Terrestrial planet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⡿⠒⠓⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠑⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣋⣩⣟⣿⠟⠿⣶⣆⠀⠀⠀⠈⠙⢲⣄⡀⠀⠀⠀⠀⠀⠄⠀⢼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢤⣶⠞⣿⣿⣿⣿⡿⣿⡿⠙⢋⣤⣶⣾⣿⣿⠗⠀⠀⠀⠀⠠⣿⣿⣦⣰⣄⡀⠀⠀⣀⠈⡿⠿⠷
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠚⠉⠁⠀⠈⠱⠎⠁⠀⠈⠉⠈⡙⠋⠁⠀⠀⠁⠀⠠⡄⣿⣿⣿⣿⣏
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⡾⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⣴⣶⣦⣄⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⢀⡿⠿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⡼⠀⠈⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠋⠻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠤⠀⠀⢐⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣶⣦⠀⠋⠾⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠐⠈⠃
⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠉
⠐⠾⠿⠀⠈⠁⠠⣄⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⣽⡛⢻⣿⡏⡇⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⠟⠁⠀⢻⡼⠀⠀⢀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣩⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠐⠁⢀⣀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⢀⣠⣎⠀⠀⠈⠁⠀⠀⢀⣄⡀
⠀⠀⠀⠀⢀⣀⣈⠁⠀⠀⢀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⢡⠄⠀⠀⠴⠋⠙⠁⠀⠀⠀⠒⠀⠀⠿⠋⠁
⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠈⠒⢤⠀⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠁⠀⠰⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⢿⣯⠉⠉⠉⠹⣿⣟⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠠⣾⣿⣍⠀⠀⠀⠀⠈⢹⣿⣠⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠈⣻⡇⠀⠀⠀⠀⢸⣿⠟⠃⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣀⣀⠀⣠⣤⣾⠟⠁⠀⠀⠀⠀⠀⠉⢀⣀⣀⣀⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠹⣷⣼⡟⢻⣷⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠛⠛⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣿⣷⣄⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠙⠛⢀⣴⡶⠿⢶⣤⣤⡀⠀⠀⠀⠙⠿⠾⠟⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⠁⠀⠀⠀⠉⠹⠷⢶⣦⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⢀⣿⠇⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⢾⣏⠀⣠⡾⠟⠛⠋⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣮⣿⣛⣋⣁⣀⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋⠉⠉⠙⠻⢿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣻⣾⣝⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠿⢿⣿⣦⣀⣀⣈⣉⣛⡻⠿⠋⠀⠀⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢻⣿⣷⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣴⣿⡿⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦
⠀⠀⠀⢀⣾⣿⡟⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⡙⣷⡀
⠀⠀⢀⣾⣿⠏⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢹⣷⡀
⠀⠀⣾⣿⡟⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣷
⠀⣸⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠛⠛⢿⣇
⢀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⣿⣿⠿⠋⠁⠀⠀⠀⠀⣿
⢸⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⣿⣦⣄⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣾⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⢫⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠈⠻⠿⣷⣄⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣀⣀⣀⣠⣴⣶⣿⣿⡇⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⢿⣿⣿⡄⠀⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⢈⣿⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠁⠀⠀⠘⡇⠀⢻
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠺⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⢀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠻⣿⠇⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣦⣀⠀⠀⢀⣿⣠⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣶⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁
⣶⣶⣶⣶⣶⡷⣿⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣷⣶⣿⣿⣶⣶⣶⣿⣶⢿⡿⠷⠿⢷⣶⠿⠿⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⢻⣿⣿⣿⣧⡀⠘⠷⣭⡙⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⢈⡉⠉⠻⠃⠀⢸⣿⣷⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣠⣶⣶⣤⡀⠀⡀⠀⠀⠀⠀⠀⠘⠁⠟⠻⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣯⣙⣫⣀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣥⣽⠋⢁⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⢸⡆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⣼⣿⣿⣿⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠛⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠈⠹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠳⠌⠙⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠖⠉⠀⠀⠀⠀⠀⠐⠦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⢻⣡⠀⠀⠀⠀⣠⣴⣿⣿⣷⣠⣶⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⡀⠀⠸⢿⣿⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢠⢮⣧⢀⣤⣧⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡿⠛⢋⠙⢮⡟⣿⠿⣧⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣛⣤⣴⣾⡆⠛⠁⠙⠀⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣤⣾⣷⣦⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣧⣭⡉⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⠟⠁⠀⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣩⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⢉⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⢄⡀⢀⣠⠴⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠛⠁⣠⡶⠛⢋⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠘⢛⣋⠁⠀⠐⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢁⣀⣤⡶⠛⢉⣠⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣥⣤⣤⡶⠶⠶⠶⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠉⢀⡤⢖⣫⠴⢋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⡁⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⡴⠾⡿⠚⢋⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⢶⣠⣤⡄⡀⠒⣂⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠐⡖⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡁⠔⠑⠉⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣀⠀⢀⣼⡟⣳⡄⠑⡀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⢀⡈⠄⠐⢀⡀⠀⡀⠀⢠⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡦⠘⠛⣾⣿⣷⠀⢘⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠤⡃⠀⠀⠁⡀⡀⠰⠀⠠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡉⠢⡀⠀⢈⡯⠟⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠈⠂⠤⠄⠂⠀⢀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⢤⣾⣿⣦⣯⣴⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡅⣈⠀⡀⢐⢈⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠔⠈⠉⠁⠡⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⡲⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣀⡤⠐⠶⠤⣤⡀
⠀⠀⠀⠀⠀⠄⠀⠀⢼⣆⠀⢠⠊⢀⢀⡨⠀⠀⠠⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠘⠀⢙⢢
⠀⠀⠀⠀⠒⠁⠄⠀⠀⠀⠀⣏⢀⠁⠀⠀⠠⠄⠀⢦⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡁⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠰⠀⠣⠔⠀⠀⠃⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠹⡄⠀⠀⠀⠠⠐⠒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠠⠤⠂⠢⢀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣔⠁⠀⠀⡠⠂⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠤⠬⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠔⠁⠈⠈⠓⡄⠀⢸⠀⠀⠀⠰⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⢀⡤⠖⠊⢉⠉⠉⠉⠑⠲⢄⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠐⠈⠁⠉⢲⠀⢸⠀⢰⠀⠀⠀⠀⠀⡇⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠱⡀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠂⡜⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠈⠉⠛⠒⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢡⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⢀⠈⠀⠀⠀⠓⠀⠒⠊⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠐⠂⣀⢀⠀⠁⠐⠀⠈⠀⠀⠊
⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡎⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠀⠘⠃⡈⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠈⠉⠉⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡈⡸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠈⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠄⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠸⠁⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣄⣀⣀⣀⣀⣠⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠞⠛⠋⠉⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠤⣀⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢉⠉⠉⠉⢉⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠄⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠌⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠐⠆⡠⠄⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠄⠀⠀⢀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⠋⡀⠀⠁⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠁⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠠⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠠⠀⠀⢠⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠰⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠙⠳⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠐⠁⠀⡐⠂⠐⠂⠀⠑⠒⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠤⠀⠀⠀⠼⢤⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠂⢤⣀⣀⡁⠀⠀⢧⠀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠂⠠⡂⠀⠀⠀⣠⠄⠀⠀⠠⠀⠀⠀⠀⠐⢄⠀⠀⠀⠁⡦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⡎⠀⢀⡀⠀⠀⠐⠀⠀⢀⡀⠀⢐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⡈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⢀⠼⣿⣄⡠⣾⡷⢄⣰⣿⡗⢄⣀⣀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⠻⣧⡀⠁⠀⡟⢧⡴⠛⠛⢆⠀⣿⠉⠀⢀⣼⣿⢷⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣄⠀⠀⠙⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢱⠇⠈⣼⡟⠇
⠀⠀⠀⠀⠀⣴⣤⡤⠚⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠈⠢⣤⣤⡄
⠀⠀⠀⡀⠀⢀⡟⠻⢦⡄⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⣠⣾⠟⢻⠁
⠀⠀⠘⢿⣿⣷⣤⣄⠀⣱⣶⣴⡾⢿⡥⠉⣿⡿⠟⠋⠀⠀⣠⣶⣶⣦⣴⣶⣿⣿⣿⣿⣿⣷⡌⠀⠀⢈⣢⣴⣦
⠀⠀⠀⢈⠂⠉⠳⠄⣾⣿⣿⣅⣰⣷⣆⠀⠉⠀⠀⠀⠠⣦⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠴⠿⠋⠹
⠀⢠⣴⣧⣤⣀⠀⣼⣿⣿⣿⣿⠿⠃⠉⠀⠀⠀⠀⠀⢰⣾⣛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡀⣉⣤⣠⡀
⠀⠈⠙⠻⠋⢉⢁⣿⡿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣶⣶⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⢉⡽⢿⠟⠉⠁
⠀⢠⣴⣮⣾⠁⠈⠿⣧⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⠋⠀⠀⢹⡏⠀⠙⠛⠈⢹⣦⣷⣄⡀
⠀⠀⠈⢣⡙⣦⡀⠀⠀⠉⠒⣾⣶⣦⣄⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠳⢠⠴⢋⠛⠉
⠀⢠⣴⡿⠿⠥⠄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣾⣷⣤⡄
⠀⠀⠀⠑⡄⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⠉
⠀⠀⢀⣠⣧⣾⠟⠁⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⣤⣰
⠀⠀⠈⠛⠉⢰⠀⢀⣠⡀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⣩⠿⠿⠿
⠀⠀⠀⠀⠀⣼⣶⡿⠋⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡄
⠀⠀⠀⠀⠀⠈⠁⠉⠑⡀⣠⡾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⡄⢰⠊⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠥⡄⣼⣠⠆⠀⠀⣄⠀⡀⠀⠀⣠⡀⣠⠀⠀⢿⣦⠀⣀⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣇⢠⡀⣼⣿⣀⡱⣶⡶⣃⣳⣿⠀⡤⠌⣿⣟⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⣿⡟⠁⠈⢻⡟⠁⠘⣿⡋⠀⠀⠀⠋
⠀⡀⡀
⠀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢢⡖⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡒⢤⡀⠀⠀⠀⠀⠀⠄⠁⠐⠂⠙⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⠌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⡠⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡈⠁⠠⢀⡜⠤⠃⠀⠀⠀⠀⣠⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢀⢠⡤⠛⢢⠤⠠⡄⠔⠀⡷⠀⠀⠀⠢⢀⣀⠠⢤⠀⠲⡓⠠⠀⠂⠅
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢄⠤⢀⠀⠀⠀⠁⠀⠰⠆⢀⣠⠂⠀⠀⠀⠠⡄⠀⠌⡆⠀⠀⠀⠀⡀⠋⠑⠤⠀⠀⠀⠀⠀⢀⣠⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣤⠀⠀⠀⢡⡔⠛⢄⡤⠀⠀⣛⣁⠀⠀⠀⠀⡬⣅⠲⠀⠀⣄⠀⠀⠀⠴⡋⠉⠈⢃⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⣠⠄⡹⠈⠀⠀⠀⠀⠀⡴⡢⠈⠋⠈⠀⠁⠈⠀⠀⢪⢟⣤⡈⠀⠀⠀⠉⠁⠂⠲⣤⢧⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⡘⠁⣨⠖⡀⣀⢠⠆⠀⠈⠠⠀⠀⠀⡀⠐⠁⠈⠀⠀⠙⠢⡀⠀⠀⣶⠐⣆⡀⠹⣃⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠹⢟⡀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⡐⠠⠀⠠⠄⠑⣄⣤⠻⢷⡌⠁⠀⡏⠁
⠀⠀⠀⠀⠀⠤⠄⠐⠂⠠⣄⠀⠚⠀⠀⠀⠀⡘⠀⠁⠀⠅⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠈⠆⠀⠀⠀⠀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠤⢁⠐⢤⠠⠐⠀⠀⠠⣴⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⡀⠀⡠⠖⠠⠀⠀⠀⢀⠀⠘⡄⠀⠠⢀⣀
⠀⠀⠀⢀⢀⡆⠀⠠⠃⠩⡉⠈⠐⠠⠀⠈⠱⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⣦⣀⡌⠠⠓⠄⠼⠠⡔⠀⠐⣸⠛⢂
⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠁⡆⠀⠀⠀⠀⢸⠀⠀⠀⠐⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠴⠊⠉⠱⠘⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡴⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠀⠀⠀⢀⠜⠁⠀⠚⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠠⠀⠄⠠⠞⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⡔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⢠⡂⡀⠀⠠⡂⢘⠇⠂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⠂⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠅⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠒⣦⡤⡐⠐⠀⠀⠀⠀⠀⠀⠒⠙⠎⢡⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠈⢙⣙⠉⠀⠀⠀⠀⠀⠀⠄⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠰⠉⠈⢐⠁⠀⠀⡀⡀⠀⢠⠂⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠐⠂⠄⠀⠀⠱⣔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⡿⢿⠿⠿⠿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢯⡁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣉⣧⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⡉⠉⡉⠉⡉⠁⠀⠀⢀⡞⠙⢦⠀⠸⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠄⠀⠀⠀⢀⡏⠀⢀⡈⣷⠒⠲⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢳⠀⠀⠂⠀⠂⠀⠂⠀⠂⠀⠀⠀⠀⠀⠳⣄⣉⣴⠇⠀⠀⢸⠆⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠹⣤⣧⡾⠀⠀⠀⠁⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⡘⠲⠤⠴⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⣈⢳⡄⢸⡇⠀⣠⠴⠲⡆⠀⠀⢀⣤⣴⠶⡶⢶⣤⣀⠀⠀⠋⠀⠀⢰⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣭⣶⡃⢸⡇⢸⢃⡄⢀⡇⠀⣴⠯⣴⣧⣠⣧⣬⣧⡼⢷⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠇⢨⡟⠶⠋⠀⢸⠃⠀⣿⠀⠀⡇⠀⢸⡆⠀⣷⠀⣾⠓⠶⣄⣀⣀⣀⣠⡴⠚⢻
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⣹⣷⣋⣀⣀⡀⠀⢸⡉⠉⣿⠉⠉⡏⠉⢹⡏⠉⣿⠀⢹⡀⡴⠋⠁⠀⠉⠙⢲⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡤⢿⡶⠶⡷⠶⣾⢤⣴⠃⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⢒⡒⠒⡒⠲⡄⠀⠀⠙⠦⢷⣤⣧⣼⠷⠞⠁⠀⠰⣯⣄⣀⠐⠀⠀⠀⠂⢀⣀⣬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⣉⣀⣈⣡⣤⣥⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⠙⢳⣛⣳⠋⢉⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠰⣤⠞⡉⠙⢲⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⣍⣽⠉⣳⡀⠀⠀⠘⣿⠀⠀⢠⠴⠓⠛⢛⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠋⠈⣿⢉⡷⢤⡀⠀⠸⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠴⠃⠀⠀⠀⢤⣄⣀⣈⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠸⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⡆⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢼⣿⣿⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠻⡎⢃⠀⡇⠀⣰⢿⡇⠀⠀⠠⠖⢴⡇⣷⠔⠦⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡃⢀⡅⠛⠁⠀⢰⣿⢳⡿⡇⣾⡧⢻⣷⠀⠀⣤⣄⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠀⠀⠀⠀⢰⣶⢰⣶⡆⣶⡦⣰⣶⠀⠀⢹⢏⣴⣾⣿⣷⣮⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣅⢭⡅⣭⢅⡭⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣛⣿⣿⡆⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢭⣟⣛⠿⠿⠿⣛⣫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣄⡀⠀⠀⠀⠉⠛⠃⠉⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⢰⣄⠀⠀⠀⠂⢸⣿⡿⣃⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢶⢂⡀⠀⠀⠸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣭⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣏⡻⣿⣿⣿⣿⣿⣶⣬⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⡙⢿⣷⢹⣿⣿⣿⡿⠟⣛⣋⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡶⠉⣡⣶⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣟⣃⣼⣧⣝⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣯⣽⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⣡⣦⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⢛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢟⣿⣿⣿⣿⣿⣯⣍⢻⣿⣿⣿⢫⣙⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⣻⣯⣙⣛⣛⣟⣩⣽⣿⢿⠿⣿⣦⠹⣶⣶⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠳⣮⣩⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⣿⡿⢿⣟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣿⣿⣦⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣬⠻⣿⣿⣿⣿⣿⣿⣷⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⡿⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢃⣿⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡜⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡹⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⢱⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣮⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠟⠻⣿⣿⣿⣿⣤⣤⣀⣀⣨⣿⣿⣿⣿⡿⠛⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣴⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣄⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠋⠤⠀⠤⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠉⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠁⢀⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠃⠀⢄⠙⢿⣿⣿⡉⠉⠉⠉⢻⣿
⣿⣿⣿⣧⣠⣴⣿⠟⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠙⣿⣧⠀⢀⣶⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠄⠤⡘⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠂⠁⢸⣿⡿⢿⣿⣿
⡏⠉⠁⠀⣿⡇⠀⠀⠀⠈⢂⠀⠀⠀⠂⠀⠀⠈⠬⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠙
⣿⣦⣄⣰⣿⡇⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢠⣿⣆⣠⣿⣾
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠖⣜⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⢠⠀⢠⣿⣿⠿⣿⣿⣿
⣿⣿⠟⠿⠁⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄⣠⣿⠟⠁⠀⠸⣿⣿
⣿⣿⣤⣀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣀⣾⣿⣷⣤⣴⣄⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⣤⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⢻⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⡟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣟⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣾⣿⡆
⢰⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟
⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⢴⢤⣶⣶⣁⡅⡠⠤⠀⠉⠛⠙⢿⠋
⣿⣿⣿⣿⣏⣀⣀⣰⣶⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⢿⠇⠛⠛⠉⠁⠀⠉⠀⣀⣉⣁⣀⣀⠀⠀⠀⠀⠀⢸⡆
⠿⣿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣆⣠⣠⣄⣀⡀⠀⠀⠀⠤⠤⠄⠀⠀⠉⠉⠀⣀⣀⣀⣀⡀⠀⣠⣤⣤⣿⣷⣶
⠀⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠛⠛⠛
⢸⡟⡴⢁⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⣰⣖⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣾⣟⡔⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠿⠿⠿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠋⠉⠀⡁
⣿⣿⠟⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡶⠖⢒⡠⡖⠁⠀⠀⠀⠀⠀⠀⠄⠦⠤⠴⠄
⣿⣿⠃⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠛⠋⠀⠀⠿⠿⢿⣿⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠖⣚⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿
⠶⠒⠒⠒⠶⠶⠶⠿⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣃⣶⣤⣤⣤⣾⣦⣤⣶⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⡯⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢋⡴⠞⠀⠀⠀⠀⠀⠀⡵⢼⠀⠤⢤⡀⠀⠀⠀⢀⡾⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣠⠃⢀⠤⠢⡀⠀⠀⡷⢼⠀⠀⠀⠈⢢⢀⠴⡃
⠀⠀⠀⠉⠀⢸⠬⠐⠲⣀⡀⠀⠀⠀⠀⡅⠀⠀⢙⢶⡢⣉⠉⠁⢲⠀⠀⠼⠋⣄⠁
⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⠉⢢⣀⠀⢀⡇⠀⣀⣠⣰⣵⠶⠤⠶⣮⣿⠤⢶⡈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⣿⡀⢲⣴⣾⣻⣿⣿⠗⠀⠀⠀⠀⠈⠑⢾⣹⡆⠐⠂⡀⣈⡅⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⢁⡆⣰⣿⣿⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠡⠿⠦⣄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣴⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡐⠂⠤⣶⣓⠄
⠀⠀⠀⠀⠀⠄⣀⡀⢳⠶⣶⣶⣿⣿⠠⠶⣆⣄⣈⡉⠀⠈⠂⠀⠀⠀⠀⠀⣠⡀⢹⣇⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣭⣻⣿⠃⠀⠀⠉⠉⠙⠁⠀⠀⠒⠀⢲⣦⣄⠀⣿⣿⢸⣿⣀⢂⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣧⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⣠⣾⣿⣿⣷⣶⣿⣿⡇⡀⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠁⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⡿⢁⠃⠙⡇
⠀⠀⠀⠀⠀⠘⡂⠀⢠⠤⠂⡀⣠⣾⢿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠲⢤⣢⢀
⠀⠀⠀⠀⠐⠃⠠⡆⠀⠀⢀⡽⠋⢀⢦⡽⢻⣧⣀⡀⠀⠀⣼⣁⣾⣿⡿⣿⡷⡠⠦⠀⠉⠑⠤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠳⢋⠎⠠⠋⡻⠟⡹⣻⠛⠯⣟⢀⠙⡶⡋⠒⠤⡞⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠘⠳⠚⠁⠈⠀⠡⠀⠀⠀⠘⢳⠗⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡁

⠀⢠⣴⠶⢶⣶⡿⠿⣶⣤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⠁⣼⡤⣏⠰⠶⣿⠰⠶⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⢔⢐⣴⡆⡄⣀⠴⢄⢤⠢⣖⠂⠀⢈⠄⠀⠀⠀⠀⠀⡄⠃⢀
⠀⠙⠷⠤⠴⠻⢷⣾⡿⠿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⣀⣀⣀⡀⢀⡀⢀⣠⠜⠀⠀⡠⠊⡀⢸⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠗⠁⠀⠀⠀⠐⠁⠀⠡⠞⢩⠙⠂⠤⣈⠂
⠀⠀⢀⡶⠀⠀⠀⠀⠀⠲⡔⢒⡊⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠛⠖⠚⠀⠀⠀⠥
⠀⡰⠁⡇⠑⡀⠀⠀⠎⡔⠉⠀⠀⠀⢢⡀⠄⠀⠀⠀⠀⠳⣴⣫⠗⣠⠞⠆⢠⠎⠙⣧⢀⣡⢀⡞⠀⠀⠀⢘⡿⡅⠈⠀⠀⠐⢄⠀⢰⠀⠀⠀⡠⠂
⠀⣇⠀⡇⠀⡱⠈⢰⠰⡀⠁⠀⠀⠈⠀⠇⡀⠒⠀⠀⠀⠀⠻⠤⠴⠻⣤⡤⠛⣦⡤⠎⠀⠈⠉⠀⠐⠀⢀
⠀⠈⠒⡇⠀⠀⠀⠄⢀⠱⣀⠠⠤⠊⠠⠁⢋⡀⠀⠀⡀⠀⠠⢄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠘⢘⠀⢢⢤⣀⠖⠃⠀⠀⠀⢸⠀⠒⠒⠃⢠⠁⣠⣈⡧⢀⠄⢀⡉⢢⡀⠀⢠⠁⠀⠒⠤⢠⡤⠴⠊⠁⠀⠀⠇⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⣀⣠⡀⢸⡀⠔⠂⠀⠀⠘⠀⠀⠀⢸⠀⠁⢹⠀⣇⠀⠈⠂⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠉⠉⠁
⡰⠨⢤⠉⠄⠀⢀⢰⠂⠐⠊⠐⢀⠀⠀⠰⠁⠀⠉⠿⢤⣀⣀⠀⠸⣄⣀⣀⡀⠸⣀⡀⠈⣠⠇⠀⠀⠀⣀⠤⠒⠁⠀⠈⠱⠄⠀⠀⡀⠀⠀⠐⠄
⠑⠊⠩⠔⠂⠀⠀⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠉⠀⠀⠙⠛⠛⠁⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠐⠃⢠⠀⠀⠀⠀⣾⡆⠀⠈
⠀⠀⢀⣤⡖⠒⠂⠒⠒⣲⣤⡀⠀⠀⠀⠀⠀⠀⣰⣊⡉⠉⠉⢱⢦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠄⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⣠⡙⢻⡷⠀⠄⠐⣋⣭⣿⣿⣦⠀⠀⠀⠀⢠⠀⠇⢮⡁⢠⣷⠣⢹⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠱⣀⠀⠀⠂⠁⢈⠕⠀⠀⡐⠀⠀⠀⠀⠂
⢰⠹⠟⣃⡀⠀⠀⠼⠛⠟⠿⢿⣿⡇⠀⠀⠀⠎⠀⠈⠉⠑⠆⠘⡇⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⡇⢸⠒⠊
⢸⣷⣿⣿⠁⠀⠀⢠⣾⣿⣧⣙⠿⡇⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣠⣾⣷⡀
⠀⣿⠉⢁⡀⠀⠀⠙⠿⠿⣿⡿⢡⠇⠀⠀⠀⢸⠈⢀⡀⠀⠀⡰⠁⠀⠀⡎⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠰⠿⠿⠿⠇
⠀⠘⢿⣿⣿⣶⠀⠀⠀⠀⢿⡧⠊⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠇⠀⠀⠀⠣⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⣀⠀⠀⠀⠀⢀⣀⣀⣈⣥⣤⣄⠀⠀⠀⠀⢰⣁⠯⠆⡈
⠀⢠⠊⠁⢀⠀⠀⢀⠀⠀⠀⠄⠸⠀⠘⠇⠒⠒⠒⠀⠀⠀⠀⠏⠀⠀⢀⡤⠚⠙⠀⠀⠀⠘⡇⠀⠀⢠⣿⢩⡍⢹⠁⠌⣿⡇⠀⠀⠀⠀⠀⠐⠁
⠀⠸⣀⡡⠃⠉⠡⠏⠌⢹⠐⠂⠂⠀⠀⠀⠀⢠⠀⠀⠠⡄⠀⠀⠀⢰⠏⠠⠀⠀⠀⡀⢀⣀⠇⠀⠀⠈⠻⢶⣶⡿⢗⣶⡿⢶⣦⡀⠀⠂⠀⢶⡄
⠀⠀⠀⠐⠒⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⡀⠠⠀⠀⠀⠀⣄⠀⠀⢀⠴⠭⠤⢤⡟⠐⠀⠀⠀⠀⢀⣿⣇⡛⣉⣇⣄⣻⡷⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⠈⠀⣀⣠⠭⠶⠆⠀⠀⠀⠀⠠⠀⣀⣀⣀⠠⠆⠀⠀⠉⠀⠠⠋⠀⣀⡴⠋⠀⡘⠀⠀⠀⣼⡏⠛⢹⡏⣿⢩⣹⣿⠁⠀⠀⠀⢀
⠀⢀⡀⠀⠞⠋⠋⠁⣀⠔⠁⠀⠀⠀⠀⠖⠰⢠⠂⠖⡔⠂⠀⡇⠀⠀⠀⣜⣴⣞⡉⠤⠀⠀⠀⠀⠀⠀⠻⣧⣷⣾⡷⢿⣮⣿⡿⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠶⠶⠶⠶⠤⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⡀⠀⠀⠀⠀⠐⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⡄⠐⠂⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⣰⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⢸⣿⣿⠿⣛⠁⠴⠀⠙⠀⢀⣤⣶⣶⣶⠦⢘⣭⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣘⠋⠷⠀⠉⠀⠀⠀⡄⠀⠿⣿⠏⣿⣿⡿⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠠⣾⣏⣁⣠⠀⠉⠀⠀⠀⠀⠀⠀⠘⢻⣤⣶⣶⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣼⣧⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⣤⣬⡿⠋⠻⣿⣿⣿⣍⣍⣻⣯⠸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣽⣿⣿⣿⣙⠋⠀⠀⠀⠀⠀⠀⢙⣯⣶⣶⣄⠀⢙⠛⠛⢛⣿⣿⣷⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢰⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣛⡿⠿⠿⣿⣿⣆
⠀⠀⠀⢀⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣎⢿⣿⣿⡿⠃⠀⠘⣿⣿⡄
⠀⠀⠀⣸⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠐⢶⠧⡄⠹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣮⣉⣭⠄⠀⠀⠀⠘⢿⣷
⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⣿⣿⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠋⠉⠹⣿⣿⣟⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⢻⠿⣷⣿⣿⡿⠛⠛⠛⠁⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⡇⠀⠀⠐⠦⣶⣼⣇⠈⠻⣿⣿⣧⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⣿⣿⣿⠋⢰⣿⠃⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣇⠀⠀⠀⠀⣸⠏⠻⢦⠀⠀⠉⠉⠙⠿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠛⠿⠟⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢻⡀⠀⠀⣈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠀⡀⢀⣶⣿⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠁⠳⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠈⣇⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠸⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡃⢀⡀⢠⠀⣠⠀⣄⠀⡀⢠⠏
⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣟⣿⣭⡿⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠈⠿⣋⣿⣽⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣯⣴⣆⡸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡀⢀⠀⣀⠀⣤⠀⠄⠐⠂⠘⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠶⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⡤⠶⣦⣶⣿⣿⠟⠿⣿⡿⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠲⢶⢶⡏⠛⠲⣖⠒⠈⠀⠈⠛⠫⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠋⠉⠀⠀⡞⢆⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢱⡀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⠀⠀⠈⡎⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣋⠜⠁⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠒⠋⠙⠂⠀⠀⠀⠀⠀⢯⠀⠁
⠀⠀⠀⢀⡤⣤⠴⣄⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⣠⠤⠤⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠡⠛⠀⠘⠛⡟⠛⣻⢿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⠶⠚⠛⣿⠛⠛⢳⡚⠁⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢨⠂⠀⠀⠀⠀⠀⠀⠉⠉⢈⣉⣉⢀⡀⢀⣈⣉⣉⡍⠉⠛⠿⠭⣉⠀⠀⠀⠀⠀⡌⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠈⠁⠬⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠚⠉⡋⠀⠩⠖⠛⠹⢿⠒⠒⠤⠤⠄⠀⠀⠀⠀⠀⢠⡀⣰⣆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⢯⣿⡟⠳⣤⣤⠴⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠐⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⢹⡏⠩⠉⣿⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢆⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠜⢨⠇⠘⡌⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢐⡆⠀⠀⠀⠀⣄⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⡇⠀⠀⠀⠀⠈⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠨⡆⠀⠀⠀⠀⣀⠇⠀⠀⡀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠰⠛⡄⠀⠀⠀⠉⠀⠀⠀⢈⢁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠂
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⢄⢖⢞⢾⣚⣈⣉⣀⣐⠿⡃⣄⡂⠀⠀⠑⠀⡀⠀⠐⠁
⠀⠀⠀⠀⠛⠂⠄⠀⢐⢞⣦⡲⡛⣿⡫⠋⠁⠀⠀⠺⠀⣼⠹⠷⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠑⠀⠀⠀⣱⢝⣝⢜⠌⠜⠓⠀⠀⠀⠀⠀⣼⠹⡄⠀⠈⠢⠀⠀⠀⠀⠀⢀⠒⣀
⠀⠀⠀⣠⡶⠀⡰⠀⣿⡮⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄⠀⠀⠀⠀⠁⠀⠀⠀⠤⠔⠊⠁
⢀⣀⣴⣦⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠃⠠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤
⠈⠀⠉⠀⠀⠀⠀⡼⠆⠸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠡⠀⠀⠊⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣀⡁⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣯⣉⣙⣛⡻⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣷⣿⣿⠉⠉⣉⣼⣿⠘⢿⣽⣷⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣽⣾⣿⣿⣿⣿⣼⣿⣷⣦⡀⠀⠉⠁⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⣿⣿⣿⡿⠿⠿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⣿⣟⢁⣀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⠀⠀⠀⠈⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⠏⠀⠁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣤⣄⣄⣶⣂⣀⣤⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⢀⣴⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⣁⣤⡈⠟⢿⣿⣿⣿⣿⣟⢠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣷⣤⣤⣍⣛⣳⡿⠟⠛⣶⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠻⠿⠿⢿⣿⣟⢻⡏⠁⠐⢮⣝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣽⣿⣾⣧⣄⠀⣸⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣿⣿⣿⡿⠛⠙⣿⣿⣿⣶⣶⣿⣿⣩⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡈⠠⣤⣦⣿⣭⣼⡫⢀⡴⢤⢟⣿⣿⣿⣿⣿⢿⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣆⣀⣉⣻⣿⣿⡷⡉⢿⣦⡾⣟⢹⡿⢹⢸⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣴⣿⣻⡿⠛⢻⣿⡯⣿⣤⣿⣿⢱⢱⡆⢸⠇⢹⣿⣷⣾⠆⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣼⡿⡟⡋⠥⠓⠀⢀⠾⡏⢰⣿⣿⠹⣿⡜⡄⠇⠘⡰⠿⠛⠫⠾⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⡼⠻⠍⠁⠁⠁⠀⠀⠀⠀⠈⢠⡤⣾⠟⣿⠀⣧⠋⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡿⠿⣿⣷⣽⡇⠀⢠⡆⠀⠀⠀⢈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣠⣿⠿⠿⠁⠀⠘⣧⠀⠀⠀⠞⠃
⠀⠀⠀⠀⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠰⠿⣿⣷⣤⣤⣤⣀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢮⡙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡀⡀⠀⢀⢀⣀⢀⡀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠘⠐⠂⡤⠀⡸⠀⢸⠀⡠⠠⠄⠀⡇⠐⠀⠒⢄⠑⡆⠀⠈⢠⠤⡄⠱
⠀⠀⠀⠀⠀⠀⡜⠁⡔⠁⠀⢸⠀⣀⣀⡀⠀⡇⠠⡠⠠⠊⢀⠂⠀⠀⠆⠀⢠⠀⡀
⠀⠀⠀⠀⢀⠎⢀⠌⠀⠀⠀⢸⠀⡤⠤⠃⠀⠇⠀⢄⠀⠂⠁⠀⢰⠀⠀⠀⠘⠀⡃
⠀⠀⠀⢀⠎⠠⠏⠀⠠⡀⠀⠸⠀⠇⢀⡀⠀⠀⢦⠈⢢⠀⠀⠀⠀⡀⠣⠠⠂
⠀⠀⠀⠘⠤⠤⠤⠤⠤⠂⠀⠰⠤⠤⠤⠃⠀⠦⠂⠁⠤⠃⠀⠀⠀⠐⠠⠠⠐⠁

⠀⠀⠀⢰⠒⡆⠀⠀⠀⠀⠀⠀⠀⠒⢲⠀⠀⠔⠐⠄⠀⠀⢀⠖⠉⠉⠲⡀⢰⠀⠀⠀⠀⠈⠀⠀⡀⠀⠖⠂⠀⠐
⠀⠀⠀⠈⡄⢰⠀⠀⡠⠤⡀⠀⠀⠃⡀⠀⠐⠀⠀⠘⠀⠀⡂⢰⠁⠀⠉⠀⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⡇⠈⠉⠉
⠀⠀⠀⠀⢡⠀⡆⠰⢡⡄⢱⠀⠰⢀⠁⠀⡀⢈⠁⠀⠀⠀⠑⠄⢉⣁⠐⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠰⠤⠤
⠀⠀⠀⠀⠘⡄⠰⠇⠎⢸⠘⡀⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⡖⠀⠈
⠀⠀⠀⠀⠀⢃⠀⡜⠀⠈⡄⠓⠁⠇⠀⢈⠀⠔⡄⠀⠀⢐⠁⣀⣀⠠⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠣⠤⢤
⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠒⠊⠀⠀⠐⠐⠀⠑⠒⠀⠀⠑⠂⠀⠒⠁⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠘⠂⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣠⡬⣤⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⣡⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡄⢀⡤⠤⠞⠁⠀⠀⠀⠀⠘⣆⡒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⡠⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡌⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰⠃⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢤
⠀⠀⠀⠀⠀⠀⠼⠀⠀⣀⣀⠀⢀⣀⠀⠀⠐⠦⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⣄
⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠈⠛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣸⠁⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢠⢀⡠⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢳⡀⣿⠀⡀⣴⠀⠀⢿
⠀⠀⠀⢀⡤⠖⠋⢀⣠⡭⠃⠀⠀⠋⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠸⣥⠇⠀⠙⣿⠀⠀⠸⡄
⠀⠀⢀⡏⠀⠂⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣏⢀⡏⠀⠀⠀⣿⠀⠀⠀⠹⡀
⠀⠀⠘⠦⠤⡄⠀⠀⠈⠉⠉⠉⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⣿⢸⡇⠀⠀⠀⣿⠀⡰⠂⢀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⣠⠖⠓⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⣿⠀⢳⡀⠀⠀⣿⠞⠀⢀⡼
⠀⠀⠀⠀⠀⢻⠀⡀⢧⠀⠀⠀⠀⢀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣿⠉⠉⠙⠦⠄⣿⢠⠴⠋
⠀⠀⠀⠀⣤⠞⣠⠇⢨⡿⠶⠀⣴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠵⠶⠖⠒⠲⠆⣿⠠⣄⡀
⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠉⠒⠀⢤⠀⣀⡀⠀⠀⢀⡀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⠁⠀⠉⠛⠒⠒⠶⠶⠶⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠢⢤⣴⠀⣀⣺⠟⠃⠀⠶⠾⣿⣿⣷⢿⠛⠂⠐⠀⠀⠀⠀⣀⡴⣿⣆⠀⠀⠀⢰⠊⠀⣀⣰⣦⠤⠤
⠀⠀⠀⢠⡙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠏⠈⠘⠀⠀⠀⠀⠀⠐⠊⠉⢱⡈⣻⡄⠀⠀⠀⠻⠼⠿⡏
⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤
⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⢀⡆⠰⢤⡷⠤⠄⡀⠀⠀⠀⠁⢸⠛⣿⠀⠀⠀⢀⡀⣤⣄⣷⣿⠷⣀⠀⠀⠰⢾⣷⡿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠸⠉⠙⠁⠉⠀⠀⠀⠀⠀⠂⠉⠀⠈⠃
⠀⠀⠀⠀⢤⣀⣠⠀⠀⣴⣒⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡤⠀⠀⢄⣀⣀⣄⣀⡀⡀
⠀⠀⠀⠀⢠⡛⠟⠀⠉⠁⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠐⢊⣆⣤⣼⡟⡄⠀⠀⠀⠹⡍⢹⠿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⢯⠷⠝⠇⡈⠀⠀⠀⠀⠀⢸⡁⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⡄
⠀⠀⠀⠀⠀⢤⣄⠿⠁⠀⠀⠀⠀⢀⣠⣴⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⣤⡾⠛⢉⣭⠿⠧
⠀⠀⠀⠀⠟⠛⡹⠁⠀⠀⠀⠀⢠⣼⣿⡿⢿⡃⠀⠀⠀⠀⠀⠀⣠⢢⡜⣿⡗⠀⠀⠀⠉⢳⡟⠻⠙

⠀⠀⢀⡠⠄⠶⠒⠶⠦⠤⣤⣠⡤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢤⡤⣀⣀
⠀⡔⢡⡄⠀⢀⡀⠤⠦⢶⣭⣀⠀⠀⣤⠈⠉⠳⣶⠤⣠⡔⣥⠐⡄⠀⠀⠀⢀⣀⠤⠤⠒⠒⠉⠉⠀⠀⠀⢀⡔⠙⡄⠀⠈⠉⠒⠦⣄⡀
⢠⡇⢨⠳⣀⣎⣀⣀⡠⣄⣀⠈⠻⣀⡟⡄⠀⣤⠹⣷⠎⠠⠄⠰⢟⣔⠛⠛⢺⡧⢤⡴⠊⠉⠻⡉⠉⢲⠊⠉⠙⠲⢇⠀⠀⠀⠀⢀⡀⠹⣦⡀
⢸⣿⡘⢄⡞⠁⠀⠀⠀⠀⠈⡷⠤⠋⣰⠁⠀⣿⠀⡝⠀⢄⠀⢀⡈⢿⡴⣷⣿⣇⠜⣰⡟⢀⠀⢱⣄⣼⠄⠀⠀⠀⢌⠳⣤⣄⠀⢸⠙⡄⢹⣷
⠀⣿⣇⠈⡇⠀⠀⠀⡠⠤⠤⠳⣶⠞⠉⡻⣤⣿⣳⠧⠤⠴⠴⠮⠴⣞⣿⣿⣿⠀⡼⢻⣵⡏⠀⠈⡆⠁⠈⠄⠀⠈⠀⠀⡸⠀⢳⣼⠀⠹⡀⣿⣧
⢸⣿⡜⣆⠹⠀⠀⢰⠀⠚⠃⠀⠉⠉⠛⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣻⣎⠻⣧⣸⣿⡇⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠑⠒⢻⠃⠀⠀⢣⢹⢸
⢸⡏⢿⣿⡇⠀⠀⡜⠀⠀⠀⠀⢰⠆⠀⠇⣿⣿⣿⢆⠀⢀⠔⠀⠀⡿⠁⡀⠈⠙⢦⡙⠻⣝⢦⣀⠀⠻⡆⠀⠀⠀⠿⠂⡀⠀⠈⠦⣀⣀⡼⢾⣘
⠀⣿⣮⣿⡏⢄⣠⠀⡄⠀⠀⣠⡞⠀⣰⣧⠟⣉⣀⣮⡀⠬⠤⠔⠚⠉⠉⠁⠉⠉⠉⠛⠚⠛⠲⠬⠯⣶⣌⢦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⡄⢹
⠀⢸⡏⠛⢷⣬⠯⢚⣥⣀⣰⣃⡠⠴⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⠷⠦⠤⠤⣤⣧⠺⣹⠀⣩⣴⣿
⠀⠈⣿⠀⠀⠸⣭⣁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠋⣰⢫⡏
⠀⠀⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⣀⡀⢀⠀⠀⢀⡄⠀⠀⢀⠀⡀⠀⢀⠠⡀⠀⣀⠀⠀⠀⢠⡄⠀⢀⡀⠀⡄⠀⣄⠤⡀⢀⡠⠡⢸
⠀⠀⢻⢻⡄⠀⠀⢰⠀⠀⠀⠀⣊⠒⠾⠀⣂⠐⠢⠃⠀⡈⡀⠀⠠⡱⠒⠅⠀⡮⠒⠴⠀⣱⠀⠀⠀⡀⠃⠀⢸⢠⠀⡇⢸⡴⠒⡀⣸⣿⡀⢸
⠀⠀⣾⢸⡇⣀⡀⣸⡇⢀⢤⡜⡇⡀⠤⡀⡙⢒⠕⠀⠀⡸⢣⠀⠐⠧⠐⠢⠸⠣⠔⠒⡀⣺⠀⠀⢀⡿⢻⠀⢸⣾⢠⡇⢸⡇⠀⣯⢸⡟⣷⠸
⠀⢠⣿⢸⣿⣇⢹⣿⣿⡝⣰⠇⠇⠁⣳⠀⢴⡜⠄⠀⢰⡉⠅⡇⠈⠉⠀⡧⠀⠉⠁⢁⡇⢿⠀⠀⢘⡈⢥⠃⢸⡍⠼⠇⠸⡇⢀⢃⠈⣏⠘⢳⡆
⠀⣾⣯⡿⣹⣼⡿⣤⠀⣸⡇⢠⠣⠐⡇⠀⠸⠈⢎⢄⡜⠀⠀⢰⠘⠇⠔⡕⠰⠣⠄⡰⠀⠹⠤⢤⢸⠀⠈⡀⢸⠇⠐⠀⠨⠧⢊⠂⠀⢻⠀⠀⣇
⠀⣿⣟⣽⣿⣛⣧⠀⢾⣿⠇⠀⠑⠈⠀⠀⠉⠀⠀⠉⠉⠀⠀⠉⠈⠐⠈⠀⠀⠑⠊⠀⠀⠑⠈⠁⠉⠀⠀⠁⠈⠁⠀⠁⠈⢢⣥⣄⣤⣼⢾⣄⣿
⠀⣿⣿⣿⣿⣻⣿⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⣑⡤⠤⠤⠤⣔⢩⠛⢿⣿⣿⣿
⠀⣿⣾⣿⣟⣼⠃⠀⠀⠠⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⠏⠀⠀⠀⠀⠀⠙⡆⢸⢿⣿⣿
⢰⢣⣿⣿⣽⠇⠀⠀⠀⠆⠀⡸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘⠻⠀⠀⠚⠃⠀⡸⡳⣾⣿⡿
⢸⣼⣿⢿⡿⡀⠳⡀⠀⢇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣧⠀⠰⡀⠈⢶⡴⠃⡆⡠⢁⢿⣿⣿⡇
⢸⡟⣿⣿⣴⣧⠀⠉⠢⣌⢣⣸⡇⠀⠀⠀⠀⢀⡀⠀⢀⡄⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣸⣇⡰⢙⢷⡚⠓⣲⠛⣡⣏⣀⣿⣏⢻
⠘⣧⣿⣿⡇⣿⠴⠦⣧⠈⡆⢹⣸⣤⠆⠀⠀⣼⢁⡶⠁⢀⣠⢠⣄⣾⡟⣦⢳⣀⠀⠀⣠⠏⢰⡄⣸⣾⣿⣿⡆⠘⡄⠉⠉⣠⠜⠀⡇⣿⣿⣿⡹
⠀⣿⣸⢻⣿⢡⡄⠀⣿⣷⣦⣾⢿⣏⣴⣣⣾⣷⣿⣥⢾⡟⠁⣾⣿⡝⣷⣿⡿⣟⣧⡾⣿⢀⣾⣧⣿⣿⡿⢿⣷⢀⡾⠠⠊⠀⠀⠀⢿⣿⣿⣿⡇
⠀⣿⣿⣸⣧⡀⣿⣼⣿⣿⣰⣏⣾⣿⣿⣱⡿⢻⣿⣷⣿⣠⡞⣽⡟⢳⣿⣿⣷⣿⣿⣿⢿⢿⡿⣿⢿⣿⢳⣿⣿⢻⡃⠀⠀⠁⢀⢀⣸⡏⣿⢿⡇
⠀⠹⣏⠿⣮⣻⣿⣸⣿⣿⣡⣟⡟⣼⣿⠛⣠⡼⡃⠸⣻⣯⡾⢯⣤⣿⠿⠬⠿⣿⣿⡻⢯⣼⣓⡇⢸⡿⣾⣿⣯⠞⠛⠒⠈⠁⣹⢟⣡⡿⢫⡞
⠀⠀⠈⠻⢌⣙⢾⣿⣿⡿⢫⣞⡼⠿⠷⠾⣭⣤⣬⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡽⠿⠟⠛⠛⢻⣿⣏⠥⠀⠀⢀⣾⠗⣛⣡⠖⠋
⣀⣀⣀⣀⣀⣉⣙⣛⣿⣟⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣻⣿⣿⣟⣛⣛⣋⣉⣀⣀⣀⣀⣀

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⣤⣶⠒⢲⣶⣶⠆⠀⠀⢒⣀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠐⠛⢻⣿⣿⣿⣿⣉⣵⣯⠀⠙⠁⠀⠁⣀⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠁
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠛⠈⠀⠀⠀⠀⠠⣼⠛⠿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⠃⡀
⠀⠀⠀⠀⠀⠹⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠈⠛⠧⣀⣄⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠻⠃⠈⠻⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⡀⠀⠀⠈⠁⠘⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⠔⠗⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⢃⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠛⠻⣭⠁⠀⠀⠉⠈⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⣠⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠄⠀⠄⠀⠀⡰⠃⠱⡀⢠⠇⢩⠀⠀⠈⢣⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠄⢠⠄⠘⠄⠀⠀⠱⡴⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⠙⠻⠧⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠶⡒⠒⠂⠀⠉⠹⡀⠂⠰⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⢀⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊
⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⢀⠎⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⡀⠀⠀⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡦⠀⠀⡀⠀⠱⡀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠱⡀⠀⠀⡔⡥⠦⠤⠠⠤⠄⡄⠁⠀⠀⠀⡠⠃⠪⠤⠤⠤⠤⠤⠬⠴⠖⠗⢠⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠑⡄⢸⡎⠀⠀⠀⠀⠀⠀⡏⠀⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠑⢦⡀⠀⠠⠀⠀⠃⢀⠀⠀⠘⢦⠀⢰⡂⠀⠀⣀⣀⡤⢞⡙⢫⣄⠀⠀⢀⠀⠴⡉⢋⠒⢄
⠐⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠈⠠⡀⠀⠀⠑⢾⠉⠉⠁⢍⠀⢴⣿⣦⣥⡍⠀⠄⠠⠾⠾⣿⣿⣣⢨
⠛⠄⠀⠛⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠈⠢⢅⣇⠠⠉⠁⠈⠄⠀⠘⠦⣉⣋⣡⠎
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡶⠶⢶⣿⣿⣿⣿⣿⣗⣦⣀⣐⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠺⠽⠚⠒⠣⠾⡆⢀⣀⣠⣯⣳⢿⣿⠋⠉⠛⢿⠟⡳⡤⡈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⡀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠁⠀⠘⢟⣩⡖⢆⠀⢙⡿⣋⣿⠀⠀⢙⣕⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⢂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣶⠽⠷⣶⣍⠀⢠⣽⣫⢘⡃⠈⠐⠀⠁⠘⣦⡀
⠀⠀⠀⠀⠀⡠⡺⢡⡔⢯⣦⠀⠀⢐⡈⠥⠀⠀⠀⠀⠀⠀⠀⢮⠰⢈⢔⢅⡿⠀⠙⣟⣿⣻⣪⡴⣻⠀⠀⣔⡲⡁⣉⡳⢄
⠀⠀⠀⠀⢨⡌⣔⠪⡂⢕⢸⠀⠀⠀⠒⠈⠈⠀⠀⠀⠀⠀⠀⠈⠘⠪⣴⡵⠇⠀⠀⠉⠀⣿⣯⠿⣒⡭⠶⠋⢛⠡⠘⠬⠋⠣⡀
⠀⠀⢀⠎⡈⢔⠲⣪⡐⠩⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠧⠃⠀⠀⠀⠀⠀⠈⠳⡞⢍⡢⠑⣀⠤⢒⠠⠔⠂⠀⡑⡄
⠀⢀⠆⠐⠌⡐⠍⡢⢙⠳⣢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⢲⠒⠞⠐⡄⠡⢐⠨⠐⢊⡠⠔⠊⠀⠰⢳⠘⡀
⠀⡌⠀⢌⡁⠊⠕⣊⢔⡣⠞⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⣀⢤⡨⢙⠢⣉⠉⢈⡠⠔⢊⠡⠐⢀⡀⠀⠈⠙⡷⠡
⠰⠀⠀⠀⢀⠁⠒⠂⠬⠍⡇⠀⠀⠀⠈⠀⢊⠡⠒⠁⠀⠀⠀⠄⢀⠀⠀⣠⢒⠃⣂⠤⢒⡨⠔⣊⠡⠐⢈⡠⠔⡪⠕⠀⠀⠄⠤⠧⢀
⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢑⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠂⠉⠐⢈⠠⠒⢈⠠⠐⡪⠄⠊⢁⠠⠐⠈⠐⠄⢢⢀⡏
⡇⠀⠀⢒⣂⠀⠨⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡔⠊⠐⡂⠡⢒⡈⠤⢒⠨⠔⢂⡁⠤⢒⡈⠔⣂⠁⢐⡂⠬⢲⠉⠉
⡇⠀⠈⡁⠤⠒⣊⠥⠀⡀⠀⠈⢿⠦⡀⠀⠀⠀⡌⢝⠡⢐⠄⢄⣈⢀⠡⠐⠊⠅⠂⣈⠠⠐⢊⡡⠔⣊⠥⠒⢈⠠⠀⠐⢂⢁⠊⠀⠂
⠃⠀⠀⠐⡈⠥⢐⠢⢑⡠⢐⡀⠈⠃⠑⠀⠀⠐⡋⠕⡪⢴⢡⠂⣂⠤⡒⠡⠀⠂⠁⠄⢒⡉⠄⢒⡩⠄⠒⣉⠠⠐⠀⠊⠀⡆
⢀⠀⠀⠀⠐⡈⠄⢂⠡⢒⠡⢊⠅⠀⠈⠒⠄⣀⠐⠊⠀⣜⣵⢒⠔⡉⢷⠩⣸⠄⢀⠔⡪⢄⠀⠡⠔⣂⠩⠐⡈⠁⠀⡂⢠⠃⢀⡭⠔
⠈⡄⠀⠀⡡⠔⣈⠄⠊⡡⠒⡡⠒⡡⠀⡀⠀⡀⠈⠁⠒⢆⠀⠁⡊⠂⣁⢎⣀⠊⢑⡩⠲⢑⠠⡀⠉⠔⣂⠡⠄⠀⠀⡂⠀⢢⠀⢀⢀
⠀⢰⠀⠀⠐⠉⡠⠐⢉⠔⢊⠔⢊⠔⢋⡠⠊⡀⠀⠀⠀⠀⠑⠛⢪⠊⠀⠀⠀⣀⠀⠈⠢⠠⡈⠐⠄⠀⠐⠂⠀⠀⢀⡂⠅⡀⠁⠁⠊
⠀⠀⢣⠀⠀⢉⠤⠊⡡⠂⢁⠔⢁⠔⢁⠤⠊⡀⠔⠁⠀⢂⠄⠀⡰⠀⡠⢔⠩⠒⠀⠀⠀⠀⠈⢤⣀⠀⠀⠀⠀⠨⠐⡀⠅⡪⠀⠌
⠀⠀⠀⢢⠀⠀⠐⢊⠤⠊⡠⠐⡁⠔⢁⠠⠊⡠⠀⠀⠨⢔⠁⠸⠀⠀⠀⢑⠨⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈⢢⢀⡨⠕⡢⡑⢈⠌
⠀⠀⠀⠀⠱⡀⠀⠁⠤⢊⠠⠊⡠⠔⣁⠔⡩⠂⡀⠄⠀⠡⢂⠌⢢⠀⠀⠀⡊⠄⠀⠀⠀⠠⡂⠀⠀⠀⠔⠡⠄⡂⢅⡨⡠⠂
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐⣉⠔⢊⠤⢊⠔⢊⠔⡀⠀⠈⠠⢂⠅⠑⠤⡀⠀⠄⠀⠠⡐⠌⠀⠀⠀⡠⠀⢀⠥⠂⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠂⠁⢊⠤⢊⠥⢊⠠⢂⢄⠀⠐⠨⢢⠀⠘⠀⠁⠀⠀⠈⠀⢀⠒⠁⣀⠠⠔⡢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠁⠒⠁⠪⠔⠅⡪⢀⠀⠀⠀⠆⠀⠀⠀⠀⣀⠔⠂⠀⠄⣂⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠄⠀⢀⠤⠊⢁⣀⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⣀⣤⣤⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣻⡇⠸⢏⣿⡟⣾⡋⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠿⠶⠶⢦⣭⣴⣭⡉⢷⣀⠀⠀⠀⠀⢻⡆⠀⠀⠘⠻⠾⠿⠿⣦⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣹⠃⠀⠀⣠⡼⠃⠀⢀⣀⣀⣀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⢻⣄⢀⡾⠁⠀⠀⠀⣿⡋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠈⠉⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣭⣉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⢰⡟⠳⣦⠀⢰⡟⠁⣀⣀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠁⠈⠙⠛⢾⣝⠛⣿⣆⠀⠀⠀⣠⠶⣦⡀⠀⠀⠀⢹⡆
⠀⢸⡇⠀⢿⡇⢸⡇⠀⠻⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠋⠀⠀⠀⠀⢀⣾⣯⣤⣈⢻⣆⠀⠀⣿⠀⠈⠻⣦⠀⠀⢸⣇
⠀⣸⡇⠀⠈⣿⠚⠷⠚⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⢿⣿⣛⣿⣯⡄⠀⠐⣿⠀⣤⢴⡏
⠀⢻⡇⠀⣾⠏⠀⠀⠀⠀⠈⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⡇⠀⠀⠙⠛⠃⢸⡇
⠀⢸⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢠⡶⠟⠀⠀⠀⣠⠶⠶⠶⣿
⠀⠀⢹⣏⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣼⠏⠀⠀⣸⡏
⠀⠀⠀⢻⡄⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⡷⠘⣷⠀⠀⣰⡟
⠀⠀⠀⠀⢻⡄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⢰⣏⣀⣴⡟
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣿⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣾⠉⣿⠞⠁⠈⣩⡿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠹⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⡾⠃⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣙⠷⣄⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣮⣿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁
⡶⠶⠶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⣶⢶⣶⠶⠶⠶⢶⡶⠶⡶

⠻⣷⣄⠀⠀⠉⠤⣶⣾⠁⠀⠈⡙⠲⢦⣄⡀⠠⠀⠀⣼⣦⡀⠄⡀⠀⠢⠀⠀⠀⢠⣴⣾⣷⠂⠀⠀⡀⠢⠁⠸⠚⠛⡛⠒⠶⠂⠀⢿⣷⣄⣷⠐
⡄⠈⠉⠃⠈⡀⠐⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣷⣄⠀⢿⣿⣟⣿⣦⠄⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⣾⣿⡇⠀⢂⣠⣤⣤⣤⣀⡀⠀⠈⢛⣿⣿⣄
⢠⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣶⣄⢹⣧⠉⠛⡁⠀⠀⠙⠟⠛⠉⠁⠀⠀⠂⠀⠀⠀⠀⢈⣤⣤⣿⣿⣴⣾⣿⣿⣷⣿⣿⣿⣿⣦⡀⠌⠹⣿⡿
⣀⠀⢈⠉⠉⡉⠉⠙⠙⢹⣻⣿⣿⣿⠿⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠀⠀⠀⣼⢿⣿⠿⠃⠀⢸⡷⣍⠉⠉⢉⣵⡟⠿⣧⡀⠀⡀⡂
⠉⠓⠶⠤⢤⡄⠀⢈⡤⣾⠿⠃⣎⢇⠀⠀⠷⣸⣇⠴⠀⣤⠀⠂⠀⢄⠀⠁⢀⣤⣶⡆⠀⠀⠀⠀⠐⡀⠀⠀⡇⣸⠀⠀⣸⠛⣄⠀⠘⠷⣤⣤⡤
⢀⣤⣄⠀⠠⠀⠀⠸⠆⠹⠂⠀⠈⠦⠒⠀⠀⢿⡟⠀⠀⡯⠀⣴⢀⡤⢀⡁⠈⠛⠻⠃⠀⠻⣙⣦⠀⠀⠘⠛⠈⢁⠀⠀⠀⠛⠋⠀⠐⠀⠀⠐⠂
⠙⠋⠉⠻⣦⠀⠄⠀⡀⠀⠀⠁⣤⣤⠀⠐⠄⠘⠁⡀⠈⠁⠀⠈⠘⠁⠾⢡⠄⡀⠀⠀⠀⠂⢘⠋⢀⠀⠀⠀⠄⠀⢀⣴⣶⣶⣶⣶⠀⠐⠀⢹⡆
⡄⠰⣄⠀⠸⣧⠀⢈⡤⠶⠾⢓⣦⡿⢾⣝⠂⠀⣠⣴⣲⣿⣦⣄⠀⠀⠀⢀⡈⠑⠃⠘⠁⡀⠀⢀⠀⠀⠀⡤⡄⠀⠊⠻⢿⣿⣿⠿⠃⠀⢠⢿⡧
⠀⠐⠦⢀⠀⣿⠀⠠⠀⠠⠞⠋⣽⠀⠀⢹⠆⠀⠛⠛⢋⣿⠇⠙⣷⣶⣶⣦⣤⣄⣠⣀⡈⠀⣀⣸⡇⠀⢸⣿⣿⠀⠐⠀⢠⣿⣧⠀⠀⠀⠸⠿⠏
⢐⡄⠀⠀⢀⣿⠀⠀⠃⢀⠀⢰⡏⠀⠀⠀⠈⠀⠀⠐⠛⠁⢐⣒⡯⠙⠛⡿⣻⠟⠿⠻⢿⢿⠻⠛⢀⠐⡀⠉⠀⠔⣀⣴⣿⣿⣿⣦⣈⡂⠠
⢸⡃⠀⠀⠰⣿⠀⠀⡀⢀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⢧⠻⡄⠀⠀⠀⠀⢀⣤⣶⣤⠀⠀⠀⠀⡉⠉⠩⠉⢉⠉⠉⠁⠀⢀
⠹⠋⠀⢀⠘⣿⣅⡀⠈⠀⠀⠉⡁⠀⠠⡤⢶⣶⣄⠀⠈⠸⠁⠀⠀⠠⡤⠞⠀⢹⡆⠀⠀⠁⣸⣿⣿⠟⠀⠈⠀⠀⠌⠛⠶⠶⠿⠇⠀⢠⣾⣿⣧
⠀⠂⡀⠐⠀⢹⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠛⠻⠃⠐⠄⠀⠀⠀⠀⠀⠀⠛⠁⢠⠂⣠⡾⠋⠀⠀⢰⣄⢰⣿⡄⣠⣴⠀⠀⠠⠀⠀⢿⣿⣿⡿
⠘⣶⠧⠄⠀⢨⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣶⣦⣄⠀⠠⠀⠀⠀⠐⠀⠀⢀⣄⠀⠄⠀⠉⢀⠀⠀⣰⣞⣻⣿⢿⣷⣿⣟⣤⣶⠆⠠⠑⠄⠉⠉
⠐⠁⠃⠀⠀⢸⢻⡏⠉⠉⠁⢠⢰⢿⡷⠀⠀⠉⠛⢿⣦⡀⠁⠀⠀⠀⠀⢈⡛⢶⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠽⢨⢿⡿⢿⣿⣶⡖⣠⣠⣠⡆
⢀⡀⠀⠀⠀⣿⢈⡇⠈⠄⠀⠀⢸⡘⣇⠀⠀⠰⠀⠀⣹⡧⠀⢀⠀⠀⠀⠀⠁⠂⡀⠀⠘⠛⠛⠉⠁⢹⣧⠀⠀⣏⠸⡅⠀⠙⠻⠾⠿⠟⡋⠀⠂
⢿⣿⣿⡆⢀⠃⠘⠁⠄⠀⠀⠂⠚⠁⢋⣀⣀⣤⣴⠾⠋⠁⠐⣀⣈⣀⣈⣤⡄⠀⠀⣠⠤⣤⡀⠀⠀⢠⠋⠂⠁⣸⠀⢱⡄⠈⠀⠀⠀⠈⢀⣠⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⠒⣶⣿⣿⡿⠉⠫⠙⠩⢐⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⣾⣿⡟⣥⣼⡃⢹⣿⣿⠁⠀⠀⠡⠀⠀⠑⢤⡀⠄⠹⣿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⡀⢠⣿⣿⣿⣿⣌⠁⠘⣿⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠂⠀⠉⣀⠉⢡⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣿⣿⣿⡿⠿⠟⠃⠀⠌⠀⠀⠀⠀⠀⠐⣀⣤⣼⠀⢀⣵⣴⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⣠⣿⡄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠁⠀⠀⠦⠠⠀⠀⠀⠀⠀⠀⠨⠄⢠⣿⣿⡿⠋⠉⣝⢮⢻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣩⣭⣷⣶⣶⣙⡊⠀⠛⠀⡈⢉⣿⣿⣿⣆
⠀⢀⣾⣿⣿⣿⣿⡿⠿⠛⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣿⣿⣿⣿⣆
⠀⠀⠈⠓⢿⣿⣿⠀⠀⣀⠐⠀⠒⠒⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠃⠉⠻⠷⠾⣿⣤⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢤⢀⣴⣤⣤⣉⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣛⣉⠉⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠔
⠀⠀⠈⠐⣄⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⣷⠈
⠀⠀⠀⠀⢁⠀⠀⠀⠐⠂⠤⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠋⠰⠿
⠀⢀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠂⠀⠀⢀
⠀⠀⢂⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠋⠀⡀⠀⠀⢀⠂
⠀⠀⠈⢦⣀⠀⠁⡀⠀⠀⠀⠡⠀⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠀⠀⠔⠀⠀⣠⠇
⠀⠀⠀⠀⠢⡀⠂⠰⢄⠀⠀⠀⠂⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠮⠐⠂⡠⠂
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠡⡀⠀⠈⢺⣿⡿⠀⠤⠤⠄⠸⡄⠀⠀⠀⠀⠀⠀⡼⠀⠤⠤⠄⠀⠐⠲⠃⠉⠁⠐⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠈⠂⢀⠀⠻⣿⣄⡀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠔⠀⢀⠔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠁⢤⣀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣠⣈⣠⠤⠅⢀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⣁⣽⣿⣿⣬⣭⣙⣁⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠚⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡂⠀⠼⡇
⠀⠀⠀⠀⠒⢦⣤⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡴⠿⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠙⠛⠉⠉
⠠⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀
⠀⠙⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⣒⣰⣖⢄⠀⠀⢠⠤⡶⣦⣤⣄⠈⠂
⠀⠀⠀⠉⠑⡀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⢰⢀⢚⣻⡟⢿⠇⠀⠀⠠⠀⠀⡀⠁⠀⠁
⠀⠀⠀⠉⠀⠀⠀⠛⠃⠋⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⠁⠀⢀⡆⠀⠀⡄⠀⠁⠀⠀⠀⠠⠈
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠀⠀⠀⠀⠀⠉⠀⠛⠠⠴⠊⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣶⣾⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠀⠁⠀⡀⠙⠛⠓⠆⠀⠀⠃⠀⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠂⠀⠀⠂⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⢀⢒⠒
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢤⣴⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣖⡓⠛⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠑⠀⠀⠀⠀⠀⠂⠀⠀⠉⠋⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⢀⣀⣀⠀⠀⠀⠀⢀⡠⠤⠤⢤⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⡠⠤⠤⠤⢄⣀⡠⠤⣄⣀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠤⠭⠽⢶⣤⣀⠈⠣⣀⣠⠴⣾⣤⣠⣴⠚⠛⠋⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣠⠴⠚⡇
⠀⢀⠤⠒⢰⡊⢠⣶⠀⠀⠀⠀⠈⠉⠳⢦⡖⠀⠀⣨⣻⣟⣉⠀⠀⠀⠀⢤⡀⠿⠛⠀⢀⣠⣤⠤⠤⠤⠤⠴⠖⠚⠋⡭⢀⣠⡴⢇
⢠⢥⡒⠉⣁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠁⠀⢀⡜⣁⡠⠤⠔⠒⠺⠷⣒⠙⠻⠥⣤⣠⣠⣤⡥⠶⠴⠞⠚⠋⠉⠁⠀⡼
⠘⣄⠽⠿⠿⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⢤⡠⢮⡉⠁⢀⣀⠀⠀⠀⠀⠀⠑⡄⣀⣀⣀⡀⡀⣀⣀⣀⠀⠀⢀⠀⡰⢠⠃
⠀⣇⠰⢎⡒⠒⢒⣊⡷⡤⠊⠀⠈⢳⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢹⡤⠦⣀⣀⣀⢸⠁⠀⠀⠉⠉⠀⠀⠈⠉⠲⣃⡜⡱⠃
⢀⠞⠉⣀⡩⠛⠁⠀⠀⣇⠀⠀⡠⠎⠀⢰⠞⠶⣀⣠⣀⠀⣀⠀⠀⢀⠼⠃⠈⢠⠖⠋⢽⠀⠀⢀⡀⠀⠀⡀⠀⢀⢀⡇⠘⠓⠢⣤⣀
⠈⠦⢎⠀⣀⠖⠀⣠⣀⣸⣄⡾⠤⠤⠔⢋⡠⢀⡂⠌⠉⠉⠔⢉⠋⠉⢍⡒⠄⠛⠉⠉⠮⣗⣒⡉⢛⠒⠉⢹⡤⠚⠉⠓⠶⢄⣠⡇⢈
⠀⠀⢘⡩⠭⠿⠮⣅⡅⠀⠀⠊⠐⠂⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠁⠀⠀⣰⠚⠓⠉
⠀⢠⠎⠰⡄⠠⠄⠈⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⠀⢀⣂⢀⣀⣀⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠘⢾⡻⡍⡹⡙⣿⢡⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣻⡄
⠀⢠⢞⢣⡱⢱⢃⢿⡎⠀⡇⢀⠔⠉⠀⠉⢢⠀⠀⡰⠈⠁⠉⠢⠀⠁⠀⠀⠈⡃⠀⠀⠌⠈⢁⠀⠀⠐⠈⠡⠀⠐⠀⠁⠀⢹⢻⢱
⠀⡏⠀⡞⡇⡧⡏⢾⢷⡸⢀⡌⠀⠔⠁⢢⠀⢃⠰⠀⠰⠈⠑⠎⠀⠀⠀⠉⠩⡁⠀⢠⠀⣄⠈⡄⠀⠰⠀⠀⠡⠀⠀⠀⠀⢸⡸⣸⡆
⠀⡇⠀⣹⡄⡇⡎⡇⣼⢻⠸⡇⠀⡀⠀⢠⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠆⠀⠭⠀⢠⠀⢸⠀⠲⡀⠙⠀⠀⢀⣾⡇⢻⢸
⠀⢱⢠⡿⣹⡑⢧⣷⠋⠈⡇⠠⡀⠁⠐⠁⢀⠃⠈⠄⠈⠂⠈⢑⠀⠀⠀⠒⠂⠂⠸⠀⢀⣀⡀⠀⠆⠈⠀⠀⠐⡀⠀⠀⠘⢩⡇⢸⣼
⠀⢸⡼⢻⢠⢿⢼⠁⠀⣰⠁⠀⠑⠂⠀⠐⠁⠀⠀⠈⠂⠀⠐⠊⠀⠂⠀⠀⠀⠂⠀⠐⠁⠀⠐⠀⠂⠐⠀⠂⠀⠘⡂⠂⠀⣻⡇⠀⣿
⠀⣸⠃⣼⣯⣿⡄⣇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣠⢿⠁⠀⣿
⢰⠁⡸⢸⢹⣿⡆⣸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⣔⡣⠋⠀⢀⣿
⢸⢰⡇⢸⣿⠹⣟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠈⠀⠀⠀⢠⢾
⢸⢸⡇⣴⠏⠀⢘⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡭⠊⠀⠀⠀⠀⠀⢀⢎⢿
⠈⣆⡿⠹⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⢒⡩⠟⠋⠁⠀⠀⠀⠀⠀⣀⣠⣾⣋⡼
⠀⣸⠁⢟⠰⠀⠀⣹⡦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠛⠐⢂⠟⠉⠀⣴⠆⠀⠀⠀⠀⠀⠀⠈⣉⣡⠞⠁
⠀⣇⠀⠈⠓⠯⠍⣠⣤⣄⣀⠀⠈⠙⠒⠢⠤⢀⣀⣀⣀⣀⣀⣀⣠⠔⠋⠀⠀⠀⠀⡖⠁⠀⠀⣀⡴⠃⠀⣀⠴⠋⠉⠉⠉⠀⠀⢀⡼
⣀⣈⣓⣒⣒⣒⣛⣋⣉⣉⣉⣉⣑⣒⣒⣒⣒⣒⣤⣤⣤⣤⡤⣚⣛⣉⣉⣉⣉⣒⡢⣬⠿⣛⣛⣛⣒⣚⣛⣓⣒⣒⣒⡤⢤⡄⢒⣋⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠱⡄⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⡇⣰⡏⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⢴⠶⡖⢶⢤⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡄⣄⢠⡀
⠀⠀⠀⠀⠀⠀⣸⢁⡇⠀⢀⡞⢳⡿⠶⡷⠾⡗⠛⣆⠀⠀⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⣬⠁⣬⡁⣩⡈⣥⣄⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⢠⣇⣼⡃⠀⢸⠦⢼⡧⠴⡧⠤⣿⠤⢾⠀⠀⣳⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢘⣛⠀⣛⡁⣛⡃⣙⣛⠀⠀⠀⡻⣇
⠀⠀⠀⠀⠀⢸⠈⣇⠳⡄⠘⣆⣨⣧⢤⡧⢤⣧⣀⡟⢀⡴⢣⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⡀⠀⠸⠿⠂⢛⡃⣛⠃⠿⠟⠀⠀⣴⢯⣿
⠀⠀⠀⠀⠀⠘⣇⠈⢧⠙⢦⡈⠳⢽⣦⣧⡾⠶⠋⣠⠞⣠⠏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣦⡀⠈⠛⠘⠃⠋⠘⠋⠀⣠⣾⣯⣿⡏
⠀⠀⠀⠀⠀⠀⠈⢢⡈⠃⠀⢳⡀⠀⠀⠀⠀⠀⣼⠁⠀⠃⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣸⠁⠀⠀⠀⠀⠀⢻⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣽⠀⠀⠀⠀⠀⠀⢸⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇

⠀⠀⠀⡀⣀⣀⡀
⠀⢰⣿⣿⣟⣿⡿⣿⣦⣄⣀⣠⣔⣠⣤⣤⣤⣦⡀
⠀⠘⠻⢿⣿⣿⣷⣨⣹⣿⣿⣿⣟⣛⣻⣿⣟⣿⣿⡄
⠀⠀⠀⢨⣿⣿⣿⠏⠉⢻⣽⣿⡟⠿⠛⢿⣿⣻⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣷⣦⣈⣿⣷⣤⣤⣼⣿⡏⣩⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣀⣿⣷⢻⣶⣌⣅⣚⠂
⠀⠀⠀⢸⣿⣿⠙⠛⣿⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⢁⡄⢩⡈⠉⣅⣀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⣀⣿⣿⡿⠀⠀⢻⣆⣿⢀⣀⣔⣺⣿⣿⣿⠇⠀⣀⠀⠉⢀⣽⡿⢿⣷⡀⠀⢯⣙⣿⣄⡀⣀⢀⣀⡀
⠈⢻⣿⠿⣿⡷⠶⠶⠿⣿⠿⠛⠉⢉⣩⢟⠟⠁⠀⠊⠛⠻⣶⣦⣥⣾⣿⢻⣿⣶⣾⣿⡥⠍⠀⠀⢀⣴⣿⣧⣄
⣠⣤⣴⣿⣿⣷⣶⣠⣠⡄⢠⣴⣶⢟⡵⡷⠆⠀⠀⠀⢀⣼⣿⣿⣿⣿⠏⡼⣿⣿⣿⣿⣾⣆⣤⣎⣤⣬⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⣾⣿⣧⣐⣢⣤⣾⣾⣛⣿⣿⣿⣿⣮⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠟⠿⠿⠿⠤
⣤⣶⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⢿⣿⣿⣿⣟⡛⡛⠛⢻⣿⣿⡿⠒⠒⠒⠒⠊⠴⢿⣿⣿⣿⣿⡿⠷⣶⣶⣶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⢟⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⡿⢣⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣣⡤⢄⡀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢾⣿⢻⠟⣃⠋⡐⣴⠀⠀⠀⠀⠀⠀⣴⣶⣶
⠀⠀⠀⠀⠀⢀⣾⠿⠿⠿⢿⣿⣿⡿⠻⣿⢻⡏⣿⣿⣄⠆⠻⠶⣿⣷⣟⠁⡀⠀⠸⣤⡶⣦⡄⣸⣿⣿⣃⣀⡀
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢸⣿⡇⠀⠀⢿⡘⠇⢿⠟⣏⣱⣶⣶⣯⣼⢋⡿⢽⣶⣶⡏⣿⣿⡷⠘⣿⣿⠉⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠈⠃⠘⠈⠀⢹⣟⣻⡿⠋⠁⠘⠁⠈⠿⠀⠀⠙⠻⠃⠀⢹⣯⡀⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⡉⠛⢷⣶⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢀⣤⡤⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣀⠀⠀⠈⠁⠀⠹⠏⠀⠀⠠⢌⣡⣦⡀⠹⡆⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⣰⡟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⣿⣿⣷⣶⣦⣄⡐⠶⠴⢤⣤⣌⣩⣍⣿⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣿⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠈⠻⣿⣿⣿⣷⠀⢸⣿⡶⢲⣦⡞⣿⣿⣿⠿⣤⡀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠙⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣷⡄⠘⢿⣿⣿⣧⠈⠈⠁⠊⠉⠰⠃⠻⠋⠰⠟⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠙⠦⣜⣿⡿⣿⣷⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢙⣦⣀⠈⠙⢧⣄⣽⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠀⠀⠀⠈⠻⣿⣿⣯⡛⠿⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣤


⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⠿⠿⠿⢿⣿⠿⠿⠿⢿⠿⠿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⡠⠐⠊
⠀⠀⠀⠀⠀⠠⠂⠀⠀⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠒⠄⠀⠀⠀⠀⢀⠄⠀⠂⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠂⠀⣀⣀⣠⠴⣊⠴⢤⠍⠀⠂⠀⠀⠀⠀⠀⠀⠈⠡⢄⠀⣠⠄⢀⠀⢈⠱⠄⠈⡠⠱⠈
⢀⠴⠤⣞⢄⣀⣠⣴⣿⣋⢈⠩⠀⢰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔
⡘⢐⠈⠡⣉⠁⠀⣀⠈⠿⡀⠤⠤⠘⠀⠀⠀⠀⣠⡴⠷⠶⠚⠁⠀⠁⠀⠀⠀⠀⠀⠊⠠⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠠⠀⠠
⠀⠃⠀⠀⠀⠁⠀⠀⠐⡄⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠰⣤⣤⣤⣤⣤⣤⣤⣼⣷⣦⡀⢰
⠀⣀⡀⢀⢀⠀⠠⡀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠩⠍⠉⠉⠉⠙⠉⠛⡛⢿⣇
⠒⣏⣋⠘⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠃⠀⠀⠀⠰⠀⠀⠀⢰⡂⢨
⣠⢈⠃⠀⢰⠀⣠⣤⣶⣾⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⢀⠀⠀⢀⠀⠘⢡⢸
⠈⠸⠆⢠⠾⠿⠿⠿⡿⣿⣿⣿⣿⣷⣷⣮⣤⠤⠂⠄⠈⢀⡀⠀⠀⢈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢎⠀⠀⠀⠀⠑⠄⠀⣠⡀⠃⡾
⠀⠘⣠⣤⡌⠀⡀⠀⠀⠀⠀⠁⢤⡀⠥⠀⠐⡰⠂⠀⠉⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠸⢧⢙⠐
⡀⠀⣣⣬⠇⣤⠀⢠⠂⡠⠄⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⡀⠄⠀⠀⠀⠀⠀⠸⠼⠀⠠⠀⠀⡠⠀⠀⠃⠇⠘⡏
⣧⠆⡼⣄⣄⠘⢣⢠⠴⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠈⠀⠁⠀⠀⠰⠈⠀⠢⠠⣴⠠⠆⢸
⣿⢸⡱⠉⡸⢀⡟⡴⢀⠆⠀⠀⠀⠽⡾⢦⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡖⢘⡇
⣿⡌⠀⡀⠐⣸⣇⣘⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠄⣀
⠟⡟⠘⠀⡀⠁⠀⢀⣰⠠⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣀⠻⢦⠀⣀⡤⠤⠼⠀⠄⢼⣉
⠀⣱⡞⣀⠅⠀⡀⠀⢁⣀⣈⡄⠀⠀⠀⣀⡘⢤⣤⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠉⠨⢙⣃⠤⡀⠀⠀⠀⠀⠋⠞
⠀⠈⡄⢟⠒⠉⣘⣶⠂⠉⠴⡦⠧⠀⠈⠁⠀⠑⠠⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠐⣽⣒⡆⡀⠨⠥⠙⠣⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠽⡧⢀⠣⣶⡖⠂⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣖⠶⣲⠖⠒⠒⠒⠠⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠻⢿⣾⣷⢸⠏⡺⠗⣄⠀⠀⠀⠀⡇⠈⣉⠶⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡴⡋⢵⠭⢟⡩⢖⡵⢻⠀⢀⡖⣫⠕⣫⠔⣫⢔⣫⠝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠙⡦⠃⠀⢈⣟⠥⣚⠝⡳⢟⡫⠖⣋⠔⣪⠔⢋⡤⢞⡡⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⢔⡫⢔⡩⠖⣩⠔⣫⠕⠋⣡⢴⠏⠀⠰⢯⠞⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⢖⡩⢖⡩⢖⣩⠔⢋⡠⠶⣿⡝⡎⢧⡴⢶⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢻⡀⠀⠀⠀⠀⠀⡀⢰⣫⢖⡩⠒⣡⠖⢉⡤⢚⡥⢚⣽⡻⢛⣡⠴⠒⠁⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡩⣇⠀⠀⣰⡦⣞⠝⣢⠟⣩⠔⢋⡤⢚⡥⢚⣥⡶⠟⣩⣶⠏⠚⡀⢀⡀⡔⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠴⣋⠶⣦⠈⠛⡗⣉⠴⢋⡤⢚⡡⣖⢥⡪⠕⣩⢔⡫⠚⣏⡀⣸⡠⢫⠧⣋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢚⡥⢊⡥⠷⣀⠙⠃⠲⠥⢴⡽⡪⠗⣩⠴⣫⠔⣋⢔⡫⢊⣽⠿⠴⠥⠞⠉⠁⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣩⠔⣋⡴⠚⡏⠀⠀⠀⠀⠀⠑⠴⣋⡵⣋⠴⣊⠔⣫⠔⣡⠇⠀⠀⠀⠀⠀⠀⢦⣀⣮⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢚⣡⠖⣋⠷⣄⠀⠀⠀⠀⠀⠀⢠⢏⡠⢚⡡⢊⡴⣪⢿⡄⠀⠀⠀⠀⠀⠀⢨⡗⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡴⢊⡡⠚⣩⠟⣲⣄⠀⠀⠀⡾⣫⠔⣩⢖⡭⣊⠕⣡⠟⢉⡽⣆⠀⠀⠀⢸⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣋⠴⢋⡤⢊⡥⠚⡇⢠⡾⢋⡴⢊⠕⣫⢞⡡⠚⢁⠔⢉⠔⢿⣀⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢥⡔⣋⠔⢋⣧⢸⡔⣩⠞⡡⢚⡵⠋⣠⠖⣁⠔⢁⠔⣡⡯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠭⣜⣹⢟⡥⢊⠔⠁⡠⠊⣡⠞⢁⡔⡡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠒⠚⠓⠚⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠄⣀⠤⢀⣄⣠⢀⠤⣠⠄⣠⠀⣠⠀⣠⠀⣠⠄⣠⠄⣠⠄⣠⠄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠁⠀⠁⠈⠀⠀⠀⠁⠈⠀⠈⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠇⡀
⠀⠀⠀⠀⠀⠀⢸⡁⠐
⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠀⠀⠀⢀⡀⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠂⠀⠀⠁⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢟⣧⠤⠒⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠠⡀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠵⢋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢮⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⠀⠊⠁⠀⠀⠉⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠙⣿⣮⡳⢄⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⢑⡒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠰⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠚⠀⠑⣀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠶⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣌⠲⡤⠀⠀⠀⢠⡇⠸⣿⣶⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⡀⢀⠀⢀⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⣉⡀⠀⠀⣿⡿⣏⠉⣠⡞⠛⠚⠛⠛⠶⢦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡙⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠹⣛⣃⠀⢸⣇⣀⣜⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⢶⣀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠥⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣋⣤⣶⣿⠶⠃⠚⠋⠉⠉⢳⣷⣦⣀⣀⣄⠀⢦⣤⡀⠈⢿⡀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⢚⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⢉⣿⣯⠿⢮⣿⠱⢦⣄⠁⡀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠚⠉⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠻⢤⣀⠀⠈⠛⠶⠾⠷⡌⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡴⡄⠀⠀⠀⠀⠀⢶⢶⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠤⠄
⠀⢠⠖⠁⠀⠀⠀⠀⠀⠑⢦⡀⢠⠞⠁⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡠⠊⠉⢀⠐⠃⠀⠀⢀⣤⡿⠶⢄
⢠⠃⠀⢀⡦⠀⠀⠄⠀⢄⠈⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠑⡀⠀⠀⢠⠊⠀⠀⠈⠀⠓⢲⣴⡛⠛⠁⠀⠀⠀⡳⡀
⢈⠀⠀⠀⠉⢀⠠⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⢀⠇⠀⠀⠀⠀⠀⣰⣴⠿⠀⠀⠀⠀⠀⠀⠁⠱
⠘⡀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⢰⠀⡄⠀⠀⢀⣷⠙⢲⡀⠀⠀⠀⠀⠂⠒
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠀⠘⠸⠀⠘⠇⢠⣼⠁⠀⠀⠁⠀⠀⠀⠀⠠
⠀⠀⠙⢄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⢄⠀⠀⠀⢺⡅⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⡰
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⣔⡴⠁
⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⡀⠀⠀⠀⢈⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠈⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢣
⠀⠀⠀⠀⠈⡟⠻⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢇
⠀⠀⠀⠀⠀⡇⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⢁⠁⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⢁⠠⠆⠦⠀⠁⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇
⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⢀⣧⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠻⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠛⠃⠛⠉⠃⠃⠀⠃⠘⠘⠟⠙⠰⠋⠃⠃⠛⠙⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠂⠑⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆
⠀⠒⠀⠀⠂⠀⠀⠐⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄
⠀⠃⠀⢀⡤⢃⠀⠤⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⢤⡄⡀
⠀⢀⣎⣌⡁⠋⣃⡈⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⣀⣄⢩⣄⠀⠠⡄⠀⢒⣑⡿
⠀⡀⠈⣧⢘⢷⣟⣶⢤⡤⠶⠤⠤⠀⠀⠰⣫⣍⣟⢲⡄⠀⠐⠒⠂⠐⠀⠀⠀⠀⣈⣉⣉⣁⠀⠀⠀⠀⠚⠻⢿⣻⣻⣻⣋⡄⠈⠁⠂⢶⡆
⠀⡇⠐⠒⣿⡆⠓⠈⠃⠀⠀⠀⠀⠀⠀⠀⡟⡏⢹⡖⢷⡄⠀⢀⠀⠀⢀⠀⢰⠫⣑⣠⣶⣮⠆⠀⠀⠀⠀⣀⡞⣙⡇⣀⣹⢻⠰⠂⠀⣸⡇
⠀⠓⠂⢀⣿⣇⡀⠀⠀⣀⣀⡀⢉⣀⣢⣈⣁⣉⣈⣁⡈⠩⠤⠬⠴⠤⢌⠀⣿⣿⡏⠀⠈⢿⢂⠀⣀⠘⠛⠉⠀⠉⢀⠀⠉⠁⠀⠀⠔⠚⠁
⠀⠀⠛⠀⠀⠀⠀⠀⠄⠁⠁⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⢘⡿⠧⠄⠀⠿⠉⣀⠀⠀⠀⠊⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⢀⠀⠊⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢋⠂⠈⢉⠬⠁⠀⠐⠒⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢩⠀⣀⡀⠀⠀⢀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⠀⠀⠀⢀⠂⠀⡰⢅⡀⠀⢸⠀⠀⠰⠀⠀⠀⢠⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠁⢠⠒⡋⠉⠀⠀⠁⢰⠀⠀⢣⡀⢀⡜⠁⠒⠐⢁⡄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⠉⠀⡀⠀⠸⣀⡠⣤⠊
⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠠⠔⠁⡠⠒⠀⡀⠑⡀⠉⠁⠑⠒⠄⠀⠀⠀⡃⠀⠄⠀⡼⠁
⠀⠀⠀⢠⢊⣤⠄⠂⡩⠁⠀⠀⠀⢰⠁⠀⠇⠀⠠⠄⠊⢀⠄⠪⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⢥⡸⠀⢧
⠀⠀⠰⠡⠞⢁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠉⠁⠁⠀⣒⡠⠤⠲⠦⣄⣀⣀⣀⣀⠔⠉⠀⠠⠘⡄
⠀⠀⠃⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠶⠈⠁⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠄⠀⣶⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⠤⡆⠯⡙⠘⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢩⣁⣇⠹⠽⠀⠃⠍⠠⠉⠼⠀⠚⢘⠀⠁⠐⣀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠠⡜⣐⠓⠒⠀⡀⠢⡐⡞⡬⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠢⡑⣠⠤⠑⠊⣀⠄⢰⡘⠆⠃⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⢰⡢⡁⠬⠐⠎⠇⠈⠈⠀⠀⠀⢀⣀⡤⠤⠔⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠘⢅⡁⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠶⠖⠚⠛⠛⠻⠿⠿⠿⠿⠷⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⢀⡀⠈⠑⠒⢦⡀⠀⠀⠀⠀⠀⣀⣠⢶⡟⢓⣸⠍⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⡋⠉⠰⣏⠉⠉⠉⠉⠙⣆⠀⠈⢷⡀⠀⠀⢀⡞⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⡛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⢋⡀⠀⠙⠓⢻⡟⢦⣄⣀⣀⣰⠏⠀⠀⠀⠙⠳⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠳⣌⠱⡌⢷⣄
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠉⠀⢀⣤⠴⠚⠁⣼⠛⠿⠛⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣸⣳⠏⠀⠙⢷⣄
⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠈⠙⢦⣄⣴⠏⠀⠀⠀⠀⠀⠀⠈⠓⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⠅⢀⣠⣄⣀⠹⣦
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡟⠁⢻⣿⠑⠼⣧
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡤⣾⣃⣠⡴⣭⠀⠀⠘⣇
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠓⠚⠉⢿⡆
⢰⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣾⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⠀⠀⠀⠈⠷⣤⡆⠀⠀⠀⠀⠀⡠⠚⠢⢄⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⣾⠀⠀⠀⠀⠙⢉⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡴⠟⠻⣦⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⠶⠤⠶⢻⡆⠛⢶⣤⣈⣉⣉⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡄⠀⠀⠈⢧⠀⣼
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣤⡤⣄⡀⠙⠉⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠙⡄⠀⠀⠘⢤⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣽⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣾⡿
⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠉⠉⠙⠲⠦⠤⠶⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢎⢣⡀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠸⠤⠇⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣀⣤⣖⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣴⠟⠛⣋⣤⣶⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⠶⢦⣤⣿⣤⣤⣾⣷⣾⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢠⡀⣀⡀⡀⠐⣿⣷⡆⡆⠀⠁⠀⠤⠔⠀⠀⠀⢠⣄⣸⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣟⣶⡿⢟⠗⠄⠀⠀⠀⠀⠀⢠⣀⡠⠎⠉⠉⠀⠀⠀⠀⢀⠄⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠢⡙⠂⢀⣠⣤⣄⢀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⢠⣿⣋⡟⢻⡘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠿⠅⠒⠈⡁⠌⠀⠀⠀⠀⠀⠀⠀⠄⡂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠈⠀⠀⠀⠀⠀⠐⣾⠀⠀⠁⠆⡀⠀⠀⠀⠀⠀⠀⠢⠄⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠈⠑⠒⠈⠀⡇⠀⡀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠀⠀⠀⠈⠀⠀⠀⠃⠀⠂⠄⠀⠀⠇⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠀⣠⠀⠀⡂⠀⠀⠀⠀⠀⠈⠠⠀⢠⣼⣭⠀⠀⠀⠉⠀⠈⠀⠀⠐⠂⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠊⢠⣀⡀⢘⠀⡄⡄⡔⢄⣌⡀⠀⡿⠓⠎⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢡⠦⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠊⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠠⠠⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠙⠀⢒⡉⠁⠀⠀⠀⠀⣀⠈⣠⣠⣰⣶⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠠⠌⠀⢂⣈⣤⣤⣶⡾⣬⣈⣄⡛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠀⠀⠀⠐⠊⠉⠓⠒⠲⠤⠤⠿⠿⠟⠛⠓⠛⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠑⠄⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣾⢀⣤⡰⣧⢄⣴⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣿⢿⣿⣯⣼⣿⡗⠛⣼⢛⣵⣿⡇⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡙⢿⣿⡿⠠⣬⣥⣬⡛⣼⣇⣀⢺⣿⢟⡰⢩⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣷⣬⢠⣆⢰⣦⡙⢿⣿⣿⣿⡟⣿⠂⣴⣿⢧⣾⣿⠟⢴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣟⢫⣼⣯⡽⠟⢘⣿⡇⣿⠈⣩⡌⣿⠉⠁⣿⣏⣠⠉⢀⣵⣶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣷⣬⠂⣙⠛⠛⣾⠻⠿⣿⡻⣼⠿⠃⣻⣧⡾⠧⢾⣯⢀⣸⣿⡿⠁⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⢟⣬⣝⠷⢦⣼⣧⣬⣙⡿⢻⡆⢷⣿⣏⣤⡶⠿⢾⣟⢣⣾⣏⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠿⠿⠋⠰⠛⠀⠀⠈⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠀⠛⠿⠇⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡶⢞⣉⣭⣽⡿⠿⠶⠦⣄⣤⣶⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢋⣹⣿⣿⣿⣿⣿⡽⠖⠛⠀⠀⠀⠙⢿⣿⣿⡿⠂⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣾⣿⣿⣿⣿⣿⣿⣏⡡⠾⢿⣦⣤⣠⡀⠀⠙⢿⡁⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠁⠀⠠⡀⠀⢨⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣾⣿⣿⣿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⡿⣿⣿⡏⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣿⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⠀⠀⠽⠻⣿⣧⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠁⠈⠙⣷⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣤⣤⣌⣡⣬⣭⡴⠟⠋⠙⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣤⣤⡄⣀⣂⣤⣶⣵⠿⠯⣭⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⡿⠻⢿⢯⠕⢶⠶⠆⢠⡘⠷⢶⣤⣤⡉⠈⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣶⢿⣻⣿⣿⣶⣦
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⢿⣿⣿⡲⠤⠤⡀⠑⠒⠛⠉⠀⠀⠀⠀⢹⣄⠀⣀⣔⢙⣷⣤⣀⣤⣤⣀⣤⣤⣝⡿⣟⡙⣿⣿⣟⠉⡀⡀
⠀⠀⠀⠀⠐⣿⣿⣿⣽⣿⣿⣷⡿⠟⠙⠛⠒⠉⠙⣛⣋⣁⠂⢂⣠⣰⣶⣾⣿⣿⡿⠿⠿⠟⣛⣋⣹⠏⣩⡍⠛⠾⣿⣿⣿⣿⣿⣷⠾⠅
⠀⠀⠀⠀⠀⠳⠾⢝⣿⣯⣯⣶⣝⣻⣤⡤⠖⣚⣯⣭⠤⠒⠀⠐⠒⠂⠀⠀⣀⣤⣤⣤⡴⠟⠙⠁⠀⢀⣤⣤⣤⢿⣿⣷⣿⣿⣿⣟⠂
⠀⠀⠀⠀⢠⣐⠒⠾⠿⠟⠉⠉⠞⠭⠓⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⢀⡚⠛⠭⠤⠁⢈⠻⣟⣻⡿⢿⡶⠆
⠀⠀⠀⢀⣈⣉⣹⣩⣤⣴⣾⣴⣤⣤⣼⡿⠭⠷⠦⠴⠲⠺⣿⣯⠓⠐⢘⢦⠤⠤⡀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⢀⣹⣺⠛⠁⡸
⠀⠀⠀⠈⠋⠻⠟⣿⣉⣿⡿⢭⠹⣏⣩⡄⠀⠀⠈⠉⠀⠈⠉⡏⠿⢻⠩⠁⡈⠁⠠⠀⠀⠀⠠⠄⠠⡥⠀⠀⠀⢂⣤⠉⢲⡾⠄⢀⠠
⠀⠀⠀⠀⠠⠤⠿⣇⠀⠹⣭⣼⡿⣿⣿⡇⣼⠄⠀⠀⡀⠀⠀⠐⣤⠏⠀⠀⡀⠀⠀⠀⠀⣄⡴⣬⣷⣦⣤⠀⠙⠂⠀⢺⣐⣿⠂
⠀⠀⠀⠀⠠⠤⣄⣀⠀⢩⡹⣿⣟⣻⣿⡅⠇⠈⡇⡠⢷⣶⣧⢸⣏⣀⠀⠀⢀⣀⡀⢠⣮⢛⣩⣡⣤⣯⣼⡷⣴⠁⢀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠁⠩⢦⣀⠊⣿⡟⡿⢿⢋⣯⠀⣥⡙⢮⣁⡩⡻⠹⣿⣶⣿⠺⠤⡔⣿⣼⣿⡿⣿⣿⣿⣿⣳⣬⣿⣧⢈⣉⣩⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠻⠀⠃⠊⠙⠘⠻⠯⢫⡿⠠⠿⠂⠟⠰⠀⠐⠛⠦⠀⠀⢸⣟⣻⣈⣿⣯⣭⣹⣟⣿⣿⣗⣫⣟⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈

⠀⠀⠀⠀⠀⢀⠤⠤⢄⣀⣀⣀⡀
⠀⠀⠀⠀⢠⣇⡀⠀⠀⠙⠗⠏⠱⣄
⠀⠀⠀⠀⠘⠧⣈⣛⣳⣶⣦⠤⡀⠘⢆
⠀⠀⠀⠀⠀⢀⣀⣈⣙⡭⠟⠈⠀⠀⠘⠦⠤⠶⠦⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡉⢉⣁⣠⣴⣒⡀⠀⠀⡀⠀⠀⠀⠉⠁⢀⠀⠈⠉⠙⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⢮⡩⠀⠀⡸⠀⢠⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢩⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⣿⠆⡏⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⡻⢶⣗⣿⠁⠀⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⡚⡩⠂⠉⠀⢿⡀⠀⠀⠐⣖⢉⣤⣖⣀⣀⣀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠻⡅⠀⢠⡏⠉⠈⠳⣀⡄⠈⠑⠦⡀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣠⡇⠀⠀⠀⠀⠉⠉⢳⡆⠈⣦⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡶⢅⡀⡼⠀⠀⠀⠀⣀⡤⠴⠚⠀⢠⠁⣷⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⢀⠀⠀⠑⢍⠳⢄⡀⠀⠀⠉⠑⠒⠚⠀⢉⡴⠃⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠚⠂⠒⠋⠉⠑⠤⣉⠓⠒⠤⠤⠖⠒⠊⠁⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⢀⣠⣴⠾⠧⢀⡀⡀⢀⠀⠀⠀⠈⠐⠂⠀⣀⡆⠀⡀⠀⣀⢸⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠏⠙⠇⢠⣴⠃
⠘⠛⠁⠀⠀⠈⠙⡷⠤⢂⠄⢀⣆⣶⣅⠀⠉⠱⠴⠶⠒⢡⣾⣶⣮⡌⠀⠀⠀⠀⠀⣒⡦⢀⠀⠘⠶⠒⣒⡤⠀⢀⠴⠃⠀⠀⠀⠀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠙⠁⠈⠲⠀⢀⣠⢀⡶⠃⠀⠀⠉⠁⣲⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⢤⡀⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠉⠚⠋⠉⢀⣠⣤⠆⠀⠈⠀⠀⠐⠋⠁⠐⠀⠒⠒⠰⠞⠉⠀⠀⠀⠀⠈⠘⠛⠚⡅⠘⠧⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⣀⡀⠂⠀⠀⠿⠏⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⠀⠈⠀⠀⠠⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣤⡉⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠉⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⡀⠈⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠸⣼⢢⡀
⠀⠀⠀⠀⠀⠀⣄⣰⠀⠀⠀⣠⣿⣧⣥⠀⠀⢠⣴⣶⣾⣧⡆⠀⠀⣄⣶⣶⡦
⠀⠀⠀⠀⠈⢄⠘⠿⠃⠀⠀⣿⣿⣿⡿⠀⠀⠙⣿⣿⠿⠿⠃⠀⢐⣿⣿⣿⠃⠀⢠⠀⣠⡆
⠀⠀⠀⠀⠀⠈⠑⢠⣄⠀⠈⠋⠉⠋⠉⠀⠀⠀⠈⠒⠉⠉⠀⠀⠀⠉⠈⠉⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⡀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣾⣿⣾⣷⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⡙⣧⡄⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠉⣠⣖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡧⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⣩⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠉⣿⠀⢠⣿⣿⣿⣿⡷⠄⠀⠀⢀⣀⣬⣻⣿⡇⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠀⠀⢻⠖⡏⠉⠙⢟⠁⠤⣆⣶⢾⠟⠛⠛⠻⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠃⡘⠀⠀⠀⠘⠀⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⢦⣀⡀⠀⠀⠰⡔⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣏⢀⣤⢤⣤⣤⣠⡾⠛⠛⠛⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⢀⣤⣴⡿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣾⠏⠀⠙⠦⠿⠱⢿⣤⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢰⣿⣋⣁⣀⣀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠈⠛⠛⠛⠛⠷⠶⠿⢷⣆⠹⣦⣄⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠉⠛⠛⠛⠻⣷⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢠⡟⠀⠀⢀⣤⡾⠃⠀⠀⣀⣀⣀⣠⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠘⣧⡀⢀⡿⠁⠀⠀⠀⠸⣿⡋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠶⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣼⣧⣀⠀⠀⠀⣴⠿⠛⠛⠛⠷⠶⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠾⠶⣦⣤⣹⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⢀⣿⠈⢻⣷⠀⢸⣿⠀⣠⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡟⠀⠀⠀⠀⠈⠹⣷⡀⠈⣿⣦⠀⠀⠀⢰⡟⠛⣷⣀⠀⠀⠀⠀⣿⡄
⠀⢸⡿⠀⠀⣿⣄⢸⡟⠀⠈⠛⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠉⠀⠀⠀⠀⠀⠀⣾⣿⣤⣤⣄⢻⣧⡀⠀⣸⡇⠀⠈⠙⣷⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⢈⣿⠜⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣛⣿⣯⣤⡀⠀⠀⣿⠀⣠⡶⣾⠇
⠀⢸⡇⠀⢀⣾⠏⠀⠀⠀⠀⠀⠈⠻⠶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⠃⠀⠀⠙⠷⠟⠀⣿
⠀⠸⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⢀⣀⣠⣀⣸⡏
⠀⠀⢸⣇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⣰⡟⠉⠉⠀⣽⠇
⠀⠀⠀⢿⡆⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣤⠀⣼⡟⠁⠀⠀⣰⡿
⠀⠀⠀⠈⢿⡄⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢘⣷⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣿⠀⣾⣧⣄⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⠉⣿⡿⠃⠀⠈⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠈⣿⡄⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⢀⣴⡿⠃⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡈⠻⣦⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⡻⣾⣟⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠠⣤⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠩⣀⠀⠐⠒⠀⡀⡀⠖⠢⠀⡩⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠂⠁⠀⠀⣘⠁⣉⢡⠀⡄⠈⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠁⠀⠀⠀⠀⠈⠂⠐⡈⠉⣤⡀⠁⠀⠀⠀⠧⠠⠄⠀⠂⠉⠠⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣬⠀⣀⡀⠀⠀⠀⠀⠐⡁⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠎⢘⠏⠐⠀⠈⠉⠢⠄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⢠⣥⣼⠀⠀⢀⣀⡀⠤⡄
⠀⠀⠀⠀⠀⠈⠉⠑⠂⠠⢄⣽⡀⠘⠿⢦⡢⠀⠤⠊⠀⢀⠀⠀⠄⡀⠀⠀⡀⠀⢀⠀⡠⠁⢐⡤⠔⠓⠋⠉⠉⠁⠀⢀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠁⠒⠤⣙⢦⠀⢲⡦⠨⠊⢔⠠⢂⠅⠪⡂⢀⠔⣨⣄⠔⠉⢠⠀⠀⠀⠀⠀⠀⡠⠁⠄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠉⠲⣆⠔⠨⢂⠄⠈⡂⢐⣀⠀⡴⢺⠔⠁⠀⢀⠂⠢⡀⠀⠀⢀⠄⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠑⠑⢄⠀⠀⠀⠀⠀⠀⠀⠑⢮⠂⢑⠠⠂⠁⠗⠨⡴⠁⠀⠀⠀⡇⠀⢰⠈⠀⡰⠁⠈⠀⠀⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⢀⠀⠂⠑⠄⠀⠀⠀⠀⠀⠀⠀⠑⣄⠊⠊⡐⢵⠊⠐⠀⢱⠀⠀⠀⢤⢠⡾⠊⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠂⠤⠬⠁⠀⠢⡀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡸⠁⠀⠐⢤⠏⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠠⠤⠀⠀⠚⠢⢄⠀⠀⠀⠀⠀⢸⡷⠁⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⢀⠀⢀⣠⠖⠋⠀⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡉⢀⣢⠤⠤⠭⣷⣦⡀⠐⡀⠀⡃⠀⠄⢀⣠⣐⣥⣄⡀⠀⡀⢀⣨⡼⠋⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠚⠋⠁⠠⡀⠐⠛⠶⠒⠛⠁⠀⠀⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡤⠀⠀⢀⣠⠔⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⠤⠤⠤⠤⠤⠤⠚⠉⠀⠄⠜⢋⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠉⠁⠀⠀⠐⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠐⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠒⠓⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢄⠈⠢⣀⠀⢀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢀⠀⠈⠢⡀⠀⠙⠥⡀⠡⡈⠒⢄
⠀⠀⠀⠀⠈⠐⠁⠀⠁⠈⠀⢀⠂⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠈⠀⠀⡇⠐⢢⠈⠢⠀⠀⠈⠂⢰⠀⠀⠉
⠀⠀⠀⠀⠑⠒⠉⠐⠊⢁⠔⠁⠀⠀⠀⠑⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⡀⢐⠀⠀⠁⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠐⠐⠒⠒⠈⠀⠀⠀⣀⣀⣀⣀⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⢀⠘⢰⠀⠀⡷⠀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠇⠀⠀⠀⠔


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠒⠄⠀⠀⠀⡠⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁⣀⠀⠀⢀⣀⠔⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠐⠅⣀⣀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠈⢉⠏⠈⢂⠀⠸⠄⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⢴⠀⠀⢨⡁⠀⢩⡀⠀⠀⠔⠢
⠀⠀⠀⠀⠀⣀⠊⣀⡠⠚⠒⢠⡠⠤⠤⡀⠀⠤⡒⠠⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⡁⠀⠬⢠⣠⠈⠄⠀⢸⠃⠘⣇
⠀⠀⠀⠀⠊⡠⠄⢉⢀⣂⣐⠈⣐⣄⡄⢈⢣⣠⡈⢒⡈⣢⠀⠀⠀⠀⡠⠀⢄⡩⠤⠤⢀⡠⠠⠄⢀⣀⣀⣪⢤⡤⣵⡀
⠀⠀⠀⠀⡜⢀⡈⠂⠀⠀⠀⢀⠄⡀⠀⠀⢀⠄⠒⢄⡀⠀⠀⠀⠀⠀⢣⠈⠀⡀⠆⠈⣀⠈⢀⠄⠀⠀⢀
⠀⠀⠀⠀⠢⣲⣀⠌⡀⠀⠈⠁⠐⠈⠂⠐⠁⠐⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⠘⢺⠀⠀⠇⠁⡄⡇⠀⠀⢇
⠀⠀⠀⠀⠀⠈⢠⢁⣠⠨⢁⠆⠀⠀⡠⠊⠀⡑⠤⡀⠀⠀⠀⠀⠀⠀⠈⢌⠂⢠⠰⢆⡇⠐⡐⠁⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠈⠉⠫⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠭⠍⠐⠁⠀⠀⠀⠀⠀⠀⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⢀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⢹⣿⡇⠀⠀⠀⠀⢀⢀⣤⣾⠀⡀⠀⠀⢀⡴⣾⣿⣶⡄⠀⠀⠀⣠⣸⡿⢦⡀
⠀⠀⢰⡝⠦⣟⣀⠀⣰⡆⠀⣤⠀⣴⣦⡠⡀⠐⠀⠀⠀⠄⠒⠃⠒⣺⣷⡆⠀⠀⡤⠔⣟⢿⠷⣿⠇⠀⠀⠾⠇⣼⣿⢫⣿⡆⠀⠐⢿⣧⠤⣐⡛⠂⡀
⠀⠀⢾⢶⣶⣬⣬⣿⡿⠃⠀⢾⣧⣼⢻⣷⠤⡄⠀⠀⠀⢀⡤⠒⠛⡿⠟⠀⠀⠀⠀⠶⠿⣅⠠⣯⣀⠀⠀⠀⠀⣿⠍⢚⢻⡶⠀⠀⣾⣯⣇⡙⠛⠦⣈
⠀⠀⠈⠑⠛⠟⡻⠻⠇⠀⠀⢸⡿⠛⠉⠂⠶⠟⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠘⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⢴⣾⣧⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡒⣠⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⣷⣠⢀⣽⣮⡇⠀⠀⢸⣿⡇⠰⣟⡂⠀⠀⣀⣀⠀⠠⣦⣤⡀⠀⠀⠀⠀⠀⠀⢄⠠⢔⡁
⠀⠀⣀⣠⡆⠳⡮⣤⣅⣀⡂⠀⠀⠢⣰⣀⣠⡿⣲⡇⠀⢰⡿⠷⠾⣿⣿⠁⠀⠀⢤⣀⣸⣁⣠⡖⠀⢈⣿⣿⣷⡿⢋⣈⣠⠄⠀⠈⡄⠀⣠⣿⡗⣼⠦
⠀⠠⢿⣿⠿⢿⣿⣯⠈⠈⠀⠀⡈⡀⢉⢤⣝⠾⠟⠀⠀⠀⡹⢂⡼⡿⠃⠀⠀⠀⠀⠫⡁⡩⠋⠀⠀⠀⠙⠿⣗⣿⣦⡝⣇⠀⠀⠀⢡⣤⣉⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠛⠂⠊⠓⠋⠁⠀⠀⠀⠀⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠉⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠄⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⣀⣀⡄
⠀⠀⣀⡄⣀⣼⣻⠟⣃⠐⣂⠀⠀⠸⠀⠀⢸⠀⠀⠐⠂⢲⣿⣿⣿⣤⡀⠀⠀⠀⢀⡀⠀⣼⡕⠁⠀⠀⠀⠀⠠⣀⠸⠟⠘⢛⡆⠀⠀⠀⢉⠁⠀⣂
⠀⠰⣿⣿⣿⡻⢛⠏⠉⠉⠁⠀⠀⣤⣠⣤⣠⡄⠀⠉⠛⢻⡟⣻⣿⣿⣾⠀⠀⠀⣚⣎⣊⣿⣦⠜⠁⠀⠀⠈⠙⠻⠂⠀⣶⠟⠃⠀⠘⢳⣦⡾⠛⡩⣦
⠀⠀⠈⠚⠉⠿⠄⠁⢄⡀⠀⠀⠀⠻⡟⠋⣻⠇⠀⠀⠀⠠⣿⠟⠉⠙⠃⠀⠀⢸⣷⣴⣿⠗⢀⣄⠀⠀⠀⠐⠦⣀⣀⢭⣿⣶⡄⠀⠀⠚⠋⣴⣾⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢹⠀⠉⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠿⠛⢿⠟⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠁
⠀⠀⠀⢀⣴⣾⡟⠋⠉⠀⠀⠀⠀⠀⢀⡀⣤⣄⠀⠀⢀⠀⠈⢙⡀⠁⠂⠀⠀⠐⠳⠐⠞⢻⡠⣾⠟⠀⠀⠀⢀⢔⣺⡶⠿⡇⠀⣐⠍⠔⣻⠟⠉⠛⠇
⠀⠀⣰⣿⣷⣿⢀⠀⠀⠀⠀⢀⢡⣄⣀⣀⣿⣿⡀⠀⠈⠙⠟⡟⣻⠿⣷⠀⠀⠀⠀⠀⡟⠻⠿⡏⠀⠀⠀⠀⡘⠘⣫⡴⠶⠆⠀⢩⠤⢤⠶⠲⣂⢺⣦
⠀⠀⢹⢽⣿⠿⠣⠹⠦⡀⠀⢀⣀⡉⢡⣭⣝⣿⣧⠆⠀⡴⡎⠀⠉⠑⣌⡃⠀⠐⠈⠹⠿⠿⠢⠘⣀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠈⠐⠂⠀⢴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁
⣿⣿⣿⢿⣿⠿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣴⣧⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠰⠖⠐⠒⠒⠒⠒⠀⠀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⢋⡡⠖⠋⠁⠐⢲⠀⠀⠀⠀⠀⠰⠀⠀⡔⠋⠈⠁⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⠧⠀⢠⠖⠊⠄⠀⢀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠠⠄⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢁⠤⠃⣴⡥⠤⠴⢃⡬⢅⠀⠀⠀⢀⡔⠂⠉⠉⠐⣆⡰⠓⠲⠃⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣀⣠⠎⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠀⣰⠋⠀⣴⣆⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡋⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠹⠶⠟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⠉⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⡀
⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⣀⠖⠲⠊⠙⠢⡀⠀⠀⣴⡩⡵⠆⠀⠀⠐⢧⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⢰⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠶⠊⣁⣀⣀⠀⠀⠀⠙⠤⠴⠈⣇⠀⡀⢤⠀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠿⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⠉⠉⠀⠀⠀⠣⣀⠀⠈⢁⣀⠀⠀⠉⠀⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⣨⢲⡆
⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠋⠀⠉⠉⠉⠒⡌⢂⠀⠀⠀⠈⢳⡉⣠⢭⡉⠉⠒⢦⠀⠀⡤⠀⡇
⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢢⠀⠀⠀⠀⠉⠁⠀⡇⠀⠀⠈⢧⠀⢇⠀⡇
⠀⠀⢸⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠧⡀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠘⣄⡈⡆⡇
⠀⠀⠸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡈⣆⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠱⢣⡇
⠀⠀⠘⡇⠀⠘⡀⠀⠀⠀⠀⠀⠀⠙⣄⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢳⢀⡇⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⢡⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⡘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢠⠏⠈⠀⠀⠀⠀⠀⠀⡜⢀⡆
⠀⠀⠀⠀⢧⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠒⠀⠉⠉⠉⠉⠉⠳⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⡼
⠀⠀⠀⠀⠘⢆⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⢦⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣀⠔⡂⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢎⡔⠁⡰⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⡰⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⢀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣀⠠⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠂⠰⠤⠤⠤⠤⠤⠤⠶⠖⠒⠋⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠤⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⡈⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡴⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠋⠁⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⡴⠆⢴⡇⠀⠀⠀⠀⣺⡏⢹⣗⠀⠀⠀⠀⢹⣷⣦⣀⣀⡀⠀⠀⠀⠰⠰⣡⣿⡇⠀⠀⠀⠀⣤⣼⣷⡀
⠀⠀⡟⣅⡀⠶⡇⠀⠀⠀⠀⠈⠛⡛⠁⠀⠀⠀⠀⠀⠙⢹⡟⠋⠀⠀⠀⠐⠿⣿⣾⠻⠿⠀⠀⠀⠀⣽⣿⣿⣿
⠀⠀⠈⠚⠓⠊⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⢠⣤⢠⡖⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠠⣂⣂⡂⠄⠀⠀⠀⢠⣶⣲⣖⣶⡆
⠀⠀⣄⠠⣿⠀⠀⠀⠀⠀⢀⢲⣸⣆⡴⠀⠀⠀⡔⢀⢊⣀⢸⠆⠐⡄⠀⠠⢱⡁⠀⢸⠬⠀⠀⠀⢸⠾⠰⠷⠿⣿
⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠇⠀⠀⠑⠀⠊⠉⠈⠂⠐⠁⠀⠀⠑⠙⡒⠍⠊⠀⠀⠀⠈⠉⠭⠯⠍⠁

⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⣠⡓⠒⢢⡄⠀⠀⠀⠀⢰⡿⢿⡇⠀⠀⠀⠀⡐⡞⣡⡙⣖⡀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⢠⣿⣿⢠⣤⡄
⠀⠀⠁⡷⠶⣪⡀⠀⠀⠀⠀⠀⣶⣾⠄⠀⠀⠀⠀⠐⠛⣍⡝⠂⠀⠀⠀⠀⠰⣿⡿⢻⠀⠀⠀⠀⠀⢹⠉⠈⡿⠁
⠀⠀⠀⠇⠀⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡏⠭⢽⡉⢷⠀⠀⠀⠀⢎⣇⣸⡡⠀⠀⠀⠀⢠⠴⠯⠷⢄⠀⠀⠀⠀⢐⣾⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⡷
⠀⠀⣿⠶⣾⡇⢨⠀⠀⠀⠀⠄⡱⢎⠱⠀⠀⠀⠀⢸⠀⣠⡄⢸⠀⠀⠀⠀⢸⡏⠶⢻⠀⠀⠀⠀⢸⡿⠆⣠⣤⣠
⠀⠰⠿⠶⠿⠏⠁⠀⠀⠀⠀⠊⠒⠒⠑⠀⠀⠀⠀⠘⠤⠬⠤⠜⠀⠀⠀⠀⠈⠿⠿⠿⠀⠀⠀⠀⠈⠁⠀⠙⠛⠁