Keroppi Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠿⠛⠛⠛⠿⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⢠⣶⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣦⠀⠀⣿⡏⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⣿⡇⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠉⠀⢰⣿⣿⡀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⢀⣾⠟⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠘⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⣿⣆
⠀⠀⠀⠀⣾⡟⠀⠀⠉⠛⠿⣶⣦⣤⣤⣤⣤⣴⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣶⣶⣶⡾⠟⠋⠁⠀⠘⣿⡆
⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⣴⣶⡿⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣦⣄⠀⠀⠀⠀⣀⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⢀⣼⣿⠇⠀⠀⠀⠈⠙⠻⠿⣷⣶⣦⣤⣤⣤⣤⣀⣉⣻⣿⣶⣴⣾⣿⣋⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣉
⠀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣋⡉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠻⣿⣄⠉⠉⠛⢿⣶⣄
⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣧⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠉⠛⠿⢷⣶⣤⣾⣿⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⣿⣧⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⣀⠀⠘⣿⣦⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡟⠁⠀⠹⣿⡿⠿⣷⣄⣻⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⢿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⠁⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠛⠛⢿⣷⣤⣶⣿⠿⣿⣶⣴⡾⠟⠁⠀⠀⠀⠹⣷⣤⣀⠀⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⡿⠶⠶⣤⣀⠀⠀⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠉⠉⠙⠾⣤⣀⣿⣶⣿⣿⡟⠋⣏⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠁⠈⠉⠉⠉⠐⠒⠒⠒⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣀⡀⠀⠀⢸⡄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⡀⠀⠀⠛⠃⠀⠀⢨⣧⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⣰⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⢰⣿⣿⣿⢿⣿⣶⣤⣤⣤⣤⣶⣿⣿⣷⣦⣀⠀⠀⠀⠀⣀⣥⣾⡿⢿⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⡟⢁⠀⠉⠉⠛⠛⠛⠋⠉⠉⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⣋⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⠁⢸⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣤⣀⠐⠃⠀⠀⠀⠀⣾⣿⣿⣿⣷⣾⡿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣿⡅⠀⠀⠀⢀⢤⣴⣿⣿⠷⠟⣿⢿⣿⣿⣷⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⡀⠀⠀⢀⠀⣆⠣⡘⢿⣄⠀⣰⣥⡾⠟⠁⣁⣴⣾⣿⢟⣻⣿⣻⣿⠆⠐⠀⠀⠈⠙⣻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⢀⣿⣗⡢⠤⣽⣿⡽⠋⢀⣴⣾⣿⡿⣿⣾⣿⣿⣋⡥⠃⠀⠀⠀⣤⣤⣾⡿⠟⢁⠀⡤⠀⢀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠉⠹⣿⣧⣩⣥⣴⣾⡿⠟⠋⣁⣨⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣅⠀⠀⠰⠌⣀⢚⡐⢴⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣸⠂⢤⣀⠈⣉⠛⣛⣉⣡⣴⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣆⠀⠀⠂⠛⠉⠙⠁⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⣻⣿⡿⠛⠛⣉⣿⡏⣭⡄⠀⠉⢻⣿⠟⠉⠀⠀⢀⡞⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⣤⣄⣀⣀⡾⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⣁⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⣦⣤⣼⣿⣿⣿⣿⠿⠿⠿⠛⠙⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣶⣾⣿⣿⣿⣶⣿⣷⣄⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⡀⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢀⠤⠒⠂⠀⠐⠒⠤⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀
⠀⠀⠀⠀⠉⠑⠒⠒⠒⠊⠉⠀⠀⠀⢀⠖⠋⠉⠙⢦⣀⣠⠤⠤⣄⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡖⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣶⡆⡏⡠⡄⠀⠈⢷⣶⠋⡉⠉⠱⣤⠖⠉⠉⠳⡖⠀⠀⠀⢠⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠊⠣⢄⣀⡠⠞⢇⠀⠀⠀⢀⡞⣇⠺⡿⠀⠀⣏⢿⡿⠀⠀⡇⠀⠀⠄⢸⡁
⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠉⡗⡾⠒⠠⠔⠊⠈⠒⠤⠤⢾⠓⠒⠂⠀⠸⣅
⠀⠀⠸⣄⠀⠀⠀⢀⡀⠤⠄⢐⡶⠛⢦⡀⠀⢦⣀⣀⣀⣤⢤⠀⢠⢏⡇⣀⠀⠀⠀⠀⠀⠀⠠⢸⡇⣤⣀⠀⠀⠐⠉⣇⣸
⠁⠀⠀⢸⡒⠂⠉⠀⠀⠀⠀⠈⠧⣄⡰⠉⠁⠒⠒⠩⡜⠁⠀⢹⣿⣩⡞⠀⠑⣄⡲⣔⡀⣀⡠⣮⣏⣱⣚⡱⠀⠁⠒⠂
⠀⠀⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠰⡏⠉⠉⣱⠀⠀⠀⠈⠒⠴⡞⠓⠁⠙⡦⠚⠀⠀⠀⠀⠀⠡⢈⡿⠒⠁
⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠉⢯⣁⡒⣒⠲⡇⠀⠀⢸⣏⠉⠉⣹⣀⣀⠀⣀⡹
⠈⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠓⠚⠁⠙⠛⠚⠛⠁
⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣴⣾⡿⠟⠛⠉⠉⠉⠙⠛⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠈⠙⠻⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣷⣶⣦⣤⣤⣄⣸⣿⣿⣆⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⢻⣿⣿⡿⠿⠟⠃
⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⣰⣿⡿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⣿⣧⠀⠀⢻⣿⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣦⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⢿⣷⣦⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠉⠁⠀⢀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠏⠀⠀⠀⠉⢻⣿⣦⡀
⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⣼⣿⠏⠈⠻⢿⣦⣄⣀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠸⣿⣿⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⢠⣿⡟⠛⠻⠿⠿⠶⠶⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠉⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋
⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⢀⣀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⡀⢸⣿⡇⠀⠻⠿⠁⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢸⣿⣷⣾⡛⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣦⣤⣀⡀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⣀⣠⣴⣾⣿⣿⡉⠉⠉⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠛⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣶⣾⣿⣋⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⢻⣿⣦⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⣤⣶⣶⡶⠾⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣧⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣥⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⢰⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⣿⣿⣀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣿⣟⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⡶⠶⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⢿⣿⡟⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣠⣄⣀⣀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣶⣾⣿⣷⣄⣀⣀⣴⣾⡿⣿⣷⣦⣤⣤⣾⡿⣿⣧⣀⣠⣤⣾⡿⣿⣷⣦⣤⣴⣿⠿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠿⠿⠟⠋⠁⠀⠀⠉⠙⠛⠉⠉⠀⠈⠛⠛⠛⠋⠉⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠋⠉⠛⠛⠛⠿⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣦⣀
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⠀⠀⢸⣿⡟⠀⠀⢀⣤⣤⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠀⠈⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠏⠀⢸⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⣼⣿⣿⡄⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⣰⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣆
⠀⠀⣼⣿⠏⠈⠙⠿⣷⣤⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠿⠋⠀⠘⣿⣇
⠀⢰⣿⡏⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⢹⣿⡄
⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⠃
⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣄⡀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠻⠿⢿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⣀⣙⣻⣿⣶⣤⣶⣿⣿⣋⣁⣀⣀⣤⣤⣤⣤⣶⣶⣾⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠉⢉⣽⣿⠟⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠛⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧
⠀⠀⠀⣴⣿⠟⠉⠀⠀⠀⣰⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠟
⠀⠀⠀⣿⣯⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢿⣿⡄⠀⠀⢀⣠⣤⣾⣿⠟⠋
⠀⠀⠀⠈⣿⣿⡆⠀⢰⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠻⣿⣷⣶⣿⣿⠁⠀⢀⡀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣏
⠀⠀⠀⠀⠀⠀⠙⢻⣿⡇⣠⣾⡿⣿⣿⣿⠏⠀⠀⠙⣿⣿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠉⠉⠀⠀⠀⠀⢸⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⢻⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠈⢿⣿⣄⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⣤⣶⣦⣤⣀⣀⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⣀⡀⢀⣀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠙⠿⣷⣾⣿⡿⠿⠿⣿⣷⣶⣿⠿⠋⠙⠛⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠛⠛⠛⠛⠻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⢀⣴⣿⡿⠛⠉⠉⠀⠈⠉⠉⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⣾⣿⡿⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠁⣰⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⣿⠟⣿⡇⠀⠈⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠙⠻⢿⣷⣶⣶⣶⣶⣾⡿⠿⠛⠉⠀⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⢠⣿⡏⠀⣠⠖⠈⠉⠐⠢⡀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⣿⡏
⠀⠀⠀⠀⢸⣿⡃⠀⠃⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠟⠛⠉⠁⢻⣿⡄
⠀⠀⠀⠀⢸⣿⡄⠀⢆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠲⢤⡀⠀⢿⣷
⠀⠀⠀⠀⠸⣿⣇⠀⠀⠑⠠⠤⠔⠊⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣄⡀⠀⠀⠀⠱⠄⢸⣿
⠀⠀⠀⠀⣠⣽⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠋⠉⠻⠿⠿⣶⣀⣠⠄⣸⣿
⠀⠀⠀⠀⣿⡿⠻⣿⣦⣀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣦⣿⡟
⠀⢠⣾⣿⠿⠃⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣿⣿⠃
⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣶⣤⣤⣙⣿⣿⣶⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⢿⢿⠿⠿⠟⠿⡟⡿⣿⣿⡿⠃
⢸⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠉⡹⠛⠛⠛⠿⡿⠿⣿⣿⣿⣿⣿⣭⣤⣼⣿⠘⠸⠀⠀⠀⣿⡿⠿⠿⣿⣦
⠀⠙⢿⣦⣄⣀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⡰⠁⠀⠀⣰⣾⣆⠀⠀⢀⣯⡈⠉⠉⡟⠛⣿⡇⡆⠀⠀⣂⣿⣧⠀⠀⠀⢻⣧
⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⠃⢀⣤⣶⣶⡅⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⠀⠀⢰⠀⣿⡇⢃⠇⠀⣿⣿⡁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣤⣿⡟⠉⠹⣿⡄⠀⠀⡙⠋⠁⠀⠙⠿⣿⠋⠀⠀⠈⡆⢹⣿⢸⠀⣸⢠⣿⡿⠀⠀⢀⣾⡟
⠀⠀⠀⣠⣶⣶⣶⣾⡿⠁⠀⠈⠉⠀⠀⠀⣿⣿⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠸⣿⣌⣀⣿⡘⣿⣧⣤⣴⣾⠟⠁
⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣘⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⢸⠀⠙⠛⠛⠻⠿⢿⣿⡟⠁
⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⡀
⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⣶⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⣠⣾⡿⠻⣷⣤⣴⣿⠟⠛⢿⣶⣦⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⣿⣿⣿⡿⠃⠀⠀⠘⡿⢶⣄⠀⠀⢀⣀⣴⣶⣄⠀⡠⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⠁⠀⠀⠀⠀⢿⡀⠈⠛⠙⠉⢹⣿⣿⡟⡛⢄⣼⡁
⣿⡿⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠘⠛⠋⢿⢵⣾⣿⣿
⡿⠃⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣏
⣇⠀⠀⠀⠀⠀⠀⠓⣷⡀⢰⣿⡄⠀⠀⠀⠀⣾⣷⠀⢀⣿⠃
⠋⠀⠀⠀⠀⠀⠀⠋⣨⢿⣆⡏⠀⠀⢶⠒⠀⠙⡇⣀⡾⠫⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⣿⣿⣷⣶⣾⣶⣶⣾⣿⣿⣆⠀⠀⠀⠀⡠⠂⠒⠠⡀⢀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡇⠀⠀⠀⣰⡇⠀⣤⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠷⣤⣄⣴⠟⢷⣄⣉⣠⡏
⣆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⡦⠈⡙⠃⠀⠀⠈⠹⢅⡇
⣿⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣮⣽⣷⣤⣶⣿⣶⣯⣄⡀
⣿⣿⡇⠀⠀⠀⠈⠻⠘⠷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠃⠃⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⢀
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠻⣿⣿⣿⠟⠀⠀⠀⠀⠈⢿⣿⣿⠋⠉⣿⣿⣿⣿⣄⠃⠀⠀⠀⣰⣾
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⡀⠀⠀⠀⣿⠀⢀⣠⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⣿⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠀⠀⢀⡏⠀⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⡾⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⢀⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⡁
⠀⠀⣰⠋⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠘⢦
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢣
⠀⡇⠀⠀⠀⡠⠖⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠲⢤⡀⠀⠀⠘⡆
⠀⡇⠀⠀⣼⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱⠀⠀⢠⡇
⠀⢻⡀⠀⠘⢦⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣠⠎⠀⠀⡼
⠀⠀⢳⡀⠀⠀⠈⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠈⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣠⠔⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠳⢄⡀
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⢈⠟⠒⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠖⠚⠏⠀⠀⠀⠀⠀⠙⢦
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢰⠀⠀⠈⣩⣿⣯⡉⠉⢉⣽⣿⣯⠉⠀⠀⢰⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢳⡀
⠀⢸⠁⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡆⠀⠀⠀⢿⣿⣿⡿⠿⠿⣿⣿⣿⠀⠀⠀⠘⡄⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⣣
⠀⠈⠓⢲⡄⠀⠀⡰⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⡟⠋⠀⠀⠀⠙⢻⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⢣⠀⠀⠀⡖⠚⠁
⠀⠀⠀⠘⠧⣤⡴⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠳⣤⡤⠇
⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢾⣀⣀⣀⣀⣀⣀⣀⣬⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣨⣄⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣱
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⢸⠀⠀⢀⡠⢤⠀⠀⠀⠀⣠⢤⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠘⢆⢀⡠⢤⡀⠀⠀⠀⣠⢤⡀⠀⠀⢳
⠀⠀⠀⠀⠘⠒⠚⠉⠀⠀⠑⠦⠤⠊⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠦⠤⠞⠁⠀⠈⠑⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠉⠁⠀⠀⠈⠉⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠉⠀⠉⠉⠉⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⢹⣿⡟⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣸⣿⡇⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⢀⣿⣿⡇⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣧⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠈⠻⣿⣶⣤⣀⣀⡀⢀⣀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣤⣀⣀⣀⣠⣤⣶⣿⠟⠋⢹⣿⡆
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⣀⣀⢀⣿⡿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⢼⣿⡿⣿⡿⠃⠀⠈⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡃
⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣿⡿⣿⣷⣶⣦⣤⣤⣀⣙⣻⣿⣷⣄⢀⣠⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠻⣿⣷⣶⣶⣆
⢰⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠟⠛⠉⠀⠀⠀⠈⠉⣹⣿⠏
⠘⣿⣷⡀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣦
⠀⠈⠻⣿⣦⡀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿
⠀⠀⠀⠈⠛⢿⣷⣶⣿⠏⠀⣀⣀⣀⠀⠀⣰⣿⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢨⣿⠃⠀⣼⣿⠿⣿⣷⣤⣿⡿⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⣤⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⣶⣿⣿⣷⣴⣿⡟⠀⠈⠛⠻⠛⠁⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠋⠉
⠀⠀⠀⠀⠀⣿⣿⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠹⣿⣧⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⣀⣀⣠⣴⣾⡿⠟⠁⠀⠀⠀⠹⣿⣧⡀⣠⣾⣿⣶⣤⣀⠀⣠⣾⣿⣷⣄⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠙⠻⠿⣿⠿⠋⠀⠙⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠉⠉⠛⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠻⣷⡀⣰⡿⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⠀⠀⠹⣷⣿⠁⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⣿⡏⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⣿⡇⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠙⠿⣶⣄⣀⠀⠀⠀⠀⣀⣠⣶⠟⠋⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠘⢿⣆
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠛⠛⠛⠁⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⢀⣀⣠⣤⣤⣤⣽⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣤⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣟⣁
⠀⣾⡟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⣷⣶⣤⣤⣤⣀⣀⣀⣀⣈⣙⣻⣟⣋⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⡿⠿⠛⠛⠛⠛⠛⠿⠿⣶⣦⣄
⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⣿⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣏⣽⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠆
⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢰⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋
⠀⠈⠛⣿⡆⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⣠⣤⣿⠇
⠀⠀⠀⢿⣷⣶⣶⣶⡾⠿⢿⡿⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢿⡟⠿⣶⣦⣄⣀⣀⣻⡏
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⠃⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠘⣿⠀⠀⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣸⣿⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣀⣀⣀⣀⣸⣿⣿⣿⣧⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣤⣄⣀⠀⢸⣿⡀⠀⢀⣤⣤⡀⠀⠀⢀⣤⣄⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⠿⠋⠉⠻⣶⣴⡿⠋⠙⠻⢷⣾⠟⢷⣶⠟⠋⠙⢿⣦⣤⣾⠋⠛⢷⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠛⠛⠷⣶⣄⡀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⣿⡏⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⣰⣿⣧⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠻⢷⣦⣄⣀⣀⣀⣀⣤⣴⠿⠋⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣀⣀⣤⡾⠛⠛⣷⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣶⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠉⠉⠁⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⠛⠁⠀⢠⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⢀⣤⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⢀⣿⣧⣴⣶⣶⣶⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⢠⣾⠟⠛⣿⡏⠀⠀⠈⢿⣯⠉⠙⠛⠷⣶⣶⣦⣤⣤⣤⣤⣤⣩⣿⣯⣥⣤⣤⣤⣤⣶⣶⠿⠟⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⣿⡇⠀⠀⠈⠁⠀⠀⠀⠈⣿⡆⠀⢀⣾⠏⠀⠀⠀⠈⠉⢩⣭⣉⠉⢉⣭⣭⠉⠀⠀⢿⡇⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⠶⣿⣿⣿⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠈⠻⣷⣄⡀⠀⠀⢀⣤⣿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠈⠙⠋⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⣹⣷⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣤⣴⣶⣮⣻⣷⣤⣀⣿⡏⠁⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟⠁⠀⠀⠉⠉⠀⠀⠉⠉⠉⢹⡿⠛⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣤⣦⣄⠀⣀⣤⣦⣄⣀⣾⠿⣧⡀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠈⠙⠛⠛⠁⠀⠉⠙⠉⠀⠈⠛⠷⠶⡶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠓⠀⢢⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠁⠀⠉⠙⠳⣄⠀⢀⣤⠶⠟⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣶⠟⠁⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⣿⣿⡧⠀⣿⢀⣶⣶⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠉⠉⠁⣰⣿⠈⠻⠿⠃⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣦⣄⣀⣀⣀⣠⡾⠋⠘⢧⡀⠀⠀⠀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⣤⣦⣍⠉⠉⠉⠁⠀⠀⠀⠀⠙⠳⠶⠶⠶⠛⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣦⡉⠉⠀⠸⣦⣀⠀⠀⠀⠀⠀⢀⣠⠀⠿⣿⣿⠇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠁⠈⠛⣷⣦⣤⣀⣙⣷⣄⣀⣠⡶⠟⠁⠀⣀⣀⣤⠾⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⢠⡾⠃⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡉⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡟⣀⡀⠀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣴⡟⠛⠿⠃⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠉⠀⠀⠀⠀⠀⣸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣀⣤⡾⠋⠀⢿⣆⣠⣤⣄⣀⣤⣤⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠀⠉⠋⠁⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠶⠶⠶⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⢿⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⢀⣼⢿⡟⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⣼⠃⠀⠙⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣿⣠⠖⢧⣀
⠀⠀⠀⠹⣆⠀⠀⠀⠀⢀⣤⣴⠶⠶⢶⣤⣀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣄⣀⣠⣴⠞⢋⡴⠛⠉⠉⠙⢮⡉⣹⠂
⠀⠀⠀⠀⠙⣷⣄⡀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢷⡄⢠⡾⠋⠁⠀⠀⠀⠉⠻⣯⠀⠀⢸⠁⢠⡀⠠⠀⠀⣿⠁
⠀⠀⠀⠀⣸⡏⠉⢻⡏⠀⠀⠀⠀⠀⣀⣀⠀⠈⣿⡿⠁⣀⣀⠀⠀⠀⠀⠀⠸⣇⠀⠘⣆⠐⠤⠴⢂⣰⡇
⠀⠀⠀⢠⡟⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⢀⣼⠛⣻⠚⠻⠍⠙⢦⠀⣀
⠀⠀⠀⣼⠃⠀⠀⢸⣇⠀⠀⠀⠀⠀⠉⠉⠁⣰⣿⣇⠈⠉⠉⠀⠀⠀⠀⠀⣸⡇⠀⢸⣥⣤⡀⠀⢀⣀⣀⡼⢃⡟⢸
⠀⠀⠀⣿⠀⠀⢠⡾⠛⠷⣤⣀⣀⣀⣀⣤⡾⠋⠀⠙⢦⣄⣀⠀⢀⣀⣤⡾⢿⡄⠀⠀⠀⠀⠙⠚⠋⠉⠉
⠀⠀⠀⣿⠀⢀⣿⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⢿⡀
⠀⠀⠀⣿⠀⢸⣏⢠⡞⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠻⡆⢸⡇
⠀⠀⠀⢸⡇⠀⣿⡈⠷⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡴⠃⣸⠇
⠀⠀⠀⠘⣷⢀⣼⣷⣄⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠀⠀⢀⣴⠟
⠀⠀⠀⠀⣹⣿⠏⠁⠉⠻⢶⣤⣤⣄⣀⣙⣳⣦⣄⣴⣾⣟⣉⣠⣤⣤⣶⣿⣥⣀⡀
⠀⠀⠀⠀⢻⣇⠀⠀⠀⢀⣼⠟⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⣷⣄⠀⠈⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠙⠷⣦⣄⣾⠋⠉⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⢻⣆⠀⠀⣶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⣿⣤⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣡⣤⣄⡀⣀⣀⣀⣀⣠⣿⣇⣀⣤⣄⣀⣠⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠛⠛⠉⠉⠉⠉⠀⠉⠋⠁⠉⠛⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠒⠐⠂⠒⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠿⠿⠿⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠉⠉⠉⠛⠿⣶⣄⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⡀
⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⡄⠀⣿⣿⠀⣰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⢀⣿⣿⡄⠸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⣼⡏⠻⣷⡄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⢀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⢀⣀⣴⣿⠟⢻⣧⡀
⠀⠀⢠⣿⠏⠈⠙⠿⣦⣤⣤⣀⣠⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠛⠋⠉⠀⠀⠀⠹⣷⡀
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠈⠙⠻⣶⣤⣤⣄⣀⣀⣀⣩⣿⣷⣦⣤⣴⣾⣿⣥⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⡋⠁
⠀⠀⠀⠀⢀⣤⣶⠿⠛⢋⣽⡟⠉⠉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⠟⠉⠁⠉⠹⣦
⠀⠀⣠⣾⠟⠉⠀⠀⢠⣾⠋⠀⠀⣸⣿⣿⣁⣤⣾⣿⡆⢀⣤⣴⣶⣿⢿⣿⠁⠀⠀⠀⠀⠀⢹⣷⣤⣀⠀⠀⠀⣴⣿⣿
⠀⠰⣿⣅⡀⠀⠀⣰⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣫⣾⠟⣉⠀⢸⣷⣼⡇⢀⣀⠀⠀⠀⠀⢸⣿⠉⠻⢷⣦⣾⠋⠀⣿
⠀⠀⠈⢿⣇⣠⣶⣿⣧⣤⣶⠿⢿⣿⣿⡟⠻⣿⣿⣟⠁⠘⠿⠗⢸⣿⠻⣿⡿⠻⢷⣶⠿⣶⣾⡟⢀⣠⣾⠟⠿⣦⣀⣿
⠀⢀⣤⣴⣿⣿⠁⠀⠈⠉⠀⠀⠈⣿⣟⣁⣀⣙⣛⣻⣷⣤⣀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠋⠁⠀⠀⠘⢿⣿
⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠿⠿⣷⣶⡶⠿⠿⠟⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⢹⣧⣀⣠⣾⢶⣤⣠⣴⡾⠶⢶⣶⣶⠟⠁
⠀⠀⠀⠈⠻⢶⣦⣤⣴⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣷⡀⡟⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠻⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⡟⣦⣀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠘⠢⣄⡀⠀⠀⠀⠀⣀⠴⠋⠈⢷⡽⣿⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⠀⣉⣑⣒⡊⠉⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⡉⠀⠀⠀⠀⠈⣷⠉⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣠⠞⠁⠘⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠈⠉⠉⠉⠉⠉⢁⣀⣤⠶⠋⣁⣀⣠⣤⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⡹⢉⠏⣹⣋⣉⡏⠉⡆⠸⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡅⠀⠀⢰⠁⡸⠀⣻⠉⠉⡇⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣠⠃⣰⠁⢀⡇⠀⠀⡇⠀⢰⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⠀⣸⠃⠀⣀⣃⠤⠼⠴⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡁⠀⠑⠲⢿⠄⠄⢯⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢄⡴⠃⠀⠀⠀⠉⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠈⠐⠢⣀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⢸⠃⠀⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠟⠀⠀⡜⢃⠀⠈⠻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠢⢄⡀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠉⠢⠄⣀⠀⠀⠀⣀⠠⠐⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⢤⠀⠀⠈⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂
⠀⠀⠀⢀⠬⠰⠀⠀⠀⠀⠈⠀⢂⠆⠀⠤⠤⠀⠀⠀⠀⠈⠐⠴⠈⠠⠤⠀⠀⠀⠀⢖⠂⠉⠀⠀⠈⠁⠒⠢
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠠⠠⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣈⡁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠁⠀⠈⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⢀⢲⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠄⠀⠀⠊⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠈⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠉⢆⠀⠎⠀⡀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢀⠌⠉⢢⠀⠀⢀⠇⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⠀⢠⠤⠖⠋⠉⠲⠶⡄⠀⠀⠀⠀⠀⠀⣠⠶⠶⠒⠦⡤⣀⠀⠀⠀⣠⠶⡄⢀⡴⢦
⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⣀⣸⠀⠀⠀⡇⢠⡇⢸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠉⠁⠀⠀⠀⣳⠊⠀⠘⡴⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡶⡀⠀⢀⡴⢻⠀⠀⣠⠖⣇⠀⢠⠟⢆⠀⠀⢀⣠⡄⢀⡏⣀⣄⢰⠃⢀⣀
⠀⠀⠀⠀⠀⢠⠿⡄⢰⡇⠙⣄⡎⠀⠈⢧⡞⠁⠀⠸⣄⠎⠀⠘⣄⠴⠋⠀⢳⢸⡟⢡⠟⣟⡴⢋⣜⡀
⠀⠀⠀⠳⣄⡞⠀⠙⠾⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⢠⠏⢰⡟⣡⠞⠉⡇
⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⣀⡴⠚⠉⠉⠉⠳⡄⣠⠖⠉⠉⠙⠲⣄⣀⣀⣀⣿⣃⠀⣸⠟⠁⠀⠀⠻
⠀⠀⠀⠤⠴⠒⠛⠉⠉⠁⠀⢸⠇⠀⠀⠀⣀⡀⢸⡇⠀⡀⠀⠀⠀⢸⡄⠀⠀⠈⠉⠉⠛⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⣇⠀⠀⠘⢿⠗⡼⣇⢿⡿⠀⠀⠀⣰⡻⢿⠓⠲⢤⣀⠀⠀⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⡞⠓⠶⠶⠖⠋⠀⠈⠳⠤⡤⠤⠖⢻⠙⠻⣖⠳⣄⠈⠳⡄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⣄⢸⡇⠲⠓⠀⡀⠀⠀⠀⠀⠀⠀⠰⠷⢸⠷⣄⠈⠳⣌⣻⡆⢸⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢠⠷⢄⣀⠀⠙⠳⣤⠴⠛⣡⠶⠦⣤⠋⠀⠈⣳⡤⠚⢉⡀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⠓⠲⠬⢭⡏⠙⠛⠛⣻⡁⠀⠀⢸⡖⠚⢉⡁⢸⢳⡎⣿⢶
⠀⠀⠀⠀⢠⡀⠣⡀⠀⠈⠙⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠉⠛⠓⠛⣀⣀⣬⢯⡛⠂⠁⠱⢟⡟
⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⢠⡤⠤⢐⣦⣎⠉⠉⠉⠉⠉⣩⢭⡍⡉⠉⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠀⠈⠉⣉⣩⠽⣝⠛⢧⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠓⠃⠀⠁⠀⠀⠀⠙⠀⠉⠉⠉⢦⠀⠀⠀⠀⢠⣄⡗⡲⣄⠀⠶⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠉⠉⣓⡲⣄⠀⡀⠀⠤⢬⣑⠃⡸⠀⠀⠀⠀⢸⣄⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠿⠿⠈⡞⢵⣷⠄⠀⠈⠓⡀⠀⠀⠀⠀⠉⠉⠙⠋⠁⠉⠙
⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠃⢀⠀⠀⠀⣀⠀⣄⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣄⠙⠂⠀⠈⠉⠉⠉⠁⠀⠈⠳⠤⠤⠤⠄⠀⠀⢀⠞⢉⡙⡶⣋⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⡼⠃⠈⠁⠀⠉⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡻⠖⠈⠑⠉⠀⠐⣇⠀⠀⡀⢀⡀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠓⠚⠉⠛⠒⠚⠉⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠿⠿⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⣰⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⡀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣤⠀⠘⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣆⠀⠙⠻⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⡀
⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⣼⣿⠋⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⣿⣿⣄
⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠹⢿⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠟⠁⠀⠈⢿⣿⣧
⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣷⣾⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⢙⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⣠⠚⠋⠉⠙⠳⣄⠀⠈⣿⣿⡄
⠀⠀⠀⣼⣿⠏⠙⠛⠿⢿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⡇⠀⢿⣿⡇
⠀⠀⢸⣿⡟⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⡇
⠀⠀⣿⣿⠃⢀⡞⠉⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠳⣄⣀⠀⣀⣠⠞⠁⠀⣿⣿⡇
⠀⠀⣿⣿⠀⢾⠀⠀⢀⣤⣤⣶⣿⠿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠉⠉⠉⠁⠀⠀⢰⣿⡿
⠀⠀⣿⣿⡆⢸⣤⣴⣿⠟⠛⠛⠁⠀⠈⠛⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣦
⠀⠀⢸⣿⣷⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⣿⣿⡀
⠀⠀⠀⢿⣿⣿⣿⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⣀⣤⣾⣿⡿⠟⠁⠀⠀⠹⢿⣿⣿⣆
⠀⠀⠀⠈⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⡿⣋⣀⣤⣴⣾⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⡃
⠀⠀⠀⠀⠀⣹⣿⣿⣾⣿⣿⡇⣿⣸⠀⣇⣿⣿⣿⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠋⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷
⠀⠀⠀⢀⣾⡿⠋⠉⠉⢙⣿⡷⣿⣿⢀⣿⠇⣿⣿⠿⣿⠿⠿⠛⢻⡟⠉⠉⠉⢙⣧⣀⠀⠀⠀⢳⡀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⣼⣿⠁⠀⠀⠀⠸⣿⣷⣿⣿⢸⢻⢠⣿⡇⠀⡏⠀⠀⣴⣿⣷⣤⣄⣠⣿⣿⣿⡆⠀⠀⠀⢳⡀⠀⠀⠀⠘⢿⣿⣧⣠⣤⣤⣴⣶⣾⡿⠟⠁
⠀⠀⠀⢿⣿⡀⠀⠀⠀⣠⣾⣿⣿⣿⢸⡜⢸⣿⠃⢸⠁⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⣿⡟⠀⠀⠀⣴⣿⣿⣿⣶⡄⠘⣿⣿⡿⠛⠛⠛⠉⠁
⠀⠀⠀⠸⣿⣧⡀⠀⠀⢻⣿⣷⣿⣿⣼⡇⣿⣿⠀⡿⠀⠀⠀⠘⢿⠿⠋⠀⠀⠀⠉⢹⡅⠀⠀⣸⣿⡏⠀⠘⢿⣿⣾⠿⣿⣿⣦
⠀⠀⠀⠀⠙⢿⣿⣶⣤⣴⣿⣟⣿⣿⣿⣷⣿⡟⢠⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⣿⣿⠀⠀⠀⠈⠉⠁⠀⠀⢻⣿⣷⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⠿⠿⠿⠿⠟⠁⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠋⠉⠉⠉⠉⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⣀⣤⣾⣿⣶⡄⠀⢀⣤⣶⣶⣄⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⣀⡀⠀⠀⣀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠁⠙⢿⣿⣶⣿⠟⠉⠻⣿⣷⣦⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠲⣤⣀⠀⢀⡾⠁⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠉⠳⠞⠁⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣤⠤⠤⠤⠼⠇⣀⡴⠖⠒⠒⠶⣤⡀⠀⠀⢘⡧⠶⠒⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⣰⠋⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠘⢧⠀⣸⠁⠀⠀⠀⢠⣾⣿⣿⣆⢸⡇⢀⣀⣤⠶⠒⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⡀⠀⠀⠀⠘⢿⣿⣿⠟⣸⣇⠙⠻⠶⣤⣀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠳⣄⠀⠀⠀⠀⠀⢀⣰⠋⠙⢦⡀⠀⠀⠈⠀⠀⣠⠞⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⠛⠲⠶⠶⠖⠋⠁⠀⠀⠀⠙⠓⠶⠶⠖⠛⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢳⢤⣄⣀⣀⠀⠈⠙⠦⣄⣠⠶⠋⠀⠀⣀⣀⣤⢴⡞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡼⣧⡈⠠⠈⠉⠉⠛⠻⣿⡟⠛⠛⣻⣿⠟⠿⠉⠉⠂⡀⢑⣰⢧⣄
⠀⠀⠀⠀⠀⢠⠞⠉⠀⠈⢹⠷⠶⣾⣤⣤⣆⣸⣿⣷⣾⣿⣁⣦⣤⡼⣶⠶⠿⣏⠁⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠈⢳⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⡿⠟⠉⠙⠛⢿⠀⠀⠀⢸⡇⠀⢻⡄⠀⠀⡞⠃
⠀⠀⠀⠀⠀⠀⠈⡿⢳⣼⠁⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡆⠀⠀⠈⣷⠀⠈⣷⡞⢿⡃
⠀⠀⠀⢀⣤⣤⡾⠁⠠⣯⣤⣤⣿⣤⣤⣤⣼⣧⣤⣤⣤⣤⣼⣧⣤⣤⣤⣿⣤⣤⣽⡄⠈⠳⣤⣤⡀
⠀⠀⠀⢿⡔⢛⠻⢛⣻⠏⠀⢀⣀⡀⠀⠀⢀⠀⠘⣟⣻⠇⠀⡀⠀⠀⢀⣀⡀⠀⠸⣟⡻⢛⢋⣌⣽
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠉⠁⠙⠳⠶⠋⠛⠶⠛⠙⠶⠚⠙⠶⠶⠋⠈⠉⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠖⠐⠒⠒⠒⠒⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⠀⠀⢿⣾⠃⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⢸⡏⠀⠀⠘⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠙⠻⢶⣤⣤⣀⣠⣤⣴⠾⠛⠁⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣠⣤⣴⠾⠛⠁⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠉⠉⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠙⠛⠋⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⣀⣤⣾⣯⣤⣤⣄⣀⣀
⠀⠀⠀⠀⣴⠶⠟⠛⠛⠋⠉⠉⠛⠛⠻⢶⣶⢦⣤⣤⣤⣤⣤⣠⣈⣙⣋⣉⣀⣤⣤⣤⣤⣴⢶⣶⠟⠋⠉⠉⠉⠁⠈⠉⠉⠙⣿
⠀⠀⠀⠘⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⠀⠉⠉⣿⣿⣿⣿⠉⠁⠀⢻⣿⣿⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢾⡋
⠀⠀⠀⠀⢰⣟⣀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠘⣷⡀⠀⠀⠀⠀⠀⣴⠾⠃
⠀⠀⠀⠀⠀⠉⣿⣃⣀⣀⣤⡶⠟⣿⠏⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣷⠀⠀⠸⣿⠻⠶⢶⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢠⡿⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣠⡶⣦⠀⢀⣠⡶⣦⣄⣀⣾⣇⣀⣤⡶⣦⡀⢀⣠⡶⢶⣄⣀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠙⠻⠛⠉⠀⠀⠉⠉⠁⠉⠉⠁⠀⠈⠛⠛⠉⠀⠀⠉⠙⠉⠁

⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⣿⡏⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⢰⣿⣧⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠻⢷⣦⣄⣀⣀⣀⣀⣤⣴⠿⠋⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣀⣀⣤⡾⠛⠛⣷⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣶⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠉⠉⠁⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⠛⠁⠀⢠⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⢀⣤⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⢀⣿⣧⣴⣶⣶⣶⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⢠⣾⠟⠛⣿⡏⠀⠀⠈⢿⣯⠉⠙⠛⢷⣶⣶⣤⣤⣤⣤⣤⣤⣍⣻⣏⣥⣤⣤⣤⣤⣶⡶⠿⠟⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⣿⡇⠀⠀⠈⠁⠀⠀⠀⠈⣿⡆⠀⢀⣾⠏⠀⠀⠀⠀⠉⢩⣭⡉⠉⢉⣭⣭⠉⠀⠀⢿⡇⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⠶⣿⣿⣿⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠈⠻⣷⣄⡀⠀⠀⢀⣤⡿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠈⠙⠋⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⣹⣷⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣤⣴⣶⣮⣻⣷⣤⣀⣿⡏⠁⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡟⠁⠀⠀⠉⠉⠀⠀⠉⠉⠉⢹⡿⠛⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣤⣦⣄⠀⣀⣤⣤⣄⣀⣾⠿⣧⡀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠈⠙⠛⠛⠁⠀⠉⠙⠉⠀⠈⠛⠷⠶⠶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠓⠀⢠⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣴⣦⣤
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⢿⣿⣯⣉⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⡞⠁⢑⠀⡄⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⣐⣽⢶⣉⣘⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣔⠛⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⠌⠌⠁⠈⠁⠀⠀⠀⠀⠀⠀⡀⠐⠡⠄⠀⢀⡤⠤⠽⢿⣿⣿⣿⡷⠖⠚⠿⣿⣿⣿⠃
⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠈⢦⡿⠀⠀⠀⠀⠐⠆⢠⠀⠀⢠⠀⢀
⠀⠑⠈⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠐⢢⡄⣸⡀⣿⣷⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠅
⠀⠈⠰⠌⠃⠀⣀⣀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⢸⣄⠀⠀⠀⢉⡴⠋⠣⣄⡀⠀⣀⡤⣿⠛⠿⠷
⠀⡄⠀⠀⠀⠀⠉⢛⡓⠜⣡⠀⠀⠀⠀⠀⠠⠃⠀⠀⢠⡏⠈⠛⠒⠛⠉⠀⠀⠀⠈⠉⠉⠉⠀⠈⣧
⠀⢃⠀⠀⠀⠀⠀⢈⠉⠃⠉⠀⠄⠙⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡟
⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡦⡀⠀⠀⠀⢀⡽⣄⡀⠀⠳⣄⣀⠀⠀⣀⣴⣏⣀⡤⠞⢳⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢰⣶⣤⣴⣄
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢈⠆⠀⠀⣞⠀⠀⢉⡿⠛⠛⠛⠋⠉⠉⠉⠉⠹⡄⠀⣠⡟⠀⠀⠀⠀⣾⣷⣿⣿⣆⠀⠀⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⢸⠁⠐⡤⠠⢤⡤⣤⢄⡰⡍⠠⠴⢁⠀⠀⣀⣼⣷⣤⣾⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠹⡿⢿⣿⣿⡗⠀⣤⡼⠿⠻⠻⠟⠛⠂⠐⠛⠙⠋⠛⠙⠓⠦
⠆⠒⢠⣿⡦⣴⡀⠃⠀⠛⠛⣿⠿⠷⠶⠆⠙⠃⠢⡈⢻⣿⠉⠁⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣯⣩⣀⠀⠉⠀⠀⡴⡂⠐⠚⠲⠒⢃⡀⣤⣼⣷⠴⠶
⠀⠔⠉⠉⠢⡀⠈⢆⡠⠋⠁⡃⠀⠀⠀⢀⢶⡄⠀⠘⣆⠀⠀⢀⠠⢼⣿⢞⡉⠉⠒⣄⢀⣠⠤⡼⠲⣷⠀⡜⠀⠀⠀⠀⠐⢹⠀⠀⠀⣰⠋⠀⠰⡻⠍⠑⢀
⠀⠀⠀⠀⠀⡇⠀⢸⠃⢀⣜⣏⣡⠀⠀⠿⠧⠜⠀⠀⢹⠀⡼⠁⠀⠛⠀⠀⠈⢆⠀⢸⡏⢀⠤⣇⡴⢢⣀⠼⠓⣄⠀⣤⠾⠚⠳⢦⡀⢿⣠⣤⣤⣅⡀⠀⠈
⠶⣄⣀⠀⠴⠃⣠⢶⠀⢀⣍⠀⠀⢀⣀⣤⣤⣴⣻⠄⣸⠀⢇⠀⠀⣄⠀⠀⠀⢸⠀⢸⠇⠲⠢⠏⠠⣦⣉⡄⠀⢸⣾⠃⢀⠖⣁⡆⣿⡾⢁⠀⢀⠈⢷⡄⠲
⠐⠟⠋⢳⠤⠚⣁⡸⠗⠚⠓⠻⣁⡼⠉⠀⠀⠀⠙⣴⠃⠀⠘⣄⠀⠘⢀⣀⠠⠶⣶⣫⠈⡏⠐⠒⠒⣤⠭⡄⠀⣘⣻⣄⠀⠈⠐⢃⣿⣇⠀⠎⢠⠀⢸⡇
⠓⠞⠉⠁⠀⣀⡟⠀⠀⠀⣠⣤⡈⡇⢰⣿⣦⠀⠀⣿⠀⠀⢀⠜⠋⠉⣹⠁⠀⠀⠀⢹⡇⠚⠳⠂⠈⢱⡾⢿⡏⡙⠃⠉⠓⠶⠖⠋⠀⠛⢦⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠻⠿⢃⠿⣌⠛⠉⢀⡴⢏⠀⠀⠈⠀⠀⢀⡸⢄⡘⠈⢀⢼⡁⠀⠀⠀⠀⠘⣄⡤⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠊⠑⠒⠤⢤⡀⠈⢳⠤⠤⠤⠒⠉⠀⠀⠉⠉⠁⠀⠈⣧⠀⢰⠧⢤⣿⣿⢠⡌⠉⠁⣸⢥⣼⠷⣄⡀⣀⠀⡀⠤⠵⣄⠀⠀⢄⠀⠀⠀⣀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣸⢟⡽⠛⠏⡉⠙⢇⠘⠀⠀⠈⢣⠈⠳⣵⠀⠀⢸⣿⡷⠶⠷⠶⣯⣄⣤⣤⣴⣞⣷⡀
⠀⢠⣦⣀⡶⣄⣠⣿⠀⠀⠀⠀⠀⣀⢀⠤⡄⠀⣀⣀⡞⠉⡝⠀⠉⡁⠀⠀⠀⢱⠀⠀⡅⠀⠀⠀⢸⡆⠀⡿⠄⣤⣿⠋⠀⣘⠂⠀⠆⠈⠛⣿⡛⢯⠀⣱⡆
⠀⠹⠿⣿⡀⣨⠿⠟⠳⣤⠤⠤⢄⣑⡒⠊⠰⡎⠀⠀⢹⠀⢳⢰⠋⢵⡶⢤⡀⡸⢀⡠⣷⡚⢲⠀⠘⠁⣰⠇⡖⠛⠉⠋⠙⡀⠀⠉⠁⠀⠀⠈⠙⠦⣟⣫⡿
⠀⠀⠀⠈⠙⠁⠀⠀⠀⢿⠀⠀⢠⣿⡡⠀⠘⠻⣤⠰⡏⢠⠞⠉⢇⣈⣥⣤⠟⠉⢯⣀⣉⢀⡟⠋⠛⠐⠷⢄⠳⣄⣀⣠⡼⠉⠉⠙⢦⣠⣄⣀⣀⣐⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠚⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⣿⠀⣠⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⡿⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠟⠀⠀⢠⠇⠀⠙⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⢀⡴⠋⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠢⡀
⠀⢠⠎⠀⠀⠀⠈⠙⠲⠤⢄⣀⣀⣀⡠⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⣀⣀⣀⠤⠔⠚⠁⠀⠀⠀⠙⣆
⠀⡞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⡄
⠰⡇⠀⠀⡰⠉⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠉⢳⠀⠀⠀⡇
⠀⢇⠀⠀⢣⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⠀⠀⢰⠃
⠀⠘⣆⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⢠⠏
⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⢀⠝⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠺⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠉⡳⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⢞⠉⠀⠀⠀⠀⠑⢄
⠀⠀⡴⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠉⠉⠉⢉⣿⣿⡛⠛⠛⣻⣿⣏⠉⠉⠉⡄⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠳⡀
⠀⢸⠁⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢈⠀⠀⠀⢸⣿⣿⡿⠿⠿⣿⣿⣿⠀⠀⠀⢰⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⢣
⠀⠈⠓⢦⠀⠀⠀⡜⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠛⠛⠀⠀⠀⠙⢻⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⡀⠀⠀⡰⠒⠋
⠀⠀⠀⠘⠤⢤⠜⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⣤⠤⠗
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠎⣤⠠⠤⠤⠤⠤⠴⠤⠤⠤⠤⠤⠤⢧⡤⠤⠤⠤⠤⣼⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⢤⡬⠄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⡌⠀⢀⡠⠴⢄⠀⠀⠀⡠⠖⢤⣠⠋⠀⠀⠀⠀⠀⠀⠀⠘⢦⡠⠖⢤⡀⠀⠀⣠⠶⢤⡀⠀⢸⡀
⠀⠀⠀⠀⠈⠊⠉⠀⠀⠀⠑⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠚⠁⠀⠀⠈⠉⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠁⣀⠴⠚⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣮⠏⠀⢀⣠⣤⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣿⠃⠀⡼⠋⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡽⠀⢸⡇⠈⣀⡀⠈⡤⣴⡀⠀⠀⠀⠀⠀⠀⢀⢔⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⢧⠔⠁⢠⡽⠯⠥⢞⠱⠦⣿⣽⣄⣀⣀⣀⠴⣫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⢀⣀⣠⠟⠀⣏⣼⣿⣻⣷⢿⣲⠷⠶⡯⣥⣶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠻⣌⣛⣬⣿⣯⢹⠏⠁⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⡀⠈⠁⠂⠤⣀
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⡄⠒⣄⠀⠀⠀⠀⢀⣞⠉⠙⢶⢋⠀⢀⡼⢁⠀⠀⢀⣀⠀⠉⠂⢄
⠀⠀⠀⠀⣀⣴⣿⠀⢀⣶⣿⣿⡿⠟⠑⡒⠒⠤⡀⢆⠀⠀⠀⠀⢿⡿⢿⣿⣿⡆⠀⡏⢵⡧⢸⡧⢠⡼⢃⡴⠊⠀⣿⣿⣦⣿⣿⣤⣶⣷
⣀⣀⣤⣼⣿⣿⣿⡤⢊⠈⡉⠀⣀⠀⠒⠈⢦⣀⡉⡈⠀⠀⠀⠀⠀⠀⠀⡈⠁⢲⡀⡗⠊⢉⣉⣀⣀⠀⠈⢣⠀⣴⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢛⣿⣿⣿⡟⠀⢸⠀⠁⠘⠋⠁⠀⠀⠘⠧⠐⣳⠀⠀⠀⠀⠐⠀⠀⢀⠀⡾⠀⢧⠋⠗⠀⡀⠀⢽⢦⢸⢺⣿⣆⣀⣀⣾⡏⠙⠛⢿⡏
⡿⠛⠒⠋⢩⡝⣿⠖⡞⢠⠀⠀⠀⠀⠀⠀⠘⢧⡗⠀⠛⠀⣤⣤⣤⣠⣶⡮⠖⠁⠀⠈⢓⣤⡤⠠⣄⣤⠼⠋⠀⠻⣿⣿⣿⣽⣷⣦⣶⣿⠃
⡘⠃⠀⡦⣀⣤⣯⡀⠓⡞⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠘⠤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠃⡃⠀⠀⠀⠭⠂⠀⠀⢿⣿⡿⠛⢿⣿⣿⣿⠅
⣤⡛⢿⠑⠛⠙⡚⣋⣈⡒⣆⢀⣤⡤⠤⣆⣰⡗⠂⠈⠉⠉⠰⣏⣙⢟⣉⠟⠀⠉⠀⠁⠀⠱⠄⠧⠰⠋⠉⠒⠒⢸⣿⡥⠀⣄⣿⡇⣀⣾⣿
⠿⠗⠸⠴⠤⠔⣃⣄⡂⢄⡉⡉⠀⠀⠀⢀⢁⠀⠀⠀⢠⡤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠅⢀⢨⡉⠁⡄⢴⣿

⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠄
⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠈⠋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠖⠒⠊⠉⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠙⢦⡀⢀⣠⣤⣤⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠀⠹
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⣤⡀⣷⠋⠀⠀⠀⠈⠻⣤⣤⡿⠚⠛⠛⠲⣄⢀⡤⠶⠒⠾⣧⣤⠀⠀⠀⠀⠀⣠⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠄⠀⠀⠀⠀⢀⣧⠀⠀⠀⠘⠛⢡⡇⠘⠉⠃⠀⠀⠀⣷⣼⢀⣴⣤⠀⠀⠸⡏⣤⣤⡀⠀⠈⣷⠀⠀⠀⠀⠀⣹⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠑⠢⠤⠤⠖⠁⠙⢄⠀⠀⠀⢀⣰⠃⢻⡈⠻⠟⠀⠀⡸⣏⠳⠿⠃⠀⠀⡿⠀⠀⠀⠑⠀⢻⠀⠀⠀⠀⢀
⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠸⡖⣾⠛⠒⠤⠔⠊⠁⠈⠓⠤⠤⠔⢾⠓⠒⠒⠒⠒⠒⢿⡀⠀⠀⠀⠁
⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣴⠟⢄⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠸⡇⠀⠀⠀⠀⠀⢀⠭⠟⢷⠀⢺
⠆⠀⠀⠈⠹⣆⣀⡠⠤⠒⠚⠉⠁⠀⠀⢼⡃⠀⠀⢱⠦⠤⣈⣙⠒⠲⠒⡿⠏⠙⢦⡤⡿⢼⢳⠜⠢⣀⠀⢀⡀⢀⠀⠀⠀⠀⡸⢧⢿⣉⣷⢤⠀⠐⢄⣀⡙⠒⠛
⠀⠠⠢⡀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣴⣁⣀⣀⠀⠀⠉⠉⢻⡁⠀⠀⢸⣯⠳⡴⣿⠀⠀⢈⡧⠤⢽⣥⡤⠤⢴⠺⢷⣳⡴⢫⡤⠞⠀⠀⠀⠀⠈⠉⠉
⠀⠈⠈⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠀⠀⣸⠀⠀⠀⠀⠀⠙⠒⠲⡏⠙⠋⠁⠘⣳⠖⠋⠀⠀⠀⠀⠀⠀⠈⢆⠀⡽⠉⠋
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠶⠋⠉⢳⡖⠒⠲⠤⠤⠤⡇⠀⠀⠀⢰⣳⠒⠋⠉⠉⡆⠀⠀⠀⠀⠈⢻⠁
⠀⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠶⠲⠶⠇⠀⠀⠀⠈⠙⢦⣄⣠⠼⠻⣇⣮⣩⣥⣺⠏
⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠉⠉⠈⠉⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⣿⣿⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⠀⢻⣿⡇⠀⣸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⣸⣿⡇⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⢀⣿⣿⣧⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠋⠀⠀⠀⠀⠀⠈⠻⠿⣷⣶⣶⣤⣤⣤⣶⣶⣿⠿⠛⠉⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣦⣀⡀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠁⠙⠻⢿⣿⣷⣦⣤⣤⣄⣀⣈⣀⣀⣈⣛⣿⣿⣶⣤⣤⣶⣿⣿⣛⣁⣀⣀⣀⣀⣤⣤⣶⣶⣿⡟⠋
⠀⠀⠀⠀⠀⣤⣾⡿⠇⠀⠀⠀⠀⠀⠈⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣄⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢿⣿⡿⠛⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠈⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⠁⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣴⣶⣿⠿⠿⣷⣄⣠⣴⡾⠿⣶⣤⣤⣴⡿⠃⠀⠀⠀⠀⠻⣷⣤⣀⡀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠸⢥⠟
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡀⠹⣆⣀⠀⣀⢀⣠⡞⠁⠀⢠⠀⠙⣆
⠀⠀⠀⠀⣤⡈⢻⡇⠀⢰⡏⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠀⢰⣏⣿⡄⠀⠿⠈⡀⠈⠀⠉⠀⠐⠀⣿⣿⠐⢸
⠀⠀⠀⠀⠙⢳⡀⠻⡤⠎⠉⣟⠀⢀⣠⡄⠀⠀⠀⠀⢀⣠⠖⠛⢻⠐⠀⠘⠿⠟⡁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⣧⡐⣸⠁
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠉⣩⠋⠁⠀⠀⣠⡴⠋⠁⠀⠀⠈⠁⠁⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⡀⠀⠀⠀⠀⠀⢴⣦⠀⣀⡀⠀⠐
⠀⠀⠀⠀⡞⡂⠀⢸⡆⠀⠀⠀⠀⣧⠀⠀⣠⠾⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠚⠲⠶⢤⣤⣬⣷⡄⣿⣦⡀⢀⣼⡇⢀⡿⢓⠀⢸
⠀⠀⠀⣖⠌⠀⠀⠀⢷⣀⠀⠀⠀⣿⢶⣴⠋⠀⡀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠤⠤⠤⠤⠴⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⡇⠙⠋⠘⠷⣟⣀⡈⣠⠈
⠀⠀⠀⠀⠀⢀⠠⡀⠈⢧⠀⠀⢸⡏⠂⡈⢷⡄⠀⣾⢦⠀⡿⣷⠞⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣤⡴⠇⠀⠀⠀⣠⠼⢷⠋⠏⢸
⠀⠀⠀⠈⣀⠀⠈⠀⠠⠈⠳⣄⢸⡇⠤⠀⠀⢻⡆⠈⢶⡟⠀⠘⠛⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢀⡘⠷⣄⣨⣠
⠀⠀⣄⠀⠂⠀⢀⣤⡀⠀⠀⠈⠹⡇⠀⠄⠀⠀⠹⣄⣼⠃⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⣀⠀⠀⢀⣀⣠⠴⠋⠉⣉⠉⠙⠏⢠⢤
⠀⠀⢸⠀⢀⠜⢈⠀⠀⠀⠀⠀⠀⣷⠀⠠⠀⠀⡴⠋⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠄⠁⠀⢀⠀⠉⠘
⠀⠀⠈⠀⠀⠈⡆⠀⠀⠀⠔⠂⠀⠸⡆⠀⠀⠘⠁⠔⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡆⠘
⠀⠀⠄⢠⠀⠹⡄⠀⠀⣈⠂⠀⠀⠀⠹⣄⣀⣠⡤⠖⠋⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠀⡀⢀
⠀⠀⠀⢾⡄⢰⡇⠀⢀⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⠤⣤⣤⣤⠤⠶⠿⣯⣀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⢀⣀⣄⠀⢠⠀⢸⡆⠀⠃⢸
⠀⠀⠈⡾⠀⠈⢰⠀⠘⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠀⠀⠂⠉⠛⢋⣉⣽⡋⠉⠀⣼⠆⠈⡇⢸
⠀⠀⠀⠸⡀⠀⡇⢠⢠⡾⠅⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⡀⠻⣅⠀⣉⡿⢿⠵⠀⠀⠃⠆
⠀⠐⢶⠀⠇⠐⠀⢸⡀⢈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⢀⣼⡧⠒⠉⢻⡋⠉⠉⠛⢿⣷⠃⣴⠸⠀⠀⡷⢀⠃⢰
⠀⠀⢈⡄⠠⠀⠠⣼⡗⡘⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣸⣇⠀⢰⣂⠬⡁⢀⠙⠀⠀⢠⠃⡘⠀⡾
⢠⠄⠘⠂⠧⠞⠛⠛⠛⠋⠻⠦⠀⠀⠀⠀⠄⠀⠀⠀⠉⣥⠶⠶⢶⣤⣄⡈⠀⠒⠒⠂⠀⠀⠈⠁⠤⠀⠀⠐⠖⠢⠍⢉⣀⠀⢈⣀⠁⣈⣀⣀⠀⡄⢀⠁⡘⠁
⠀⠉⠁⠀⠘⠀⠠⠦⠄⠛⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠐⠚⠐⠋⠈
⠀⠀⠤⠐⠂⡠⠄⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠠⠴⠂
⠀⠀⠀⠀⠀⠀⡐⠋⠀⠀⠀⠀⠐⠉⢠⠂⢉⠀⠂⠀⡌⠻⡋⠉⠍⠛⠋⠁⠀⠀⠈⠉⠁⠀⠒⠦⠀⠀⠀⠐⠒⠖⠀⢄⠈⠉⠒⠀⠀⠈⠁⠄⠀⠒⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠈⠲⢀⡀⠀⠈⠁⠀⠀⠰⠎⣲⠁⠁⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠠⠈⠀⠊⠀⢀⠔⠁⠀⠀⡠⠂⣀⠀⢀⠂
⠀⠀⠉⠀⠒⢠⠀⢀⡀⠈⠀⠂⠠⠄⢀⣀⠈⠁⠀⠀⠐⠒⠉⠁⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢁⠀⠤⠄⠒⠈⣀⠠⠀⡂⠥⠐⠊⠀⠂⠁⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠒⠒⠦⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠶⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠉⠙⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⣠⣴⠾⠟⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠘⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⣴⡿⠻⢷⣄⠈⣿⠏⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠉⢀⡿⠀⠀⠸⠏⠉⢻⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠙⠛⠳⠶⠤⠤⠴⠶⠚⠋⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⢀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⢢⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠉⠛⠻⠶⠾⠟⠛⠉⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣼⠃⣰⡟⠀⠀⠀⠀⠀⣸⠇⠀⠀⢈⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠟⠀⠰⠏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢠⡄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⢻⣦⡀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢈⡿⠛⢶⣶⣶⣤⣤⣀⠹⣿⣁⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⣠⠞⠀⢀⠎⢠⠃⠀⠀⠀⠈⠛⠉⠁⠉⠈⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⢀⡎⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢀⣀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⡞⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢻⣶⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⠶⢴⣅⣴⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠉⠉⢻⡟⠛⠲⠖⠲⠶⠒⠀⠀⠀⠤⢤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠘⢷⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠀⣤⣦⣄⡿⠁⠀⠀⢹⣆⢀⣤⣀⣀⣀⠀⢈⡏⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠋⠁⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⢀⣀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠴⠞⠉⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⣿⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⢹⡄⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⢷⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⢀⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢯⡀
⠀⠀⠀⡴⠋⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠙⣆
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠘⣇
⠀⢰⡇⠀⠀⢀⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⢤⡀⠀⠀⢹
⠀⠘⡇⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⣸
⠀⠀⢻⡀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣀⡴⠁⠀⢠⠏
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢀⡤⠊⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠳⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡨⠉⠓⠲⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⠖⠚⠙⡄⠀⠀⠀⠀⠀⠙⢆
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡄⠀⠀⠀⣼⣿⣯⣉⣉⣉⣿⣿⣧⠀⠀⠀⠆⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢼⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⠁⠀⠀⠀⣿⣿⣿⠿⠿⠿⣿⣿⡿⠀⠀⠀⢰⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠈⠙⢳⠀⠀⠀⡜⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⢦⠀⠀⢠⠞⠋
⠀⠀⠀⠀⠘⠦⢤⠎⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢷⠤⠼
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠮⣤⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠴⣤⠤⠤⠤⠤⠠⣴⠤⠤⠤⠤⠤⠤⠵⠤⠤⠤⠤⠤⠤⣤⠷
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⣾⠀⠀⣠⠴⢦⡀⠀⠀⢀⡴⠦⣄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠶⢤⡀⠀⠀⢀⡴⢤⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠙⠚⠋⠁⠀⠀⠙⠢⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠋⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠿⠿⠿⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⠀⠀⢀⣠⣶⡿⠿⠿⠛⠿⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⢸⣿⠁⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⣸⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣿⣿⠀⠈⠿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠈⠻⢿⣦⣤⣀⣀⡀⣀⣀⣠⣴⡾⠟⠁⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⣀⣀⣉⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⣤⣤⣤⣤⣤⣴⡾⠟⠋⢿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⠻⠿⠿⠿⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸⣿⠇
⠀⠀⠀⠀⠀⢀⡀⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠻⣿⣿⣿⣿⠏⢀⣿⡿
⠀⠀⠀⠀⢸⣿⡿⡿⠟⠀⠙⠻⣿⣦⣄⣀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⠁
⠀⠀⠀⣠⣼⣿⠇⠀⠀⠀⠀⠀⢨⣿⡿⠿⢿⣷⣶⣶⣤⣭⣿⣿⣶⣤⣴⣿⣿⣛⣁⣀⣀⣀⣀⣤⣤⣶⣾⠿⠛⠹⢿⣿⣿⣦
⠀⠀⠸⣿⣟⠁⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⢿⣿⠉⠀⠀⠀⠀⠀⠈⣿⣯⡀
⠀⠀⠀⠙⢿⣧⣀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠙⣿⣿⠄
⠀⠀⠀⠀⠈⠙⢿⣷⣦⣾⠟⠀⣀⡀⠀⠀⣰⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⢀⣾⡿⢿⣷⣴⣿⠏⠈⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⢰⣿⠿⣿⣾⡿⠁⠀⠈⠛⠋⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⣀⣀⣀⣀⣠⣤⣾⡿⠋⠀⠀⠹⣿⣆⣀⣴⣶⣦⣄⡀⢀⣴⣶⣦⣄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠙⠻⠿⡿⠟⠉⠛⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠉⠙⠻⣦⣄⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⣧⡀⣰⡟⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠘⣷⡟⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⢹⡇⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠈⠛⠷⣦⣤⣤⣤⣤⣶⠾⠋⠁⠀⠀⠀⠀⠈⠙⠷⢶⣤⣤⣤⣤⣤⡶⠟⠋⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⠛⠛⠋⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠉⠉⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣻⣶⣄⡀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⣃
⠀⠀⠀⠀⠀⠀⠀⢰⣟⠋⠉⠉⠉⠉⠉⠉⠙⠛⢷⣶⣦⣤⣤⣤⣄⣀⣀⣉⣛⣛⣉⣀⣀⣀⣠⣤⣤⣤⣴⣶⠾⠟⠛⠛⠛⠛⠛⠛⠿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣿⣿⡏⠉⠉⠉⣿⣿⣿⣿⠉⠉⠉⢿⣿⣿⣧⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣶⠶⣿⠃⠀⠀⣾⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡀⠀⠙⣿⠷⣦⣤⣀⣀⠀⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⡏⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢹⡆⠀⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠶⠶⠾⠿⠿⠿⠶⠶⠶⠶⠿⢿⣿⠿⠶⠶⠶⠾⠿⠿⠿⠷⠶⠶⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣀⣴⣤⡀⠀⠀⣠⣤⣄⡀⢸⣧⠀⢀⣠⣤⣄⠀⠀⢀⣤⣀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠈⠛⠷⠾⠋⠈⠉⠛⠛⠙⠛⠛⠉⠈⠙⠷⡶⠟⠁⠙⠛⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠻⠷⣦⣄⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠻⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠈⣿⣿⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠀⢀⣿⣿⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣾⠃⢹⣆⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⣼⠿⣦⣄⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣠⡾⢿⣄
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠙⠛⠷⠶⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠾⠛⠉⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠀⠀⠀⠀⠀⣠⣿⡁
⠀⠀⠀⣀⣀⣿⠉⠻⢶⣄⣀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⣀⣤⡾⠋⢹⣇⣠⣀
⠀⠀⠈⣿⡍⠉⠀⠀⠀⢉⣿⢻⠷⠶⢶⣤⣤⣽⣷⣦⣴⣿⣭⣤⣤⡶⠶⡾⠻⣯⠁⠀⠀⠀⠉⢹⡟
⠀⠠⣾⠛⠀⠀⠀⠀⢠⡾⠁⣼⠀⠀⠀⢸⠁⢸⡇⠀⠀⢸⠀⢹⠀⠀⠀⢳⠀⠹⣧⡀⠀⠀⠀⠈⢛⣷
⠀⠀⠙⢷⣄⡀⠀⢠⡿⠁⠀⡇⠀⠀⠀⡟⠀⢸⡇⠀⠀⢸⠀⠘⡆⠀⠀⠘⡇⠀⠘⣷⡀⠀⢀⣴⡾⠃
⠀⠀⠀⠀⠉⠛⢷⡿⠁⠀⢸⠇⠀⠀⢰⠇⠀⢸⡇⠀⠀⢸⠀⠀⢧⠀⠀⠀⢿⠀⠀⠘⣷⡟⠛⠁
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣸⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⢸⡀⠀⢸⡀⠀⠀⢸⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣯⣀⣀⣀⣏⣀⣀⣸⣇⣀⣀⣨⣇⣀⣈⣇⣀⣀⣨⣇⣀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢹⣏⣩⣽⠿⣯⡉⣉⣭⣭⡉⢩⣿⣯⠉⣩⣭⣍⡉⣉⣿⢿⣭⣉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠛⠋⠁⠈⠛⠛⠁⠘⠛⠋⠀⠉⠛⠋⠁⠀⠈⠉⠁

⠀⠀⢠⠤⠞⠓⠋⠲⢤⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠘⠲⣄⣀⣀⡤⠔⠁⠀⠀⢀⡽⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠀⠀⠈⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰
⠀⣴⠉⠱⡄⠀⠁⠀⠀⢀⣤⣶⣿⣷⣿⣿⣶⣶⣾⣿⡀⢠⠊⠉⠉⠀⠀⠀⠈⠉⠓⠲⡄⠀⠀⠉⠲⣀⣀⡀⣠⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⢠⠋⠀⠀⠙⡾⠉⠉⠉⠉⠛⢛⣏⣰⣿⣿⣹⡉⠉⠉⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡤⠤⠃⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠸⣄⠀⠀⣜⣀⣀⣀⣀⣀⣠⢮⠎⢀⣹⣿⠟⢿⣦⠀⠀⠀⠀⠙⠒⠒⠙⠂⠒⠊⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠸⣄⣀⣽⠀⢠⣍⣇⣀⣥⣯⣠⣯⣤⣺⣄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⡆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈
⣀⣠⠤⠗⠚⠋⣍⣹⠤⠤⢤⣀⠀⢀⠴⠒⠛⠒⢮⡏⡓⠲⠤⣀⠀⠀⠀⠀⢰⠉⠀⠀⠙⣄⡔⠉⠀⠀⠉⠳⣴⢲⠖⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀⠉⠉
⢁⣠⣄⣀⠀⢀⡎⠁⠀⢀⣠⣈⢳⣏⣤⣤⠀⠀⠀⢹⡁⠀⠀⠀⠉⠲⢤⣀⣸⠦⠔⠒⠋⣻⠀⠀⠀⠀⣠⣄⠸⡏⣠⣄⠀⠀⠀⠀⢱⠀⠀⠰⡓⠛⣲
⠸⣄⣠⠏⠀⠘⡇⠀⠀⠸⣿⣿⢿⣿⢿⡿⠃⠀⠀⣸⠃⣀⣠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠘⠃⠈⢠⡇⠉⠘⠃⠀⠀⠀⢸⠀⠀⠀⡿⣿⢵
⠸⣝⣟⡽⠀⠀⠙⣤⣀⣀⣀⡴⠋⠈⠲⢤⣀⡤⠖⢻⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⠦⢤⣤⡤⠖⠁⠘⢤⣀⠀⠀⢀⡠⢯⠀⠀⠀⠉⠛⠉
⠀⢀⡀⠀⠀⠀⡼⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠄⣠⢤⡀⠀⠀⠀⣀⣤⣠⠀⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⠈⠉⠉⠉⠀⠈⡇
⠀⣏⣹⡴⢶⣊⣇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣯⣀⡤⣏⣠⠇⠀⠀⠀⠳⣤⣜⡀⢧⠀⠦⠳⠀⠀⠀⡇⢸⠀⠀⠀⠳⠙⠀⣰⠁
⠖⠋⠉⠓⠺⣤⡜⣿⠉⠋⠧⣬⠓⠒⠚⠁⣀⣠⡴⠛⠥⠜⠒⠃⠀⠂⠀⠀⠀⠻⠽⠥⠃⣤⠗⢤⣀⣀⠀⠀⠱⠞⠀⠀⣀⣀⡤⠾⣅
⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⡠⠋⠉⠉⠉⠉⠙⢯⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⢠⠋⠈⠉⠉⠉⠉⠉⠉⠁⠙⡄⠀⣹⠆
⡒⢚⡛⢒⠒⠒⠛⡛⠣⠤⠤⢤⡖⢒⡛⣒⠢⠬⠧⠴⢚⡲⢤⢤⡤⢤⠴⣒⠒⠲⠤⢤⣤⡤⠿⠓⠒⠒⠒⠒⠦⠤⠤⠔⢒⠃⣛⠺⡥⠖⠊⣉⣉⡛⣉
⢭⠁⢩⣽⡤⢾⣉⠉⢫⣇⠤⣮⣍⠁⠉⡸⢆⠤⣼⣭⠉⠉⣩⣇⢤⣯⡍⠈⢩⣧⢤⣏⡋⠙⣻⣆⢤⣏⡋⠙⢋⣧⣠⢤⣯⡍⠉⢩⢽⠴⣼⢤⠁⢩⠞
⠾⠊⠻⠶⡆⢰⠺⠖⠺⢶⠄⢰⡟⠚⠓⠗⡆⠀⢰⡟⠖⠛⠷⢦⠀⣴⠳⠊⠳⢶⠀⡶⠧⠖⠧⢤⠀⢴⠳⠚⠚⢲⠀⠀⡴⠧⠒⠾⢶⠀⢰⠚⠚⠛⠒
⣳⣤⣠⢔⣓⣙⣦⣀⣀⣜⣓⣊⣳⣄⣠⡴⣙⣲⣊⣳⣄⣀⣠⣟⣒⣙⣦⣀⣀⣜⣒⣳⣄⣀⣠⣞⣒⣙⣦⣀⣠⣞⣓⣒⠳⣄⠀⣀⠞⣒⣪⣧⡀⠀⣠
⡙⢿⡿⠋⡽⢸⡙⢯⡿⢉⡇⠰⡛⠻⣽⠛⢹⠂⠀⢏⠻⣿⠟⢉⠆⣏⠻⣇⠿⢻⠇⢞⠻⣿⠟⢹⠀⢾⠙⢿⡿⠛⡇⠈⢿⠻⣿⣯⠝⣲⠠⡦⢼⣻⠴
⠙⠚⠓⠊⠀⠀⠙⠚⠒⠉⠀⠀⠙⠒⠗⠒⠁⠀⠀⠈⠑⠛⠒⠁⠀⠈⠓⠚⠒⠋⠀⠈⠓⠓⠒⠁⠀⠀⠙⠚⠒⠋⠀⠀⠈⠑⠺⠧⠒⠁⠀⠙⠲⠿⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⠀⠀⠀⠀⠀⢠⠁⠀⠑⢔⠈⠀⠀⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠂⠐⠈⠁⠁⠀⠀⡑⠉⠈⢲⡈⠈⠣⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠒⠀⢤⠒⠀⢀⠆⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠘⡑⠀⣀⠀⠒⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢫⢵⠃⠀⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠰⠀⠀⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠐⠓⠂⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠑⠀⠐⠠⠀⠀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄⡄⠀⠠⠄⠐⠒⠁⠀⠀⠀⠀⠘⢦⢠⠠⠂⠒⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⠠⠄⢀⣀⢀⠀⠜⠈⠢⣀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠢⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠠⡀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡖⠒⠂⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠇
⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡈⠄⠀⠀⠀⠀⠀⡊⠀⠀⢠⡆⣀⠄
⠀⠀⠀⡐⠀⠀⠮⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠂
⠀⠀⡁⠀⠀⠁⢀⠀⡐⠀⠀⠤⠤⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠒⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠘⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠉⠂⠀⠁⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡣⠂⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⡖⠋⠀⠈⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣗⡠⣄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⣄⡠⠋
⠀⠀⠀⠀⠀⢀⡰⠉⠙⢆⢀⣼⣁⠀⠈⠉⢢⢀⡞⠁⠀⠀⠉⢳⣤⠚⠉⠉⠙⢦
⠀⠀⠀⠀⠀⡏⠀⡀⢀⣴⠻⣀⡨⠦⠤⠒⠚⢸⠀⠀⠀⡴⠢⢀⡇⠖⣆⠀⠀⠈⡇⠀⠀⣠⠤⣀
⢀⡴⠒⠢⡀⠉⠉⠉⠁⡎⢸⠁⠀⠀⠀⠀⠀⡴⠳⣄⣀⣀⣠⠞⠣⣀⠀⠀⣀⣼⠁⠀⣞⠀⠁⠌⡇
⠸⡈⣐⠡⢇⠀⠀⠀⣀⣇⣸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⡇⡴⠉⠉⠳⡖⠁
⠀⢸⠁⠀⠀⣷⠀⠈⠀⠀⠈⠉⠉⠀⠀⠀⠘⣇⠀⢀⣤⠀⠀⠀⠀⠀⢀⡀⠀⢀⡗⡧⣄⡀⣠⠇
⠀⠀⠳⣶⢾⡏⢀⡤⣄⢀⠄⢤⡰⢻⠀⠀⠀⠈⣹⠋⠉⢹⣦⣤⣤⣴⣋⣤⠴⠻⣼⣯⠿⠛⠃
⠀⠀⠀⣽⣾⣽⠸⢄⡿⠘⢯⠔⣣⣟⣉⠗⠀⠀⣹⣦⠴⡋⠓⠤⠴⢊⠀⠹⡄⣀⡽⠃
⠀⠀⠀⠑⠒⢋⣩⣞⢉⠉⢉⡉⣗⡂⠀⠀⠀⢸⡉⠉⠉⢹⣦⣤⣤⡏⠑⠛⠿⡅
⠀⠀⠀⠀⠀⠀⠫⠝⠤⠭⠥⠜⠛⠂⠀⠀⠀⠀⠓⠦⠴⠋⠀⠀⠀⠳⢤⣤⠞⠁
⠀⠀⠀⣤⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⡀⠀⣀⡤⢄⡀⠀⣠⢄⡀
⠀⠀⠀⣏⠀⠧⠖⢊⣹⣀⠤⠐⡆⢺⡄⠀⣤⡄⢱⢠⠖⣉⠑⣄⠛⡆⢰⢦⠘⡖⡇⢰⣶⠘⣆⡏⢠⠇
⠀⠀⣴⠉⠀⣄⠀⢏⠁⢻⡆⢚⡇⠀⡇⠀⡉⠡⡏⢿⠘⠭⠃⡼⣴⡃⢈⡩⠞⠀⣷⠀⡡⠞⢸⠃⣸
⠀⠀⠙⣷⣀⡟⣧⣨⠆⠘⣇⣘⣳⠀⣧⡴⠻⣦⡼⠈⠛⠓⠛⠁⠈⣧⡼⠀⠀⠀⢿⣤⠇⠀⠻⠶⠃
⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠉⢣⣰⠋⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣴⣶⡄⡇⠠⠒⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠉⢠⠿⣄⠀⠁⠀⠀⣠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠉⠲⠤⠤⠤⠖⢁⣀⠈⠉⠒⠒⠋⠁⠈⣇⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⡀⠀⣿⠀⠀⠠⠄⠀⠀⣼⠀⡇⠀⢀⠂⠀⠀⠀⣸⠀⡙⠤⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⡄⠸⡄⠐⠄⠠⠃⠀⢹⣀⡇⠀⠈⠢⡔⢀⡰⢣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠌⢳⠖⠒⠲⣤⢤⡖⢒⡖⡶⠉⠈⠹⡄⠁⢀⢀⠀⡰⠒⠒⡄
⠀⢀⢔⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⡀⣀⡰⠚⠙⣍⢱⠋⠉⠧⠤⡴⢻⡆⠙⠘⠐⡇⣀⣠⠇⠀⠀⠀⢀⣀
⠀⠐⠿⢿⣦⡀⣠⠴⠒⠒⢴⣺⣃⣀⡀⠀⡿⠭⠥⠤⠴⠺⢹⡏⠝⠒⢒⠒⠚⢅⡇⠀⣸⡙⢿⣿⢩⣳⠤⡄⣰⠋⠀⢹⢠⢠
⠀⠀⢀⣴⣶⣶⡇⠀⠁⠆⠀⣯⠞⣿⣷⡄⣿⠓⠒⠒⠒⠋⢹⡏⠑⠒⠒⠒⠋⠉⡇⠀⠙⢯⣽⠯⢏⣻⢥⣏⣽⢀⡴⠋⠈⠘
⠀⠀⠻⠿⢿⠀⡷⣤⣄⡤⠾⡟⢠⠏⠉⠀⢹⣀⡀⣀⠀⣀⡾⣧⠤⣤⣤⡤⠤⢾⠃⠀⠀⠽⡟⠢⡤⢌⣿⡟⣭⡝⠁
⠀⠀⠀⠀⠈⠢⠬⢇⣀⣀⡠⠋⠁⠀⠀⠀⠈⠫⠭⠭⠭⠼⠁⠘⠲⠤⠴⠖⠒⠋⠀⠀⠀⠀⠉⠒⠒⠚⠏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠿⠿⠿⠿⢿⣷⣦⣄
⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⣷⣦⡀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀
⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⠀⠀⣿⣿⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠀⠀⣿⣿⡀⠀⠻⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⢀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄
⠀⢀⣾⡿⠉⠛⠿⣶⣤⣀⣀⣀⣀⣀⣤⣴⣶⡿⠛⠁⠀⠀⠀⠀⠙⠻⣷⣤⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠁⠘⣿⡄
⠀⣸⣿⠁⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⢹⣷
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄⡀⠀⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⣀⣠⣤⣾⡿⠟⠛⠿⢿⣷
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣬⣿⣿⣷⣿⣿⣿⣤⣤⣤⣶⣶⣶⣾⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠸⣿⣧⡀
⠀⠀⠀⣠⣾⠿⠋⠉⠀⣠⣾⣟⡉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⢁⣀⣀⣀⣀⣈⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⢸⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣆⠀⠀⠀⠀⣀⣴⣾⡿⠃
⠀⠀⠈⢻⣿⡆⠀⢰⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣶⣶⣾⠿⠛⠋⠁
⠀⠀⠀⠸⢿⣷⣶⣿⡏⠀⢀⣀⠀⣶⣷⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡁
⠀⠀⠀⠀⠀⠉⣻⣿⣠⣾⡿⠿⣿⡿⠁⠀⠈⢿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⡿⢿⣿⣅
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠉⠉⣿⣯⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⠀⠀⠀⠀⠀⢀⣤⣿⠋⠀⠀⠀⠈⠻⣷⣤⣴⣾⣿⣿⣦⣤⣴⣾⠿⠻⠿⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⢀⣴⣾⠟⠛⠉⠉⠉⠉⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣄⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠀⣸⡿⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠃⠀⣿⡇⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠐⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠁⠀⠀⠙⠿⣷⣦⣄⣀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠹⣿⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠛⠉⠂⠐⣀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠂⠁⠂⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣶⣤⣶⣶⣾⠿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠔⡄⠀⠀⢠⡀⣀⣄⠀⠰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣌⡀⠀⠈⠂⠁⠘⢿⣷⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⣿⣿⣷⣤⣄⡀⠀⠈⠻⣿⣆⠀⢰⣀⣀⡀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⡿
⠀⠀⠀⢠⣾⡿⠛⠛⡛⠛⠛⠛⢛⣿⣿⣿⣷⣶⣤⣙⣿⣷⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢰⣿⠇
⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⣠⣴⣿⠟⠁⠈⠉⠛⠛⠿⢿⣿⣿⣿⣭⣍⣉⡁⠀⠀⠠⠤⡔⢀⡀⠀⠀⠀⠀⠀⠀⠀⠨⠐⣠⣿⠟
⠀⠀⡀⠀⢹⣿⣷⣦⣤⣾⡿⠟⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⢀⣾⡿⣷⣿⠿⠛⠻⣿⣿⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉
⣾⣿⠀⠠⢄⠀⡀⠀⠀⠉⡉⠉⠉⣿⣿⠀⠀⠀⠀⣀⣤⣾⡿⠿⠛⠛⠉⠉⠉⢉⣿⡿⠋⠁⠀⠀⡉⢻⣷⡄
⣿⣇⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⢠⣿⣿⣀⠀⠀⠀⢹⣿⡅⠀⣴⣷⡆⠀⠀⢀⣿⡿⠁⠂⠀⠉⠀⢀⡀⣿⡇
⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠛⠻⢿⣷⣶⣤⣿⣿⡄⠈⠉⠀⠀⠀⣸⣿⣤⣦⣤⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠙⠿⣷⣶⣤⣤⣤⣤⣴⣾⡿⠋⠀⠀⠀⠀⢀⣿⡿⠿⣿⣿⣦⡀⠀⠀⠀⠈⠛⠉⠙⣿⣶⣿⣷⣄⣼⣿⡥⠿⠿⠦⣤⣤⣶⣾⣿⠁
⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⣈⡻⣿⣦⣄⡀⠀⠀⠀⠀⠈⠁⠀⠹⠿⢿⠏⠀⠀⠀⠀⠈⢯⣥⠟⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠿⢿⣮⡙⠻⢿⣷⣶⣶⣤⣤⣤⣴⣶⣶⣿⠀⠀⠀⢰⣶⡆⡞⢀⣀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠿⣿⣿⣭⣭⣿⣿⡟⠉⢷⣄⡀⠀⣉⣴⣇⠙⠿⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⣿⠀⠀⠀⠈⠙⠛⡉⠁⠙⢦⣀⣀⣀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⢷⡜⠂⠔⠨⠅⠂⠈⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡋⢉⣽⠟⠾⣿⣶⣿⣛⠛⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠿⢷⡆⠀⣠⣴⠿⢿⡿⠿⢷⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣈⣀⡾⠛⢶⣿⡜⠀⠾⣧⣄⣸⢧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠶⠿⣷⣤⣤⣬⠿⠒⢻⣽⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢦⣤⣤⠤⠤⣴⣿⣿⣿⣿⣿⣦⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠛⠁⠀⠀⠀⢠⡖⠒⣦⠀⠀⠀⠈⠉⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⡾⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⡁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠌⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣯⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠶⡶⣀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⠻⠿⠿⠟⠉⠁⠀⠀⠀⠉⠛⠿⣿⡿⠟⠃⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠅⠉
⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠄⠀⠀⢀⣴⠾⠛⠛⠛⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣶⣄⠈⣷⠀⠀⠀⠀⠀⠀⢀⣿⢀⣾⠛⠉⠀⠈⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠛⠻⢷⣤⠀⢰⡿⠁⠀⠀⠀⠙⣷⠙⢷⣄⣀⣀⣀⣤⡾⠃⢸⡇⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣠⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠙⣧⢸⡇⠀⠀⠀⠀⠀⣿⠃⠀⠈⠉⠉⠉⠁⠀⠀⠘⣷⡀⠀⠀⠀⠀⣠⡿⠀⢠⡿⠋⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢠⡿⠈⠻⣶⣄⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠟⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣤⣴⠟⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠙⠳⢦⣌⠻⣦⣀⣀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⣠⣤⡶⣦⣤⣄⠉⠉⠉⠀⠀⠀⠀⣀⣤⣴⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⣠⣶⠟⠋⠉⠀⠀⠀⠉⠙⠻⣦⡀⠙⢷⡈⠉⠉⢉⣡⣤⣤⣀⡀
⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⡀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠈⠁⢀⣴⠟⠉⠁⠈⠉⠻⣦
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢀⣼⠏⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠈⣿⡇⢀⣶⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠘⣷⡀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⡶⠟⠋⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣇⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠛⠷⠶⠶⠿⠋
⡄⠀⠀⢀⣤⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⣿⢿⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏
⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠙⢷⣤⣀⡀⠀⠀⣀⣀⣤⣴⠟⠙⢿⣆
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣸⡿⢷⣤⣀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⢰⡟⠀⠀⠉⠙⠛⠻⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠙⠛⢷⡄
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠈⠻⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⣿⠇⠈⣿⡄⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⣴⡿⣧⡀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⢀⣴⡟⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣀⡀⠀⠀⣀⣤⡾⠟⠁⠀⠀⠀⣀⣠⣴⠿⠋⠀⠈⠻⠶⢶⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⢀⣤⣾⠟⠻⢶⣤⣀⣀⡀⠀⢀⣀⣉⣙⣻⣿⣿⣿⣭⣤⣶⡶⠶⠿⠛⠛⢿⣤⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡄⠀⠀⠀⠈⠉⣹⡿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⣀⠀⠀⠀⠀⠀⢀⣀⣹⣷⣄⠀⠀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⡐⡎⢹⣼⡋⣀⠠⠖⠈⣉⣉⡀⠤⠬⠿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⣀⣾⠗⠒⠒⠀⣉⣉⣉⠠⠇⢠⠀⣦⣈⣩⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡄⠀⠀⠀⠀⠀⠈⠙⠛⣿⡟⠁⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡴⠶⠾⠛⠛⠉⠉⠀⢀⣀⡀⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡶⠶⠶⠾⠿⠿⠛⠛⠛⠋⢹⡏⠀⠹⣦⣀⣀⣴⣶⣤⣤⣴⡿⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣀⣠⣤⣄⣀⣠⣴⣶⣤⣴⠿⠃⠀⠀⠈⠛⠛⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠛⠿⢿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⡀⠲⠀⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠆⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⡷⠀⠐⠿⢏⡇
⠀⠀⠀⠀⠀⣾⣿⣿⡟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣦⣴⣶⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣤⣀⠀⠉⠉⠉⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⠁⠀⢠⣶⢶⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⢡⢸⣿⣿⣿⠄⠀⠀⠀⠀⠰⠀⠀⣰⣾⣲⠀⠀⠀⠀⠀⣼⣟⣦⠀⠀⠇⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣀⠀⢻⣿⡿⠀⠀⠠⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⣄⣄⠀⠻⣿⠟⠀⠀⢸⠸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠌⠀⠈⠋⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠂⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⣀⣀⣀⡀⢀⣀⣀⣤⣤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡤⠀⠀⢀⡀⣀⡀⠀⠤⢔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠠⠁⠀⠀⢀⠠⠀⠀⢾⣦⣵⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠇⠀⠀⠀⠀⠁⠀⠀⠀⠘⠿⣿⣿⡷⠂⠀⣤⣴⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡿⠛⠉⠉⠀⠀⠀⠉⠉⠙⠗⣁⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢰⠄⠂⠁⠀⠀⠀⠀⠀⠈⠑⠏⠀⠉⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⡀⠀⠄⠀⠀⠅⡷⠚⢱⣉⡦⡎⡂⡏⣷⡄⣲⢖⣁⢖⣑⢴⢑⠄⠀⠀⡀⠠⠀⠀⢠⠁⠀⠀⠀⢠⠜⢿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⢀⣁⣀⣀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠧⠀⠀⠠⠃⠀⠀⠀⠀⠀⢸⣼⣮⣿⣿⣿⢿⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠿⠿⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣠⡶⠟⠛⠉⠉⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⡀⢸⣿⠃⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠁⢸⣿⠀⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⡄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠻⣦⣄⣀⡀⢀⣀⣤⡾⠟⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠻⠷⣶⣤⣤⡶⠾⠛⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡟⢿⣦⡀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⣻⡏⠛⠀⠀⠉⢻⣷⣦⣤⣀⣀⡙⢿⣦⡀⢀⣠⣶⠿⠋⠁⠀⠀⢀⣀⣤⡾⢿⣧⣤⡄
⠀⠀⠀⠀⠀⠠⣿⡛⠁⠀⠀⠀⣠⡾⠃⠈⠉⠉⠛⠛⠛⠿⠿⠿⠿⠷⢶⠶⠶⠾⢿⣟⠋⠉⠀⠈⠉⣿⣇
⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠏⠀⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣀⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠶⠶⣤⣤⣤⣤⣤⣄⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢀⣼⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⢀⣴⠾⠋⠉⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⢻⣿⠁⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣷⠀⢸⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⣼⣿⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⣦⣀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⣠⠞⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣉⢷⢃⣤⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠿⢻⣯⡛⠁⠀⠀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠏⠈⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉

⣿⣿⣿⣿⡇
⣿⣿⣿⣿⡇⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠛⠲⣤⡀
⣿⣿⣿⣿⣷⡟⠋⠁⠀⠀⠈⠙⠳⣄⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⣠⣤⡀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⢁⠀⠀⠀⠀⠈⠛⣶⡄⠀⣿⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⢸⠇
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠛⠉⠀⢀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠙⠦⣄⡀⠀⠀⠀⣀⡴⠞⠉⢷⡀
⣿⣿⣿⣿⢟⠓⠶⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⣀⣀⠀⠈⣧
⣿⣿⣿⣿⣾⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠈⢳⠀⣿
⣿⣿⣿⣿⣿⡟⠁⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠻⠤⠴⠏⢀⡟
⣿⣿⣿⣿⡟⠙⠶⠖⢋⣀⡘⣧⡀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⣟⠀⠀⠀⠀⠀⢀⣴⣦
⣿⣿⣿⣽⣿⣦⣤⠞⠋⠉⢿⣀⠙⠓⠶⠶⠶⠞⠋⠁⠀⣀⣠⡴⠞⠉⠉⣿⠀⠀⣠⣴⣾⣿⠿⠟⠛⠳⢦⣄
⣿⣿⣿⢽⡇⣸⠃⠀⠀⠀⠀⣽⡶⠶⣶⠖⠒⣲⠟⠛⠉⣉⣿⡀⠀⠀⠀⠈⣻⠆⠙⢿⠟⠁⠀⠀⠀⢀⡀⠙⣧
⣿⣿⣿⣾⡇⢹⣆⡀⠀⠀⢀⣈⣿⢦⣬⣷⣾⣧⡴⠶⠛⠉⠈⢷⣀⣠⡴⠛⠁⠀⠀⣾⠀⠀⣈⠁⠀⢈⡤⠀⣿
⣿⣿⣿⣿⡇⠀⢨⡟⠉⠋⠉⠉⠀⢠⣯⠿⠻⢼⠇⣰⠶⣦⣴⢾⣯⣁⣀⠀⠀⠀⠀⠸⣆⠀⠉⠙⠒⠉⠀⣰⣏⡀
⣿⣿⣿⣿⡇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠉⠉⢹⠀⠀⠀⠀⢰⠟⠛⢳⡶⠶⣶⠛⢉⣼⠇
⣿⣿⣿⣿⡇⠀⢹⣶⣦⣤⣤⣤⣤⡤⠤⢤⣤⠤⠴⢿⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠈⡷⠀⠈⠁⠀⠀⠀⠀⢻⡆
⣿⣿⣿⣿⡃⠀⢸⣥⣴⠶⣤⣀⣤⠤⣄⣼⠇⠀⠀⠈⠙⠒⠶⠶⠞⠋⠀⠀⠀⠀⠀⠘⢧⠴⠞⢶⣤⡶⠲⠶⠾⠃
⣿⣿⣿⣿⡇⠀⠀⣄⣀⢀⣀⢉⣁⠀⢀⡀⢀
⣿⣿⣿⣿⡇⠀⠀⣿⣧⢸⣿⣺⣿⡗⣿⡿⣿⣟⣸⣿⢸⣿⡇⣾⣷⢸⣷⠃⣿⡁⢸⣿⢴⠖⣦⣾⣻⢼⣿⠆⣇
⣿⣿⣿⢿⠇⠀⠀⠁⠀⠈⠁⠈⠀⠁⠀⠀⠉⠉⠉⠉⠈⠉⠁⠈⠁⠘⠉⠁⠙⠃⠙⠉⠈⠉⠉⠋⠀⠘⠀⠀⠛
⣿⣇⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠛⠿⢶⣤⡀⠀⠀⠀⢀⣠⣴⠶⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⣰⡟⠋⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⣿⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⣿⠃⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣀⣀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⢠⣿⡄⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡾⠛⢻⡏⠙⠛⣶⡄
⠀⣴⠟⠋⠙⠻⣦⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣿⠁⠀⣼⠇⢀⣾⠋⣿
⢸⣿⠀⠀⠀⠀⠙⣷⣴⡟⠙⠻⠶⣶⣦⣶⡶⠾⠛⠁⠀⠀⠈⠻⢷⣤⣀⣀⣀⣀⣤⣴⠿⢿⡆⠀⢿⣦⡾⠋⠀⢸⡇⢠⣿
⠀⣿⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠘⣿⠀⠀⠙⠷⢶⣤⣼⣿⠟⠁
⠀⠘⣷⡀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠹⠷⠶⠂
⠀⠀⠈⢿⣄⠀⠀⠀⢻⣆⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⣸⡟⠀⠸⣦⣤⡄
⠀⠀⠀⠀⠙⣧⡀⢀⣤⡿⢷⣄⡀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⣠⣾⣿⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⢻⣾⠟⠀⠀⠉⠛⣿⣶⣶⣿⣿⣶⣶⣶⣶⣶⣾⣿⣭⣤⣤⣶⡾⠛⠉⠀⠈⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣻⣦⣀⠀⠀⣼⣿⣿⣿⠇⠀⢠⣴⣿⣿⣿⣦⡀⠀⢻⣿⣿⣷⡀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣨⣿⣷⣾⣿⣿⣿⣯⣤⡀⠘⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣷⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣴⣿⡿⠛⠛⠋⠈⢿⡄⣾⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣷⣤⣤⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⣀⣼⠃⠀⠈⢷⡄⠀⣀⡀⠀⢀⣤⣀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠙⠛⠋⠙⠳⠟⠋⠙⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⣁⣠⣤⡤⠤⢤⠀⣤⡤⢤⣤⣤⡤⠤⢤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡔⠉⢠⢿⢤⠻⢱⢸⠀⡇⠀⡔⠉⢀⠉⢢⠀⡇⢸
⠀⡠⠒⠉⠉⠉⠒⢤⡀⠀⠀⡇⠀⣜⣐⣰⣐⣜⡄⠀⠀⠀⠀⠀⠀⢰⠃⢸⢀⠤⡼⣶⡚⠉⢻⢸⢀⡇⠀⢇⠈⠰⡆⢸⢤⡇⢸
⡜⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⠇⠀⡇⢠⢺⡳⡀⡇⠀⠀⠀⠀⠀⠀⢸⣀⣘⡚⠚⠚⠛⠛⠿⠷⠞⠀⠳⠖⠟⠓⠒⠺⠥⠞⠁⠸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⣗⠁⠀⠀⡧⠬⢷⠮⡤⡇⢸⣁⠢⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠤⢄⡠⠠⡄⡬⢍⡩⠅⢍
⠀⠀⣀⣄⡀⢀⣤⡀⠀⢸⠀⠀⠀⡇⢹⠃⣌⠀⡵⠚⢦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⢔⠃⠀⣵⠀⠸⡀⠘⢍
⡆⢰⠁⢀⣹⡇⢀⡘⡄⡸⠀⠀⠀⡇⢸⠁⠠⠀⣧⣀⣀⣱⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣑⣁⣠⠳⣀⠀⣀⣷⣘⣁⡰
⣹⣼⡀⠸⢿⡆⠘⢿⣧⠇⠀⠀⠀⡇⢸⠀⠦⠀⢁⠨⠥⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⠁⠀⠉⢲⡲⠋⠀⠀⠉⢳
⢸⠋⠑⠒⠁⠙⠒⠉⢻⢤⡤⠗⠒⠷⣘⡶⠛⠉⠛⣷⠆⠛⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠴⠛⠂⡇⠴⣄
⣸⡀⠀⠀⠀⠀⠀⠀⣼⢸⠁⠀⢴⣷⣾⣶⣿⠆⠀⢸⡔⣤⠈⡆⢀⢾⣄⠀⠀⠀⠀⢀⣀⣀⢠⠷⢄⣀⣀⣠⠞⠙⢄⣀⢀⣀⠼
⢡⣵⣦⡬⣵⣯⣥⣶⣅⠈⣦⣄⣀⡭⠋⠙⠦⠤⠴⢻⡀⠈⢀⠕⢘⣾⣏⣀⡀⢠⢪⠵⠒⠒⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⡞⢹⠉⠩⡏⠉⠉⢻⠻⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢴⠊⠀⢎⠀⠀⠀⡷⢃⡏⢰⢋⡩⢿⡭⣉⡛⠦⣄⠀⠀⣀⡄⠀⠀⢀
⡷⡿⠶⢶⣿⣷⠤⠾⢶⣽⠳⡤⡄⠘⠦⠴⠃⢀⣠⣼⣳⡟⢀⣀⣈⣉⣉⣉⣁⣀⣷⡈⡏⠀⣸⣵⠛⢿⡑⢶⠷⢯⣥⠤⣤⣖⣉
⠩⣇⣀⣐⣇⣀⣀⣖⣺⢿⡀⠈⡏⠉⠋⠉⣹⠉⠈⡯⠻⢿⣻⠆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠷⢽⣟⠛⠑⡏⠀⠀⡹⠀⠈⢧
⠀⣼⠀⢈⡏⣏⠀⢹⠀⠀⣿⣉⣀⣀⣀⣀⣉⣑⣒⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢥⣭⣛⣉⣩⣭⣤⣤⢤⢤⡇
⠀⠳⠶⠚⠁⠸⠶⠚⠃⠘⠥⠦⠴⠦⠞⠣⠶⠴⠲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠢⠾⠤⠖⠢⠴⠒⠲⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⡴⠞⠛⠛⠛⠛⠷⣤⠀⠀⢀⣤⡶⠶⠛⠷⠶⣦⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡟⠁⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠇⠀⠀⠀⠀⠀⣤⣶⣶⣄⠀⣿⠃⢠⣴⣶⣤⠀⠀⠀⠀⢸⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⣿⣿⣉⣿⠇⣿⡄⣿⣿⣟⣿⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⠻⠿⢋⣼⢿⣇⠘⠻⠿⠟⠁⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢶⣤⣤⣤⣤⣴⠾⠟⠁⠀⠙⢷⣤⣤⣀⣤⣤⣶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣰⣶⣰⣶⣦⣄⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⣶⣶⡦⢠⣿⣿⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣄⣤⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣠⣶⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠋⠈⠉⠉⠈⣻⣶⠿⠛⣷⣤⣄⠘⢷⣦⣄⣠⣶⠟⣃⣶⠶⡿⠻⣶⡟⠛⠛⠉⠀⠀⠸⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⠹⢿⣦⣤⣌⣙⣋⣥⣼⣟⠋⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣍⣩⣽⣿⣿⣆⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⣤⣶⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⢿⣧⣀⣀⣾⣿⣿⣿⣿⠙⠛⢛⣿⣧⣄⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣀⣠⣿⣿⣿⣏⠀⠈⣻⣿⣷⣶⣾⣋⣀⣈⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠋⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠛⢷⣴⡶⠟⠳⢶⠾⠛⢷⡶⠟⠻⣦⡶⠟⠷⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠈⠙⠲⣄⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⠀⠸⡀⠀⢼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣇⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⢠⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠙⠶⣤⣀⣀⣀⣀⣠⠴⠚⠁⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⣤⣀⣀⣀⣀⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣠⠞⠉⠙⢳⡄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣈⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠋⠀⠈⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠳⠶⠶⠛⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣤⠞⠛⠋⠀⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣰⣏⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡯⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⣠⠞⠉⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠓⠒⠲⠶⠶⠦⡶⢧⣄⣀⣀⣀⣀⣤⠴⠚⣉⣀⣀⣤⣶⠋⠁⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠙⣳⠀⠀⠀⢀⣧⢤⡤⠴⢿⠟⠓⢻⣟⠉⠉⢯⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⡄⠀⠀⢸⡇⡾⠀⢸⠋⠛⠒⠋⠈⣧⠀⠈⠧⣀⠀⠈⢳⣄⣤⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠐⣿⠀⠀⠀⢸⢠⡇⠀⠸⣦⡴⠛⠓⠶⡇⠀⣠⠏⠉⠳⠴⠶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣾⣀⣀⣀⡿⢸⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⡏⠀⠀⠀⠀⠀⠀⠛⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⣉⣀⣀⣛⣀⣀⣀⣉⣀⣀⣀⣀⣘⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⣉⠉⠉⠉⢉⠁⠀⠀⢀⡟⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠶⠛⠉⠳⠤⠖⠋⠳⣄⣠⠞⠁⠀⠀⠀⠀⠈⠳⢤⣤⣤⠴⠚⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠖⠀⠀⢠⡶⠟⠛⠛⡛⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠀⢹⡇⢀⣤⣶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⢀⣴⠟⠛⠛⠿⣦⢻⣄⠀⠀⠀⠀⢀⣾⢃⣾⠃⠀⠀⠠⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠉⠙⢿⣆⢸⡏⠀⠀⠀⠀⢹⡇⠙⠳⠶⠶⠾⠛⠁⠸⣷⠀⠀⢀⠉⠀⣸⡟⠀⣠⡾⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠠⠇⠀⠀⣿⠙⣧⣄⡈⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⡶⠟⠁⠀⣿⠀⠀⠃⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⣡⡾⠋⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⡀⠐⠲⣤⣀⢻⣄⡀⠈⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣌⡙⠛⠛⠉⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠛⠻⣦⣄⠙⢷⡌⠛⠛⠛⣁⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⢠⠀⠉⠻⣆⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠈⠙⠻⣦⡀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠉⢀⣴⠟⠉⠉⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡆⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⡇⠀⠀⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠃⠀⣠⡟⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠘⣿⠀⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢷⣄⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⠶⠛⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡇⠀⣿⡆⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢰⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠉⠻⠶⣦⣤⣤⣶⠶⠟⠛⠁⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣾⠋⠙⠿⢶⣦⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⡉⠙⠻⣷⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⢠⡿⢁⠐⠀⠄⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠐⠂⢸⡇⠈⣿⡄⠀⠀⡀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠂⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠂⢈⣠⡾⠃⠀⠘⣿⣦⡀⠀⠀⠀⠈⠙⠿⣶⣤⣀⡀⠀⢀⣠⣴⠿⠋⠀⠀⣀⣀⣤⡾⠟⠁⠈⠛⠶⢶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⣤⡾⠟⠻⢶⣦⣄⣀⣀⣀⣀⣉⣙⣿⣿⣿⣿⣤⡶⠶⠿⠛⠛⠛⢿⣄⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⢩⣿⠋⠉⠉⠉⠉⠉⠉⠁⠀⣠⠀⠀⠀⠀⣀⣀⠄⠿⣷⡄⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⠀⠀⠀⠀⣾⡃⠀⣀⠀⠠⠤⢤⡼⠁⠻⠯⣤⡄⣯⡥⠤⠄⠒⠒⠚⠻⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠉⠛⠿⢶⣦⣼⣟⠉⠤⠤⠤⠐⠒⠒⠀⢦⠴⠦⠔⠃⠀⠀⠀⠀⠀⠀⠀⣀⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠛⠀⠀⠀⠀⠀⠀⠀⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⠿⠛⠛⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡦⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣴⣶⣶⡶⠶⣾⠟⢻⣏⠉⠁⣀⣄⣀⣀⣴⡶⢶⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⣉⣁⠀⢀⣠⣤⣀⣴⡿⠀⠀⠙⠿⠿⠛⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣤⣾⣿⠿⠛⠛⠛⠛⠛⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣶⣤⣤⣀⣀⣀⠀⣿⣿⣧⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠛⠉⠉⠉⠉⠉⠉⠙⠻⢿⣿⣶⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⣿⣿⠃⠈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⣿⣿⡄⠀⠈⠋⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣄⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠉⠛⠿⠃⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠈⠙⢿⣿⣦⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⡿⠹⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠙⠻⢿⣶⣦⣤⣤⣤⣴⣶⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢰⣿⡇⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣤⣄⣀⣀⣀⣀⣤⣴⣶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠹⠿⠃⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⢠⣿⡿⠀⠈⠉⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠈⣿⣿⣆⣀⣀⡀⠀⠀⣤⣄⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣆⠸⣿⡿⠀⠀⠛⠋⠀⠀⣴⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣄⣀⠀⢀⣠⣾⡿⠋⠀⠀⣀⣠⣤⣶⣿⣿⣿⣧⡀⠀⠀⠉⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠋⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⣿⣿⣿⣭⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⢿⣿⣆⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠻⣿⣷⣶⣶⣶⣶⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣼⣿⣿⣆⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣯⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⢀⣾⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣾⣿⡃⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⡶⠶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠾⠿⠟⠛⠛⢿⣿⡟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣤⣴⣶⣿⣦⡀⠀⢀⣠⣾⣿⣿⣶⣤⣀⣠⣾⣿⣿⣧⡀⢀⣠⣴⣿⣿⣷⣤⣄⣀⣾⣿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠙⠿⠿⠿⠿⠛⠉⠀⠈⠛⠛⠛⠛⠋⠁⠙⠛⠿⠟⠛⠛⠁⠈⠉⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⣤⠴⠶⠶⢶⣤⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⢀⡤⢤⠴⢦⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣆⠀⠀⠀⠀⠈⢧⠀⣠⡴⠶⣤⡀⠀⣀⣾⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠻⢶⣤⣤⣴⡶⢶⣿⠋⠀⠀⠈⢿⡟⠋⠉⠁⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣟⣻⠿⠛⢶⣤⡴⢶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⣀⣽⣇⠀⠀⢀⣿⣄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠳⢶⡟⠓⠋⢀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠛⠙⣧
⠀⠀⠀⠀⢀⣀⣠⣿⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣴⣿⠶⠶⠤
⠀⠀⠀⠀⠈⠉⠈⢿⡀⡀⠀⠀⠸⠿⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⡷⠀⠀⠀⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠚⠛⣿⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢭⡽⠂⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠛⠳⢦
⠀⠀⠀⠀⠀⠀⣨⡷⠟⠻⣦⣽⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⡛⠉
⠀⠀⠀⠀⠀⠸⣏⠀⠀⢠⡟⣠⡾⠋⠁⠸⣯⣭⣽⣽⣯⣭⣽⠇⠈⠛⢯⣙⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣾⣝⣿⣤⣀⠀⣰⠟⣹⠏⠀⢻⣎⢷⡄⢀⣠⡴⣿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠉⠙⠋⣰⠏⠀⠀⠀⢹⣎⠛⠋⠁⠀⠘⢧⣀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠓⠲⠶⠶⠤⠤⢤⣤⠤⠤⠤⠶⠒⠚⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡄⠀⠀⠀⠀⡆⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⢄⡀⠀⣀⣀⣤⣤⣀⡀⠀⠱⣸⡄⠀⠀⠀⠳⠃⠀⠀⠀⠀⡠⢖⠆⣀⣀⣠⠊⠉⠉⠉⠉⠉⠉⢳
⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⠄⠀⠀⠀⠀⠐⢥⡞⠀⠀⠀⠀⠀⠹⡄⢀⡭⠚⠉⠉⠉⠉⠑⠢⣄⠀⠮⠔⠁⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠸⠥⠤⠤⠤⠤⠤⠤⠤⣤⠎⠀⠀⠀⠀⠀⠀⠀⠈⢮⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⠓⠒⠠⠤⠀⠐⠒⠒⠒⠂⠄⠒⠁
⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠠⠖⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡇⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⢀⡤⠴⡟⠤⠄⠤⠚⠉⠑⢦⡀⣠⠔⠊⠉⠒⢤⣀⡠⠔⠤⡑⣄⠀⠀⠀⠀⡼⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢣⡄⠈⣾⣤⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣤⠊⡤⢶⣯⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡱⠆
⠀⠀⠀⠀⠀⠀⢀⣸⡛⠃⢀⣿⠛⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣦⡽⠓⠓⠚⠓⢲⣞⠳⠶⠶⠷⢇⣀
⠀⣠⠖⠓⣤⠖⣻⠋⠑⠒⠋⠈⠓⠒⠊⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣏⣿⣉⣿⡝⡵⢮⢻⡓⣖⢲⣶⣏⡀
⠠⡿⠀⠀⣎⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⡠⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠀⠀⠀⠠⠯⠮⠤⠤⢷⣽⡍⠉⠉⠀⠱⢄⡀
⢸⠶⠶⠴⢾⡀⠈⣢⣄⣐⣦⣤⣒⣀⣠⠞⠀⣀⣀⡀⠀⣇⣀⣐⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⢟⡻⣉⣉⡛⠛⠛⠓⠒⢒⠶⣖⠒⡖⠊⠓
⢸⠀⠀⠸⣍⣉⣹⢱⠇⣽⠉⠉⢹⠙⣎⢳⠋⠁⠀⠉⢳⡟⢁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⣤⠞⠵⠵⣏⣙⣽⡍⠉⠉⠉⠉⣽⣷⣋⣻⣿⡝⢦⡀
⢸⠀⠀⣀⣸⣴⠉⡟⠀⠙⠓⠒⠚⠁⢹⢿⠀⠀⠐⠿⢪⣇⠿⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⡅⠀⣼⢈⠟⢋⠉⠳⡄⠲⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⡤⠛
⢸⣴⣾⣿⣉⣿⣶⣧⡀⠀⠀⠀⠀⠀⠸⣯⠓⠦⠤⠔⠋⠈⠲⠤⠤⠞⢹⡛⠓⠲⠦⣤⣀⣾⣀⣀⣸⢿⣄⠢⠌⢁⡇⡸⣟⣻⠋⢻⠛⣟⣛⡳⠲⣒⣺⠓⢦
⢈⡁⢈⣛⡍⠉⢹⠁⡟⣦⡤⣤⣤⣤⣤⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠒⠲⠤⣈⡧⠀⡩⢬⡇⠘⠛⠲⠋⢩⡗⡜⠉⠑⣼⠲⣋⡸⢆⡴⢇⣀⡖⠘
⢈⠀⠀⠉⠁⠉⢹⠀⡟⣹⢀⣼⠀⠀⢳⡼⠳⣤⣙⣲⣤⣠⣴⣋⣠⡴⠿⡶⠤⣄⡀⠀⠀⡇⠀⠙⢾⣦⡤⣄⡤⣄⣽⢼⠋⠀⠘⣯⠛⠛⠧⡘⢧⢜⠈⠷⠤
⠈⠉⢉⣗⣲⡖⠚⠛⠛⣣⠟⠉⠓⠒⠻⢤⣠⠋⠀⠀⠀⠀⠀⠀⠹⣄⡠⠗⠀⣠⡟⠛⠲⡇⠀⠀⢰⡇⠉⠓⠦⣄⡈⢹⠛⠒⢒⣻⠛⠛⠋⠛⠚⠃⠹⠚⠙
⠀⢀⢎⡜⢳⡱⡄⢀⡾⠁⠀⠀⠀⠀⠀⠀⡿⠤⠤⢤⣤⣤⠤⠤⠤⣿⠀⢀⡴⠋⠀⠀⠀⠳⢤⣠⠼⠳⢤⡀⠀⠀⠉⣻⠀⠐⣏⠉⠳⢤⡀⠠⢤⠀⠀⠀⠐
⢠⢪⠎⠀⢰⢱⡘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⡖⠛⠚⠓⠚⠒⠛⠚⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⠉⠓⢦⣀⣿⠀⠀⠈⡷⢄⠀⠙⢦⡀⠀⢀⣀
⠀⠃⠀⠀⠈⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠃⠀⠙⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⣶⠀⠀⠀⠀⠀⣴⣶⡆⣶⣤⣴⣶⣄
⠀⣠⡀⢀⣴⣷⣠⣤⡈⢁⡼⣿⡳⣄⣤⣴⢶⡒⢦⣾⣸⡏⠈⠳⢟⣋⣀⠀⣶⠗⣾⣶⡄⣀⣀⠀⣠⡤⡄
⢸⠉⡇⠚⠚⡟⡏⠉⠀⠚⠉⠁⢈⣧⠈⣀⣤⣮⠜⠯⠋⠀⠀⠀⠻⠿⠟⠁⠷⠶⠏⠸⠟⠿⠾⠸⠁⢇⡇
⠈⣇⢿⠀⢠⡇⡗⠀⠀⠀⠴⠶⠟⠁⠈⠋⠁⠀⠀⠀⠀⣠⡴⠊⢱⡤⠒⣦⣄
⠀⠙⢚⡃⠀⠉⣤⠀⠀⠀⢀⣀⣤⣤⣶⣶⣒⣒⠢⢄⡘⠀⣰⠾⠞⣰⣾⣷⣀⡠⠤⢄⣀⠀⢀⣀⣀⡀
⠀⣄⠈⣿⣄⢰⡏⠀⢀⣾⠟⠉⠁⠀⠀⠀⠀⠈⠙⠲⠹⡌⠓⣺⢛⡽⠿⠋⠉⠋⠙⠓⠾⣝⣏⠉⠉⣽⣲⡷⠶
⠀⢨⠞⢉⡈⢹⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⡸⣾⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡴⢩⠄⢀⢀
⠀⣏⠰⠟⠙⣦⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣫⣿⣷⠀⢸⣿⣧⣾⣿⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠁⠈
⠀⡈⠓⠒⡶⠋⠘⣿⡀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟⢠⣿⣿⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡜⡷⠶⠛⠦
⠸⠋⣠⡄⢠⠴⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣾⠜
⠀⠐⠟⠀⠸⠀⢡⣿⠛⠳⣄⣀⣠⣠⣤⣒⣊⡥⠖⠋⠁⠀⠙⠿⣤⣀⠀⠀⠀⢀⣀⣴⣾⡿⢿⣿⣧⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⣁⠀⠀⠀⢻⣿⡟⠋
⠀⠀⠀⠀⢀⣼⡏⢰⣞⠛⡙⠻⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠑⠀⠀⠀⣿⣧⠀⠀⣠
⠀⢀⣤⣞⡁⣿⢁⠼⣧⣊⣴⣠⠞⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⣀⠀⠀⣠⡿⠀⣿⣿⠀⠚⠁
⢀⡟⠁⠀⢉⣿⣧⡈⠀⠉⠉⠀⠀⠀⠈⢫⡢⣀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠙⠛⠛⠁⠀⣰⣿⠇
⠞⠀⠀⠀⡾⠁⠈⠛⠷⣦⣤⣄⣀⣀⣀⠀⠈⠛⠷⣦⣤⣤⢴⡾⠋⠁⠀⠀⠀⠀⣀⣀⣠⣤⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⢈⣿⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠉⠉⠉⢻⣿⡉⠉⠙⢿⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⣿⢿⡀⣠⢾⢿⡀⠀⠀⠀⠀⠀⢻⣗⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⣾⠖⢡⡷⠊⠀⠀⠀⠀⠀⠀⠸⡏⡇⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢰⡧⢶⡆⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠳⣶⢻⡧⣄⠀⠀⠀⠀⠀⠀⠀⢳⣡⠀⠀⢀⣬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⠤⣯⠻⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⠖⠲⠏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠒⠒⠒⠶⠶⠶⢶⠦⠤⠤⠤⠤⢤⡤⠤⠶⠶⠶⠶⣶⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣠⢄⣀⣄⢀⡾⠀⠀⠀⠀⠀⢸⡇⢀⡀⣀⣀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠈⠋⠀⠀⠀⠀⠀⠀⠈⠛⠁⠙⠃⢈⣩⣭⡀
⠀⠀⠀⠀⠀⣤⣶⡆⠀⢀⡀⠀⢀⣀⣸⣧⣶⡆⢀⣀⣼⣦⣴⡆⠀⠀⠀⠀⠀⢸⠁⢸⡇
⠀⠀⣀⣷⣤⡉⠁⢶⡄⠈⢿⠆⠻⠛⣉⣿⠀⠀⢈⣭⡼⢿⣾⠛⠃⠀⠀⠀⠀⡿⠀⣻⡀
⠀⠙⠛⣿⣽⠶⠆⢿⣇⢀⣄⠀⠀⠈⠛⢻⡇⠀⠀⢀⡀⠈⠋⣀⠀⠀⠀⠀⠀⠓⡾⡛
⠀⠀⢠⡿⠶⢶⠶⠌⠙⠛⠉⠀⠀⠀⠀⠛⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⢸⣁⣿
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⡞⢸⡯⠅⣻⢼⡇⣞⣹⣦⣷⡞⢁⣶⡒⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣎⣷⢿⣨⠗⠙⠉⠁⠉⠉⠈⠀⠀⠈⠉⠈⠃⠉⠘⠧⠅⣼⣷⠟⣤⢄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣯⡖⡀⠻⠉⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠀⠓⠚⣱⣯⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣧⡬⠉⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉⠉⠙⠷⣄⠀⣠⠞⠋⠉⠉⠉⠛⢷⡄⠀⠀⠀⠉⠀⠾⠳⢟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣠⣀⠘⣿⠋⢀⣀⡀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣿⣿⠇⣿⠀⢿⣿⡿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⣰⡿⣧⡀⠉⠀⠀⠀⠀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠿⢶⣶⣶⣶⠾⠋⠀⠈⠛⠿⢶⣶⣶⠾⠛⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣄⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⡴⠛⠛⠛⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣷⣤⣄⣠⠿⠺⢿⣧⣀⠀⠾⣶⣤⣀⠀⠀⠀⢀⣠⣶⠟⠁⢀⣠⣾⣏⣾⠁⢠⡄⠀⣀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡮⣿⡸⠇⢸⡏⠛⢿⡶⢶⣿⣿⣿⣶⣾⣿⣯⣶⢶⣾⠟⠉⠉⢹⣿⠀⢤⡁⢀⣉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣦⣤⠾⠋⠛⠛⠻⣆⣰⠟⠁⠀⠀⣶⣶⣦⣾⣿⡆⠀⠀⠻⣧⡀⣠⣤⠿⢷⣤⣙⣋⣁⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣩⣬⢻⣿⣦⡀⣰⣤⣀⣿⡟⠀⠀⠀⠀⠻⠟⠉⠙⠿⠃⠀⠀⠀⢹⣿⢿⣄⠀⠘⠋⠉⠙⠿⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢿⣏⣸⣧⡞⠉⠛⠀⢉⡼⠿⠿⠷⠾⠶⠶⠶⣶⠶⠶⠶⠶⠶⠷⠾⢿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠛⠋⠀⠀⠀⠀⠘⠻⠶⠶⢶⡴⠶⠶⠶⠟⠷⣴⠶⠶⠶⠛⠓⠚⠁⠙⠛⠛⠻⠶⣦⠶⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⣀⢱⡔⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⢛⡹⡝⠛⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠉⢿⣯⣷⣿⣷⠒⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢶⣶⣿⣿⣻⣽⢿⣤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡟⢽⣿⠍⣿⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⡽⠃⠺⣿⣤⣿⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠏⣿⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣬⣷⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣰⣟⣲⣗⣆
⠤⠤⠤⠤⠄⠰⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠁⠉⢀⠀⡁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠡⠀⠀⠰⠶⠶⣿
⠤⠴⠶⠷⠖⠆⠡⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠲⣄⡀
⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣀⠀⠀⠀⠀⣷⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡟⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⢀⡇⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⠁⠀⠀⠀⣼⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⢀⡴⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣄
⠀⠀⢠⠏⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠈⢳⡀
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⡿⠀⠀⠀⠀⣠⠤⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⢤⣀⠀⠀⠀⠈⡇
⠀⣇⠀⠀⠀⡾⠁⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠘⡆⠀⠀⠀⡇
⠀⢹⡀⠀⠀⢧⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⠇⠀⠀⢰⠇
⠀⠈⢷⠀⠀⠈⠑⠲⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠒⠋⠀⠀⢠⡏
⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠻⣄⡀
⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⢻⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⢶⠋⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠉⡟⠙⠛⠒⠶⣶⣶⠶⠶⠶⠶⢶⣶⣶⠒⠚⠛⠛⢋⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⣿⣿⣷⣤⣤⣴⣿⣿⣿⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠰⣇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢻⣿⣿⡟⠛⠛⠛⣿⣿⣿⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠈⠙⢳⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡝⠉⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢠⡟⠉
⠀⠀⠀⠀⠸⢤⣤⡴⠁⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠹⣤⣤⡼⠃
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠈⠉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠋⠉⠉⠉⠉⠉⠻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣟⠉
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⡞⠀⠀⣠⠴⠒⢦⡀⠀⠀⢀⡴⠚⠲⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠞⠳⣄⠀⠀⠀⢠⠖⠲⢤⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠞⠁⠀⠀⠀⠈⠙⠚⠁