Pigs Emojis & Symbols

⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⡴⠈⠙⡆
⠀⠀⠀⠀⣷⡑⢤⠀⠀⠀⡸⣷⡄⡀⠰
⠀⠀⠀⠀⣿⡁⠀⠙⠉⠉⠁⠸⣿⡇⠀⣦⡀⣀⣀⣀⣀⢀⠀⠀⠠⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄
⠀⠀⠀⢠⡽⠀⠀⢀⣠⣀⠀⠀⠹⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⣀⠔⠀⠀⠀⠘⠛⠟⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⢯⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠻⣶⣵⡶⡶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠈⠙⠓⠶⠦⣀⠀⠀⠀⠀⢀⣀⡤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠄⣠⣅⣄⡀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⢱⣄⠁⠀⠀⠀⠀⡈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⣷⣾⣿⣧⡙⠀⠀⠀⠀⣼⣇⣰⣧⣴⣿⣧⣴⠆⢀⣠⣶⣾⣿⡆⠀⠀⠀⠈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⡿⡯⠁⠀⠀⠀⠜⠉⠉⠉⠉⠉⠙⠛⢿⡿⠛⠉⠀⠘⡿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢰⠁⡆⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣼⡇⠰⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⣴⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⢰⣷⣴⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣺⣿⣀⠾⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⣴⣶⣾⡿⠻⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠿⢿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⢿⡏⠉⠛⢷⣦⡀⠈⠻⣦⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣴⠟⠁⢀⣴⡾⠛⠉⢹⡿
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠙⣿⣤⣴⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣦⣤⣿⠋⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⡀⠀⣠⣶⠿⠿⠿⠿⣶⣄⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡇⣼⡟⠁⣤⠀⠀⣤⠈⢻⣧⠸⣿⣿⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠿⠀⠀⠿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠘⠻⣶⣦⣤⣤⣴⣶⠟⠃⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠶⣶⣶⣶⣶⣶⣶⠶⠶⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⢻⣦⣤⡶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣀⠀⣠⡶⠷⢶⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⠀⠀⣀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⣾⣿⠟⠉⢙⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡔⠙⢦⡀⠈⠛⢷⣆
⠀⠀⠀⠀⢀⣿⣿⣄⡀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⣴⡟⣷⡀⠀⢠⣿
⠀⠀⠀⠀⠀⣿⡻⣿⣟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠦⣄⣀⡀⠀⠀⠀⠀⡏⣠⡦⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠉⢉⡹⣧⡈⠻⣦⣾⠃
⠀⠀⠀⠀⠀⠘⢷⣄⡙⠛⠛⠛⠛⠛⠻⠶⠶⠶⠶⠶⠶⠾⣿⠃⠀⠀⠀⠈⠉⠙⠛⠓⠚⠁⢤⣄⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠉⠛⢶⣤⣿⠘⢷⣄
⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⡇⢀⡼⠁⠀⢠⠖⢳⡄⢠⡶⢤⡀⠙⢧⡀⠀⠙⢷⡄
⠀⠀⠀⠀⢠⡿⠉⠡⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⠏⠀⠀⢰⠏⠀⢸⡇⠈⣇⠀⠹⡄⠀⠳⡄⠀⠈⢻⡆
⠀⠀⠀⢀⣿⠁⠀⠠⠀⠀⠀⠀⠀⣀⠑⠄⣀⣀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢿⠀⠀⣼⠁⠀⠘⠦⣴⠇⠀⠀⣿⠀⠀⠈⣿
⠀⠀⠀⢸⡇⠀⠔⠀⠀⠠⠀⠈⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⡏
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠈⠂⠀⠐⠈⠀⠈⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠈⠳⠦⣄⣀⡀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⠀⣰⡟
⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠳⣄⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠉
⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣦⣤⣤⣀⣠⣤⣤⣴⠶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⣀⣴⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢸⠙⠲⢤⣀⣀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣼⡥⠖⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣦⡀⠘⣿⠙⠛⠛⠛⠛⣿⠀⠀⠀⢰⣿⣇⠀⢀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠀⠸⣿⠛⠛⠛⠁⠀⠀⠀⠀⢻⡧⠀⠀⣾⠋⣿⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣿⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⢲⢶⡄⣀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠒⠲⠤⣀
⠀⠀⠀⠀⠳⣘⠒⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⣄⣀⠠⠤⢺⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⡔⠠⠀⠀⠀⠀⡐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣹⠇⢀⣀⡠⠞
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢠⠐⠈⠀⡜⠖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠢⠁⠠⠤⠀⢀⠀⠀⠃⢀⠀⠣⢣⠈⡄⢀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⢠⣤⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠐⠠⠀⢠⡁⠀⠀⠴⢤⣀⡀⠀⠀⠐⠀⠐⠀⠈⠂⠂⢃⠐⢁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠉⢁⠄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠈⢀⡞⢳⠀⠈⢃⡏⠀⠉⠉⠐⠒⠤⠤⠥⣤⣤⣬⣬⡤⣼⡄⠀⠀⠸⢀⠧⠴⢄⣀⠀⠈⠂⠀⠢⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡨⢀⠞⠀⠈⡇⠈⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠘⡄⠀⠀⠀⠉⠉⠑⠚⠳⠦⣄⣘⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢁⡏⠀⠀⠀⠘⣆⠠⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⡎⠱⣄⢀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡇⠀⠀⠀⠀⠘⣄⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠰⡄⠀⠈⣆⠡⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠗⠀⠀⠀⠀⠀⠘⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠀⠀⠈⠳⣤⣨⡷

⢸⣷⢤⣀⣀
⠀⠻⡶⢄⠉⠉⠉⠙⠒⠦⣄⡀
⠀⠀⢹⠀⠑⢄⠀⠀⠀⠀⣀⣉⣦⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⣄⣀⣀⣀⣀⣤
⠀⠀⢸⠀⠀⠈⣦⠔⠊⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⣦⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡨⢥⡷⠋
⠀⠀⠘⣆⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠁⡔⠁
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⡼
⠀⢀⡏⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⠜⠁
⢀⠜⠋⠉⠉⠉⠑⢦⡀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠧⠤⠤⢤⣀⣀
⡏⢠⢦⠀⢀⣤⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠳⡈⠉⠀⠈⠒⠁⢀⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⣴⠿⢿⣆⢀
⠀⠈⢳⡒⠀⠒⠊⠁⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢿⣦⣼⣿⠿
⠀⠀⠀⠙⣶⢤⣀⣀⣀⣀⠤⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠿⠋
⠀⠀⠀⠀⠈⠻⡄⠀⠀⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠘⢦⣤⠬⣋⡴⢯⣤⡤⠤⡔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡑⢤⣤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⡄⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⠬⢆⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡄⠀⠀⠀⠀⢀⠏⠁⣠⠧⣀⣈⣆⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡶⠠⢼⡀⠀⠀⠀⡞⠰⣞⣡⠞⠀⢀⣿⣀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣊⣀⣀⡼⢧⠤⠠⡼⠀⠀⠈⠓⠛⣽⣋⡡⠂⠈⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣯⠴⠃⢀⣰⠃⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠤⠤⢄⣀⡀
⠀⠀⠀⠀⢀⣀⠀⠀⢠⣶⡿⠿⠻⠟⠻⠋⠉⠉⢉⠁⢒⠩⠗⠏⢋⠉⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀
⠀⠀⠀⣰⣯⣙⢻⣿⣿⠏⠀⠀⢀⡀⠀⣠⢶⠈⠀⠛⠀⢔⡯⠖⠁⠨⠕⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣦⣀⣀⣠⣤⣤⣴⡶⢶⠦
⠀⠀⠀⠹⣿⣿⣾⡛⡁⠀⣠⠖⠉⠁⢊⡠⠖⢁⢄⡠⠖⡫⠂⡴⠠⠔⣃⡈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣛⣿⡟⠫⠕⠀⢀⣤⣞⣁
⠀⠀⠀⣠⣿⣿⣷⣇⠀⠐⠡⠲⠷⣶⣻⢋⢔⡵⠊⠀⣨⠴⠋⢀⡠⢊⡥⣒⢋⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣭⠹⣿⣷⣏⣁⣵⣿⣿⣛⡩⠟⠛
⠀⢀⣼⡿⢻⣿⣿⡄⠀⠀⠀⣠⠔⠋⣥⠗⠉⠀⢁⠀⠉⠀⠀⢤⣠⣵⠿⣛⣫⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡽⠗⢎⣿⣿⣿⣿⣿⣿⣏⠁
⣠⢊⣼⠁⢸⣿⠟⢁⠀⠀⠚⣡⣵⣿⡢⢂⠀⠔⢀⠄⢠⠔⣒⠋⣠⠴⣻⣛⣣⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣬⡜⠛⠉⣼⢟⠛⠿⡯⢿⣿⡆
⣿⠟⠁⠀⠈⣿⣷⣟⣤⣚⣞⣽⣟⣵⢞⣁⣴⡊⠐⢁⡴⢛⢵⢚⣥⣾⠿⢫⡿⣻⣄⠀⠀⠀⠀⠀⠀⠀⢐⣺⣏⠈⠀⠀⢾⡞⠀⣀⣠⡜⠉⡟⢦⡀
⠏⠀⠀⠀⠀⢻⣿⣿⢏⣼⠋⠀⡠⠴⠾⠧⣪⣴⣽⣻⣾⣿⣟⣯⢉⣴⣡⡶⢫⣿⣿⣁⠀⠀⠀⠀⠀⠀⣐⢺⣷⠲⠀⠀⠸⣴⣿⣿⣾⣴⣷⣶⡖⣉⡶⢦⣶
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣨⣄⣔⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⣴⣿⡿⢛⡰⠤⠤⠀⠀⠀⠀⢻⣿⣷⣶⣆⣥⣾⣿⣿⣿⣿⣝⣛⣛⡻⢷⣶⣾⡻
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢿⣿⣿⣿⣿⣯⣥⣤⣴⣶⣾⣿⣿⣵⣶⣶⣿⣿⣾⣷⣶⣾⡓⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⡿⣷⡿⠛⠉⠈⢻⣿⣿⢿⡏⠉⠉⠛⠻⠿⠿⠟⠛⠛⢻⣿⠟⠙⣿⡂⠀⠐⣿⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⠋⠀⠀⠀⠀⢸⣿⣿⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠠⠈⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢷⠀⠀⠀⠀⠀⠘⣿⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡰⠃⠀⠈⢷⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣇⠀⠀⠀⠀⠀⠹⣿⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠘⣧⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣟⣧⠀⠀⠀⠀⠀⠉⠻⢯⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⡦⠀⠀⠈⠋⠷⢼⡦
⣿⣿⣿⢿⣿⠿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣦⣴⣧⣾⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣠⣤⣤⣀⣀⣀⡀
⠀⠀⢀⣀⡀⠀⠀⢀⣠⣴⣶⠿⠏⡩⠟⠻⠟⠫⠈⠊⠛⠿⠙⠻⠻⡻⣻⡛⢿⣿⣷⣆⠀⠀⠤⠤⢤⣀⣀
⠀⠀⢺⣯⢙⣧⡔⢿⠏⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠼⠟⢳⣿⡆⠀⠀⠀⠀⢹⣿⣿⣶⣤⣤⣀⠀⡀
⠀⠀⢄⡷⣿⡟⠙⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢧⠀⠀⠀⠀⠀⢿⡿⡟⠛⢿⣿⠝⠻⠓⠀⡀⠀⡀
⠀⠀⠀⢰⡟⠄⣠⠀⠀⠀⠀⠀⠀⠀⠙⣤⠺⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠗⡎⠀⠀⠀⠀⠀⢾⡇⢻⠀⢰⡆⠘⣵⣤⣶⣷⠯
⠀⠀⠀⢾⢷⠀⡃⠀⠀⠀⠀⠀⠀⢀⢄⣡⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⢌⡄⣸⢀⠺⣿⣷⣤⣾⣿⠇
⠀⠀⠀⢻⢄⠸⡄⠀⠀⠀⠀⠇⠠⠛⣷⣿⣷⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡝⠀⠀⠀⠀⠀⢀⠆⢀⣿⡏⠀⢹⣿⣿⣿⢿⡆⠢⢀⡄
⠀⠀⠀⠈⣿⣄⠙⠃⠀⢐⡀⠀⠠⠤⣟⣿⣛⠛⢟⡋⠌⠄⠀⠀⠀⠐⠀⣰⣷⣾⣿⠆⡄⠀⠀⠀⠀⣎⠃⢠⣿⣷⣴⠃⣿⣷⣹⠿⠧⢤⣶⠟
⠀⠀⠀⠀⠘⣧⣦⠀⠁⣈⣴⣠⣾⣿⠏⠙⠻⠿⣿⣿⣛⡻⣶⡰⢀⣀⣚⣉⣷⣿⠏⢸⡁⠀⠀⠀⠀⢿⣷⠿⠟⠛⠿⠾⠿⠿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣿⠆⢀⣊⣾⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣿⡇⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⡄⠉⠐⠖⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠛⠋⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣟⠍⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⢢⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⠋⡀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠈⠀⠀⠀⣤⣄⠀⠼⢇⡀⠳⠤⠄⠠⠠⠦⠀⠤⠴⠄⠤⠀⠀⣂⠲⠂⠙⠃⠚⠁⠀⠀⠆⠘⢶⣄⠀⠐⠆⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠹⠁⠀⠒⠀⠐⠚⠂⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠋⠑⠈⠁

⠀⠀⢀⣤⣤⠠⣀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠠⣠⡤
⠀⠀⠈⠛⣻⣷⡄⠳⠈⠀⠀⠀⠀⠀⠊⢀⣾⠟⠀⠀⠀⠀⠀⠐⡠⠤⠀⢤⠆
⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠇⢸⠃⠀⠀⠀⠀⠘⣷⠺⠀⠀⠁⠀⠀⠀⠠⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠗⡀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠠⢤⣤⠴⠀⢀⡜⠀⠐⣶⣴⠒⣿⠀⡀⠀⠈⠫⢀⡀⢀⠀⢰⡇⠀⣰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡝⠢⣄⠀⢰⣥⠖⠋⠀⣠⠀⢼⡉⣱⡄⡈⢿⣿⣶⠀⢢⢹⢉⠀⡜⠉⠉⢟⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠁⠐⣄⡀⢀⡠⠀⠀⢠⡟⠀⠀⠈⢻⣾⡧⢾⣿⡏⠀⣈⡀⢀⣨⠅⠀⠶⣞⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠛⠿⠇⠀⠰⠁⠀⠀⠀⠀⠰⠿⠀⠜⠹⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣠⣤⣤⣿⣿⣀⡴⠋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣇⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠉⠉⠁⣿⣿⣭⠄⠚⣷⣿⡍⠱⣶⣄⠀⠀⠀⠀⣰⣿⣤⠄⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⢙⣽⣿⣼⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⣴⣿⡀
⠀⠀⠀⠀⠀⠻⣶⣤⣤⠴⠶⠶⠿⠿⠿⠿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⠷⠀⠈⠙⠿⣿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣀⡀⢺⣿⡅⣷⣰⠹⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⣀⠈⠛⠛⠺⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠟⠛⠿⣷⣼⣿⣠⣫⠅⠀⠀⠀⠛⠉⠛⠿⢿⡛⠛⠿⠟⠛⠛⠒⠾⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⣀⡠⠶⣿⡴⢤⣜⡄⣳⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠀⠀⠊⢹⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠠⠀⣀⣆⣠⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣏⠁⠀⠁⠀⠀⢁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢨⣿⣿⣿⣿⠇⠀⠘⣧⠞⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣵⣏⡀⡀⢀⠀⢹⣿⣿⣿⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀⠚⣠⣾⢿⣿⣿⠛⠤⠴⠶⡄
⠀⠀⠀⠀⠀⠀⣯⢿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠠⠀⣾⣿⣿⠟⠁⠀⠀⠀⡀⡀⠀⠁⣺⣿⣇⠠⠄⠄
⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠙⣷⡀⢀⣿⠛
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡏⠛⠿⢿⣶⣄⣂⠀⠘⠻⣿⣯⣥⣀⠀⢀⣤⣴⣦⣽⢿⣾⣿⣆⠀⢴⣄⡆⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⠃⡼⣿⣿⣿⡇⠀⠀⠀⠈⠙⠛⠂⠈⣠⣿⣿⣿⠃⢼⣿⣿⣿⣿⣿⡿⠿⠛⠛⠶⠼⢿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⡅⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠐⣿⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡇⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⠇⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡅⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠘⢿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠯⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⣀⣀⠀⠀⢀⡠⠤⠒⠒⠚⠉⠉⠋⠓⠒⠒⠒⠒⠒⠒⠒⠠⠤⠤⠤⣀⣀
⠀⠀⠀⠸⡘⠬⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣄
⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣹⡦⠤⠐⠒⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠃⢰⡔⠊
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠂⢰⡀⣒⠂⠚⠆⢰⡞⡟⣿⠂⢖⢂⢰⠲⢒⠒⡂⠀⠀⢀⠀⠀⢰⡄⠁⠀⣀⠀⠸⡁
⠀⠀⠀⠀⠀⠈⢢⠀⠀⢠⠀⢐⠁⠀⠩⣑⣂⠀⠒⠙⠊⠑⠂⠂⠐⠒⠓⠀⠀⠐⠂⠈⠚⠄⠀⡀⠐⢋⡀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⢠⠛⡆⠀⢂⠇⠈⠉⠐⠒⠠⠤⠤⠤⠤⠤⢤⣆⠀⠀⠁⡴⠐⠤⣀⡀⠀⠀⠡⠀⠀⡑⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠈⣠⠃⠀⢹⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡀⠀⢡⠀⠀⠀⠀⠈⠁⠙⠒⠤⠕⠁
⠀⠀⠀⠀⠀⠀⢈⠂⢠⡇⠀⠀⠀⢱⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠈⢦⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠈⠧⣈⡇⠀⠀⠀⠀⠱⠬⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠌⠷⠀⠈⠳⣀⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠀⠀⠀⠐⠒⡀⢀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢰⣿⠏⠐⣆⣠⣀
⠀⠀⠘⠦⣤⣬⡅⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡀⣴⢄⠀⡀⠈⢛⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠉⠸⠏⠀⠈⠙
⠀⠀⠀⠀⠀⠀⢷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠠⢨⠇
⠀⠀⠀⠀⠀⠀⠘⣿⡥⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠠⠲⢤⠄⠀⠀⠀⠀⠀⣠⣼⣷⣮⣤⣄⣀⣠⣤⣤⠭⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡄⠀⠀⠀⠀⢰⣿⣿⣵⣶⣖⣂⣼⣭⣤⣤⣄⣴⡤⣤⡦⢴⣷⡄⢀⠀⠀⠀⢀⣰⣿⠟⠋⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⢠⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠠⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠐⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠀⠀⠸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠁
⠀⠀⠀⠤⠤⠤⠤⠄⠤⠤⠽⠟⠳⠶⠖⠐⠛⠛⠒⠲⠒⠲⠦⠀⠀⠀⠀⠐⠒⠂⠐⠒⠐⠒⠛⠂⠘⠷⠤⠤⠤⠄


⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⡇⠀⠀⣔⡆
⠀⠀⠀⠀⣶⡃⣖⡎⣧⠴⠒⠚⠉⠛⠓⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⡞⣇⠴⢊⢾⠃
⠀⠀⠀⠀⠘⠣⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠓⠈⡽⠋⠀⢀⡞⡸⠳⡖⠁⡼
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡰⠋⠀⠁⠀⠘⣾⠁
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠊⠀⠀⠀⣀⠀⠀⠸⡄
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠌⠀⠀⠀⣳⡀⠀⡀
⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⡊⣹
⠀⠀⠀⠈⢏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣀⠀⠀⢀⣀⣏⡽
⠀⠀⢸⠩⠋⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠩⠀⠀⠀⠀⡀⠀⣠⡤⠴⠖⠒⠲⠭⢝⡏⠁
⠀⠀⣸⠀⢀⡴⠒⠊⠉⠒⠦⡀⠀⠀⠀⡧⣄⣀⣸⠀⠀⢀⡾⠟⢿⠉⠀⠱⡀
⠀⢾⢛⣁⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠸⠀⠀⡎⠀⠀⠈⠒⢤⡀⠈⢢⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡀⢀⣧⡀⠀⣴⣄⡜⠀⠀⠀⠀⠀⠀⠹⢿⡯⣑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠬⠃⠀⠘⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣼⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠠⠆⠀⠀⠀⣀⠠⠐⠂⢩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠀⠈⢳⠀⣠⡾⠀⠀⠻⢦⡀⠀⡀⠀⠀⠈⠲⢤⣤⠤⠂⠉⠀⠀⠀⠈⣿⠈⢳⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⠜⠛⠸⡟⠁
⠀⠀⠢⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⢾⣅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢤⣴⡿⢀⢸⣿⣦⡀⠀⠠⠋⠉⠀⡾⠿⣿⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣨⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⢠⠀⠁⢠⠀⢀⣀⣼⣿⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠈⠳⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢸⡁⢀⡀⠀⠀⠀⢠⡀⠀⠀⢀⣼⣿⡟⠀⠀⠠⠃⠀⠀⠘⠀⠈⠻⢿⣿⡀⠀⠀⢸⡿⠛⠀⠀⠀⠄⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠺⣦
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⢿⣧⣾⣿⡏⠀⠀⠰⠁⠀⢠⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠰⠀⠀⠘⠉⠀⠀⢀⠠⠾⠗⠀⠈⠷⠀⠀⠹⡆
⠀⠀⢀⡆⢀⣠⠄⠀⠀⠘⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠘⠉⠀⠘⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠈⡳⠚⣻⠶⡖⠠⣾⣤⡀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠺⣿⡶⠀⠀⠀⠀⠀⡀⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⣤⡯⠀⠉⠀⢻⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢘⠀⠀⣶⣿⠓⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⣶⠀⠤⡤
⠀⠀⠀⠛⠘⠃⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢁⣻⣧⣆⣀⠀⠀⠀⠻⠆⠀⠀⠹⣇⠀⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⣰
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣸⣷⠸⡇⠀⠀⠷⠔⡇⣤⣽⡿⢿⣯⠳⡄⠀⠀⠀⠀⠤⠠⣿⣷⡄⠀⠀⠀⠀⣠⣄⡈⣀⡀⠉⠀⠀⠀⣀⣀⠀⢀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠘⠿⠄⠀⠀⠀⠠⠄⠙⡁⠁⠀⠀⠙⣷⢹⡄⠀⠀⠈⠀⠀⢸⣿⣿⡄⠀⠀⣠⣻⣿⢹⣿⣿⠀⠀⠀⠀⠈⠻⠷⠎⢘⠿⠚⠃
⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢀⣲⠔⠀⣴⠂⠁⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡀⠘⠿⣿⡆⢿⡿⠀⣀⣀⠀⠀⠀⢀⠰⠃⣴⡶⣶⣶⣆
⠀⠀⠀⠀⠉⠀⠀⢀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣰⠉⡷⡈⢿⡀⠀⢿⣷⣤⢡⣇⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠠⠀⣤⣠⣤⡴⠀⠀⠀⣀⣀⣀⣀⣤⠀⠀⣀⡄⠀⠀⠘⣧⣑⢼⡾⠁⢰⣮⣿⣿⡗⠙⠉⠛⠁
⠀⠀⢀⣀⣤⡴⠖⡁⠀⠀⠀⠻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠀⠀⠀⠀⢹⡟⡶⠭⠛⣚⣟⣿⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠻⠟⠀⠀⢀⡄
⠀⠀⠀⠀⠉⠀⣠⣡⡶⠠⢤⡤⠦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⡆⠀⠀⠀⣐⣦⠀⠈⠐⠫⠔⠃⠉⠉⢿⠓⣀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢠⣽⡿⢿⡔⠋⠁⠀⠀⢠⣀⡀⠀⠀⠈⣷⠀⠀⠈⠋⢀⣤⣾⣫⠏⠀⠀⠀⣠⠇⠀⠀⠄⠈⠸⠏⠀⠀⠀⠀⠀⢠⠀⠀⠈⢀⠇⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣰⣄⡜⣽⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢠⣤⡀⡀⠀⠀⠀⠀⠘⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣶⣿⣥⡀⠀⠠⠄⠠⣤⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⢻⣿⣿⣿⣿⣾⠇⢰⠟⢻⣿⣿⡿⠔⠀⠀⠀⠛⠀⢀⠴⠿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣿⡿⠟⢻⠀⠀⢠⡟⠻⠏⠁⠀⠀⣠⣤⣤⠖⢻⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣾⠀⢰⡆⠀⢰⣤⣀⡀⠀⢰⡟⣴⣶⣿⣷⣏⣻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⣴⠀⣸⣿⣦⣩⣿⣿⣇⣾⣿⣯⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠿⠿⠷⢶⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣤⠤⣤⡄⠀⠀⠀⢀⢀⢄⠄⠁⠀⠈⠉⠀⠉⠀⠀⠈⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⢰⡇⠘⠧⣄⣁⣈⣀⣉⣉⣷⣦⣠⡦⠀⠀⠐⣿⣿⡵⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠇⠀⠢⡦⣤⠤⡤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣣⣾⡿⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⣿⣿⣿⣇⠀⢠⡀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⢀⣴⣾⠟⠀⣿⣿⣾⠷⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⠸⣿⣿⣷⠀⡞⢣⡀⣠⣶⠶⠂⠄⠈⠿⣶⣦⣼⣿⣟⡊⢠⣿⣿⠁⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣉⠀⠻⣿⣿⡀⣰⣿⠛⢋⠡⣀⠁⠀⠀⠓⠀⠉⠃⠙⣿⡇⣸⣿⡯⠀⢠⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⠀⣹⣿⣷⡟⠀⣸⣏⠐⠟⠃⠀⠄⠀⠀⠀⠀⠀⠙⢰⣿⣿⣆⠀⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠂⣠⣼⣿⣿⢁⣾⠯⠽⠒⢿⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⣲⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⢠⣆⣤⠀⠽⠶⣶⠀⠸⣼⡇⡼⠇⠀⠀⠠⢎⡀⢀⣷⡦⢈⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢍⡝⢿⣿⠄⣿⣿⣯⡀⠀⠻⠃⢠⠀⡀⠀⠀⠿⣟⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡘⢀⣼⡇⠀⠛⣁⠀⠈⢣⡄⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⣄⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⣺⣿⠀⢰⢯⠗⢀⠴⠉⠁⣀⣤⠀⠀⠀⠀⠀⢠⣥⠀⢙⡀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⢫⣿⡏⠀⣸⠁⢰⡿⠀⣰⠟⢋⣉⡀⠀⠈⠲⠀⠈⠈⠀⢘⣥⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠤⢟⣿⡇⠀⣸⠁⣾⠃⠀⡿⣶⠛⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⠶⢾⡇⠀⠛⠀⠟⠀⢀⡴⢁⣴⡿⠃⠀⠀⢿⣿⣦⠀⠀⡠⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣾⡇⠥⣼⣆⠸⣆⢁⠀⣿⠁⠈⠉⣀⣀⠀⢀⣀⠀⠼⠀⠀⠛⠂⣈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢳⣛⣡⣭⣷⣌⠺⠁⢸⡄⠀⠸⠿⠋⠀⠘⠛⠛⡁⣀⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⡭⠄⣐⣋⡹⢻⣶⣦⡑⢀⣀⣀⣀⣠⣤⠄⢊⣤⠃⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠩⣟⣃⣀⣉⣷⣶⣿⣟⢻⣷⣄⣩⠍⠉⣀⠲⢈⢷⣲⡆⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣛⣻⣶⣷⣤⣾⣽⣟⣽⣯⡟⠀⠠⣜⣷⣋⣛⣴⣷⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢉⣩⣭⠉⠭⠟⡋⣽⣧⣾⣳⡆⢘⠦⢛⣦⣉⣻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠭⣿⣶⡆⣰⣊⠃⢻⡟⣿⠀⢈⠷⣄⣼⠚⡡⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠈⠸⢿⣷⣿⣷⣄⠘⠻⠻⣿⣾⢿⣛⠮⠁⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⠀⢡⡮⢿⣿⡇⠀⠀⢀⣿⣯⣆⠁⠀⢠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡷⢻⠀⣱⣿⡇⣇⠀⠀⠈⣽⣿⣟⠁⠀⢸⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠈⣇⣨⣟⡿⣿⠀⠀⠀⣿⣧⣽⡇⠀⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⣈⢈⡄⠀⠀⣿⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⣿⡯⠈⠃⠀⠀⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠓⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⡶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠢⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢆⠈⠳⣄⠀⠀⠀⢀⣎⡔⠂⠀⢀⡴⠚⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡄⢸⡄⠀⡹⠖⠒⠛⠉⠉⠛⠒⠶⣏⠠⠎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣝⠋⠀⠀⠀⠀⣠⠴⠦⠄⠀⠀⠀⠀⠶⠶⢄⠀⠙⣦⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡤⢄⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠀⠀⠀⠀⠀⢰⣯⣶⠒⣿⠀⠀⠀⠀⢸⣾⡃⣷⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠱⠃⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⠀⠀⠀⠀⡘⣿⣿⡿⠇⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡀⠀⠀⠀⠀⠖⠀⠀⠈⠙⠟⣡⣢⠴⠒⠒⠻⢮⡁⠀⠀⠀⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⡥⠤⡀⠀⢠⠒⣝⢦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣇⣀⠇⠀⠙⠴⠅⢸⠃⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⡡⠴⠛⡲⠦⠖⠁⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⡏⠀⡠⠖⠋⠉⠉⠙⠲⣌⣦⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣹⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡀⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣞⠁⣀
⠀⠀⠀⢰⣀⢔⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣈⡛⢦⡀⠀⠀⠀⠀⠠⡇⠀⣠⠋⠈⡉⠘⣷
⠀⠀⠀⠀⠙⠪⠽⠭⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢤⡼⢹⡆⠙⢦⠀⠀⠀⠀⡇⠀⣇⣀⠐⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⢤⣤⣀⠘⠀⣸⢉⡾⠤⠴⠚⣇⠈⢉⡀⣹⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠲⠷⠊⠀⠀⠀⠀⠈⠛⠛⠈⠁

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

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⡒⢄⠀⡀⡠⠊⡡⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠘⣿⠀⠀⠀⠀⡰⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣃⢾⣠⠊
⠀⠀⠀⠀⠀⢀⠀⡆⠀⣰⣴⡛⠀⠀⠀⢶⡅⠀⢠⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠟⠉⡫⣿⡇
⠀⠀⠀⠀⠀⢸⠀⡇⢰⠟⣉⠙⢶⠤⠤⠀⠙⡶⢠⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⡴⢋⢰⠈⠳⡈⢣⡀
⠀⠀⠀⠀⠀⢸⠘⡇⠛⠀⣈⠀⢸⣷⣶⡶⢶⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⢾⠀⠀⠀⠛⡶⠃
⠀⠀⠀⠀⠀⠀⠭⣀⣄⣸⡇⣀⣸⣥⠤⠤⠬⠧⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⣏⡀⠀⠀⣿⠉⠀⠁
⠀⠀⠀⠀⠀⠊⠄⢀⠤⠚⠉⡉⠀⢄⠀⠠⡀⠢⡐⠄⠑⠀⠀⠀⠀⠀⠀⠀⠒⡉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢠⢂⡖⣄
⠀⠀⠀⠀⠀⠀⠘⠂⡿⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠉⡐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⢰⢧⠺⢀⣤⠤⠤⠤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣬⣆⡤⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡼⠆⢰⠏⠈⢳⡤⠤⠤⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢙⣀⣹⣴⢯⣏⢳
⠀⠀⠀⠀⠀⠀⣀⡗⣆⠸⠀⡷⢸⡌⡗⢸⡇⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣸⣏⣿⢣⢺⣿⣿⣿⣼⢿⣯⠄
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⣀⣀⣼⣧⣧⣀⣠⣇⣀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣸⣯⠥⠼⠿⠾⠿⢿⣬⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⢀⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠛⠛⠶⣦⡘⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠻⣿⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠲⠶⠶⣶⣶⠿⠿⠿⠿⠿⠿⠿⣷⣦⣄⠀⠋⠀⠀⣿⣇⣀⣤⣶⠶⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠛⠒⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠙⣿⣆⠀⢠⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⢙⣷⡦⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡉⠁⠀⠀⠤⠤⠤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠛⠳⢦⣄⢘⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣛⣿⣃⣀⣀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⡿⠋⣍⣿⣤⣴⡶⠾⠿⠿⠶⣶⣤⣄⡀⠀⠀⠀⠉⠉⢉⣩⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⡐⠼⠶⠶⠛⣋⣡⡴⠶⠛⢋⣩⡿⠟⣿⠗⣨⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⢟⣋⣥⣶⣶⣿⠟⠁⢀⣾⠃⣰⣿⣿⣯⢠⣤⠤⣂⡤⠄⠀⠀⢀⣠⣤⣤⣤⣤⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⣻⡿⠛⠁⣠⣶⣿⡏⢰⣿⠉⠻⣿⣦⣝⡛⠛⠛⢉⣀⣀⣠⣤⣤⣭⣝⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⢀⣼⠟⠀⣠⣾⠟⠉⣾⠃⢸⡇⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣾⣏⡀⠀⠀⢠⡾⠁⢀⣼⠟⠁⠀⠀⣿⠀⢸⠁
⠀⠀⠀⠀⣠⣾⡿⠟⠋⡉⠉⢩⡿⠟⠛⠿⠿⣶⡿⠁⣠⡟⠁⠀⠀⠀⠀⣿⠀⢸
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠻⣦⣈⣤⠆⠀⠀⠀⡿⠁⣰⣿⡀⠀⠀⠀⠀⠀⣹⡄⢸⣄⣀⣀⣀⡀
⠀⢠⣿⠏⠀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣸⠃⣰⡏⢿⣷⠀⠀⣠⣶⣿⣿⣧⠈⣿⠿⠿⠿⣿⣿⣷⣤⡀
⠀⢸⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡟⠀⢸⣿⣧⣾⣿⠟⠉⠀⠘⣦⠘⣦⡴⠀⠀⠀⠉⠙⢿⣷⡄
⠀⢸⣿⡀⠸⣿⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⡇⣼⣥⣤⣾⣿⣿⡿⠁⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⢿⣷⣄⠈⠃⢀⣴⣾⡿⠟⠋⠉⠉⢹⡃⡏⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠈⠻⣿⣦⣴⣿⠟⠉⠀⠀⠀⠈⢷⣼⣅⣧⣤⠞⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⣸⣿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⢀⣴⣿⠏
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢠⣿⡿⠻⢿⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠠⢤⣤⣤⣤⣤⣶⣿⠟⠁⢀⣴⣿⡿⠁⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣤⣬⣍⣉⣉⣉⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠈⠠⠀⠂⣀⣀⡀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠁⠀⠀⠀⠀⡀⠀⢴⣤⣠⣴
⠀⠠⠀⠀⠀⠀⡴⣻⣿⣿⣿⣶⣶⣤⡧⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣧⠀⠈⠀⠉⢠
⠀⠀⠆⢸⣄⣼⢷⣿⣾⣿⣿⡿⡿⣿⣿⣿⡀⠀⠐⠀⠀⠀⣠⠀⠀⠀⢸⢸⡇⠀⠀⣰⣤⣾⠿⣧⡄⠈⠐
⠀⠀⠼⣆⣿⣷⣾⣿⣷⣤⣿⠟⠛⣿⣿⣿⣷⠀⠀⠠⠁⢀⣸⠀⣠⠀⣇⣾⠀⠀⣺⣟⡅⢇⣠⢈⢙⠀⠻⢈
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣂⠠⣴⣿⣿⣷⣦⣤⣀⣸⣮⣡⣸⣼⣷⣿⣛⣻⠋⠙⡿⣿⣾⣿⡆⠂
⠀⠀⠀⣿⣿⡟⢿⣿⡿⣴⣿⡿⣻⣿⣀⣹⣿⣿⡿⣿⣿⢿⣿⢿⣿⠿⣿⣻⣿⡿⣿⣧⣾⣟⡿⢟⣿⣿⣾
⢀⠀⠙⢿⡿⣿⣿⣿⣘⣧⣤⣿⣿⣦⡶⡛⢛⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣯⢹⣛⣾⡏⠽⢿⡿⣿⣿⣿⣿⢀⣀
⠙⠀⡀⢀⡿⡿⢂⣿⡻⡿⡛⠋⣩⢎⣙⣛⣇⡻⣿⡇⣘⣿⣿⣿⣿⣿⣿⣿⡳⣿⢻⣇⠀⣸⣿⣟⣻⣯⣿⠀⠁
⠀⠙⡅⠃⢀⣤⣿⡞⢝⣯⣼⠻⣴⣠⠟⡸⣶⢃⣿⣿⣿⣻⣿⣿⡿⡿⣿⣿⣧⣿⡿⡽⣿⣿⡟⣯⣟⡻⢟⡇
⠀⠀⠰⡛⣏⣹⣷⣃⣅⣯⠿⣹⣾⣭⣴⣿⣸⡿⠿⢿⣿⣿⣿⣿⣷⣿⣿⡏⣈⡙⣽⣿⣿⣷⢻⡟⣿⣷⣿⡇⠂
⠀⣀⣀⢰⣿⢿⣯⣭⣙⣿⣿⣿⣿⣿⣿⣿⡏⣠⣷⣗⣿⠿⡇⢉⡉⢘⠛⣓⠾⣷⡏⣿⣿⣟⡟⣋⢿⣾⣉⠁⢁
⠰⠐⠢⢼⡗⢼⣿⣿⣿⣿⣙⣿⣿⣿⣿⣯⣿⣩⣿⣿⣿⣷⣥⣮⣤⠒⣷⣿⣴⣾⣿⣿⡟⠛⠢⡐⠖⣿⣼⡋⠁
⠀⠀⠀⠈⣿⣻⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⡟⢿⣧⢴⡿⠟⡛⣿⣃⣸⣇⣴⣾⣷⢴⡏⣹⠋
⠀⠀⠀⠀⢿⡿⣽⡵⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣧⣰⣤⣾⣿⣿⣿⣀⣋⣥⣀⣽⣿⠏
⠀⠀⠀⠀⠘⠀⠻⠐⠁⠀⠀⠁⠙⠋⠁⠈⠙⠁⠀⠉⠉⠙⠛⠙⠛⠛⠛⠛⠙⠋⠉⠙⠋⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢌⠙⠂⠀⠀⠒⠉⠙⠛⠲⢤⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠈⢉⠉⠉⠓⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⢀⡇⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠸⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠑⢀⡼⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠈⢧⡀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⣉⣁⣀⣀⠉⠙⠆⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢆⠀⠀⠀⠀⠑⠀⠀⠀⠐⠉⠉⠀⠀⠉⠛⣆⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⠈⠳⣤⣀⠀⠀⠀⠀⢠⠀⠋⠛⠀⠀⠰⠦⠘⠂⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⠃⠀⠀⠀⠈⠉⠉⠀⠀⠘⢷⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⠏⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠙⠻⠿⣯⣭⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢷⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⡀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴
⠀⠀⠀⠀⠀⠀⢸⣷⣶⡿⠋⠉⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣤⣾⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠈⢻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⡿⢫⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣄⣀⡀⣀⣀⣠⣼⣿⣿⡎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⣿⣿⡟⠀⢸⡏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣷⡘⣮⡑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⣦⣾⣿⣿⣷⣐⠸⡇
⠀⠀⠀⠀⠀⠀⠻⣄⣉⣅⣩⣍⣭⣩⣭⣽⣿⣿⣧⣿⣿⡷⢹⡆⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣭⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡗⢺⡦⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⢻⣿⣇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠵⠿⠁⣴⠟⣉⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣞⡻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡭⠟⠉⣩⠛⣩⣵⣾⣿⢁⣴⣿⣾⣿⣿⣦⡐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠘⠉⣩⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠗⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠇⢀⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡽⢣⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⢀⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣰⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⡎⠈⣿⣿⣿⠇⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣀⡀⠸⣿⡆⣿⣸⣿⣿⠿⠟⢿⠿⠿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢸⡇⢀⡿⠹⡿⠀⠀⠀⠀⠐⠈⠈⠀⠀⠠⢐⣴⣿⣷⣤⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡰⠀⠀⣻⡃⣾⢃⢰⣿⠀⠀⢠⣴⣶⣀⠰⠛⠶⣿⣾⣋⠁⢙⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⠁⠀⣰⣿⣷⡇⢸⠀⠻⣷⣶⣦⣤⣥⣀⣤⣤⣶⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⣿⣿⣿⣿⣤⠀⣤⣙⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⡇⠘⣻⣿⣿⣿⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣤⣀⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠻⢧⠺⠟⣿⡿⠿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠗⠀⠀⠀⠀⠀⠡⡐⠆⡄⡰⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣊⣲⣿⡇⠀⣉
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠍⠹⡑⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⢸⣑⣿⠄⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠁⢰⣶⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠒⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠰⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻⠀⠀⠸⡇
⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠙⠃⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠉⢀⠀⠀⠀⠀⣤⣟⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠐⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⠀⠛⠃⠀⠀⠀⠋⠿⠀⠐⠈⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠱⡆⣾⠀⡠⠀⠺
⠀⠀⠀⠀⠀⠰⠂⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠹⣿⣠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠠⠦⠒⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣠⡇⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⢀⠀⡀⠀⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣢⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠀⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠒⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠁⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠊⠀⠁⠀⠀⠀⠀⠰⠤⠀⠔⠃⠀⠐⢄⠀⣀⡀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠⢄⣀⠀⠒⠀⢄
⣀⣀⣀⣀⡀⢀⡀⠤⠤⠤⠤⠄⠀⠀⠁⠒⠒⠒⠒⠒⠒⠐⠒⠒⠂⠙⠛⠲⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠤⠂⠈⠙⠉⠉
⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠈⠉⠉⠁⠉⠁⠂⠀⠁⠀⠀⠢⠄
⠀⠀⠀⣴⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠄
⠤⠶⠚⠛⠃⠑⠂⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠀⠀⠰⠶⣤⠠⠴⠚⠈⠉⠁⠀⠈⠁⠈⠉⠂⠀⠀⠀⠀⡈⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠤⠤⠒⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠙⠛⣛⡋⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⠄⠤⠒⠒⠂⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠰⣾⣿⠟⠀⣿⣿⣿⡄⠀⠀⠤⠀⠐⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠠⠀⠛⠛⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠖⠒⠚⠯⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⣀⣤⣴⣀⣠⣤⣄⣤⣤⣤⣴⣶⣶⣦⣠⣰⣄⡤⣼⣗⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⢠⣶⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣿⣿⣿⣿⡟⢃⡒⠙⠪⣇
⠀⠀⠀⠀⠀⠀⢲⣄⣀⡾⢁⣤⣠⣶⣯⢻⡋⠰⣿⣿⣿⣿⣿⡿⣟⣉⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⣦
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣖⢿⣿⣿⣿⣋⣠⣶⣧⣹⣿⣿⡿⠿⡷⢿⣿⡶⣿⣯⡟⢛⣿⣿⣿⡟⠛⠻⣿⣿⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢻⣿⣿⣿⣇⢹⣿⣿⣿⣿⣧⣤⣶⣤⣿⣿⣿⣾⣿⡿⠋⢻⣿⣷⣤⣼⣟⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣷⡈⢃⣿⣿⣿⡈⣿⡿⠛⠛⠻⠿⠿⠿⣿⡿⠿⠿⠛⢳⣶⣶⡏⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡀⠻⣿⣷⠾⠋⠉⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠚⠉⣀⣀⣠⣤⡖⠀⣿⣀⣀⣠⣤⡀⠀⠀⢴⣶⣶⡦⢶⣽⣿⡴⠟⠿⠆⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠎⠠⠞⠛⠛⠋⠉⠁⠁⠀⠀⠀⠀⠉⠁⠊⠉⠁⠀⠀⠀⠠⠭⠏⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⢸⡃⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠦⢉⣡⣰⣆⡔⣄⣆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣼⣿⣾⠃
⠀⠀⠀⠀⢀⣤⡸⠇⡐⠀⠀⠂⠲⠀⠀⠀⠀⠠⣀⣸⠆⣘⢶⢿⠿⡦⡖⠞⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⢊⣡⣤
⠀⠀⠀⣰⠞⢉⡔⠊⣩⢀⠀⠠⠈⠀⠀⢀⣻⠧⣄⣸⠇⣼⣷⣿⡟⠁⣉⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠘⠿⠟⠁
⠀⠀⢰⠏⠀⢼⠀⣼⠦⠦⢤⠀⠀⡆⠀⠀⣿⡖⣳⡀⢐⢛⣻⣿⣿⣿⠛⠿⠘⠄⠀⠀⠀⠀⠀⣰⣾⣅⣦⣶⣤⡀
⠀⢀⡞⢀⡿⢁⣿⢋⣩⠂⠀⠂⠄⠀⠀⠀⠸⠿⣿⣤⣁⣨⢉⣩⠇⡛⠄⠀⠀⠀⠀⡤⠀⠀⣤⣿⣿⣿⣿⣿⣿⡏⡿⢰⡄
⠀⠀⣿⣿⣽⡟⣱⣟⠉⠀⠀⠰⠷⣄⠀⠀⠀⠈⠛⢿⣷⣾⣉⣵⣤⠣⣀⣴⣤⠎⠈⠀⠀⣶⣿⣿⣿⣿⣻⡏⡝⠁⠀⠘⣱⡆
⠀⠈⣿⣯⣾⣿⣻⣄⡄⢡⡄⠁⠀⠀⠑⠀⠀⢀⠤⠀⠁⠛⠩⠿⣧⠀⣧⢉⠂⢀⣦⣼⣿⣿⣿⣿⣿⡿⢿⣿⣀⠀⠀⠈⠉⠰
⠀⠀⠸⣿⣿⣿⠛⠝⠁⠀⠀⠀⠀⠀⠀⢠⣆⣈⡠⢀⣮⠆⠀⣠⠀⠈⣿⠀⢠⠀⢻⣿⣿⣿⣿⣿⣋⣘⠐⣿⡯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠠⣤⣀⡀⠀⢠⡀⠀⠿⣿⣿⣾⡏⡀⠀⣿⡇⠀⢸⢠⠏⣀⠈⣿⣿⣿⣽⣿⣿⣿⣿⡟⠃⢢⣔⠒⠦⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣷⣿⣶⠢⠄⠱⡀⢱⢰⣾⣿⣿⣶⢰⡏⠀⠈⣆⠜⢻⢟⣽⡿⠉⢏⡋⡄⠀⠀⢉⣳⣦⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⣦⡘⢳⠸⣾⣿⣿⣿⣿⣸⠀⢀⡾⠁⠀⡜⠻⣯⣴⠄⣸⢣⣇⢴⡳⡼⠞⠁
⠀⠀⠀⠘⣿⣇⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡍⢻⣿⣿⡇⣿⢠⡞⠀⠀⣼⢁⡤⡄⠁⠈⠉⠋⠙
⠀⠀⠀⠀⣉⣉⣳⣞⡠⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⣸⣿⣿⣥⣻⠟⠀⡄⠀⠇⢸⠿⠃⠀⣠⠁
⠀⠀⠀⠐⠻⠟⢁⣜⠁⠠⣀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠞⣿⣀⣃⣿⠀⣶⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢳⣴⡷⠒⠒⠂⣉⣀⡐⢀⣨⣿⣿⣿⣿⣿⣟⠠⠀⣀⣴⣿⢿⣿⣿⣿⣿⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠦⠾⠁⠾⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠏⢰⣿⣿⣿⢿⡜⣸⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⡿⠟⣿⣦⡿⠋⢀⣴⣦⣜⠷⣿⡟⣸⣃⣴⣾⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⢀⣴⣿⣿⠧⠂⢈⣉⣛⡿⡆⢿⢹⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠹⢿⣿⣿⢰⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢆⠤⢀⡀⠀⠀⣀⣘⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠢⢌⠓⡄⠀⠀⠈⠉⠙⠒⠤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡄⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠊⠩⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠉⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠲⠲⠛⠁⠀⠀⠀⠀⠀⣇⢉⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠦⠄⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⣀⡤⠖⠋⠘⣇⠀⠀⠘⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⣶⠲⣟⣉⠁⠀⠀⠀⠀⢹⡀⠀⠀⢧⡀⠀⢳
⠀⠀⠀⠀⠀⠠⡀⠀⠈⠷⣿⠾⠛⠁⠀⠀⠙⠂⠀⢀⡀⠀⠀⠀⠈⠳⣄⡀⢸⡃⠀⠀⠀⠀⣧⠀⠀⢸⠑⣼⠙⠇
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣀⡀⠀⠀⠉⠛⣻⡟⠀⠀⠀⠘⣆⡶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠄⠚⠋⠀⠀⠀⠀⠘⠃⠈




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

⠀⢠⠖⠉⠙⠢⣄⠀⢀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠴⠊⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢠⠃⠀⠀⠀⠀⠀⢱⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢣⣀⣀⡤⠤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠈⠗
⡇⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠃⡔⠢⠱⠀⡇
⡇⠀⠀⢀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠱⣑⡴⢁⣏⠔
⢇⢀⡔⠁⡇⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠈⠣⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡒⣊⡡⠊⠁
⠈⠉⠀⠀⡇⠀⠿⠿⠃⡠⠒⠂⠐⠒⢄⠀⠿⠿⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢳⠀⠀⠀⢰⠁⢶⠀⠰⠆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠳⢄⡀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⢦⡀⠀⠀⡄⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠑⠲⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⡇⠀⠀⠀⡼⠉⠉⠉⠉⠉⠉⢏⠉⠉⠀⣿⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⡸⢧⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠻⡀⠀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠤⡀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⢳⠤⠓⠒⢘⠃
⠀⠀⢀⣀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢎
⢀⣀⢅⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡀⠀⢀⡀
⠈⠁⠈⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠿⠂⠈⠈⠙⣼
⠀⠀⠀⠀⡷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸
⠀⠀⠀⢠⠁⠘⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠼⢁⡰⠖⠋⠉
⠀⠀⠠⠃⠀⠀⠈⢢⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⣀⣀⡠⠔⠊⠁
⠀⠀⡇⠀⠀⣀⡠⠄⠓⡄⠀⠀⢀⠧⠤⠀⣀⣀⣀⠀⡇⠀⠀⢀⠾⠓⠉⠉⠙⡀
⠀⠀⢆⢀⣏⠀⠀⠀⠀⢰⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠆⠀⢀⠎⠀⠑⠢⢄⡀⠐⣄
⠀⠀⠀⠉⠛⠁⠀⠀⠀⠈⠑⠢⣀⢈⣦⡀⠀⠀⣴⡉⢀⠴⠃⠀⠀⠀⠀⠀⠈⠂⢬⣧⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢤⠤⠀⠀⠀⠠⠤⣤⣀⣤⣤⡀⠀⠀⠄⠀⠀⠀⠤⠄⠀⢀⣀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣶⣷⣿⠶
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣟⣽⣭⣒⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡿⡍
⠀⢀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣘⣨⣿⣊⣻⣽⣍⣡⣤⡄⣠⡶⢾⣷⣀⠀⠀⠨⡯⠃⠀⠀⠀⠀⣀⡀
⠀⢈⣤⣀⣀⡈⣉⠛⢿⣿⠿⣿⣿⣿⡏⣽⡯⣻⣿⣿⡿⣛⣛⣛⣶⠮⠵⢿⣿⠋⢉⣐⣿⣿⡗⠂⠈⠉⠉⠛⠃
⠀⢠⣤⣤⣤⣉⣩⣉⣒⣶⣾⣿⠿⠿⠇⠻⠓⣻⣟⠛⠛⠛⠛⠋⠛⠂⠀⠸⠿⠿⠿⢿⣻⣭⣽⣤⣤⣤⣄⣠⡄
⠀⠘⢟⡛⠋⡉⠉⠉⠀⣤⣴⣶⠀⠀⠀⠀⠀⢹⣿⣥⣤⣴⢤⠶⠒⣶⣤⠖⢠⣤⡄⢠⣽⡿⠛⠿⠿⠟⠛⠛⠃
⠀⢠⣾⣷⣶⣷⣴⣷⣾⣌⠻⣇⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡈⣿⣿⡇⣶⠀⣿⣷⡆⢁⣾⣶⣮⣠⣤⣠⣦⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠦⡤⢼⠄⠀⠀⠀⠙⠻⣿⣷⣇⡷⢹⣿⣤⣿⣭⣿⣬⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣄⣀⣀⣹⣿⣀⣤⣾⡄⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣟⣿⣻⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠛⠋⠉⠉⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣴⣿⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⣿⣤⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣐⢻⣿⣿⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⣤⣤⣤⣼⣿⣷⣶⡄⠉⠁⢀⠀⠀⠀⠀⠀⠀⢀⡸⢿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣦⠀⠶⠈⣇⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣻⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⢧⠀⡄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⣻⣿⣿⠀⠀⠀⡄⠶⠶⠂⠀⠀⠛⠁⢸⢇⡇⢸⣿⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⢏⡼⠁⢸⡿⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠲⠾⣿⣿⣿⣿⠃⠀⣼⡃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠷⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣠⣾⠗⢠⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠉⢷⣤⡀⠉⠀⣤⣬⣭⣿⡿⠟⣁⠴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣿⣦⡀⠈⢻⣿⣦⣄⡀⢁⡐⡦⠖⢈⣤⠞⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠈⠁⢹⠍⠙⠻⠷⠤⣤⠤⠤⡤⡽⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠉⠁⣲⠐⢎⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠃⠀⠀⠱⠄⠀⠀⠀⠀⢠⣾⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠻⣿⡿⠏⠀⣀⣀⣤

⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⡄
⠀⠀⠀⠀⠀⠀⢠⠄⠈⢄⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠛⠫
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠐⠀⠀⠴⠋⠀⠠⠀⠀⠀⠠⠄⠤⠄⠻⣿⣿⣿⡇⡀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠑⠀⢄⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠉⠡⠂⠁⠀⠀⢰⣿⣿⣿⠃
⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠉

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣷⣶⣦⡀⣦⣀⢀⡀⠀⠀⠀⠀⠀⢼⣿⢘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣴⣦⡀⠀⠀⠀⠀⣠⠸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⡗⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢟⣵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⣿⢾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⢎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⣭⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢸⣿⣿⡟⣿⣿⣷⠀⠀⢸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣼⣿⣿⢠⣿⣿⣿⠀⠀⢸⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠿⠟⠿⠛⠛⠛⠛⠿⠅⠛⠿⠀⠒⠈⠛⠈⠓

⠀⠀⠀⠀⠀⣀⠀⠗⡀⠈⠀⠀⠀⠀⠀⠠⣠⣤⣤⢦⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⡄
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢐⠓⠊⠨⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⢎⠰⠈⡟⠉⡵⡄⠀⠀⠀⠀⠀⠀⠀⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⠢⣤⠤⠔⠉⠀⡀⠀⠀⠀⠂⠟⢳⡋⠛⣲⣾⠁⠀⠀⠀⢠⠊⠵⠇⢪⠓⠂⢑
⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠎⠀⠀⠀⠀⠀⠀⠑⠂⠤⣀⡀⠤⠊⠀⠀⠀⠀⠀⠲⠦⠉⠙⠀⠁⠀⠀⠀⠀⠈⠂⠤⠠⠛⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⢀⠀⠀⠀⠀⠀⠀⠀⣁⢓⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠈⠤⠀⢀⡦
⠀⠀⠀⠀⠀⠈⡸⠶⡇⠀⠀⠀⠀⠀⠀⠢⠜⠫⠙⣉⣃⠖⠀⠀⠀⠀⠀⠀⠘⢃⡀⣄⣀⠀⠀⠀⠀⠦⠊⠀⠉⡉⢢⣀⡠⠀⠀⠀⠰⠃⠀⠀⠈⣄⡀
⠀⠀⠀⠀⠓⢺⠀⠀⠐⠂⠀⠀⠀⠀⠈⢈⠃⡉⢰⡈⡐⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠂⣸⠉⠀⠀⠀⠀⢠⡀⠀⣠⡟⡠⢤⡱
⠀⠀⠀⠀⠀⠀⠁⠐⢀⡠⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠬⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠿⠃⠀⠀⠀⠈⠓⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠣⡊⣉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⢀⡜⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠐⠶⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⣀
⠀⠀⠀⠐⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⡡⠀⠀⠀⠀⢺⠮⣿⢿⠆⠀⠀⠀⠀⠀⠀⣢⣄⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢛⣬⣇⣐⣨⣻
⠀⠀⠀⠠⡀⠀⣠⠶⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢜⢎⣷⡦⠀⠠⠀⠀⠀⠀⢰⣿⣿⣳⣦⣀⠴⠋⠀⠀⠀⡈⣿⢫⠞⢁⠏⡠⡅
⠀⠀⠀⠀⠈⠉⠛⢄⡑⠖⠊⠀⠀⠀⠀⠀⢀⣦⣄⡀⡠⠃⠀⠀⠀⠀⠀⠣⣳⢟⡅⠨⠀⡀⠀⠀⠀⠀⠑⢿⣿⣿⠿⠒⠀⠀⠀⠀⠀⠈⠻⠴⠚⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠜⢂⠍⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠾⣷⣶⣤⠀⠀⠀⠈⢢⡀⠀⠀⠀⣤
⠀⠀⠀⠀⢆⣤⣶⣶⣆⡘⠂⠀⠀⠀⢠⡄⢠⣀⣀⣠⣿⣀⡀⠀⠀⠀⠀⢘⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡻⣿⣇⠀⠀⢀⡀⠃⠐⢓⠚⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠄⠀⠀⠹⡀⠀⠀⠀⠀⢀⣀⣀⣠⡬⣿⠿⣿⡾⠏⠀⠀⠘⡀⠀⠁⣴⠋⠉⠲
⠀⠀⠀⠻⣿⡿⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠠⣠⣀⣠⣀⠇⠀⠀⠀⠀⠈⠈⢷⣼⣀⣼⡷⠃⠀⠀⠀⠀⠀⠀⠒⠚⠻⣄⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣶⣷⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢰⣇⠀⣴⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⢠⣶⣾⣿⣿⡍⡅⠀⠀⠀⢠⡀⣼⣟⣩⣁⡀
⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⢿⣿⣿⣿⣧⣗⠀⠺⣿⣄⠀⢹⣿⣟⣋⣠⡐⢀
⠀⠀⣴⡈⢤⠄⠀⠀⠀⠀⠈⠁⠀⠉⠀⢻⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣟⣁⣀⣿⡟⢩⢹⣿⣟⣟⠩⢉⣯⡤⠆
⠀⠶⠿⣭⡤⠶⢖⠉⠉⠉⠁⠈⠃⠋⠉⠙⡛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠋⠀⠈⠙⠛⠛⠐⠊⠐⠀⠉⠀⣀
⠀⠀⠀⡔⣤⠡⢄⠀⣤⣀⡠⣤⠀⡠⠤⢠⢄⢄⠀⠀⠀⢀⣠⡄⢠⢀⠀⠀⠀⠠⣀⢀⡀⢀⡀⡀⡀⢀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⢹⡶⡌⢱⢛⠀⣿⡌⠉⣢⡽⢇⣦⡏⢀⢜⣮⣆⠀⢇⢁⠡⣉⣬⢠⣴⡧⣌⡅⣚⡤⣡⡶⠗⠠⠄⠀⠵⢹⣅⡠⡄
⠀⠀⣹⣽⣇⣷⢡⠲⣦⡆⢼⡣⡇⣻⡀⣧⠨⠞⢸⡟⠻⣤⡘⢹⣫⡍⣊⡡⢿⢳⣼⠽⢿⠾⠃⢜⡋⠦⠟⠃⢨⣏⣀
⠀⠀⢸⡇⡏⢾⢸⡟⢫⡇⢻⡟⣇⢺⣆⡟⢻⡯⢱⡏⠿⡳⢻⢾⣷⡄⣿⢠⣬⡀⢸⡷⣺⣧⡴⣦⢶⡖⡐⢺⣫⠌⠐
⠀⠀⣹⣏⡉⣺⠘⠒⢸⡇⢤⠮⣯⣼⠇⣷⢸⣋⣸⠎⠑⡟⡴⠛⢻⠂⠿⠠⠾⠉⣸⣏⠟⣻⣐⡗⣻⡿⠆⣶⠡⡆
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠚⠷⠤⠤⣭⣤⣄⣹⡅⠉⠈⣿⠀⠉⠃⣛⠄⠣⠀⢸⡇⢀⣹⣎⡟⣹⠛⠁⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠒⠒⠦⠿⣀⣀⡀⢸⡇⠀⠀⢸⡏⠈⠐⠋⡟⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠓⠒⠓⠠⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠖⡒⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⡈⡆⠍⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠄⠐⡀⠀⠀⠀⠀⢀⡊⠐⠁⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠀⠸⠀⠀⠀⠠⠈⡉⠰⠃⠰⠆⠘⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠘⠁⢰⠂⠀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⣀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠘
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠂⠀⠀⣁⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣯⡀⢋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⢱⡖⠂⢀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⢰⠀⠙⣄⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠰⠙⢘⡠⢇⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠅⠘⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠷⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠠⢀⠹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠝⠀⠒⠂⢈⡉⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⡀⢒⣾⠀⢤⡀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠠⠐⠂⠌⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠸⠀⠀⠀⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡉⠤⠈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣀⡀⠄⢀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠐⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠓⠠⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢼⡤⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠉⠄⠡⣄⡗⠋⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡐⠀⠛⠛⠈⠀⠐⡽⠦⣀⣀⡀⠀⡀⠈⣃⢀⠊⢉⢧⡀⢁⠨⠧⡀⠀⡀⠈⠀⠀⠀⠀⢀⠀⠀⣾⠛⠂⢤⡠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠉⣈⠀⠀⠿⠀⠀⠐⠲⠀⢀⠀⠐⢌⠂⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠂⡂⢀⡍⠀⠠⠋⠈⢠⠠⡂⠌⠐⠀⠀⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢐⠡⠀⠐⠁⠄⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡜⠀⠀⠀⠀⠂⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠒⢒⡄⠈⡄⠀⠀⠀⠀⠀⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠓⠒⠉⢀⠄⢰⠀⠀⠀⠀⠀⠠⠀⠀⠅⡀⠀⡀⠀⠀⠀⡀⠀⢊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠀⡀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⣀⣀⡀⠄⠀⠈

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣿⡟⣦⠀⠀⠀⠀⢠⣀⣸⣿⣿⡏⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣿⣿⣧⡿⠿⠓⠒⠀⠀⠙⢷⣿⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⡧⣶⣂⠆⠀⠀⠀⠀⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠉⠉⠉⠉⠉⠙⠉⠹⣿⣿⣿⡟⠋⠀⠻⠿⠇⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠳
⠀⠀⠀⠀⠀⢀⣴⢠⡎⠁⠀⢠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢰⡛⠠⣾⠠⡷
⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣾⡄⠙⣦⣄⠀⠀⠀⠀⠀⢿⣿⠷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⡄⠹⢿⣷⣶⣶⣦⣶⣮⠙⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢿⣧⡀⠀⠀⠀⡀⢸⡁⠀⠀⠀⣺⣿⣿⣷⣜⠛⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣸⣿⣇⠀⠀⠈⣧⢸⡁⠀⠀⢘⣿⣿⣿⣿⡟⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⣿⣿⣷⣶⣄⣿⡼⣄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⣀⣿⣿⣿⣿⡟⠛⠿⢷⣷⡀⠀⣿⠿⠿⠟⢻⣿⡟⢘⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣼⢻⣿⣿⡟⠀⠀⠀⢸⣿⠇⠀⣿⠀⠀⠀⢸⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⠀⢻⣿⣧⠀⠀⠀⢸⣿⣷⠀⣿⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⣿⡀⠸⠻⣿⡄⠀⠀⠀⢻⣿⡀⡇⠀⠀⠀⢸⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣇⠘⢶⣿⡿⠆⠠⠄⢾⠉⢙⣧⣤⣤⣤⣼⣀⣤⣵⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠶⣿⡿⠟⠉⠁⠀⠉⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠦⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣗⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡤⣌⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠈⣣⠈⠃⠐⠂⠉⠉⠉⠉⠒⠁⠐⠃⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢒⣠⣤⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⢠⣴⢴⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠉⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⢤⢴⢶⠃⠀⠀⠀⢐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣬⠄⡄⠀⢠⠀⠤⠠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠲⠶⢺⡃⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡸⠀⠀⠀⢀⠈⡈⠀⠀⠀⣀⣀⣀⠀⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⡤⠐⢒⣾⣇⣉⣿⣿⣃⣀⣀⣲⡀⠘⡄⠀⠀⠀⠈⢆⡈⠊⠔⠕⠐⢐⡴⠃⣀⠀⠀⢈⡈⠁⠀⢀⣍⠩⢁⣄⢈⣩⣁⣀⣀⣈⠑⣂
⠀⠀⠀⠀⠀⠀⣿⠒⠺⡾⡧⢼⣟⠂⠤⠧⠶⢿⡇⠀⠈⣦⡀⠀⠀⠀⠈⢁⡒⠲⠒⣋⡠⠚⠀⢀⠠⠋⠀⠀⠀⠈⣏⡛⠀⣛⣛⣹⡇⠠⡿⣿
⠀⠀⠀⠀⠀⠀⢾⣍⣹⣟⡗⠲⢿⣉⣐⣛⣛⣻⣧⠀⠀⠂⢙⡢⡀⠀⢀⣀⠈⠉⠉⠀⡀⠀⡀⡀⡀⢸⠀⠀⠀⠀⣶⠄⢨⣭⡭⠷⣯⢉⣯⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠢⣤⢭⣭⠿⠟⠒⠀⠲⣄⡐⡠⠊⠔⠋⣽⣿⡏⠫⠨⠊⠌⠄⠂⠼⠀⢰⠮⠭⢁⣠⡴⡬⣿⣻⣷⢤⢷⠟⠚⠌⠚⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠇⣀⣀⣴⣳⡍⠙⠋⠛⠋⠍⠈⠝⠒⠶⠲⠖⠞⠋⠐⠀⠘⠗⠲⠲⠒⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠬⢥⠥⠶⠗

⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠤⠤⠀⠀⠀⠠⠀⠀⣀⡤
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠋⢢⣀⢀
⠀⠀⠑⠦⠬⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⣶⠆⣀⡀⠻⠁
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠈⠃⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠐⢺⢬⡜
⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⢠⣴⣞⣠⣄⠀⢠⣄⣀⡂⢀⡀⢀⣀⣤⣍⠀⠀⠀⠀⠀⣽⣿⠿⠻⠿⠶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣯⠌⠀⠀⠠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠈⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢧
⠀⠀⠀⣀⠀⢀⠀⠀⠹⣾⢤⣀⣈⢻⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⢀⠀⢈⣷⡀⢠⣄⣀⡀
⠀⠀⠈⠉⠈⠉⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⡄⠀⠀⢀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⣹⡿⠟⠿⢦⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣶⣶⣿⠟⠀⠁⠀⢉⡟⠉⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡛⠂
⠀⠀⡆⢸⠀⡆⡀⠀⠀⠚⠛⠛⠛⠛⠉⠙⢻⣿⣿⠋⠀⠀⠀⠀⣞⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⣄⣠⣼⣿⣿⣧⠀⠀⠒⠒⠶⠛⠀⣿⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣹⣿⣿⣿⡀⢰⡄⡦⠀⠀⠀⠉⢠⢜⣿⣿⣿⣯⣼⣿⣿⣿⠟
⠀⣀⣤⡤⠤⠤⢐⣒⣄⡨⣤⠤⠖⢒⣣⣬⣼⡭⢽⠛⠛⣿⣶⡶⠶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧
⢉⢩⣀⣤⢴⠞⠍⠉⢠⣦⣴⡶⠟⠉⣉⣡⣴⣶⡾⠟⢋⣭⣰⣤⣄⣼⣧⣯⣹⡟⣟⠛⠛⠉⠉⠉⠁
⠛⠛⠉⣀⣤⣤⠼⠚⠛⠥⣤⣴⣶⣿⠛⠙⡋⣠⣦⣼⣿⣿⠏⠛⠋⠉⠉⠀⠀⠀⢳⡝⡄
⣶⡞⡿⠿⠷⠶⠶⠶⢿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⡠⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠕⠆
⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠒⠀⠀⠚⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠀⠀⠣⣄⠀⠀⠐⠠⣾⣡⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠈⠀⢳⣦⡵⡈⠉⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠷
⠀⠀⠀⠀⠐⠀⠃⣀⠗⠁⢤⡍⡉⠋⠁⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⢰⣄⠐⠠⠄
⠀⠀⠀⠀⠀⣈⠋⠉⠢⣨⠂⠁⠁⠤⠐⠈⠑⠐⠀⠀⠀⠀⠀⠃⢀⡀⢀⣀⡤⠚⠙⠚⠀⢀⠃
⠀⠀⠀⠀⠀⠋⠀⠀⠈⠁⠇⠀⠀⢀⣴⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠉⠙⠇⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠤⢤⡀⠘⡤⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⠀⠈⣿⣗⣼⠏⠉
⠀⠀⠀⠀⠀⠀⢀⢈⣄⠨⠇⠠⢏⡀⠕⠀⠀⠀⠀⠀⢠⠂⠀⠀⡀⠀⠖⢤⢐⡯⠁
⠀⠀⠀⠀⠀⠐⠏⠀⢙⠉⢢⡌⠈⢱⡄⠀⠀⠀⠀⠀⠈⠁⠀⠄⣠⠚⠁⠉
⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠴⠛⠦⠀⠀⠀⠀⠐⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣬⠉⠉⣷⣦⢶⣄⢊⡀⢳⡀⠀⠘⢿⣷⢀⣴⣿⣿⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⣀⣰⣧⠛⠃⠀⠹⠛⠻⠛⢁⡶⠆⠹⡷⡞⠋⢁⠿⢁⣨⡄⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠒⠛⠛⠁⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠘⢰⣤⣤⣷⣿⣿⡇⠀⣺⣤⣤⡀⠀⡄⡀⠀⠀⡠⡀
⠀⠀⠀⠀⠄⠀⢀⠢⠷⣦⣀⠀⠉⠙⢶⣤⣿⢃⡁⣩⣏⣿⣿⢿⣿⣅⣈⣿⢉⣐⢾⢟⡄⡀⣀⠁⠠⣄⠀⠈⢀
⠀⠀⠀⢄⠠⠴⠎⠃⠀⣽⣈⣄⣀⠀⠀⢍⡉⣲⣿⣿⡿⣷⣿⣿⣿⣿⣷⣿⠁⢸⡃⣤⣹⣿⣿⡴⣶⢋⢀⣀⡆
⠀⠀⠀⢸⠇⡄⠙⠃⠀⢹⡟⢻⣿⣷⠰⢾⣴⣿⣿⢻⣷⣿⣿⣿⣿⢿⣿⣿⣧⢘⣿⢙⣩⣿⣿⣿⣿⣷⣔⠸⠓
⠀⢰⠀⠰⠀⡇⠀⠀⠀⣾⡆⢸⡟⢙⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣍⣸⡿⠀⢀⣿⣿⣇⣼⣶⣛⡑⠓
⠀⢸⠀⣂⢸⣇⣀⣴⣴⣿⡇⢹⣴⣿⣟⣻⣖⣿⣿⣿⣿⢯⣽⣿⣿⣷⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘
⠀⢸⣁⠈⢘⡏⠛⠡⣭⢹⣏⢹⣯⣿⣿⣍⣫⢿⣿⣿⣿⢿⣿⠏⠉⠹⣿⣿⣿⣿⣿⣇⣿⣿⢋⣏⡴⠠⠆
⠀⠺⣿⢇⡐⡇⠀⠀⠠⣼⣟⣸⡏⣉⣽⠛⠉⠛⣻⣿⣿⣛⣿⣷⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠄
⠘⠲⡽⠊⠈⠃⠀⠐⠂⠙⣿⣿⡇⠀⢹⠀⠤⠶⠀⠰⠼⠿⣷⣤⡤⠄⢻⣿⣿⣿⣿⣿⣿⣿⠏
⢀⣠⣽⠏⠀⠀⠀⠀⠤⣿⣟⠋⠀⠀⢹⡀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠠
⢀⠽⡯⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⢀⣈⡄⠀⠀⠀⠶⠿⠉⠉⠛⠛⠛⠟⠛⠻⠿⡋⠙⠻⠿⣧⠠⠀⠀⠀⠒⠲⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⡟⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⢉⣻⣿⣿⣷⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣼⣿⣿⣿⡟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⣙⡻⣿⣿⣿⢰⡎⣦⠶⠟⢹⡇⢸⣿⣟⠶⢖⣷⡇⣿⣿⣿⡽⠗⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⢯⣬⣿⣯⢈⣿⣿⣤⠤⡎⠀⠈⢹⡟⣾⢟⣿⡱⣿⣿⣽⡽⢇⣶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣶⣶⣝⣿⣯⠚⡛⠁⠀⠀⠀⠀⠸⠀⠈⠁⠈⢉⠙⢿⣿⡻⠿⠿⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢈⢸⣿⣤⠆⣴⠺⠀⠀⣀⣠⣤⢀⣀⡀⡞⣢⡀⣨⣿⡥⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠻⢿⡇⠼⣿⡷⢂⡳⠷⠋⠙⠈⣿⠁⢻⢟⠷⢺⡿⠳⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣾⠁⡘⠍⠠⠖⠉⠀⣤⣠⣄⠈⠲⣄⠈⣥⣀⢻⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⢠⡅⠸⠃⠀⠆⢀⡴⠋⠀⠉⠉⢷⣤⠹⡆⢨⡋⠸⣧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⢠⣖⡁⠀⠀⢊⡴⠖⠛⠛⠓⠦⡀⠄⢸⡼⢡⠀⣿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠈⠙⠁⠀⠠⠸⢶⣿⠇⠀⣿⡷⠾⢤⠀⠁⢿⠂⣿⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⡆⠁⣤⠀⣶⡘⠆⠀⠀⠀⠈⠀⠘⣾⠆⢀⠎⠠⣿⡂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠁⣷⣿⣿⣇⣀⣵⣶⣶⠾⠷⣶⣶⣾⡟⣻⡙⣿⣿⡉⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠠⠾⠿⣛⣿⣟⣌⡉⠻⠶⠶⠏⢘⣰⣎⣛⣻⣿⢥⣉⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⣿⡳⣟⠰⠺⠿⣿⣿⣿⣄⣠⣶⣿⣿⣯⣋⣱⠄⣸⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣿⣟⠓⠂⢶⣿⡿⣿⣿⣿⣿⣿⣿⣮⡋⣩⣿⡿⣃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠊⢻⣿⣷⣷⣾⣿⡃⢺⡇⣹⣝⣏⣲⣶⢿⣿⢖⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠷⢼⣿⠻⠿⣿⣷⣎⣿⣿⣿⣿⣿⣿⡟⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡿⣷⣶⣬⡿⢿⣿⣫⣿⣧⣿⡷⠄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⠛⣿⢿⡇⠈⣿⣿⡿⠟⢿⡯⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠏⣽⡇⢰⣿⣻⣃⠀⢀⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⠀⣀⣿⡇⠰⢶⡿⠯⠀⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⢻⣿⠀⣸⣿⠗⣶⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠿⠿⠷⠿⠿⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠄⠤⢤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣤⠎⠩⢞⠀⠅⠉⠒⠠⢬⣃⡉⠉⣹⠋⠐⠤⡀
⠀⠀⠀⠀⣚⠿⠦⠁⠡⠀⠋⠓⢒⠒⠃⠐⠌⠉⡁⠀⣤⡀⠈
⠀⠀⠀⢼⡛⣠⢡⠰⡀⡔⣲⠀⠀⢀⠬⣤⠀⠀⠀⠀⠊⠀⠀⠐
⠀⠀⠀⠈⠁⠁⠉⠷⠃⠂⠠⢸⣆⣁⢠⠰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠄⣠⠖⢀⡴⠋⣠⠞⠁⣠⠞⠁⣠⠞⠀⠀⡠⠂
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢤⠀⠀⠁⠀⠀⠉⠛⠁⠀⠀⠀⠀⢀⣠⣀⠀⠀⠉⠘⠁⠚⠀⠞⠀⠴⠋⢀⡜⠁⢀⡔⠁⢀⠔⠁⠀⢀⠘⠁⠀⢀
⢀⠀⠀⠠⣀⣠⡄⣤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⢦⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠜⠀⠀⢠⠂⠀⠀⣠⠋
⠈⠐⠱⣶⠟⠁⠀⠹⠛⣶⠖⠲⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⠋
⠀⠀⠠⠿⣧⣄⣀⣾⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢣⡿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠂⠀⠉⠉⠉⠛⠃⠦⠤⢯⣄⣀⡀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⢀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠃
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣤⣶⣿⣠⣴⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢱⣿⣿⣿⡏⢘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡼⢿⣿⣿⡟⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡦⠀⠀⠀⠀⢀⣿⣿⡇⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⡟
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣴⡆⠀⠀⢻⡿⢻⣦⠀⠘⠃⡄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠛⢠⡀⠀⠀⠀⠀⢨⠢⠀⠀⠀⠀⠀⢄⠑⠶⠀⣰⣦⡀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣦⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣼⣿⣿⣧⠀⡇⠀⠀⠿
⠀⠔⡀⣿⣿⣿⣻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢧⢹⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡖⡋⠿⣿⠏⠀⡇
⠀⠀⠀⢿⣿⡟⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠈⣎⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡆⠁⠀⢸⠀⠀⡇
⠀⠀⠀⢸⠁⠁⠀⠀⠀⢀⡘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢹⡄⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⢀⡄⢰⣿⡄
⠀⢰⠀⢸⡄⢠⣤⠀⠀⠘⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣤⡌⣧⠀⠀⣮⠛⢀⠀⡀⠀⠀⠉⠀⠀⢹⡌⢆⢠⡄⠈⡗⢤⡀⠀⠀⠀⠈⠀⠾⠛⠏
⠀⢸⡇⢸⣷⣿⣿⠀⠀⠄⠀⣶⠈⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⣄⢹⡄⠔⠉⠀⡏⠀⠛⠀⢀⣀⡤⠀⢸⡇⠘⡎⡇⢈⡇⡀⠳⡄⠀⠀⠀⠀⠂
⠀⠀⢻⣿⠊⢻⣿⣶⣿⢟⣿⠃⠀⠀⢀⠀⠈⠙⢿⡉⠉⠟⣇⠀⢹⡎⣿⡆⠀⣸⡇⠀⠀⠀⠐⠻⠆⠀⠀⣷⠀⢻⣷⢰⡇⢡⠀⢹⡄⠀⠀⠀⠀⠀⢀⡔
⠀⠀⢸⠸⡁⢹⡟⠉⣙⣯⣿⣀⡀⢀⣸⠀⠀⠀⠀⡿⣄⠀⣿⠀⠀⣷⢹⡁⠀⡿⠀⠀⢠⠀⠀⢀⠄⠀⢀⣿⣀⢈⣿⣾⡇⢸⣤⠀⢻⡀⠀⠀⠀⣠⡾
⠀⠀⣼⠀⣇⣹⣿⣿⢿⣿⣿⣯⠛⢉⣿⣶⣾⣷⡄⢹⣿⣷⣼⡆⠀⢸⣾⡇⢰⡇⠀⠀⣴⠀⠀⣼⠀⠀⠈⢻⡙⠛⢿⣿⡇⢸⡿⠀⠈⣧⠀⠀⠾⣿⠃
⠀⠀⣿⡄⠹⡇⢸⢹⡀⢟⠛⢿⣿⠾⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⣷⣿⢸⡇⠀⣀⠃⢀⣼⣃⣴⠏⠀⣿⡿⡄⣸⣿⡇⢸⡇⢡⠀⢹⡇⠀⢠⡟
⠀⢠⣇⡇⣦⣇⢸⡇⣷⠈⢳⡀⣷⠀⢸⣿⣿⣿⡿⠀⣿⣿⣿⡇⢠⠀⢹⣹⣼⠀⠀⢹⢰⣠⡿⠻⣇⠀⡜⢹⡇⢳⡏⢹⡷⣾⣇⠈⡆⠘⡇⣧⣾⠇⢰
⠀⢸⠉⡟⣿⣿⢻⣷⢸⣵⣾⣷⢸⣆⣼⣷⣽⢻⡇⠀⣟⡏⠈⣇⢸⠀⢸⣿⣿⣶⣿⡿⣿⣿⠿⣷⠿⣸⠁⢸⡇⢸⣇⢸⡇⣿⢹⠓⢷⠀⡇⣿⣹⡀⠀⡇
⠀⣿⠀⣿⡇⢿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⢸⡇⠀⣿⡇⠀⣿⢘⡇⢘⣿⣿⣿⠙⣇⢻⡏⣰⠋⢀⡏⠀⢸⣁⣸⣿⢸⣇⣏⢸⠀⢸⠷⣟⡿⡿⠃⠀⢱
⠀⣿⠀⣽⣧⣼⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⡇⠀⣿⣧⠀⣿⠸⡇⢸⡿⣿⣯⣠⡏⣼⣡⠏⠀⢸⠃⡤⢾⠏⢸⣿⣿⣿⣿⣸⠀⠈⡇⣿⣇⡿⣼⠀⢸⡀
⠀⣿⢠⣿⣏⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⡇⢠⣿⣿⡀⢿⣐⣇⢸⡇⣿⣿⣿⢻⣿⣾⣦⣦⣿⠟⠀⢸⠇⢸⣿⣿⣿⣿⣿⣢⠖⡏⣿⣿⡇⢹⡀⠀⡇
⠀⣿⣤⣿⣿⢸⡇⣿⡏⣿⣿⣿⠛⣿⣿⣿⣼⣿⣿⣾⣿⣿⣧⣿⣿⣿⢸⡆⣿⢻⣿⢸⣿⣿⣿⣹⣿⣄⠀⡾⠀⠘⢿⣿⣿⣿⣿⡅⠀⡇⣿⣿⣇⠸⡇⠀⡇
⠀⣿⡟⣻⣿⣸⡇⣿⣷⣽⣿⣿⣠⣿⣸⡟⠈⡿⡿⡟⢻⠃⣟⢻⠛⡋⣾⡄⡇⠀⣿⣼⣿⣿⣿⣿⡇⠀⢀⡇⠀⡇⢸⣿⣿⣿⠘⣧⠀⡇⢹⣿⣿⠀⣧⠀⣷
⠀⣿⠁⢹⣿⣿⣷⣿⣿⠿⣿⢻⠿⣿⢹⡇⠀⡇⣿⡇⢸⢰⢸⣸⠀⡃⣿⡇⡇⠀⣿⣿⣿⢏⡟⣼⠁⡀⢸⡇⢠⣧⠿⣿⣿⣿⠀⠀⠀⣧⢸⣿⣿⠀⣿⠀⣿
⠀⣿⠀⢸⣿⡿⡃⢹⡿⣆⣿⢸⠀⢿⢸⡇⠀⡇⣿⠃⢸⠸⢸⣿⠀⠁⢸⡇⡇⠀⢻⠃⡇⣾⣷⣿⣟⡉⢹⡇⢸⣿⠀⣿⣿⠉⠀⠀⠀⣿⡿⣿⢻⠀⣿⠀⣿
⠀⣿⠀⢸⢹⡇⠀⣿⡇⠀⣿⢸⠀⢸⢸⡇⠀⡇⣿⠀⢸⡇⢸⣿⠀⠀⣿⣷⡇⠀⢸⠀⡇⡿⠋⣼⠈⠃⢸⡇⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⠇⣿⢸⠀⢻⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡾⠋⠉⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠛⠭⠀⡀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣤⡀⣠⠞⠃⠀⠉⣉⣉⣉⣀⣤⣿⣦⠀⠀⠀⠀⠠⠀⠀⠙⠿⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⣠⠀⠀⢠⣿⠀⠀⠀⠙⠷⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣿⣦⣤⣾⣿⣿⣿⣟⣻⣟⠂⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⣷⠤⢀⠆⢀⠀⠸
⠀⠀⠀⠀⠀⠀⢠⠴⣶⣿⣤⣤⣾⠛⣻⠿⠿⠧⠞⠛⠈⣥⡤⠾⠷⠶⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣾⣿⣿⣿⡶⠛⣶⡟⠀⡀
⠀⠀⠀⠀⠀⠸⡄⢀⣾⣿⣿⣿⣿⡄⠀⠀⣀⣀⣴⣶⣾⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠛⣿⠟⣷⣸⣷⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢻⡟⢫⣷⢩⣿⣿⡿⣦⣸⢿⣍⣭⣽⣿⣿⣿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠗⠒⠒⠿⣿⣿⣿⣤⣠⣶⣄
⠀⠀⠀⠀⠀⡄⣠⣽⣧⣼⣿⣯⡥⣿⣾⣿⣧⣿⣿⣿⣿⠟⠛⠟⢷⣶⣤⣶⣶⠂⠀⠀⢀⠀⠀⠲⠀⠠⠙⢀⣸⣶⣶⣿⣿⣿⡛⠛⠛⠛
⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⠿⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣧⣸⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠙⠻⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⢉⣭⣍⢩⣭⣭⣭⣝⠓⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣐⣿⢷⣿⣿⣿⣟⣿⣽⣿⡧⣿⣿⣶⢆⣉⡓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⣾⠁⣼⣿⣟⣿⣿⣷⣾⣿⡿⣿⣼⡿⣷⢷⣿⣿⣞⣯⣻⣷⣦⠍⠲⣄
⠀⠀⠀⠀⠀⣼⣿⡆⠸⣿⣿⢿⣿⣿⣷⣾⣿⣾⣿⡋⠀⠀⢭⣻⣋⣽⣿⡷⣿⣿⡷⣈⠱⣄
⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⢶⣿⣿⡷⣿⣿⣿⣿⣿⣾⣷⣞⣿⣯⡿⠾⢷⣾⣭⣽⣚⣲⠷⠘⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠙⠿⣿⣿⢟⣽⣾⣿⣿⣿⢿⠿⢁⣼⣮⣄⠱⠀⢉⠝⢿⣷⠀⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣘⣽⣿⣿⣿⣿⣍⠀⣥⣽⣿⣿⠆⠀⠀⠂⠀⠉⢾⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⡟⠁⠀⠡⠄⠀⢀⣠⣷⣶⣾⣿⠿⠷⢶⣦⣄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⠶⡒⠀⣉⣻⣷⣾⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⣭⠲⠆⣘⡃⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⡿⣽⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢏⣌⣭⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢶⡝⠷⣿⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡦⠀⢠⣴⣶⠒⡄⠙⣿⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡦⠀⠀⠀⠈⢠⠀⠀⠀⡏⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⡀⠀⡀⣠⢾⠈⠃⠀⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⣙⠙⠻⢿⣿⣿⣿⣽⣿⡴⠃⠀⢀⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠉⠻⣿⣿⢟⣣⣞⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⠿⢿⣿⣿⢿⣿⣾⣤⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡋⠀⡁⠐⠀⠄⢀⢀⡉⠁⠙⣿⣿⣧⣄⣤⣤⣠⣀⠙⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⠈⡀⢈⠠⠀⢀⣤⣤⡘⢿⣿⣿⣿⡿⢥⡉⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⣆⣤⣴⣾⣿⣏⠠⣶⢽⣿⣿⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⢶⠶⣶⣶⠶⢶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡿⣛⣪⡿⣟⡋⢛⢋⡉⢉⠉⡛⠛⠛⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⡿⢿⡿⣶⣿⠁⠀⢈⡙⢋⣳⣶⣶⣤⣩⣵⠤⠀⠘⠙⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⣿⡇⠀⠀⠀⠈⠀⣿⣿⠁⠀⠠⣌⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢀⣼⣯⣿⣷⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠂⣠⣮⡿⠐⠀⠀⠀⠀⠀⠈⢿⣷⣾⣿⠿⠟⠛⡉⠙⠏⣿⡇⠀⣀⡠⠀⣶⣞⡿⣿⣿⣿⠿⡶⣿⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⡅⢲⣀⣿⠇⣋⠀⣱⡀⠀⠀⠀⠀⢾⣿⣿⣭⣭⡷⢄⡨⣇⡠⣄⣿⣿⣿⠁⢠⡄⠀⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠠⢾⣿⣧⣤⣴⠟⣿⠁⠂⠙⠩⠳⣼⠇⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀⢀⣽⣷⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⢸⢛⣴⠳⠾⠀⢀⢠⣴⣿⡾⠋⢸⠆⢠⣷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣶⡛⢻⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⣿⠇⢸⣿⣿⣿⣿⣿⠇⡍⠁⠀⣿⠉⠉⠉⠉⠉⠉⠙⠻⠟⠛⠋⠉⠀⢻⣿⣷⣿⠲⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢼⣭⢽⣿⣦⣼⡿⠟⠉⠁⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠻⢷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠠⣠⣻⡿⠟⠋⠉⡀⠀⣀⡀⠀⠰⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠚⠿⢿⣿⣿⣿⢇⣀⣚⣿⣾⣷⣶⣦⣷⣄⣄⣤⣤⣶⣶⣿⡄⢉⣛⣏⣴⣶⣤⣰⣆⣼⣧⡙⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⠁⠈⠁⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⠁⠀⠾⠿⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠈⠂⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠛⠀⠀⢁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡀⠀⠀⠀⠄⠀⢀⠀⢀⡠⠄⠐
⠀⠀⠀⠀⣀⣁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⣠⡀⠀⠀⡀⠄⠀⠅⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠁⠀⠈⠀⠅⡀⠀⠀⠀⡀⠀⠶⣆⠰⠀⠲⠐⢶
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⡀⠀⠠⠂⠀⡀⠐⠀⠀⠁⠀⠀⠑⢦⡓⠙⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢠⠤⢤⠀⠀⠀⠙⠢⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠠⢀⠁⠐⠁⠀⠀⠸⠦⠼⠀⠀⠀⠀⠀⠈
⠀⠐⠁⠠⠂⠀⠓⠄⠀⢄⠀⠈⠁⠒⠀⠑⠀⠂⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠚⠂⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡠⠀⠄⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡤⢤⡼⠀⠀⠀⢲⡖⢲⡆
⠀⠈⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠂⠀⠀⠠⠄⠀⠀⣀⠀⠀⠂⠀⠀⠀⣿⣰⡆⠀⠀⠀⢸⢻⣼
⠀⢨⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠂⠦⠴⠂⠀⠀⠄⠤⠄⠤⠄⠀⠀⢐⠈⡅⠀⠀⠀⠀⠀⢻⣏⡅⠀⠀⠀⢸⢸⣷
⠀⢈⡅⡉⠁⠉⠀⠀⠀⠁⠠⠈⠩⠀⡏⢁⠀⠠⠀⠀⠀⠀⠀⣀⡤⠜⠙⠀⡇⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⢸⡟⢸⣇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠄⡐⠠⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⢒⠤⠉⢙⠀⠀⢀⠀⠀⣇⢀⠠⠀⠀⠀⠸⠑⠛⠒⠒⠀⠈⠉⠉⢉⡀
⠀⠀⡄⣀⠀⠀⠈⠀⠁⠀⢥⡀⢤⠀⡧⠄⠠⠖⠂⠀⠀⠀⠀⠈⠙⠀⠉⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⡍⠉⠉⠉⠀⠐⠂⠀⡀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⢈⠓⢧⢈⡂⡄⢠⡖⠍⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠩⣁⣨⡇⣨⡶⠈⡀⠒⠂⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡰⠐⡐
⠀⢠⡌⠉⡳⣈⣤⣾⠫⣀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⠘⠛⢙⠁
⠀⠀⡀⠈⢻⠷⠌⢶⠶⠘⣠⢅⣠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢻⣯⠏⠠⠁
⠀⠀⠉⠀⢲⠀⠀⠀⠁⢈⡋⠡⠀⠄⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣐⣠⡡⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢋⡁⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣈⣉⣩⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠛⠁⠀⠁⠈