠈⠐⠀⠀⠀⠀⢀⡀⠈⠢⣱
⠀⠀⢰⡿⣮⣵⡕⠀⠀⠀⠠⣏⡤⠤⡀⠀⠀⠀⡀⠀⠀⠀⠘⠽⠓⡠⠀⠀⡘⠀⠀⠑⠀⡀⠀⠂⠋⠀⠀⠀⠀⢠⠄⠀⠀⠀⡉⠒
⠀⠀⠘⢵⣭⣻⢤⡁⠀⡠⠺⣧⡽⠢⠀⠀⡠⠊⡀⠄⠀⠀⠘⠖⠋⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠂⠐⠀⠀⠀⠀⠔⡁⢀⠠⢀⠀⡀
⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠈⠁⠉⠁⠀⠪⢄⡘⠄⣄⠀⠀⠀⠀⡤⠴⠀⠀⡀⢀⠀⠀⠀⠀⢆⠀⠀⡒⡊⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⠀⠀⠀⠉⠀⠈⢀⠂⠀⠧⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠚⠤⠤⠀⠤⠖⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠠⠀⠀⠀⠈⠰⢿⠱⠀⠀⣠⡖⠒⠦⠤⢀⠀⠀⢀⡀⠀⠀⠀⠀⢴⢻⠞⠁⠀⠀⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠐⠂⠀⠀⠀⢁⣠⠋⠀⠈⠃⠀⠄⠀⠀⠠⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢂⠄⢠
⠀⠀⠀⠀⠀⢂⡀⠐⡀⠁⠀⢠⠘⡂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠂⠂⠁⠀⠈⢁⠀⠔⡄
⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠇⣂⠀⠀⢰⠀⠀⠁⠈⠀⠀⠀⠂⠀⠀⠀⢸⡏⠀⠂⠀⠀⠢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠶⡵⢄⠀⠀⠑⣧⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⡜⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠟⡱⠦⠙⠀⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠆⠀⠀⠀⠀⠀⡉⠀⠐⢸⠅
⠀⠀⢀⡄⠐⠊⠉⡙⠧⡁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠶⠶⠶⢬⣠⣤⣤⣄⣁⡞⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠐⠀⠠⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀
⠀⠀⠈⢀⠠⡄⠴⠠⠀⠀⠀⢀⠤⣀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⡄⠉⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠈⠈⠀⡀⠀⣀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠄
⠀⠀⠀⠀⠀⠀⡶⠛⢯⠛⣢⠀⠀⠠⠁⠀⠀⠀⣀⢂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠈⠀⠀⠀⠀⡐⢀⠀⠀⠄⠀⠀⠣⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣇⣀⠀⠀⠠⣾⠇⠀⠈⠈⠉⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠛⠉⠑⠀⠀⠈
⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠴⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠋
⠀⠀⠀⠀⠁⣄⠀⠀⠁⠀⡆⠀⠀⠀⠀⠸⠀⢀⠀⠀⠦⠄⠀⠀⠀⠢⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⡀⠀⠈⠋
⠀⠀⠀⠀⡰⠉⠉⠀⠀⠀⠁⢄⣀⣤⠰⠊⠀⠄⠀⠸⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⠀⠀⠰⠶⠁⠀⠀⠀⠀⠀⠉⠀⠛⣉⠄
⠀⠀⠀⠀⠀⠐⠄⠀⢖⡀⠀⠀⠀⠀⠀⠤⠈⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⢸⠃⠀⠒⠀⠀⠠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢠⠀⠆⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⡀⠁⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⣇⡼⠀⠀⠀⢀⢄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠘⠁⠃⠀⠀⠀⠀⠀⢠⡄⠀⢀⡠⠤⠐⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠀⠀⠀⠆⠘⠈⠴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⡂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠄⠀⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⡴⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠠⢀⡀
⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢚⣄⠀⢨⡆⠘⠊⠀⠠⠁⠀⢀⢠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡄⠀⠀⠀⠁⠵⡋⠀⠀⠀⠳⢄⠀⠀⠀⢀⡠⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣾⡯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣀⡁⠀⠀⠀⠂⠐⠀⠀⠂⡀⠀⠀⠀⠁⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀
⠀⠀⠀⠀⠀⠌⢄⠀⠀⠀⠀⢩⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠠⠀⠃⠀⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠂⢀⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠈⠀⠑⠴⠃⢛⠆⠤⠌⡀⡀⡀
⠀⠀⢀⢄⣀⠀⠀⡀⢀⠤⠀⢤⠄⡄⠀⠀⠠⣤⡊⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠐⡐⡉⣆⣀⠀⠀⠀⠋⠀⠄⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢜⢀⠁⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠁
⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠐⠀⠀⠀⢀⡀⠆⠀⠠⠘⠃⢀⠀⠀⢀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⢠⠀⠀⠠⠀⠉⠀⠰⠀⡄
⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠂⠠⠄⠐⠀⠀⠀⠈⠀⢰⠀⠠⠈⢀⠀⠁⠀⠀⠂⠐⠄⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠣⠀⠀⢀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠙⠀⠀⡀⠀⢉⣵⣆⠀⠀⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠄⠀⠀⠀⠠⠀⠘⠋⠀⠐⢁⡴⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣤⡔⠁⠀⠀⠀⢀⣴⠞⠉⢀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠶⣄⠀⠈⠛⠷⣦⣴⡶⠓⠈⠁⣨⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢈⠂⠰⠦⢤⡙⣿⡄⠀⠀⠞⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣷⡄⠀⠀⠀⠙⠧⠀⠔⠂⢋⡤⠦⠈⡣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠉⠛⠻⡦⠐⠿⠿⠶⠁⠀⠀⠞⠁⠚⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣶⣤⠾⠶⣶⠮⠐⢶⡾⠂⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢰⠆⣀⣁⣤⡶⠦⢶⣦⣾⡷⡄⠀⣄⡈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣨⢉⢹⣿⣯⣀⣾⠋⠸⣿⡿⢶⣼⣿⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢻⣿⠃⣿⡟⢠⠀⠈⣿⡡⠄⠸⢧⠀⠙⡎⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠸⣷⢴⣿⡇⠉⠀⠀⣹⠀⠀⣄⠀⢃⡿⠀⠉⢠⡔⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⣤⡘⢷⠃⠙⣇⣠⠴⠚⠹⣆⠀⠉⠀⢈⢷⡶⢄⣤⠀⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢿⣷⠋⠀⠀⠈⠁⠐⠶⡄⠈⣷⣀⠔⠁⠀⠛⣄⢀⡄⠁⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠁⣄⡈⠻⡴⠚⡉⠙⢇⠀⠋⠀⢀⣼⠿⡠⠴⠶⠄⠘⡟⠀⠸⡇⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢠⠀⣀⣾⡅⢻⣓⡀⢘⣧⣠⠔⠉⠀⠀⠻⣆⢀⠤⠂⢻⡂⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢾⡟⣉⠉⢏⠉⠀⢉⣠⠴⢏⡒⠶⠿⠦⠄⡟⠧⢤⣄⡀⣷⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡇⠧⡄⠈⢣⡴⠋⢀⡀⠀⠹⣀⣀⠤⠐⢿⣄⠘⠩⠉⠈⠉⠒⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣤⣧⡀⣤⠖⠘⢧⠲⠟⠧⢄⠠⣿⠀⢠⣆⠀⢘⣇⠀⠀⣠⡸⡇⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⢻⡇⣴⠃⠀⢀⡘⢀⣤⠄⢾⣀⠤⠟⠉⣉⠸⢷⡴⠋⠁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⠻⣦⠁⠀⠈⣿⠉⠀⣀⠀⠙⣆⢠⠞⠁⠀⠀⠻⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⢡⣼⣿⣶⠶⠾⠟⣢⡴⠿⡄⠀⠙⣟⠀⠠⠞⠣⠀⠧⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣇⣶⣄⠀⢱⡄⢠⡶⠒⠉⠉⠳⣀⡄⠀⠘⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣆⠛⠽⢡⡼⢉⡛⠀⠠⣄⡀⠠⠥⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⢄⡙⣦⠀⠀⠀⠀⠀⠀⠀⠓⣤⣇⠀⠀⠀⠀⠀⠀⠫⣉⣲⡴⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄
⠀⠀⠀⠀⠀⢠⢖⠉⠛⠓⠂⠒⢄⠀⠀⠀⢀⡎⠀⠈⢇⠀⠀⠀⠀⢠⢋⠀⠌⡉⣉⡆⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠀⠘⢆⠀⠀⠀⠸⡠⠀⠄⠄⢠⠃⠀⠀⠀⠀⢀⡠⠞⠁⣠⠀⢨⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡜⠀⠀⡎⢰⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢄⠂⣂⠎⠀⠀⡴⠖⠍⠡⠤⠴⠚⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢆⣀⡤⡠⠞⠀⠀⠀⠘⢼⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠓⠒⠐⠒⡒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡀⠀⠀⠀⠀⠀⡠⣒⠒⠚⢖⠳⢄
⠀⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣠⠒⢾⡽⠓⠻⣼⠒⠒⢤⠀⠀⢸⢱⠁⠀⠀⠈⡇⠀⢳
⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡞⡳⣤⠼⣇⠀⣠⡿⠷⢖⠉⠀⠀⠸⡘⠀⠀⠀⠐⠁⠀⡜
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⣛⠼⠣⡄⠀⡏⠉⣣⣀⠜⠀⠀⠀⠀⠑⠤⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⡠⠔⠃⠀⠀⠀⠐⢇⡸⠦⠤⠚⠒⠋⠚⠁⠀⠀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢇⠒⠀⠂⠀⡀⠁⠀⠁⠀⠢⠀⠂⡇⡬
⠀⠀⠀⠀⠀⠀⠀⣦⡀⡼⢳⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢦⡈⢠⠄⡀⠘⠀⠈⠠⡀⢉⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡴⣌⢣⠔⢉⢼⡀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⠤⣁⣈⣀⣉⡠⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡤⣿⡴⠥⣜⠀⠀⠀⠀⠮⣤⡤⢾⠟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⢀⡜⢇⢀⡼⠳⣄⡏⢦⠀⠀⠀⠀⠀⢠⢣⠂⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢸⣤⡴⠻⢄⣠⠊⠉⡿⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠉⠒⠊⠁⠒⠂⠉⢉⠆
⠀⠀⠀⠀⠀⢻⡀⢑⣤⣞⠉⢲⠾⣸⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⢟⠻⢤⣈⡽⠛⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠫⠥⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠻⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣴⠀⣰⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣇
⠀⠀⠀⢐⠀⠀⢰⠉⠛⡙⠦⡀⠈⣙⣀⣮⠀⡄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡎⣠⡿⢀⢻⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣦⡆⠀⠈⣼⡀⠀⠈⢢⠱⠆
⠀⠀⠄⠈⢳⣄⡼⣄⠀⠐⠄⠸⣄⣸⡟⢉⢫⣧⠀⠠⢀⠀⠀⠀⠀⠀⠈⠃⣻⡇⡾⣧⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢐⣾⠄⠀⢸⣧⣄⠀⣿⣶
⠀⠀⠠⠌⠉⠙⠋⡈⠷⣿⡆⣀⠀⠁⠈⠑⣷⣌⢷⡀⠈⠧⠀⠀⠀⠀⣠⠈⣿⣶⣵⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⣣⣌⠰⡿⢡⠂
⠀⠀⠀⠀⠲⡀⡈⠀⠀⠈⢹⢿⣣⣘⡀⠀⠈⣋⣄⡳⢄⡀⠄⠀⠀⠀⣿⢸⢠⡻⠉⠄⣴⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠢⠘⡦⠀⠉⡉⠰⠃⠁
⠀⠀⠀⠀⠀⠘⢹⣤⣀⠀⠀⠀⢴⠿⠟⣁⠰⢏⡁⠐⠄⡈⢁⠄⠀⠀⡟⣶⡈⠃⣰⢧⡿⠀⠀⠀⠉⠸⢷⡀⠈⠃⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁
⠀⠀⠀⠀⠐⠒⠤⠬⠟⠋⠈⠁⠋⠁⠀⠀⠀⠀⠈⠁⠀⡈⢦⣦⠂⠀⠘⠌⠻⠜⡷⠋⠀⠀⠀⠀⠣⠀⠛⢯⡀⠀⢰⠀⠀⢠⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⢿⣧⠂⠀⢸⣇⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘⡄⠀⠀⠙⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣷⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⣏⠀⢸⡃⢁⠀⣾⠃⠀⡹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢉⢀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣄⠀⡆⠀⠙⢷⣼⠃⢸⡏⠁⠀⠀⡇⣧⠂⠀⠀⠀⠀⠀⠀⠑⠂⠀⢾⠣⠠⠇⠂⠀⠀⠈⣱⡇⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⠖⡔⠈⠂
⠀⠀⠀⢰⣇⠀⠾⠀⠿⠀⣾⣝⠀⠂⡠⢡⣵⠀⠀⠀⠀⠀⠈⠀⠀⡠⠀⢠⡀⠀⠀⠀⠠⠤⠀⢈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢦⢀⡼⠃⢆⡤⠄
⠀⠀⢸⠀⣿⠀⠂⢠⡆⢻⣫⠋⣴⠟⢁⡿⡙⠀⠀⠀⠀⠀⠀⢘⡀⠁⠀⡘⠷⠈⣀⣀⣀⠀⣠⣠⣴⡷⢒⠎⠀⠀⠀⠀⠀⢀⢠⣇⣴⠟⠩⢅⡈
⠀⠀⠀⠳⣟⡆⠀⣨⠄⢼⣇⠀⠁⣄⣾⡷⠀⠀⠀⠀⠀⠀⢰⠈⠟⠀⣠⡴⠂⠈⢀⢩⣿⠻⠋⠙⠋⢀⠘⡀⠀⠀⠀⠀⠀⣬⣵⡟⠉⠄⠊⠁
⠀⠀⠀⠀⠸⣧⡤⠀⡠⠀⢈⠀⣴⢿⡟⠁⠀⠀⠀⠀⠀⠀⠘⢠⡙⢴⢫⠁⠀⢰⡏⠀⠀⠀⢀⠀⠀⣸⠦⠀⠀⠀⠀⣰⡾⠋⠈⠁⠀⠰⣄⢀⡀⡄
⠀⠀⠀⠀⠀⣿⠁⣼⣁⠤⡌⠀⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢠⡉⣠⣴⣯⡀⠐⣆⠀⠈⠲⣴⡷⠁⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠄⠁⠀⢹⠗
⠀⠀⠀⠀⠀⢷⠺⣘⠋⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠂⠒⠲⠽⡟⣛⠡⠾⠛⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠐⣦⣤⠏⠈
⠀⠀⠀⠀⠀⢸⠀⡍⢡⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠤⢸⡼⢖⠸⠀⠄
⠀⠀⠀⠀⠀⠀⠛⠡⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢔⣂⡱⠄⡀⠄⠀⠀⠀⢀⣉⠂⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢏⡅⢨⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠰⠀⢀⣙⡛⠀⣿⢿⣋⡁⣴⠁⡂⠀⠀⠀⠀⠙⣤⢀⣤⠀⠖⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢦⠁⣦⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡾⣷⡀⠀⡉⢀⡌⣁⡤⢹⠟⡬⢤⡄⠀⠀⠀⠀⣀⠘⠐⢿⣛⣾⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⡸⡇⠠⠀⢹⣠⠂⠐
⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢀⠌⣼⣧⣌⡿⠌⠛⠭⠂⠉⡤⠋⠂⠤⠴⠆⠀⠀⠀⠀⠀⢤⠀⠄⠠⠝⠳⢿⡷⣌⠃⠀⠀⠀⠀⠀⠏⡇⠀⠀⠻⡟⢁⡇
⠀⠀⠀⠀⠀⣨⠁⠀⢠⠾⣋⣀⣡⣬⠒⢀⣾⣌⠙⠃⠉⠁⠲⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡴⣿⣿⠈⠓⢄⠀⠀⠀⠀⠘⣿⡆⣰⢘⡀⡼
⠀⠀⠀⠀⠒⠒⠒⡀⠀⠹⠄⠀⠄⠰⢥⠀⠀⠰⠐⠶⠦⡔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣡⠃⠀⠀⠀⠱⡀⠀⠀⠀⠈⠓⠇⠞⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠲⠀⠘⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠐⠛⠦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠠⣀⠄⣑⠄⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣄⣠⣊⣄⠐⠃
⠀⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠘⣄⡄⠀⠀⠀⠀⠀⠀⠠⠆⡐⠳⣸⠆⠉⠾⣀⠁⠒⠀⠀⠀⠀⠀⠀⠀⣴⠖⠉⡀⠁⠈⠀⠉⠲⡕⠂
⠀⠀⠀⠀⣠⠴⠒⠃⠀⠠⠀⠀⠀⠀⠲⡶⠦⢄⠀⠀⠀⠀⠀⠀⢀⣉⡤⠻⢀⢀⣈⠙⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠰⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠈⠠⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⣹⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⢟⠉⠀⠀⠀⠀⡰⠁⣀⣀⡀⠀⠀⢀⣀⢀⠀⢳⠀⠰⠶⠻⠿⢻⡧⠤⠤⡦⠤⠤⠤⠤⡴⠤⠴⢟
⠀⠀⠀⠀⢀⡇⠀⠀⣠⣄⠀⠀⠀⣤⡄⠀⠸⡀⠀⠀⠀⢠⠻⣾⡿⢟⣡⣆⣠⣿⠟⣩⣶⠧⣇⠀⠀⠀⠀⡜⠀⢠⡼⠗⢄⠀⢤⣴⠟⣤⠤⢸⡄
⠀⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⡐⠀⠈⠲⣿⠟⠁⠀⠱⣾⡿⠁⠀⢁⠀⠀⠀⢠⠀⠀⠀⠔⠺⡇⠀⢀⠴⠺⢏⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠁⠈⠈⠳⣄⣀⠄⠢⢄⠀⣠⣒⠦⠤⠁⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠰⠶⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⢀⠐⠋⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⠔⠋⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⠐⠏⣠⠄
⠀⠀⠀⠀⠀⢀⣀⠀⢣⠐⡆⢰⢃⡄⠤⢤⠀⠀⠀⠀⠀⠀⢀⣀⠈⣆⠱⠆⠸⠊⡄⠀⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣆⠱⠆⠸⢂⡄⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠠⠐⢀⣱⡄⣤⣀⠔⠢⡀⠀⠀⠀⠀⠀⠀⠈⢁⠴⢌⢰⡀⣦⠊⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠶⢌⢰⡀⣥⠊⠰⠎
⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⠈⠙⢇⠒⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠈⠉⠲⣖⠧⠀⠀⠀⠀⠀⠀⠀⢠⡵⠖⠋⠀⠀⠈⠉⠲⣖⠧
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⢣⠀⠀⠀⠀⣜⣠⣤⡤⢄⣄⣀⣠⣤⠤⣤⣄⣡⠀⠀⠀⠀⠀⣎⣴⣶⠖⢀⢄⢀⣶⡾⠃⡠⣢⣧
⠀⠀⠀⢀⠁⠀⣀⠼⠿⢤⣀⡠⠼⠯⢄⡀⠘⠆⠀⠀⠰⠉⠽⠏⠤⣾⡿⠟⢿⡁⠴⠿⠿⠻⠄⠀⠀⠀⠘⠹⠟⢁⢔⣵⡿⠛⠟⢁⢔⣼⣿⠻⠆
⠀⠀⠀⢘⡠⠊⢀⡀⢀⣀⡽⣀⣀⠀⣀⠈⢢⡆⠀⠀⠘⠀⠀⡠⠊⠉⠙⣶⠉⠉⠱⣄⠀⠀⡄⠀⠀⠀⠎⠀⠀⠃⠛⠉⠀⠀⠀⠁⠛⠛⠁⠀⡄
⠀⠀⠀⢸⡷⡶⠋⠗⠙⠁⠤⠀⠉⠑⠏⠳⡶⡇⠀⠀⢸⠀⠻⢤⣀⡠⠔⣉⠦⢀⣀⠬⠛⠀⠆⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠺⡃⠀⠠⠄⠀⢀⣀⡀⠀⠠⠄⠀⢘⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠰⡁⣠⠊⠉⠖⢠⠤⢤⢀⣀⣠⡤⠤⠄⠒⡁⠁⡀⢰
⠀⠀⠀⠀⠀⠀⠓⠠⠤⠄⠀⡀⠤⠄⠚⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⢀⣀⣀⡠⠔⠉⠀⠀⠀⠀⠒⠀⡎⢀⡄⠀⣄⠀⣄⠀⣆⠀⠷⢄⡑⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈⠚⠉⠐⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⢿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠁
⠀⠠⠀⠂⠠⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡼⠀⣤⠈
⢠⠀⠀⡀⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⢇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢧
⠀⢀⠐⡇⠃⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠁⠀⠂⣀⠐⣀⠐⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡀
⠀⠈⡄⣐⢁⡼⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠄⡄⢀⡀⠀⠠⠁⠀⠀⠀⠀⠄⠀⢀⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢀⢀
⠀⠀⢣⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠣
⠀⠀⣸⣿⢣⠀⠀⠀⠀⠀⠀⠸⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠀⠀⠐
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠂⠈⠃⠀⡀⠀⠀⠄⠢⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠀⡉⠠⠀⠐⠂⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣜⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡇⢹⡴⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣇⠀⠀⠀⠀⠀⢠⠌⠳⣊⡐⠻⢄⣮⡁⠀⠀⠀⠀⠀⠀⢀⠀⡈⠤⠀⢠
⠀⠁⠀⠀⠀⢤⠀⠀⢠⠀⠀⠀⠀⠀⠸⡿⠘⠀⠀⠀⠀⠀⠀⠹⠁⡁⠈⡎⠀⠈⠁⠃⠀⠀⠀⡀⠀⠀⠀⠁⠀⢠⠈⢠
⠀⠀⠀⠄⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠋⢀⠀⠶⠊⠀⠀⠀⠀⠄⣀⠁⠀⠠⠖⠀⡀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠈⠠⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⠂⠂⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⠀⡇⡇⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⣻⠀⡁⠀⠀⠀⠀⠀⠄⠁
⡌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⢠⠙⡄⡅⠀⠀⠀⠀⠀⠂
⠀⡀⠐⠁⠀⠀⠀⠀⠠⠀⠀⡎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠁⠀⠀⠀⠀⠀⠄
⡈⢀⠄⠀⠀⠀⠀⠀⠀⠀⡴⢀⠀⣁⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⠔⢉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠠⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠝⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠈⠀⠀⠀⣘⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠳⣾⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢤⣤⣤⣴⣶⡶⠾⠶⣶⣤⣀⠸⠃⠈⣷⡀⣀⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠃⠀⠀⣀⣀⣀⣀⣀⣀⠈⠙⢷⡄⢠⣿⠟⠋⠀⠀⠀⠀⠈⢉⣷⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠚⠉⠉⠉⠀⠀⠀⠀⠉⠙⢦⣼⠿⣿⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠨⠽⠧⠤⣴⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢠⣤⡤⠖⣂⣤⠴⠖⣲⡿⣿⠇⣺⣿⠟⠉⠉⠉⠉⠉⠛⠳⠶⠤⠤⠴⠶⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣛⣭⣶⣶⠟⢁⣴⠏⣼⣿⣿⢠⣤⣂⣤⡀⠀⠀⣤⣤⣤⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢉⡽⠋⢁⣴⠿⡟⢸⡏⠘⠻⣷⣭⣭⣭⣤⣤⣶⠶⠶⠾⠿⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠟⠁⠀⢠⡟⢁⣴⠟⠁⢸⡇⢸⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⣠⣶⠿⠛⡉⢉⡿⠿⠿⠷⣶⠏⢠⡞⠁⠀⠀⠸⡇⢸
⠀⢠⣾⠏⠀⠀⠀⠳⢮⡶⠂⠀⢀⡏⢠⣿⡄⠀⠀⢀⣠⣧⢸⣤⣤⣤⣤⣀
⠀⣾⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⣸⢠⡏⢸⣿⣀⣶⡿⠟⠻⡄⢫⣉⠉⠛⠛⠿⣦⡀
⠀⣿⡇⠸⣇⠀⠀⠀⣀⣠⣤⣤⡇⣼⣀⣼⣿⣿⠏⠀⠀⠀⠚⠾⠋⠀⠀⠀⠀⠈⠻⣦
⠀⠘⣿⣆⠉⢀⣴⡿⠟⠉⢁⠘⡇⡏⠉⠉⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠈⠻⣷⡿⠁⠀⠀⠀⠈⠻⣷⡷⠏⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⡇
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣿⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⡴⠾⠋⣠⣾⠟
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢰⣿⣤⣄⣀⣀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠙⣷⣄⠀⠀⣀⣀⣀⣀⣤⡾⠏⢀⣴⣿⠋⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠙⢿⣶⣦⣭⣭⣭⣭⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢄⠀⢊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⣠⣶⣿⣿
⠀⠀⠀⠀⠄⠀⡀⠀⢠⠠⠈⢠⡷⠐⠱⠀⠀⡀⠀⠀⠀⠀⣠⣤⣤⣯⣾⣿⣿⣿⣿⣿⣿⡆⠀⢀⡀
⠀⠀⠀⠀⠈⠢⣀⠑⢜⡡⠐⠊⡄⠂⠀⠒⠁⠐⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠁
⠀⠀⠀⠀⠡⡀⠈⢢⢎⢀⠀⠀⠘⠉⠀⣰⠄⠂⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣉⢂⡀⠀⠺⠁⢳⡷⠒⠲⠃⠠⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠡⡈⣡⡐⢄⣀⠈⠐⡘⢠⡔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠁⢰⣜⡁⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣷⣧⣄⣷⣯⣼⣝⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣃⣠⠄
⠀⠀⠀⠀⠀⠀⠀⡳⢻⠛⠟⡻⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⡀⣘⠀⣁⢁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠦⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣸⡁⣷⠴⠄⠳⡤⠀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣉⠉⠛⢶⡔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢍⠑⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣀⠐⠀⠀⠀⠠⡶⠀⠄⢀⡀⠀⠀⠀⠈⠈⠂⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠐⠒⠧⠀⠀⠀⠀⢐⣋⡤⠂⠁⠀⢁⡀⠐⠃⠀⠀⡄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠞⠀⠀⠀⠀⠀⠀⠑⡀⠀⡜⠞⠀⠀⠄⣰⠯⠀⣦⡠⢆⣈⠁⠈⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣦⣄⠀⣼⠿⠦⠐⠛⠒⠀⠥⢌⣉⠗⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠅⠁⢸⡀⠀⠀⠀⠀⠀⣴⣿⡀⣏⣼⢛⣋⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠈⡠⠂⠀⠀⢰⠃⡇⠀⠀⠀⢸⡯⣉⡹⣏⣿⡉⢤⣺⠃⠀⠀⠀⠀⠀⠀⣄⠀⠇⢀
⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠈⠀⣠⠆⠀⡼⠀⣄⣀⡤⠔⠛⠉⢙⣷⡟⡧⠙⠁⠀⠈⢢⠀⠀⠀⠀⠰⠞⢪⠀⠟⣠⣚⠅
⠀⠀⠀⢁⠤⠀⠐⠒⠀⠀⠀⠀⠠⠔⠊⠁⠀⡰⣡⢞⠍⠉⠀⠁⠆⣠⠋⣼⠟⠁⠀⣀⣤⠄⠈⠓⢏⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠠⢀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡠⠊⡜⠁⠀⠀⠀⠀⠀⢰⠃⡀⡈⠀⠀⡾⡿⣮⠏⠀⠀⠈⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⢧⠀⠐⠄⠀⠀⢀⡏⡐⠀⢣⣀⠄⠂⠉⠁⠀⠀⡠⢂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣀⣀⠀⠠⠀⠈⠀⠈⠳⢦⠤⠤⠴⠊⠀⠀⠀⠀⠙⠦⠀⠀⠀⢂⠀⠔⠁⠀⠀⠀⠁⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⢰⠉⠘⠀⠄⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠚⠀⠀⠀⠄⠀⠃⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠈⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢧⡄⠀⠀⠐⠀⢀⢂⠀⠀⠁⠀⠀⠀⠀⣰⡤⡇⢸⡆
⠀⠀⠀⣆⠀⠀⠈⠄⠀⠀⠀⠄⠀⠀⠃⠦⠀⠀⠘⠀⠀⠈⠀⠌⠈⠀⠀⠀⠀⢰⡥⠄⠀⠀⠀⠉⠀⠀⠀⢀⣴⡤⠀⠀⢩⡄⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠒⠦⠀⠊⠀⠀⠀⠀⡀⠀⠞⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠈⠎⠀⠀⠈⢀⠴⠀⣀⠄
⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠑⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⡀⠀⣠⣶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠠⡂⠀⠀⠀⠀⠲⠁⠄⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠘⠀⣰⠯⣠⠀⠀⠀⠘⢂⠄⢀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⣠⠀⠀⠀⢈
⠀⠟⠲⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣔⠭⢓⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢰⣎⢁⣔⣁⡋⡂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⢀⢴⠖⠻⠏⠥⠀⠀⣞⠪⡵⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠄⠠⣀⡠⠈⠉⠉⠁⠀⠀⠉
⠀⠀⠄⠀⠀⠀⡀⠀⠚⠀⠀⠀⢀⡴⠍⠂⠀⠀⠘⠁⠀⠈⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠂⠎⠀⠀⠨
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠶⠶⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠓⠒⠲⠶⠶⠦⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠈⢿⠉⠙⠛⠛⠒⠒⠲⠶⠶⠤⣤⣤⠤⠤⠴⠶⠖⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠀⢠⠀⣿⡆
⠀⠀⠀⢀⣤⣾⣧⣀⣀⣀⣀⡀⠀⠀⠀⠤⣂⣿⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠾⢶⡟
⠀⠀⠀⠀⣿⠈⠉⠉⠓⠲⣾⠛⠛⠛⠛⠛⠛⠓⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⣿⡀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⣒⣒⣚⣩⡇
⠀⠀⠀⠀⠈⠙⣷⠒⠦⢤⣽⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠶⠶⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠁⠀⢸⣇
⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠈⢉⡙⢻⡏⠰⠒⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣷
⠀⢶⡾⣯⣭⣥⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠍⣿⠀⠀⠀⠀⢀⡠⠀⢀⣀⣀⣤⠤⠤⠶⠒⠚⠋⢉⣠⣿⣀
⠀⠈⡷⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠶⣤⣤⣿⣤⡤⠶⣾⣛⡿⠛⠋⠁⠀⠀⠀⠀⣀⡠⢔⣚⣭⠤⠖⠛⢿⡄
⠐⢿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠈⠀⠀⣄⣀⠠⡌⣷⠀⠀⢀⣀⣤⠶⠟⢛⣋⡩⠄⠂⠀⠀⠀⠈⣿
⠀⠘⣷⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠯⣭⣿⣛⣓⣒⣺⣿⡶⣿⠴⠚⣋⠥⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠁
⠀⣀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠭⠥⢖⣒⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉⠁⢸⡇
⠀⠉⠛⢻⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠒⡉⠭⢝⣒⣺⡇⠀⠀⠀⢀⣀⣤⠶⢚⡭⠟⠁⠀⠀⠀⢀⣼⣧⣄⣀⣀
⠀⠀⠀⠈⢹⣯⠉⠙⠛⠛⠛⠛⠻⠷⠾⢶⣶⣶⣮⣭⣒⣿⣀⣤⠴⠚⠋⠁⣠⠶⠋⠀⠀⠀⠀⢀⣰⠋⠀⠀⠈⣉⡽⠟⣷
⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⡉⠛⠛⠿⢿⣇⠀⡀⢇⠀⠀⣠⠞⠁⢀⣠⠶⠋⠁⠀⠀⢸
⣠⣴⠚⠋⢩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠠⠔⢒⣈⣈⣿⡄⣧⢸⣠⠞⣡⡴⠚⠉⠀⠀⠀⠀⠀⣀⣼
⠈⣿⠙⠛⠛⠿⢷⣶⣶⡦⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⡴⢒⣡⣾⠥⣶⣿⡇⣿⣾⠗⠋⠁⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋
⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣍⣉⡉⠛⠛⠓⠶⠶⠦⢶⣶⣶⣿⣯⣿⠟⠉⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠁
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣀⣠⡴⠞⠉⠉⠁⠀⠀⠀⠀⠀⣠⢴⣫⡿⠛⠁
⠈⠛⠻⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⢖⣩⢽⢛⣿⡀⠀⠀⠀⠀⠀⠀⣠⢔⣫⡾⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⣀⠀⠀⠐⠀⠀⠂⠈⢔⣋⠯⢾⣇⠀⠀⠀⡠⢔⣫⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣤⣀⣀⡀⠠⢀⣊⠽⣿⠀⢀⣨⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣷⣶⣽⣧⡶⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⢠⠟⢡⡀⠀⠀⡀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⠀⠀⠀⢀⣾⡄⠀⣰⠇⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣜⠀⠀⢀⠹⣿⣁⠀⣿⠀⢀⣼⠁⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⢿⡄⠱⡄⠀⣿⣿⢠⡟⢀⣾⠇⣸⣏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠛⣿⣦⠀⠀⢿⣿⡇⢠⠟⢠⠚⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣆⠻⡇⠀⠀⢰⣿⡰⠇⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣄⡲⣦⣈⣑⠉⢿⣄⠂⠀⣸⣿⡇⢀⣴⡿⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢳⣌⠛⣷⣤⡟⠀⠠⠋⣸⣷⣾⠟⣣⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣤⣄⣈⣻⠿⣿⣮⡛⠀⠀⢠⣿⡟⠁⣾⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣿⣆⠸⠉⢿⣆⠀⣹⠏⢀⣴⣃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣽⣿⣇⠀⠘⠛⣿⣁⣰⡝⠛⠉⣡⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠀⠀⠛⣿⡁⣠⠾⣿⣧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡛⣿⣷⣀⠰⠛⣿⣤⢎⣹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣻⣧⣉⣫⣿⣦⣾⣿⡛⠾⠛⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣿⣯⣭⢉⣿⠉⣿⣷⣄⣹⣷⣶⢢⣽⣏⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣴⠋⢻⡄⣼⡟⠙⢷⣿⠁⢈⡿⠟⢿⣀⢈⡿⠻⡝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⣿⠃⠁⣸⠷⣿⠀⠁⢰⡿⠤⣾⡇⠘⠀⣿⣬⣇⠈⢘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠈⣧⣼⡇⠠⢸⣇⣠⡟⠀⠀⠈⣷⣀⣶⠁⠀⢻⣄⣸⠃⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠹⡇⣶⢃⠘⣷⠀⣼⠃⡉⢳⡄⠀⢠⡟⠉⠹⣧⠀⣸⠏⢹⡆⢰⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⣠⠿⢿⠀⢰⡿⠾⣿⠀⠁⢺⠷⠶⣿⠀⠘⠐⣿⠴⣷⠀⠀⣿⣿⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣷⡏⠂⣼⣤⣿⠀⠂⢹⣦⣤⡿⠀⠂⢸⣧⣤⣾⡃⠠⢸⣇⣸⡇⢸⣇⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣢⡟⡀⢹⡄⢠⣞⠁⠈⣷⣀⣀⣼⠃⠀⠙⣵⠂⡼⠋⠹⢇⢰⡉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⡿⠙⣇⠀⣼⠛⠛⣯⠀⠀⣾⠋⠉⠿⠀⠀⢀⡿⠲⣷⠀⢀⡾⢷⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣼⡇⠃⣽⣴⣏⠐⠂⢸⣦⣼⣏⠈⠁⢸⣧⣤⣾⠀⠀⢸⣇⣸⠇⢸⣇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣻⣱⡏⡄⢹⣂⣠⡏⢠⠀⢿⣅⣠⣾⠃⡀⢹⡆⠀⡜⢉⢹⡆⡸⢋⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⣿⠙⣇⠀⣼⠋⠙⣧⠀⠀⣾⠋⠉⢿⣀⠀⢰⠟⠺⣧⠀⢸⡿⣷⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣏⠁⣿⡤⣿⠀⠀⢸⣧⣼⡇⠀⠀⢸⣧⣤⡿⠀⠀⣿⣤⣿⠐⣽⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣂⡛⠄⢸⣆⣐⡟⠀⠀⢹⡄⣰⡎⠡⠈⢷⡀⣰⠏⠀⢿⡀⢏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠉⣿⠄⣨⠋⡉⢿⡀⠀⣼⠋⠙⣧⠀⢠⡟⠉⢻⡄⢀⡞⠻⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣬⠗⠻⣆⠁⣸⠗⠚⢧⠀⢐⡿⠒⢿⡆⠀⣼⠷⣾⢈⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⡻⠖⢿⡀⠁⣸⠷⣿⡀⠀⣸⡷⢴⡏⠀⣨⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣷⣀⢈⣿⠴⣯⠀⣨⣷⣼⣇⠀⣠⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠿⣿⡿⢿⣿⣿⠿⠿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠄⠀⡀⠀⠌⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠡⡰⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢀⣀⠀⠀⠠⠀⣒⠂⠒⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠉⠁⣵⠂⠻⡐⠂⠠⣀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠊⠉⠀⠆⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⡀⢸⠃⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⣠⣾⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠭⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠘⠢⣤⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠉⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠂⠀⠀⠠⠞⠉⠀⠤⡀⠀⠀⢀⠤⠤⠤⠦⠸⢿⣿⣿⣿⡿⢀⠀⠀⠀⠀⢀⣤⣶⣦
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠓⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠯⠉⢉⠔⠉⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠊⠀⠐⠆⠀⠀⠀⠀⠀⠈⠉⠀⠁⠑⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⡇⡤⠤⠀⠀⠀⠒⠒⠂⠀⠠⠄⣀⡀
⠘⢄⡒⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠀⠤⠄⢀⣀⠀⠀⠀⠠⡀
⠀⠈⠙⢇⠤⣀⡠⠇⠈⠉⠁⠹⠁⠀⠀⠀⡙⠉⠁⠙⠒⠒⠂⢠⠭⠅⢒⣤⣄⠀⠀⠠⠄⠀⠀⠈⠻⢓⣈⡦⣶⠒⠀⠀⠣
⠀⠀⠀⠀⠈⠐⠩⠍⣒⡒⠠⠬⠄⠤⠤⠀⢣⣀⣀⣠⣄⠀⡀⣠⣀⣀⡤⢽⣽⠛⠋⠈⠀⠀⠀⡠⠒⢣⠀⡰⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠐⠒⠐⠒⠀⠀⠀⠐⠂⠂⠀⠉⠁⡠⠀⠀⠀⢀⡄⠉⠙⡆⡾⡪⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠳⠤⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⢢⠠⡴⡪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠻⣀⢀⣡⡲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠻⡀⠀⢀⡧⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠠⢔⠒⠉⠻⡀⠀⢀⣋⢝⠫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⡀⠀⠈⠄⠀⣀⡉⢔⡫⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠚⠓⠀⠁


⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⠉⠉⠉⠀⠀⠀⠐⠒⠒⠂⠀⠢⠤⠄⠀⠀⠠⠤⠤⠤⢆⠀⠀⢀⡀⠀⠀⠀⡰⠄
⠀⠀⠠⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠺⡷⠛⠋⠉
⠀⠀⠀⠀⠉⠒⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠄⠀⠀⠤⠤⠤⠤⠤⠀⠐⠒⠈⡿⠔⠂⠁

⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣤⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣾⣿⣿⣿⣿⣿⠏⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⢿⣿⣿⣿⣿⣯⢰⣿⡿⢡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣟⡛⠛⣷⣝⣿⡟⠅⠀⢿⢹⢰⡟⠁⢀⣼⢳⡾⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠻⠟⠻⣿⣜⣷⣎⠀⠈⠈⡿⠁⠀⣾⠟⠋⣴⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣧⣌⠻⣟⢿⡀⢄⠀⠁⠀⠀⠋⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⡻⡛⣦⠘⢾⣃⠀⡴⠉⠀⠀⠀⢀⣿⣿⣿⡿⢛⡿⢻⣿⣿⣭⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢉⣹⡿⢷⣾⣩⠻⠶⣍⣧⡀⠹⡄⠀⠐⠀⠀⠀⠀⠈⠛⣣⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣶⣍⡙⢿⣾⣆⠘⢷⠀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣬⡿⢷⣮⣙⢿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⣠⣿⡿⠿⠟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣋⣉⠺⡉⠃⠹⣆⠀⠀⢀⠀⣀⠀⠉⠀⣉⣤⣆⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⡛⠻⣿⢐⣦⣙⡇⠀⠀⠀⢈⣤⠂⡼⠉⠛⢛⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅⠐⠿⠿⣖⣊⣻⠷⠌⢭⡛⢷⣶⠷⠞⠁⠀⠠⣠⡶⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠒⢾⡷⢏⣙⠲⣇⠀⢙⡾⠧⠤⢀⣾⡷⠃⢴⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡉⠀⣈⣿⡷⠠⣭⡿⠶⠶⢀⡼⠟⢠⣼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢏⣉⠩⣝⣦⣤⡯⠓⣣⠾⠦⢴⡟⣲⢏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠇⠐⢠⠶⡦⣾⣋⣉⣁⣄⣈⣃⣹⣦⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⠿⠋⠁⠐⠃⠀⠰⣿⠓⣼⣿⣿⣿⣏⡘⢿⣧⠀⠙⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⢀⠄⠐⠆⣀⠠⠛⡿⠁⠈⠹⣦⠉⠉⠛⣇⠀⠀⢃⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢻⡏⠀⠀⠀⠀⠁⠀⡃⠐⠢⣧⣤⡔⠂⠀⠠⣤⣰⠁⠀⠰⡾⠁⣰⣽⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣲⣄⡜⠓⢶⡃⠀⠀⣏⣀⢀⡸⠃⠈⢣⣤⣤⡤⠀⡈⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠢⣴⠇⢬⣽⡋⠈⠉⣿⣂⣀⣼⠋⠀⢱⠖⠁⠀⠛⢼⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣭⠓⠐⣧⠀⣀⣹⣋⢀⣚⡟⠉⠉⢻⣄⣀⣼⠖⡇⠀⢖⠤⡀⠀⠀⠀⠀⠀⠈⠉⠚⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⢲⣿⣤⣵⣎⣁⠉⢹⣗⠚⣀⣿⢁⡍⣿⠊⢳⠶⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢛⣿⣿⣿⣿⣿⣿⣏⡉⠙⣿⣉⣤⣿⣂⣿⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣨⣿⡧⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣉⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⢟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣰⣾⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⣼⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠋⢙⣿⣿⣿⣿⡿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣯⠀⠀⠈⠙⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⢁⡼⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣉⣁⣀⡀⢺⣇
⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠷⢄⠀⠀⠀⠀⠀⢀⣶⣾⣿⣉⣙⠲⣇⣀⠉⠉⠛⣿⣳⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⢀⣾⣟⣉⡡⣤⢬⣹⠟⠛⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿⣿⣟⣻⠏⠀⠀⠠⠀⣱⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣿⣧⣼⢿⣶⠖⢛⣾⣾⢁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⣿⡿⣿⣋⣿⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀