Buoy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣦⣴⣾⣿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣠⣿⣿⣿⣿⣄⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣾⣿⠟⠁⠈⠻⢿⣷⣮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣽⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⣿⣿⣛⠛⠛⣛⣿⣿⣿⡿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠈⠙⢻⣿⣿⣿⣿⣟⠋⠁⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢃⣠⣴⣾⣿⠿⠛⠛⠿⣿⣷⣦⣄⡘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⣀⠀⠀⢸⣿⣧⣴⣾⣿⣿⣿⣶⣦⣄⡀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣼⣿⡇⠀⠀⣀⣤⣶⣾⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠻⠟⠋⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣶⣤⣤⣤⣴⣾⣿⠿⠟⠛⠿⢿⣿⣶⣤⣤⣤⣤⣶⣿⡿⠿⠛⠻⠿⠇⠀⢠⣤⡀⠀⢰⣿⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣶⣦⣄⡀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⢀⣀⣀⠀⣀⣠⣤⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⣠⣤⣾⣿⣿⣿⡄⢻⠈⣿⣿⣿⣶⣤⣀⠀⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⢰⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣉⣉⡙⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠿⠿⠿⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⣉⣉⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠤⡤⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇⢰⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡈⠛⠿⣿⣿⣿⣿⡇⢸⡇⢹⣿⣿⣿⣿⡿⠟⠋⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠚⠛⠛⠛⠛⠐⠓⠘⠛⠛⠛⠿⠶⠶⠛⠋




⣿⣿⡿⠿⢿⠿⠿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣾⣾⣷⣶⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣒⣂⠰⠦⢞⣒⡦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡊⠅⠂⠉⠁⣀⣀⡀⠀⠀⠈⠉⠒⠮⣑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⣨⣿⣭⣾⣷⣿⠉⠁⠀⠀⠀⠀⠈⠉⠒⠠⢀⠀⠈⠑⡌⢦
⠀⠀⠀⠀⠀⠀⠂⠕⠉⢀⢼⣿⡛⠁⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠘⡎⢆
⠀⠀⠀⢀⢔⡔⠁⠀⠰⠋⠀⠙⢄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡸⡘⡄
⠀⠀⢀⣠⠊⠀⠀⠄⠀⠀⠀⠀⠀⠻⣆⣠⠴⠟⠒⠛⠒⠒⠲⢄⡀⠀⠀⠀⣀⠤⢺⣷⣿⣿⣄
⠀⠀⡘⡈⠀⠀⡘⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡤⠞⠁⠀⠀⢹⣿⣷⡛⣄
⠀⠀⣟⠀⠀⠀⠁⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⠀⠀⢀⣷⣿⠓⢎⣆
⠀⠀⡞⡀⠀⢀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠋⠉⠉⠉⠁⣽⠀⠈⣆⡄
⠀⠀⢰⣱⡀⢸⠁⠀⠀⠀⢀⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣼⠀⠀⠸⠖
⠀⠀⠀⠳⡳⣼⢶⡞⠉⠉⠉⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⡃
⠀⠀⠀⠀⠘⣿⣯⣷⡀⠀⢀⡴⠞⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⠀⠀⠀⠀⡸⠀⠀⠠⠰
⠀⠀⠀⠀⠀⠹⡛⣾⢿⡤⠊⠀⠀⠀⠀⠈⠑⠢⠤⣤⠤⠤⢾⠋⠁⠘⠓⢤⡀⠀⠀⡴⠁⠀⡰⡡⠁
⠀⠀⠀⠀⠀⠀⠱⡘⡝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⣽⣦⠞⠁⢀⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠹⡀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣤⣴⣾⣿⡇⠀⠚⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣙⢄⡀⠈⠒⠠⠀⣀⣀⣀⣀⣀⣀⣠⡤⠼⡿⢏⠵⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠬⢑⡦⢤⢀⣀⠀⠈⠉⣉⡡⠤⣒⠭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠯⠩⠣⠐⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡰⢖⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣋⢁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢐⡿⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⣶⣷⣀⣠⣤⠤⠤⠶⠦⠤⡤⢼⣿⣿⣿⣶⡏⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⢯⣒⣈⡀⣀⣠⣤⣤⣤⡿⠏⠉⠙⠛⠳⢦⠀⠀⠀⠀⠙⣧⢀
⠀⠀⣀⣤⠤⠞⠁⠀⠀⠀⠀⣴⠏⠉⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⣷⣦⣄
⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⡧⠉⣞
⠀⡞⠀⠠⠆⠀⠀⢀⡤⠶⠚⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⢸⡇⠀⢿
⠰⣕⠀⠈⣇⠀⡰⠋⠀⠀⠀⠀⡡⠭⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠒⠉⡩⠖⢦⡀⠀⠀⠀⢸⠁⠀⢘
⠀⠈⠳⣄⢻⣾⣷⣦⡀⣀⡔⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠙⢲⣀⠀⣉⣙⣆⣀⣰⣯⢔⣯⠋
⠀⠀⠀⠈⢿⣛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠈⠹⠿⣿⡛⢷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣲⣷⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣡⡀⠉⠑⠲⢤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢾⣻⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢥⡢⠀⠀⠀⠉⠉⠩⠛⠶⠖⠶⠶⠖⠛⠛⠛⠀⣪⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣄⣀⣤⡤⠶⠖⠤⣤⡄⠀⠀⢀⣀⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇⣀⣹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠗
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢠⡤⠼⠤⠤⠤⠤⠤⠤⠼⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣤⣤
⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠐⠒⠦⠬⠷⠖⠒⠒⠦⠤⠤⠖⠛⠒⠦⠤⠀⠀⠀⠀⣉⡓⠶⠶⠛⣋⣉⡛⠻⠿⠛⣋⣉⡓⠶⠄
⠀⠀⢈⣉⡓⠒⠒⢋⣉⣉⡓⠒⠒⢋⣉⣉⡓⠒⠀⠀⠀⠀⣤⣉⡛⠚⣋⣡⣬⣉⡛⠚⣋⣡⣬⣉⡛⠂
⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠉⠙⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⠀⡀⢀⣀⣀⠀⢀⣀⢀⢀⠀⢀⣀⣀
⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁
⠀⠀⠀⠈⢿⠿⠋⢻⡿⠋⠈⢿⠏⠹⡿⠿⠿⠿⠿⣿⠿⡟⠻⡿⠿⠛⠛⠋⣿⢳⡄⠀⠀⠀⠀⠀⠀⣀⢀⡠⣀
⠀⠀⠀⠀⠀⢣⣤⣼⠁⠀⠀⡟⠀⠀⠁⠘⠀⠈⠚⠃⠀⠀⠚⠀⢰⠀⠀⠐⠿⠛⢧⠀⠀⠀⠀⢸⣽⣿⣯⣟⢸⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠹⣿⣿⢹⣁⢀⢧⣤⣤⣼⣣⣤⣤⡟⣤⠤⣼⡇⠀⠀⠇⠀⠸⣄⠀⣼⡿⠀⢶⣦⣾⣿⣿⣿⡇⠀⠹⠀⡀⡠⣤⡤
⠀⠀⠀⠀⠀⢐⠀⠘⡌⠉⠘⠋⠉⠉⠁⠈⢻⡟⠁⠉⠀⠁⢃⣀⣀⡆⠀⢀⣈⠀⣏⠉⠸⢻⣿⣽⡇⡀⡀⠁⠀⠀⠈⢋⠀⠁⡧
⠀⠀⠀⠀⢀⠘⠀⠀⠉⠀⡆⠈⡁⠈⠀⠀⢙⡇⠀⠉⠀⡌⢈⠁⠍⠛⣟⣉⢀⠀⠈⠁⠀⢸⡟⠩⣥⠀⡄⣀⠀⠁⠠⠼⠭⠬⢷
⠀⠀⠀⠀⠈⠉⠟⠈⠉⠉⠙⠉⠁⠈⠉⠀⠈⠇⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠱⠆⠸⠤⠤⠤⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠁⠠⢀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⣴⡀⣠⡤⢭⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣼⠀⠉⢿⡁⠈⣀⡀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡋⢿⠀⢉⡈⠛⢠⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⡇⣾⣀⢠⡤⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣀⡐⠤⠀⠒⠋⣻⡏⣥⠀⠀⢠⡄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠁⠀⠀⠀⠀⠠⠟⠛⣾⣿⠀⠀⣠⡄⠀⠀⠸⠟⢃⡀⢠⡴⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢀⡀⡄⡤⣀⠀⠘⣻⣿⡆⠀⣈⡃⠀⡘⠁⠈⠛⠻⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⣈⠾⠧⣬⣯⣅⣤⣿⠿⠇⣈⣍⠁⢸⡇⠀⠀⠀⠀⣴⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠷⡶⢾⡷⣺⡍⢹⠻⠛⣿⣿⣶⠶⠞⠉⣤⣾⠃⠀⠀⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⣲⣿⣿⢿⡛⠁⠈⢇⠀⣼⢍⠑⢀⠀⠄⠀⣿⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⡼⠛⠉⠀⠀⠡⠤⠤⢬⣟⣁⠈⣠⠟⢀⣀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⠀⠀⠀⠀⠀⠀⢀⣰⠏⠂⠀⠈⠀⠆⠙⠛⠳⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣇⡇⠀⢀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⢀⣀⠄⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣵⡾⠃⠀⠀⠀⢰⠀⠀⠐⠂⠀⠀⢨⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠉⠀⠀⠀⠀⠀⠀⠓⠤⠤⠀⢀⡠⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠈⠀⠀⠀⠈⠲⠤⣤⡄⠸⣿⡇⠀⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⢀⣠⡤⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡄⠀⠀⠀⠆⢀⠄
⠀⠀⠀⠀⠀⠀⠠⣀⠁⠑⠘⠎⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⢠⡴⠒⢤⠀⠀⠀⡒⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⢺⠀⠀⠀⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠶⠒⣚⣉⡭⠷⠖⢲⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠓⠒⠋⠉⠁⢀⣀⣠⣤⣎
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣴⠖⠚⠋⠉⢁⡴⠋⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠲⢦⣤⣟⠁⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⡾⠉⠉⠛⠲⢦⣄⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠋⠀⠀⢀⣀⣠⣤⡴⠿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡴⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠞⣻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡴⠶⠟⠛⠋⠉⠁⠀⣀⡴⠟⠁⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠛⠒⠶⢶⣤⣴⣶⣾⣛⢳⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⣷⣛⠡⠭⠹⠛⠛⠓⠶⢶⣤⣿⡦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⠞⠋⠁⢸⣀⣶⠤⠷⠖⠒⠋⠉⠁⠀⢷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⡿⠵⠖⠒⠋⠉⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠐⣏⠁⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⢤⣤⠤⣄⠀⠀⠀⠻⣄⡀⠀⠤⣶⢤⣀⠀⠀⠀⠀⠀⠀⠠⢶⡶⢤⡀⣼⠃⠀⠀⠀⠰⢶⡦⣤⡀
⠀⠀⠈⡆⠀⠱⡄⠀⠀⠈⠻⢦⣀⢹⠀⠈⢧⡀⠀⠀⠀⠀⠀⢈⠇⠀⠙⣇⠀⠀⠀⠀⠀⠈⡇⠀⠙⣆
⠀⠀⠀⡇⡸⣆⠘⢦⡀⠀⠀⠀⠙⡟⣰⣆⠀⠑⢄⡀⠀⠀⣠⢎⢜⣧⡀⠘⢆⠀⠀⠀⠀⡠⢃⠦⡀⠘⢆
⠀⠀⠀⠀⠀⠈⠳⢄⣉⣒⣀⣐⠭⠊⠀⠉⠳⠤⣄⣈⡩⠍⠒⣡⡾⠁⠑⠦⢄⣑⠒⠒⠊⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⡤⠖⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠉⠁⠀⢀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣴⠞⠋⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡭⠄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣒⣀⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣓⣒⠂⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⣤⣤⣤⣄⣀⣀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢀⣤⠦⣄⠀⠀⠀⣿⡆⡠⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠻⣦⡄⠀⠀⣠⣾⠟⠉⠻⣷⡀⠒⠒⣴⡟⠁⠀⠈⢧⡛⠛⣛⠞⠀⠀⠀⠈⢷⣄⣀⣠⡶⠟⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠈⠻⠷⠾⠛⠁⠀⠀⠀⠙⠿⣶⠾⠋⠀⠀⠀⠀⠀⠉⠋⠁⠀⢀⣀⣀⠀⠀⠉⠉⠉⢀⣀⣀⡈⠻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣄⠀⠀⠀⠀⢀⣤⡶⢦⡀⠀⠀⠀⠀⡰⠋⠁⠙⢷⣄⠀⣀⡴⠋⠀⠀⠈⠀⠈⠛⠓⠒⠒⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠳⠤⠴⠟⠁⠀⠀⢻⣧⠀⠀⣠⡿⠃⠀⠀⠹⣄⠀⣀⠜⠁⠀⠀⠀⠀⠙⠛⠋⢀⣤⡶⠶⠶⣄⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⣤⣄⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⣾⠿⠿⣶⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠳⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠹⣷⡀⠀⢀⣴⠟⠁⠀⠙⣆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠟⠁⠀⠀⠀⠀⠈⠉⠉



⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠶⠤⣤⣠⠞⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣤⡤⠶⠒⠻⣄⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢀⣈⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⢸⠁⠀⠀⡏⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣤⣼⠀⠀⠀⢧⣤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠾⠧⠤⠤⠤⠾⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⡖⠒⠒⠒⠒⠒⠒⣶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⠤⡤⠤⠤⠤⠤⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣇⠀⠀⣆⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡏⠉⠉⡏⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣤⣤⡄⣤⣷⣤⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠿⠃⠻⠿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⠜⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠷⢀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀⠸⠃⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿




⡿⠉⢹⡟⠿⠻⠿⠟⠿⡛⠿⠻⠿⠿⠟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⢂⡤⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢉⡒⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⢊⡩⠖⣉⠀⡙⠓⠦⣤⣄⡀⣀⠀⣀⡀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠁⠖⠋⠖⠉⠒⠠⠄⠤⠀⠈⠉⠉⠉⠉⠉⢉⣉⢀⡄⠍⠉⢓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡴⠀⢆⢣⠃⠁⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠊⠴⠃⠜⠐⠁⠁⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣶⠦⢤⣤⣀⣀⡀⠀⠀⠀⠀⣀⣤⡤⠶⠚⠁⠀⠀⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠶⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠒⡷⡷⢻⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠉⠙⠶⠶⡷⢷⠿⢋⡴⠛⡷⣤⡀⠀⢀⡀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣠⠖⠋⢁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠣⠞⣁⠔⢋⠴⢊⡹⢦⡀⠙⢦⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠞⢀⡴⠋⠀⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠊⣁⠔⠉⣠⠖⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣀⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⢁⡠⠊⣁⠔⢁⡼⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠖⠉⣠⠞⢁⠔⠋⣀⠜⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣠⠞⠁⣠⠞⢁⡴⢋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠔⠊⣀⠴⠋⣠⠖⢉⡴⢋⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠴⠋⣡⠔⢋⡥⠞⣁⠴⢋⡴⢻⡀
⠀⠀⠀⠀⢀⠴⠖⣀⠤⢒⣺⡇⢠⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⣡⠴⢋⡵⠞⢉⡴⠚⣡⠖⣩⠔⣹⡶⠶⢤⣀⡀⢀⡀
⠀⢀⡄⢰⡃⠀⢸⠁⠀⣏⠀⠳⣄⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⣉⡴⠊⣁⠴⠚⣁⠴⠋⣠⠞⣁⠞⢁⡟⠑⢦⠀⠉⢳⡈⠳⣄⠀⣀
⣇⠸⡅⠀⢣⡀⠈⠳⣄⠈⠳⣄⡈⠛⠲⠦⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡥⠖⣋⡥⠖⢋⣡⠴⢋⣡⠖⢋⣤⣾⠷⠞⠋⢀⡤⠞⠀⣠⠏⠀⠀⢸⠀⠙⣦
⠈⠃⠙⠦⣀⠙⠦⣀⠈⠀⠀⣀⡉⠓⠲⠤⣀⣀⣉⡉⠒⠒⠒⠤⠤⠤⠮⠥⠴⠶⠯⠥⠴⠶⠯⠤⠾⠛⠒⢊⣉⣁⡠⠤⠔⠚⠉⣀⠤⠚⠁⠀⣀⠴⠋⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢤⣀⠉⠓⠶⠦⣤⣄⣀⡉⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠘⠛⠉⠉⠉⠁⢀⣀⣠⡤⠶⠚⢋⣠⠴⢒⣉⣭⠤⠖⠊⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠒⠶⠤⠤⠭⠉⠛⠓⠒⠶⠶⠤⠤⠤⠤⠤⠤⠀⠀⠦⠤⠐⠒⠒⠛⠉⠉⣁⡀⠤⠖⠚⠉⠀⠘⠉⣀⡤⠄⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⢄⣀⣀⡀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⣀⡀⠤⠴⠒⢉⡠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠲⠦⢬⣭⣉⡛⠛⠒⠲⠶⠦⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠈⢁⣀⣄⠀⠛⢁⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⣉⣉⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠋⠉⠙⠙⠛⣉⢉⣀⣀⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⠩⠤⠔⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⢔⣂⣶⣵⣗⣒⠋⠉⠙⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣚⡭⠼⢒⣒⣭⣭⠤⠴⠶⡖⠉⠄⢀⢀⠀⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢊⠔⠋⣡⠴⠺⠉⠀⠀⠀⠁⠀⠀⠃⠐⠀⠀⠑⠊⠐⢴⡄⡀⢂⣜⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⡴⢁⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⢙⣮⡑⢬⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠩⣈⡟⠛⠅⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢬⡙⢦⡑⣜⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡝⡀⠀⠀⠀⠉⠐⢤⣐⢀⣒⣪⡽⠿⠷⠤⢤⣄⣂⡀⠀⠀⠀⣠⠃⠀⠀⠛⠙⣳⣹⡹⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠢⣨⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣤⠜⠁⠀⠀⠀⠀⠀⢖⢹⡳⡱⡀
⠀⠀⠀⠀⠀⠀⣼⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠰⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡥⠀⠀⠀⠀⠀⢀⠉⣧⢳⣵
⠀⠀⠀⠀⠀⠀⢧⡀⠠⡀⢀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠆⢽⠘⣞⡆
⠀⠀⠀⠀⠀⠀⢸⣾⠹⣇⠐⠀⠀⠀⠀⢠⠺⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⢀⣀⣀⠠⢰⢸⠀⣷⡇
⠀⠀⠀⠀⠀⠀⢸⢽⠀⣿⠂⠀⠄⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⠀⠀⠀⠀⠠⠨⢹⣦⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣽
⠀⠀⠀⠀⠀⠀⢻⢸⠀⠸⡟⠀⠀⠀⠀⠀⠀⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣔⡟
⠀⠀⠀⠀⠀⠀⠈⣎⢧⠀⠹⡝⠥⠄⠀⠀⠀⡠⠊⠬⠑⢦⣀⡀⠀⠀⠀⠀⠀⢀⣠⡾⠣⢄⠀⠀⠀⠀⠀⢀⡀⠂⠀⢌⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢮⠳⡀⠹⣆⢰⡤⢁⠀⠀⠀⠀⠀⠀⠀⠩⢙⡛⠲⠶⠛⠉⠀⠁⠀⠀⠁⢢⢄⡀⠀⣈⠎⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⠶⣌⢷⣁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣲⢴⡶⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣍⢿⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢄⣐⡁⢘⡭⢚⡵⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠈⠑⠓⠤⣐⠤⣀⡠⠄⡘⠠⡤⢑⣂⠬⣒⣻⠵⠚⢉⣤⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠈⠀⠋⣗⠓⠚⠛⠓⠛⠉⠁⢀⣠⣶⡽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⡤⠛⠿⢷⣶⣤⣤⣴⣾⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣐⡂⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠔⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⢁⠭⠛⠷⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠁⠐⠂⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠙⠖⠢⠬⣐
⠀⠀⠀⠀⠀⠀⡀⠁⢀⣀⣀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠂⠀⠀⠀⠀⠘⠢⢄⣀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⠳⡐⡄
⠀⠀⠀⠀⠀⠰⣶⠂⠉⠀⠀⠁⠉⠢⡀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠁
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠰⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗⠀⠈⠉⠕⠲⡄⠀⠐⢀⠇
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⣯⣠⠊
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠙⢦⠀⠀⢰⠟⠁
⠀⠀⠀⠀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣷⢠⠏
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣼⡃
⠀⠀⠀⠂⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠋
⠀⠀⠀⠀⠙⠦⢄⣀⡀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢬⡊⠁⠢⢤⣀⡄⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠄⡀⣀⢈⡯⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠑⠒⠬⢌⣐⡒⠐⠀⠂⠒⣈⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠉⠉⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡠⠖⠋⠉⠉⠙⠲⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡞⠀⡴⠊⠉⠉⠑⢄⠀⢣⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢰⠀⠀⠀⠀⠀⠈⡆⠈⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡆⠀⢆⡔⠊⠐⢲⠉⠁⠲⡁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠦⣀⠀⠀⠀⠈⡆⠀⠀⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡈⠀⠀⠀⠀⣏⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣸⣆⠀⡏⠀⠀⠰⠋⠉⠉⠉⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⢹⠉⠀⠀⢰⡀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠐⠂⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠓⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠇⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⠛⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠎⠩⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⢀⡀⠀⠧⠤⢄
⠀⠀⠀⠀⡠⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠰⣾⣷⠄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⢄
⠀⠀⢀⠞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢤⠀⢸⡇⠀⡤⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠣⡀
⠀⢀⠎⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢪⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠱⡀
⠀⡜⠀⣰⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢸⠀⣼⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⣆⠀⢣
⠸⠀⢀⣿⣿⡄⠀⠣⡠⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢰⢠⣿⣿⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠜⠀⢠⣿⣿⡄
⡇⠀⣸⣿⣿⣿⡆⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⣾⣿⣿⣧⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢰⣿⣿⣿⡇
⡇⠀⠈⠉⠻⣿⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢰⣹⣿⣿⣿⣿⣆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠀⢀⣿⠟⠉⠁
⠰⣀⠔⠢⡀⠈⠁⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⣸⣿⣿⣿⣿⣿⣿⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠀⠀⠁⢀⠔⠢⣀
⠀⠀⠀⠀⠈⠦⡀⠀⠀⠈⠑⠢⠤⠄⢀⣀⠀⠤⠤⠒⠙⢄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠑⠒⠤⠤⠀⣀⡀⠠⠤⠔⠊⠁⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣶⣿⣄⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣄⡀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⣀⠠⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠤⣀⡀⠈⠙⠻⢿⣧⣄⠀⠀⠀⠈⠹⢿⣿⠟⠋⠁⢀⡀⠤⠔⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠉⠻⢿⣆⡀⠀⠀⠀⠀⠋⡱⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠙⠋⠐⡢⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣭⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⠛⠿⣿⣷⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣦⠀⠀⠈⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣀⡀⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡞⣽⣿⣿⣶⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡀⠀⠈⠐⠀⠈⢷⣄⠁⠙⠻⣿⠀⣤⠀⠀⠰⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⣀⡀⠀⠠⠤⠌⠐⢒⣀⣐⣐⣒⣒⡉⣆⢨⣸⠁⣀⠠⠤⡬⠁⠀⠀⣀⡀⢠⣀⣀⡀⢀⡀
⠀⠀⣀⠤⠖⣒⠭⠋⠉⠉⠀⡀⣠⡴⠶⠓⢛⣉⣉⠥⠤⠒⣀⡀⠀⢰⠇⢠⠷⠤⠬⣭⣉⣉⡉⠛⠒⠢⣤⣀⠀⠀⠉⠑⠐⠌⢁⡒⠒⠠⣄⡀
⠐⠉⠀⣠⠎⠀⠀⠀⠀⢔⠈⣞⠁⠀⢰⣾⠋⠁⠀⠀⢎⠀⠀⠐⠂⠁⠀⣀⣘⠢⡄⣀⠀⠬⡙⢿⢮⡅⠈⠛⢷⣤⡢⠀⠀⠀⠀⠘⣲⣄⠀⠈⠑⠦⣀
⠀⠀⠀⢯⡠⠀⠀⠀⠀⢕⡨⣷⠀⠀⠐⠽⣆⠀⡂⠀⠀⠁⠢⢤⣀⡀⣀⣈⣉⣑⡊⠎⠠⠔⠁⣼⠯⣻⠀⠀⠈⡍⣋⠀⠀⠀⢀⠢⡒⢽
⠀⠀⠀⠈⠲⣡⢂⢔⢄⠀⠈⠉⢶⡔⢄⠀⠈⠉⠒⠢⠦⣎⣦⣴⣮⣥⡤⢶⣲⣶⣆⣴⡶⣐⣑⠥⠚⠁⣠⢶⠕⣅⠎⠀⠀⢌⠢⠑⡬⠎
⠀⠀⠀⡀⠀⠀⠉⠉⠈⠊⢎⣆⡄⡈⠚⠊⠊⠃⠂⠠⣰⣒⡤⠤⢬⣭⣉⣊⣭⠉⡉⠉⡀⠠⠴⣶⣊⡪⠨⠖⠊⢁⢀⢊⣄⠦⠒⠉
⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠉⠉⠙⠓⠲⠦⠤⠄⣄⣄⡉⣉⣉⣹⣻⣬⣭⠝⠻⢇⢙⢉⣉⣤⣤⠠⠤⠆⠛⠚⠈⠉⢀⡀⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠀⠀⠀⠀⠠⠤⠄⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠄⠀⠀⠒⠒⠀⣉⡉⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠐⠒⠀⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠋⢠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⣉⠘⠀⡰⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⢡⠀⠀⠀⠀⠀⠀⡎⠰⠁⠐⠐⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡠⠀⢀⡜⣆⣰⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡐⠁⢀⠊⢇⠳⡈⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠐⠀⠀⠀⠀⢀⡜⠀⢠⠃⡰⢈⠜⡸⠆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡰⠁⠀⡇⢸⠘⣀⠇⠀⢀⠔⠁⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⡠⠃⠀⡔⠁⠀⢰⡉⡞⢀⠇⢀⠴⠃⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⡐⠁⢀⠜⠀⠀⠀⡎⢸⣠⡎⠠⠁⠀⠀⠈⠀⡌
⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⢀⠜⠀⢀⠎⠀⠀⠀⠀⢇⠸⠉⢃⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠸⡀⠈⡄⠀⠀⢀⠊⠀⠠⠃⠀⠀⠀⠀⠀⢨⢜⠇⢸⢀
⠀⠀⠀⠀⠀⠀⠣⠀⠈⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣀⡳⠟⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⠒⢈⣁⠴⢺⣍⢦⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠤⠤⠤⠤⠄⠒⠊⠁⠀⠀⠀⠛⠛⠲⣶⢝⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⣡⠀⠀⠀⢸⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⢤⣶⣶⣦⡀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠔⠃⡀⠘⠆⢸⢿⣿⣿⢿⠋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡠⠒⠂⡟⠂⢄⣟⡘⣙⠘⢻⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣇⣀⣀⣇⢀⠀⠀⡄⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⡀⠀⠀⠀⠈⢋⣭⡉⠉⠉⠁⠀⠇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡙⠢⣤⡤⠴⠋⡍⠒⠀⠀⠀⠀⠆⢪⣥⣌⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠷⠊⠁⣄⢀⠀⠁⠀⠸⠀⠀⠀⠀⣀⣸⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠖⠋⠙⠃⠀⠠⡏⢹⠀⠀⠀⢠⠀⠀⠸⠀⣶⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡅⠀⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⡀⠀⣥⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡄⠀⢸⠃⢀⠀⡼⠀⠀⠠⠀⢀⠃⠀⠀⠀⡟⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠇⠀⠰⠆⢁⡼⠁⠀⠀⡀⠀⠸⠄⠀⠀⠀⡇⣄⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠒⠺⠷⡶⠶⠒⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢸⠇⢸⣀⠴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣇⣀⣀⡘⡇⠀⠀⠀⠀⠀⠀⠀⢨⣅⡾⠀⠋⢀⢠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠀⠀⠀⡏⢸⠀⠑⠛⠲⣶⡄⣀⠠⠀⠀⠀⣼⠁⠀⠀⡼⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡿⠺⣇⠀⠀⠀⠚⠑⠫⡄⠀⠀⡜⠳⡧⠀⠀⠷⠀⢠⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠀⢻⣆⠀⠀⠛⠀⠀⠀⣠⢾⠇⣾⠆⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⢰⠋⠀⡾⠋⡷⣄⣀⣀⣠⠞⢁⡎⣠⠁⠣⡉⢀⠙⡀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠈⢯⣸⠃⠁⡗⠛⡁⡸⠣⣤⡞⡰⠋⢠⠀⣧⣰⣦⢧⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⣸⠀⠀⡧⢀⡟⣁⢠⣿⠃⠀⠀⢸⠀⡟⠁⠙⠚⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⢧⣄⡘⡇⣰⢂⡇⠀⣼⠀⠀⣀⠋⠀⣋⣠⠴⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⠈⣧⠉⡱⠃⠸⢱⡀⠘⠳⠲⠟⠊⠉⠁⣤⢼⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠒⠒⣶⠒⣿⣤⣌⣳⡀⢚⣠⡗⠀⠀⠀⠃⠀⠀⠀⢹⣹⠦⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠴⠤⢤⣌⠭⠭⠥⠝⢙⠿⠭⠿⠶⠶⠶⠶⠂⠠⠴⠶⠤⢷⠤⠤⠤⠤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠤⠭⢤⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠠⠀⠀⠀⠂⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡿⠟⠻⢿⣿⣮⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡏⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⡷⠔⠒⢖⢲⣞⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⣤⡗⠛⣯⢹⣿⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⠛⡇⢰⣿⣾⢻⡅⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⡗⠺⣴⡇⠀⣿⣿⣦⡇⢸⠁⢀⡤⠤⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣹⠶⠶⠶⢶⣒⣋⣹⣄⡹⢧⣀⣿⣿⣦⣏⢻⣷⣿⣿⣷⠐⣷⣏⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⣮⣉⠛⣿⣟⡧⢽⡶⢳⣼⣿⣼⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢙⣿⣶⡏⠻⡧⠶⠞⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣿⡇⣿⡆⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⣿⡇⣿⣱⠞
⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠀⢘⣿⡇⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀
⠀⠀⠀⠀⣠⢋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣴⡟⠀⢸⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣄
⠀⠀⢀⣼⠇⣼⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣐⣳⣇⡀⠸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢳⣜⢧⡀
⠀⢀⣾⠏⢰⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⡋⢙⠿⢿⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣎⢷⡀
⠀⣼⡏⠀⣼⣿⣿⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠻⣷⣿⢦⣞⡉⣣⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⣿⣿⣿⣧
⢰⡟⠀⢀⣿⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⣿⣿⠀⣏⣿⣹⠆⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⣿⣿⣿⣿⣿
⡼⢀⣴⠿⡿⣿⣿⡛⠷⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⣿⣿⡆⣿⣡⠏⠀⠀⠀⠀⠀⠀⢠⡾⠷⢛⡿⣹⢻⠿⣟⠻
⡷⠋⠁⠀⢳⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡏⠸⠦⠐⣿⣿⣿⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣰⡿⡟⠀⠈⠙
⠀⠀⠀⠀⠘⣆⢈⡻⢿⣿⣶⣤⣄⣀⣀⣠⠞⣧⡞⠀⠀⠀⡼⢿⣿⣿⣧⡑⠦⢤⣀⣀⣀⣤⠤⠖⠉⣠⣾⡿⣱⠃
⠀⠀⠀⠀⠀⠘⣞⣿⣷⣍⡛⠿⠿⣿⣿⡟⢤⣿⣖⣀⠤⠚⠀⠀⠙⠿⣿⣿⣷⣶⣤⣤⣤⣴⣶⣷⣿⣿⢟⣴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣝⡛⠛⠁⠀⠀⠀⣷⢬⡏⠉⠙⠲⡄⠀⠀⢠⠴⠛⠛⣻⣿⣿⣿⣿⣿⡿⢟⣫⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣹⡦⣽⡀⢀⣠⣾⣆⢰⠃⠀⠀⠐⠛⣛⣫⣭⣿⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠼⡗⠿⢿⣿⣿⡇⣀⡤⠶⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠢⡇⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⣛⣛⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣿⣿⡏⠁⠀⠉⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣄⠀⢀⣤⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⣡⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣠⣾⣿⣷⣶⣖⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣲⣿⣿⣷⣄
⠀⠰⣿⣯⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⠆
⠀⠀⠈⠻⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⣿⡄
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⣿⡇⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⣿⣧⣿⣮⡻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢻⣿⣿⣿⣿
⢹⡟⠉⢻⣿⣿⣦⡙⢷⣤⡀⠀⠀⠀⠀⠀⣿⠇⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣤⠾⢋⣴⣿⣿⡟⠉⠻
⠀⠀⠀⠀⠻⣿⣿⣿⣶⣌⡙⠳⠶⣤⣶⡾⠟⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣟⣋⣥⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣭⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣬⣙⠻⠟⣡⣴⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠗⠠⠞⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠒⠷⠧⠤⣤⡶⠶⠷⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠷⢧⣤⣤⣶⠶⠷⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣇
⠀⠀⠀⠀⠀⡏⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠀⢀⠀⠉⡏⠙⢶⡀⢀⡔⡇
⠀⠀⠀⠀⠀⠳⡉⠀⠀⠀⠀⠀⠳⠀⠀⠀⢈⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⠀⠰⡏⠀⠀⠻⠀⢸⠇⢈⡽⠃
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣀⣀⠀⢀⣁⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⢋⣀⠀⢀⣉⣯⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢴⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⣷⣟⡿
⠀⠀⠀⠀⠀⠀⠰⠾⠶⠶⢌⠉⣹⠦⠶⢦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⣌⠉⣹⠷⠶⢦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⡇
⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⣿⣟⠳⣤⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠛⣏⠀⠀⠀⠐⠈⢿⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⠀⢰⠞⠀⠘⠿⠀⢸⡇⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢧⣤⣀⣤⠤⡦⣐⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣜⣃⣠⠤⣦⣐⣛⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢰⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢰⡿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠇⠀⠀⠀⠀⠀⢀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⡠⠔⠤⡐⠛⠀⠀⣰⠭⠏⡀⢀⢞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠉⠓⡄⠀⠀⠉⠀⠀⠱⠴⠖⠀⡠⠖⣋⠀⢀⠤⣈⢹⣗⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣠⡗⠁⠀⢀⡔⠒⣢⣀⡠⠔⢫⠒⠛⡾⠃⣞⡶⡿⠀⠉⠰⠉⠱⡄⠀⣎⣱⠄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠁⠀⡔⠁⣨⡷⠛⡇⠀⠀⠱⢤⡾⠃⣴⡌⠁⠀⣠⠔⠃⡤⠤⡘⣆⠌⢥⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢃⢌⣀⡳⠾⠃⡤⠒⣤⣤⡀⠀⢠⢄⠀⡞⠀⡠⠚⠣⣴⠃⠈⢦⣐⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢒⢦⣠⠴⠊⠁⠀⠳⠞⠉⡕⠀⡠⠗⠒⣿⠉⢀⡀⠈⠛⠀⡇⢨⡀⠀⡔⡐⠀⠀⠀⠻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠚⢇⠀⡀⡰⠘⡘⠸⣰⠀⠀⣅⢀⣴⡟⠀⢧⠯⠀⠀⠀⠘⡄⠉⠀⠉⠀⠀⠀⢠⣄⠱⣤⡄⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠙⠛⠒⠋⢰⢡⢁⢣⢁⠗⢣⠀⠀⠈⠁⠉⢠⠶⣽⠂⠀⠀⢆⡆⢨⢀⡄⠀⠀⣔⣢⠀⢡⠠⡟⠀⣠⠼⣄⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢃⢁⢃⠆⡌⡐⡜⠛⠋⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡠⠖⠶⡁⠘⠶⠀⠀⠉⠁⠂⢡⠐⢡⠀⢇⣠⢀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠀⢢⠀⠈⡘⡜⡸⢠⢱⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⢄⣼⢂⠀⠀⠀⢀⠀⡂⡄⠈⠀⣸⠀⠀⠉⠠⣎⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⡇⠀⠡⢂⠱⢁⢃⠇⡌⡜⡠⠀⠀⠀⠀⠀⣀⡀⠀⢠⣇⠀⢔⠌⠁⠿⠀⢀⢀⠰⠟⠁⠀⣶⠀⡼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡄⡄⠙⢢⡀⠱⣂⠘⡘⢠⢡⢠⠃⠀⠀⠀⠀⠮⣀⡼⠀⡆⠈⠉⠉⠀⢀⠀⠀⠐⠈⠀⠀⠀⣀⠘⠤⠃⡉⣈⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠠⡄⠘⣷⡀⠀⠱⡈⠡⡀⠁⡎⡈⡌⠀⡠⢊⡹⣄⠴⡌⢀⡴⠁⠀⠀⢀⠰⠘⣀⢤⡀⡎⠉⢧⡀⡧⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠘⠤⡨⠇⠀⠙⡇⠀⠀⠳⡀⠀⠀⠀⠁⠁⠇⡇⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⣨⠔⠋⠀⢰⠁⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⢇⠆⠠⡀⠘⣄⢀⠴⢦⡈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⡇⠀⣦⠂
⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⣁⡀⠘⠊⠣⡑⡀⠈⠁⠀⠀⠓⠔⠋⠀⢀⠄⢂⡠⠖⡆⠰⡇⠀⠀⠀⠀⠀⠻⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢌⠂⠀⠀⠙⢌⠠⠀⠀⠀⠀⢀⠄⢂⡤⠚⠉⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠑⠢⡄⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢸
⠀⠀⢀⡠⢄⣠⢄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⡴⠒⣢⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠎⠤⠌⠽⣃⣃⣘⢤⠀⢉⣒⣒⣀⣩⣯⡑⣤⣤⠔⢒⣈⠉⢑⣲⣤⠤⠌⠉⣭⠥⠤⠤⠔⠋⠀⢙⠦⠤⠤⢤⢄⠀⣄⠈⠂⢒⣚⠂⠀⠀⡤⠠⡖⠒⣄
⠀⠀⠀⠀⣆⡀⣀⣀⡠⠤⠴⡖⠒⠒⠒⢲⣒⣒⣒⡒⠀⢘⣋⣀⣠⡼⠧⣄⣀⣀⣀⣀⣀⣈⠉⠀⠉⠉⠀⢀⠀⠵⣎⣷⢮⡭⡥⢤⣬⡌⣓⡌⣁⡚⠉⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠄⠒⠒⣲⡶⢤⣀⢱⠞⠣⢀⣀⣬⠿⢍⣁⡚⠛⣮⠔⠛⠛⠛⢮⡘⠃⢘⠉⠙⠮⡛⠓⡎⠀⠀⠉⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⢤⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⢀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠋⠁









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

⣄⠀⠀⢤⠀⠀⡀⠀⢀⠀⠷⠀⠀⠀⡄⠀⡦⠀⢀⠀⢰⡄⠀⢀⡀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⡀
⠚⢰⡀⠈⠀⠀⠇⠀⠸⠆⠀⠀⡆⠀⠁⠀⠀⠀⠘⠀⠈⠀⣄⠘⠇⠀⠀⠀⠋⠀⣤⠈⠃⠀⠐⠖
⠀⠈⠁⠀⢸⠀⠀⢠⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣹⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⣆
⢲⠀⠀⡄⠀⠀⠀⠐⠃⠀⠀⣆⠀⢲⠀⠈⠀⠀⡄⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴⠀⠗⠀⠸⠀⠀⢈
⠈⠀⠀⠋⠀⢰⡄⠀⢰⠀⠀⠁⠀⠀⡀⢀⡀⠠⣧⣀⡀⠀⠀⠛⠀⠀⠀⢲⠀⠀⠘⠀⠀⠀⡀⠀⡀⠘
⠀⢀⡆⠠⡆⠀⠀⣀⠤⢐⣠⠻⢛⠥⠢⠐⠀⠀⢈⡄⠂⠌⠉⠙⠒⠶⣤⡬⠀⣀⠀⠀⠀⠸⡥⠀⣥
⢀⠀⠋⠀⣠⣔⠚⠉⡴⡫⠡⢊⠩⡂⠈⠀⠀⠀⠀⠐⠈⠂⠉⠀⠀⠀⠈⠙⠲⡠⠈⠁⠢⢄⡀⠀⢠⡄
⠸⠀⡠⠊⠀⠁⠀⡜⢘⠨⡂⢑⢅⠂⠁⠀⠀⠀⠀⠀⠁⠁⡀⠀⠈⡀⠀⠀⠀⠘⢦⠀⠀⡀⠈⠢⡈⠁
⢀⢎⣢⠴⠀⠀⢰⢐⠕⠨⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⡀⢀⢀⠀⠀⠀⠈⣧⢐⠀⠀⡄⢝⡄
⠟⠉⠀⠈⠉⠀⣬⡵⠖⠓⠉⠈⠉⠉⠈⠙⠓⢦⣤⡀⢠⢠⣤⠴⠿⠓⠂⠡⠠⠤⠾⢜⡵⠚⠉⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣗⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣉⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠁⠀⠂⠀⠀⠂⠔⠄⠠⠢⠠⠈⢄⠁⠌⠀⠨⠢⢀⠕⢔⢄⢀⢀⠀⡠⡂⡠⢀⢄⠔⢀⠄

⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⢷⡟⠁⠀⠀⠀⠀⠀⢹⣿⠿⣿⡏⠀⠀⠀⠀⠀⠈⢻⡾⠀⠀⠀⠀⠀⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⡞⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣄⡀⠀⠀⣀⣤⠟⠀⠀⠀⠻⣦⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣿⣿⣿⠿⠁⠀⠀⠈⠻⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣷⣄⠀⢀⣴⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⢦⣤⣤⣄⣀⡀⠀⣀⣀⣤⣤⣴⢶⣤⣤⣤⣤⣀
⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠸⣿⣿⠋⠀⠀⠀⠀⠈⠙⣿⡿⠿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⡟
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂


⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⠦⡄⠀⠀⠀⠀⡤⠖⠚⠓⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢤⣤⣤⣤⣤⡤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠘⣆⣀⣀⡞⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣾⡯⣭⣭⣭⣭⣭⣭⣽⣧⢼⡯⣭⣭⣭⣭⣭⣭⣭⣷
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢸⡯⠭⠭⠭⠭⠭⠭⣽⠇⠘⣯⠭⠭⠭⠭⠭⠭⠭⡇
⠀⠀⠀⠀⠀⠳⣄⡀⠀⢀⣠⠞⠀⠀⠀⠘⢦⣀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠘⢯⣭⣭⣭⣭⣭⡽⠋⠀⠀⠘⢿⣭⣭⣭⣭⣭⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⡇⠀⠀⠀⡼⢁⡀⢀⠀⠄⠈⠁⢀⣠⣶⣾⡿⠿⠿⢛⣛⣯⡽⠟⠁⠀⠀⠀⠀⠀⣬⡛⢯⡿⠶⠾⣿⠯⣽⣿
⡇⠀⢀⡼⠛⡞⠀⣀⡭⠅⣠⠌⢉⣉⣡⣤⣤⣶⣿⣿⣿⡏⠀⢀⣀⠀⠀⠀⠀⠀⢨⣙⡧⣾⣿⣿⢹⣿⣿⡟
⣇⡴⢁⡖⣉⣅⣉⢀⡀⠀⠤⠶⢟⣻⣭⢾⣿⣿⣿⣿⠻⠇⠀⠈⣭⣿⡋⠁⠀⠀⠈⠻⠟⠋⢹⣿⣾⣿⠋
⡷⠘⠋⠀⢁⣤⣤⣤⣤⠐⣶⣿⣿⣯⣾⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⡏
⣇⡀⠀⣀⣠⢟⡴⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⡏⠁⢴⣯⣿⣷⡞⡻⠋⣰⣿⣿⣿⣿⢿⠟⠋⣰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁
⡧⠚⠋⡹⣩⢋⠀⣠⣾⣿⡟⢻⠹⡟⠓⢀⣼⣿⣿⣿⣿⣿⠃⠀⠲⣄⠀⠀⠁⠀⠀⠀⢰⣿⠋
⡇⡠⢀⢞⣥⡵⠾⠟⢻⡟⠀⡌⢰⣇⣴⣿⣿⣿⣿⣿⡿⠃⠀⠱⡄⠀⠙⠂⠤⠤⠀⠊⢸⢇
⣏⢀⡴⡙⠋⠀⢁⠎⣼⠁⢰⢃⣿⠼⣿⣿⣿⣿⣿⣏⠤⠤⠤⠄⡈⢦⠀⠀⠀⠀⠀⠀⢸⣷⡱⡀
⣇⠚⡜⠀⢀⡴⠃⡼⠃⣠⣿⠋⠄⢠⣟⣬⣿⡿⠉⣀⠤⠄⠀⠠⢌⣻⡳⣖⠲⠄⠀⠀⢸⠀⢻⣷
⡏⢰⣄⡠⠊⣠⠴⡁⠚⣰⠃⡴⢚⣫⣵⢿⡿⠖⠉⠀⠀⠀⠀⠀⠀⠙⣷⡈⠳⣄⠱⡀⠸⠀⠀⠻⣆
⣇⣾⠋⣠⡞⢁⡞⢀⡟⠃⢀⡴⢚⡭⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣷⡀⠸⠷⣕⠀⡀⠀⠀⠙⣧
⡟⠡⢂⡼⠀⢋⡠⠋⢀⠔⣉⠔⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣷⣄⡀⢘⣷⣇⠀⠀⠀⠘⢷⡀
⡇⠹⢉⣴⠞⠋⠀⡰⢃⢒⣵⡠⢚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡽⣧⢈⡙⠷⡿⣆⠀⠀⠀⠘⣿⣄
⣧⠴⠋⠀⠀⣠⠞⣠⣾⠟⣩⠃⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣆⡿⠂⢡⡌⡳⡀⠀⠀⢸⡟⣦
⡏⠀⢀⡴⣾⠟⣨⢛⡡⠞⡠⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⠷⡀⢸⣿⣟⢞⣆⠀⣸⣏⢻⡆
⣇⠔⣡⠾⠗⠈⢸⢁⡴⠊⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢋⣷⢄⣼⣾⠉⠹⣟⣾⣷⡏⠘⣮⠇
⡇⢠⠁⠀⣠⠟⣀⣿⣤⣡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢠⣿⢋⣥⣾⡏⠹⡽⣆⠀⣿⣾⣿⣇⠀⡽⠁
⡧⢡⠴⣽⠃⢭⡽⠋⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣼⣷⡄⢿⣿⣇⠈⢻⣽⣦⠘⣿⣿⡿⠚⠁
⡗⠀⠀⠀⠐⠣⠄⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡼⢋⠻⣧⣼⣿⣿⠀⣿⣿⣿⣿⣿⡿⠃
⡇⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⡴⠟⠁⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡁
⡇⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⢶⠶⠞⠛⠛⠶⣽⣄⣀⣀⣂⣬⣼⣿⣿⣿⣯⣷⡹⣧
⡇⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢻⣿⣿⣧⡠⠀⠆⠀⡀⠉⠻⣛⠛⠉⠭⠲⠶⠶⣉⣭⣝⢻
⡇⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢻⡿⣿⣿⡷⣶⠾⠀⠀⠀⠀⠈⠑⠂⢈⡑⢮⡿⠷⣿⢿⡆
⡇⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⣷⣾⣿⡖⣯⣾⢦⠀⢀⠀⠀⠀⠀⢺⠻⣦⠙⢷⡐⢾⡇
⡷⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⣎⢀⣀⠀⠀⠀⢐⣼⡇⠀⢹⣾⠁
⡇⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠟⠉⣼⣷⣽⣇⣠⢤⡀⠀⠊⠹⣯⣦⡀⣿
⡇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣽⣷⣶⣷⡿⣿⢋⠎⡔⠘⣀⢠⡀⠀⠑⢇⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣉⢻⡿⠟⣊⠵⣫⠞⣠⡬⠤⠀⠵⡴⠄⠨⡇
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠈⠙⢿⣛⠛⠴⠎⠤⢚⣡⡤⠓⠤⢎⣻⣨⡄⣷
⡇⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠈⢿⡀⣀⠃⠖⣿⣷⣧⢃⠀⠀⢸⣿⡇⡿
⡇⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠈⢧⡶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⣯⡶⠋⢐⣿⠸⢸⠀⠀⢸⣿⣷⡇
⡇⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠳⣷⠀⠀⠀⠀⠀⠀⢀⣠⡾⡿⢺⠗⠐⠤⢤⣉⣄⢸⠀⠀⣾⢿⣿⠃
⡇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⢧⣤⣤⣤⡴⠞⣫⣽⣄⣷⡘⠀⠈⠔⣠⣿⣿⢶⡃⢠⡟⣽⡟
⡇⠀⠀⠀⠀⢀⣴⣉⣳⣦⡀⠀⠀⠀⠀⠀⠉⠳⢴⣄⣠⡙⠿⣏⠻⢻⣶⣶⣾⣿⣻⣼⣆⣱⡞⣼⣿⠁
⡇⠀⠀⠀⠀⣾⠉⠉⠙⢿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢶⣉⠋⣹⣿⣯⣿⣿⣿⣏⠰⢿⣿⠃

⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢠⣿⣿⣿⣿⡆⠄⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠿⡿⠿⠋⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠁⠀⠘⢿⣿⣿⠿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠂⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠛⠿⠟⠋⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠁⠀⠘⢿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣤⠀⢠⣤⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀⠠⡥
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠜⠧⠵⠔⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣤⣄⡀⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡗⠁⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢠⣤⣷⣄⠀⠀⠀⣴⣷⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠄⠀⠀⠍⠛⠉
⠀⠀⠀⠀⠀⢼⣿⣿⠏⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠀⠀⠀⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⡖⢊⣙⣉⣙⣛⠒⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣴⢚⣫⠴⠒⠋⠉⠉⠁⠀⠀⠈⠉⠙⠲⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠲⠶⠶⠶⠲⠖⠒⠢⠤⣤⣾⣤⣭⠛⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣆
⠀⠀⠀⠀⠀⣠⡴⠞⣋⣩⡤⠤⠒⠐⠓⠋⠉⠉⠉⠉⠙⢒⣶⣶⣷⣿⣶⣿⣷⣿⡿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⣆
⠀⠀⠀⢀⡼⢃⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣿⡟⢟⠳⡜⠌⢛⠜⣈⣱⣎⣧⠛⠛⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠘⡇⣻⡀
⠀⠀⢠⠏⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⡋⠔⠀⠈⠻⣦⣡⡘⢎⡎⠘⡿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⡇⢸⡇
⠀⢠⠟⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠊⠀⠀⠀⠀⠀⠸⣷⣿⠸⣟⠐⠄⠿⢻⣿⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⢰⡇⣾⠃
⢀⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡆⡆⠀⢼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣸⣿⡏
⣼⢧⡇⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢡⣤⡄⣾⡸⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⣦⣿⣿
⣿⢼⠃⠀⠀⠀⠀⠀⠀⣼⢯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣦⣠⠀⠀⠀⠀⠀⠀⢀⣼⡃⠀⢹⣿⣿⣆
⣿⠘⡄⠀⠀⠀⠀⠀⣼⠇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠋⠉⠉⠉⠛⠿⣿⣿⣿⣷⣄⠀⠀⣠⣴⣿⣿⣧⠜⡡⢻⣿⡾
⢹⡆⢃⠀⠀⠀⠀⣸⠇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣽⡖⡫⠉⡩⣿⡾⣿⣖⡀⢈⣿⣷⣄
⠘⣷⠘⡄⠀⠀⢀⡟⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡧⢀⠡⠐⡻⢿⣽⣋⠀⡁⣿⠿⣿⣦⣀
⠀⠹⡆⠰⡀⠀⢸⠁⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢋⡀⠐⠁⢐⢾⣿⣿⣷⣴⣿⡇⠀⠑⢌⡱⢄
⠀⠀⢹⡆⢳⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⣧⠑⢊⡁⠐⣋⣼⡟⠁⢻⡇⠀⠀⠀⠙⢮⠳⡄
⠀⠀⠀⢻⣞⣧⣿⡄⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣍⣢⣠⡵⠞⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⢳⠙⡆
⠀⠀⠀⠀⠹⣿⣿⣷⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢽⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⡇⢹
⠀⠀⠀⠀⠀⢻⣿⣿⣯⣸⣀⣀⣀⣀⣤⣴⣶⡞⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠉⢽⣿⡿⣿⡭⠞⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⢸⣟⣿⣿⠀⠀⠀⠚⢩⣷⣿⣷⠄⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠧⠊⡝⢦⡀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢀⠏⣹
⠀⠀⠀⠀⠀⡏⢿⣿⣿⣤⠀⢐⠀⢈⣿⡿⣣⢎⣤⠀⠫⢿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⢏⢢⠑⣕⣜⣦⣻⡄⠀⢰⣿⠃⠀⠀⠀⠀⠀⢀⡾⣴⠇
⠀⠀⠀⠀⠀⠹⣤⣉⣉⣽⣇⠀⢂⠤⠋⣸⢟⣾⡿⢠⡤⢠⠟⠻⢿⢷⣶⣶⣶⣾⣿⣿⡿⢿⣫⣇⠨⣦⢳⣬⠻⠿⡟⢷⣼⣿⠏⠀⠀⠀⢀⣀⣴⣯⡽⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⠂⢁⠠⠂⡴⢻⡿⣹⣿⣾⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⣊⠷⣻⣦⢻⣆⠹⠗⠀⠀⢸⣿⢏⣠⡴⣖⡾⠯⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣽⡝⣿⣏⣤⠀⢀⠐⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢡⡿⠿⢿⠀⠀⠀⣠⣾⢻⡥⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⢼⠁⠘⣿⣿⣤⣀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡟⢣⡄⠘⠀⣰⣾⢿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⡟⡼⠀⠀⠈⠻⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣧⣼⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠀⠀⠀⠈⠻⣿⣶⣤⡔⢦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⡿⣿⣟⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢦⣶⣤⣉⡛⢛⣖⣶⢶⡤⣴⣶⣶⣿⡿⠟⠋⣰⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠘⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⣰⠛⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢷⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡑⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢋⡰⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⢍⡙⠒⢤⠤⣤⠤⠤⠤⡴⢶⠚⣫⡭⠖⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣶⣷⣶⣷⣶⣧⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠛⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣴⡶⠷⠶⠦⣄⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⠏⠀⠀⠀⠀⠈⣧⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣀⣠⠤⠤⢤⣀⠟⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠛⢰⡇⠀⠀⢸⣿⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢽⠿⡇⠀⠀⢸⣿⠟⠋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⢲⣳⡟⠊⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠶⢰⣯⣀⡀⢀⣀⣀⣀⡀⢀⠀⠀⠀⡀⣄⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣾⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢻⡜⣿⠛⢻⠻⢿⣿⣿⡛⠋⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⣦⣸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣿⡟⠳⣟⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣿⡇⠀⠈⢧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⢸⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣠⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⢹⣧
⠀⣾⣇⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⢻⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣽⢁⣎⣿
⠀⣿⣿⡈⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⣄⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣾⠃⣸⣯⣿
⠀⣿⣿⣷⡌⢿⣧⡵⠶⠀⠀⠀⠀⠀⠀⠀⢀⡠⣣⠴⠊⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠃⣰⣿⣹⡿
⠀⠸⡿⣿⣿⣆⠳⣄⠀⠀⠀⠀⠀⠀⢀⣔⣣⠿⣇⡤⠆⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⢿⠃
⠀⠀⠹⠏⠘⢿⣧⡀⠑⠦⣀⠀⢀⡔⣣⠟⢁⡜⠉⠀⠀⢸⣧⣿⣿⣦⡀⠀⠀⢀⡀⠄⠂⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠉⠉⠙⠓⠊⠁⠀⠀⠀⠀⢸⣿⡟⠝⠛⠉⠀⠉⠁⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣷⣶⣤⣀⠀⠀⠀⠀⢸⣿⡫⣴⣦⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠀⠀⠉⠛⠿⣿⣶⣤⡀⣸⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠷⠀⠀⠀⠀⠀⠉⠻⣿⣷⣿⡿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣤⣔⢀⣤⣤⣤⣴⣖⣶⣶⣦⣤⣤⣀
⠀⠀⠘⣯⣽⠋⣽⡉⣿⡹⣿⡍⣿⡻⢿⣿⣿⣷⣄⣠⣤⣴⣴⣶⣶⠿⢿⠿⣿⡿⢿⡿⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠸⣿⡀⣽⣷⣿⣧⣿⣷⡜⢿⡸⡟⣿⣯⢿⣿⣷⣾⣉⢰⣼⡘⣿⣇⢿⣧⡘⢿⣷⢳⣽⣯⣽⡿⠛⠛⠻⠿⠿⠿⡿
⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣷⡘⣷⢡⣿⠇⠀⠙⢿⣿⣹⣀⣿⣿⣾⣿⣾⣿⣿⡈⢿⣯⠟⣿⡟⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⢸⣿⠿⠛⠿⣿⣿⣿⣿⣷⢛⣾⡟⠀⠀⠀⠈⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢲⣿⠃⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠻⣦⣄⣀⣹⣿⣿⣿⣯⣾⠋⠀⠀⠀⠀⠀⠈⢿⣿⠛⠉⠹⢿⣿⣿⣿⣿⣿⡿⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⣘⣿⠿⢿⣿⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⢀⡀⠀⡀⠀⠠⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠐⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠂⠐⣀⡀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠉⠄⡄⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⢄⡀⡀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠰⠠⠀⢈⠀⠁⠐⠄⢔⠀⠉⠛⠲⠒⠺⠁⠀⠀⠑⢔⠀⠁⢅⠔⣐⡀⠁⠈⠁⠀⠈⠮⠤⡀⠀⠀⠉⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠞⠉⠱⠒⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣄⡴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡉⠣⠀⠅⠈⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠁
⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣄⡤⠀⠠⣊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠀⡄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠀⠀⠋⠀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⢀⠄⠀⠀⢀⠄⠀⠐⠀⠈⠉⠀⠀⢀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠤⠀⠠⠄⠀⠐⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠁⠀⠀⡀⢀⢀
⠀⠀⠀⠸⠔⠀⠀⠆⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢈⡀⠀⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠀⢥⠀⠀⠀⠀⣀⠀⠀⡄⠀⠚⠀⠀⠁⠈⡁⠀⠀⠈⠀⠀⠁⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠃⠀⠉⠀⠀⠌⠀⠀⠘⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⣄⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠿⡿⠷⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠷⠶⠤⣶⣶⣶⣶⡶⠴⠶⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣶⣶⣶⣴⣦⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢦⠀⠀⠀⠀⠀⠀⠀⡇⣸⡇⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⣸⠀⢧⡀⠀⠀⠀⠀⠀⡇⢹⣷⠀⠀⠀⠀⠀⢠⠏⢸⡆⠀⠀⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿
⠀⣿⡄⠉⣳⡄⠀⠀⠀⢀⡇⢸⣿⠀⠀⠀⠀⣰⡋⠀⣼⡇⠀⠀⣿⣿⣿⡆⠀⣹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡋⠀⣸⣿
⠀⠻⠻⣄⠈⠦⣀⠀⢀⣸⠃⣼⣿⣄⠀⢀⣠⠞⢁⣾⠻⠃⠀⠀⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿
⠀⠀⠀⠙⢷⣄⡈⠛⠛⠁⠀⣿⣿⣿⣭⣭⣤⣶⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡈⠛⠛⠁⠀⣿⣿⣿⣭⣩⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⢒⣨⠽⠯⠿⣏⣽⠿⠟⣋⣁⣤⠤⣤⣀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠦⠾⠒⠚⠧⠤⢤⡤⠴⠋⢁⡴⠊⢿⠁⠀⠀⣽⣿⡆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠖⠚⠛⠒⠒⠒⠒⠒⠛⠛⢷⣶⠒⠈⠁⠀⡀⣤⡶⠲⡶⠲⢶⣤⣄⠀⠀⠀⠀⣾⣗⠀⣿⠀⠀⠀⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⢀⠞⣡⠖⠀⠀⠀⠒⠤⠤⠄⠀⢀⣤⣿⣿⡀⠈⣠⣾⠀⠘⠁⠀⠇⠀⢸⣿⣿⡆⠈⠙⣆⢻⣿⠀⢹⠀⠀⠀⣸⣿⡇⡇
⠀⠀⠀⠀⠀⢀⠏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⠀⠘⠀⠀⠀⠀⠈⣿⣿⢃⠀⠀⠘⡜⣿⡀⢰⠄⠀⠸⣿⣿⢡⠁
⠀⠀⠀⠀⢀⠞⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⡘⠀⠀⠀⠱⡜⢧⣰⣤⣶⡿⢟⡡⠁
⠀⠀⠀⠀⠘⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⡇⠀⣀⣠⠄⢸⣿⡿⠁⠀⠀⠀⠀⠀⠙⠒⠐⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠻⣇⠀⣧⣤⣼⠿⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠄⠂⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣖⣻⠿⠿⠿⠿⠿⠟⠛⠉⠁⠀⠈⠉⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⡀⣠⣴⣾⣿⡿⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣿⣿⣿⠃⠀⠘⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠭⠿⠟⠁⠀⠀⠀⠙⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣝⣛⣿⣿⣟⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⢀⡖⢚⠀⣀⣀
⠚⠲⢤⣀⣀⣀⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⡆⢒⠀⠀⢀⡀⠀⠀⢸⡈⣁⠀⠀⢀⡘⡦⢶⢤⢾⡇⠿⠯⠋⠁⠁
⠀⠀⠀⠈⠀⠚⠠⠍⣅⡐⠒⠀⠀⠀⠀⢀⡶⢺⡗⣤⣀⣀⣀⣴⠀⠚⠗⢺⡩⠉⠩⢹⡅⠀⢘⠯⣬⢸⠛⠻⣇⠁⢠⠰⢸⣷⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⠀⣿⡇⢤⠚⠏⠀⠀⢠⣉⡣⠀⠀⠉⠛⢿⡀⢰⠿⡄⠈⢀⡽⡏⠀⣠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢈⣇⠄⠀⠀⢀⡀⠀⠀⣠⠂⠀⠀⠈⠀⠀⠀⠉⠉⡄⠘⡀⣸⠀⢧⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠓⣾⣿⠛⠀⠀⠀⠐⠀⠀⠀⡀⠃⠀⢹⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠖⠸⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡉⠭⣀⠀⠄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠄⡅
⠀⠀⠀⠀⠀⠀⠀⢐⠁⣰⠒⡄⢱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠠⠜⠉⠁⠀⠉⠙⢇⡇⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠘⢌⡑⠒⠲⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⠤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⡦⠴
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠂⡈⠀⠀⠃⠒⠂⠀⠚⠘⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣂⣀⡀⠄⠀⠀⠀⠄⠀⠴⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄⣤⣤⣴⣶⣶⣶⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣉⣡⠔⠚⢹⣿⣿⣿⣿⣿⣿⡙⠛⠿⣟⡓⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢏⣴⠞⠋⠀⠀⠀⣟⣉⣉⣄⣁⣩⣙⡇⠀⠀⠀⠙⠢⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠈⠻⣟⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣰⣿⠃⠀⠀⠀⠀⠀⢠⣦⠾⠛⠛⠛⠛⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠈⢧⣱⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣰⡿⠁⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣧⣤⢤⣀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⣠⡤⢀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠁⠛⠻⡇⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠋⠉⠐⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢄⠀⠀⠀⠀⠸⣤⠶⠛⠋⠉⠉⠙⠛⠳⠶⣤⣀⣀⠀⢀⣼⠏⠀⠀⠀⠀⢀⡿⡏
⠀⠀⣠⣧⣾⡶⢆⡄⡀⠀⠀⠀⢻⢿⣇⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⠿⠁⠀⠀⠀⠀⠀⣸⡷⠐⠀⠀⠀⠀⠀⠀⡠⡀⣀⡀
⠀⡞⠙⠻⠟⠃⠀⠈⢯⠀⠀⠀⢸⡄⠻⣇⡀⠀⠀⠀⠀⠈⠹⢶⣤⣄⣀⣀⣀⣀⣤⠴⠿⠁⠀⠀⠀⠀⠀⠀⣰⠿⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢂⡀
⠈⠋⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⠻⣦⠙⣯⣄⡀⢀⠀⠀⠀⠀⣼⣿⢿⢿⠿⢿⡇⠂⠀⠀⠀⠀⠀⠀⣠⡾⠟⠃⠀⠀⣤⣄⡀⠀⠀⢸⡂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣰⡓⠀⠀⠀⠀⠀⠉⠻⠩⣝⠿⣷⣤⡀⠀⠀⣿⣾⣾⣷⣿⣾⡿⠀⠀⠀⠀⢀⣠⣾⣵⠂⠁⠀⠀⢸⣿⠈⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣹⣽⢿⣮⣙⠻⠶⣄⣿⣿⣿⣿⣿⣿⣇⣀⡤⠔⠊⠉⡿⠱⠁⠀⠀⠀⠀⠀⠙⠿⣸⡴⡰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⣠⠶⠛⠋⠙⠻⣿⢛⣻⣶⡾⠿⠿⠿⠿⠿⠿⠧⣦⣤⣤⣤⠦⠚⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠉⢠⡟⠂⠐⠖⠢⣄⠀⠈⠢⡙⢧⠂⠂⣇⢠⡾⠁⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣴⠀⡎⠜⣱⠂⠀⡼⢡⡟⣠⠞⡙⠻⠖⠈⡙
⠀⠀⡶⠁⠀⠐⠀⠁⠀⠱⣄⠀⠁⡌⢣⡐⡌⠎⠁⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⡄⣿⡄⢠⠇⢸⣣⠋⡐⠀⠀⠀⠀⢈
⠀⠰⠁⠀⢀⡑⡀⠀⠀⠐⠈⢧⠀⠘⢆⢻⡌⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣾⣈⣤⡇⣴⠀⠀⠀⠀⠀⠈
⠀⣱⣎⢐⣉⣈⡀⠐⠄⠀⠄⠀⠱⠀⠀⡛⠀⠀⠀⠀⣸⣿⣿⣿⠟⠋⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣻⡛⢿⣧⣹⠦
⠀⠁⠐⠎⠀⠂⡈⠓⠀⡁⠢⣄⢀⠀⡛⠀⠀⠀⢀⣼⣿⣿⣿⠋⢀⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣄⣂⣿⢟⠿⡿⡶⢾⠙⠿⣦⡀⠂⡀
⠀⠀⢣⡄⠀⠈⠀⠀⠀⢘⠢⣙⡆⡶⠁⠀⠀⣠⣾⣿⣿⣿⠃⢴⣤⡄⠀⠀⣨⣭⣁⢻⣿⣿⣿⣿⡿⠽⠿⠇⢹⠗⠚⠓⠐⠛⠋⠘⠛⠂
⠀⣄⠀⠐⠀⢲⠀⠀⠀⠈⣀⠡⠞⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⣿⣿⣷⡄⠀⠀⠈
⠀⠀⠀⠁⠀⡀⢢⠐⠀⡎⠀⠠⠅⠀⠀⠒⣳⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣝⣶⠶⠒⠶⣶⣶⣤⣤⠤⠄
⠀⡟⠀⠺⢦⡈⠂⠇⠰⠈⠀⣂⣀⣀⣤⢶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⢀⠹⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣆⢂⠀⣸⠦⠋
⠀⣽⠁⠀⠀⢩⡐⢄⢀⠀⠚⠉⠉⠉⣰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡾⠞⠁⠀⠀⠀⠀⠀⢀⣴
⠀⡀⠘⢭⠀⠂⢱⠶⠌⢳⢄⣤⣤⣾⣿⢿⣿⣿⣿⣿⣿⣿⡇⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠠⢀⠂⡀⠛⠃⣸⠞⣩⣤⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⢲⡎⢀⠄⡰⢊⠀⣨⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠐⠟⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠻⣽⠃⠨
⠀⢡⠈⢇⣠⠼⠄⠤⠊⡰⢋⣼⣿⣿⣿⣿⣿⣿⠳⣘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠂⠟⡐⢀
⠀⣼⣠⢋⢁⠠⠤⠄⢀⠙⣻⣿⣿⣿⣿⣿⢳⡏⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡄⠀⠀⠀⢀⣾⡿⣿⢋⡴⡀⣴⢁⣟
⠀⣄⡀⠈⠑⠳⢈⠓⢀⣼⣿⣿⣿⣿⠟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡈⡇⠀⠀⢠⣿⣿⡿⣁⠌⠱⣰⢃⡾⢠
⠀⣦⠄⣁⠆⠀⠈⠱⠈⣿⣿⣿⣿⣇⣴⡿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣷⠀⣠⣿⠇⡌⠛⠄⠠⡴⢡⠊⠁⢸
⠀⠁⠀⠄⡀⠀⢀⣀⠈⢮⣿⣿⣿⣿⠏⠀⠈⢿⡙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⠏⠘⣿⣿⡿⢛⡤⠶⠶⠚⠃⠐⠁⠘⣰⠶
⠀⠀⢀⡀⢐⠈⡀⢉⡑⠾⠿⣿⣿⡿⠀⠀⠀⠀⢻⡄⠘⢷⡀⢠⡾⠀⠀⠀⠀⢀⡾⢃⡾⠁⠀⠀⢹⣿⡏⡶⠈⡿⠀⠠⠔⢀⠴⠁⠤⣨
⠀⠋⠀⠈⠏⠠⠠⠞⠉⢀⡴⢿⣿⡇⠀⠀⠀⠀⠀⢻⡄⠈⣷⣾⠃⠀⠀⠀⢠⡾⢡⡟⠀⠀⠀⠀⢸⣿⣇⡹⢀⣤⠊⢤⣤⠔⠒⠒⠶⢬
⠀⠰⠄⠘⣤⠋⠀⣠⠨⡘⣡⢞⡻⣿⡀⠀⠀⠀⠀⠀⢿⡀⣿⡏⠀⠀⢀⣴⣟⣴⠏⠀⠀⠀⠀⠀⣸⣿⠞⣡⠛⠩⠉⠒⠀⠠⠅⣀⣂⣀
⠀⡀⠈⢣⠀⠀⠐⠄⠐⢧⡁⠆⣸⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣷⣶⣶⣦⣶⣶⢟⣵⢆⡝⠉⠑⠒⠦⢤⣤⠀⣀⠀⢰
⠀⠂⠀⢸⡀⠒⠁⠄⠠⠀⢳⠘⣽⠟⣿⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣾⣿⢣⠇⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠄⢀⡆⢹⡀⠄⠐⠄⠃⢈⣧⠏⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠻⡤⠀⠀⠄⠀⠐⢀⡀⢀⠠
⠀⠤⠘⠁⡎⢰⡀⠀⠰⠀⢸⢉⠠⡏⣿⣇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠂⢄⡈⠓⢂⠒⠒⣈⠀⠁⠈⣡
⠀⢀⠈⠠⠁⡌⢧⠀⠀⡆⢹⣞⢀⡁⣿⣿⣷⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣳⣌⣙⠒⠤⠭⠬⠍⠥⠩⣄⠰⣎
⠀⠌⢀⠃⡘⠀⠀⠾⢀⠂⡾⠛⢹⡇⢻⣿⣿⠂⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠈⠙⠋⠙⣂⣐⣮⡛⢌⡑⠌⠙
⠀⡶⠀⠀⡔⢀⠌⢠⣿⡞⢀⠎⠘⣇⢸⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢸⣿⣿⣵⠦⣌⡐⠂⠄⠈⣀⣁⠢⣍⡂⢠
⠀⠀⠀⠐⢠⠃⠐⠙⠇⢡⠎⢀⠝⢿⣸⣺⣿⠁⠀⠈⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠃⠀⠀⠐⠶⣿⣆⣒⠦⣭⣉⠛⢛⣛⣂⣉⣥⠤⢬⣉
⠀⠞⠀⠀⠀⠘⢰⡎⠀⠆⠀⠌⢠⠆⣹⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠉⠀⠿⢿⣄⠐⠶⢈⡙⠻⢤⡶⣴⠶⢾⠛⣹
⠀⡜⠀⠂⣠⠂⡟⠀⠌⠁⡜⢠⠟⢠⢿⣵⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢈⡳⠎⠑⠈⠖⢡⡾⠁
⠀⣁⠈⡄⠡⡘⢀⠁⠀⡘⢀⠋⣰⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠁⣜⢠⣧⠖⣩⠖⠜⡡⣾
⠀⠁⠘⠀⡄⠇⡈⠀⠀⠁⢆⡜⠋⢑⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠟⠉⣠⠚⡉⠆⠰⡀⢹
⠀⡀⠄⠀⠱⡂⡁⠀⠠⢈⣞⣁⣠⣿⣯⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣬⣥⣶⣷⠈⡄⢱⠘⡀⢛
⠀⡇⠀⢈⠀⡇⢄⢨⠖⠚⡉⣉⠼⣿⣿⣿⣮⣻⣿⣿⣶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⡿⠘⢧⡈⠈⡄⡇⢸⣅
⠀⠁⠀⠆⡀⢰⡎⠑⠊⢀⡶⢉⠜⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡄⠢⠘⠤⠟⢋⣉⠤
⠀⠾⡅⢖⢁⡞⠀⠀⡔⢀⢁⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⡿⣄⠈⠲⣉⠋⠀⠰
⠀⠰⢀⡄⠾⠠⢀⡾⢠⠏⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢹⣿⣷⣄⡙⣀⠞⠡
⣀⣢⣉⣙⣆⣀⣜⣴⣁⣀⣁⣀⣀⣀⣀⣀⣀⣈⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣋⣀⣀⣀⣀⣀⣀⣘⣿⣧⣉⣉⣉⣚⣓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠔⠈⠁⠢⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡐⠂⠒⠓⠀⠬⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠒⠵⠤⠄⠀⣀⡐⠁⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠒⢁⠶⢀⢀⡠⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠂⠀⠐⠐⠀⢦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⢅⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠊⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠋⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠁⠀⠀⡄⠂⠁
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⡠⠐⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡔⠀⢷⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡘⠀⠀⠈⠕⠄⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠂⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌
⠰⠁⠀⠀⠀⠈⢆⠂⡀⠀⡇⠀⠰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠜⠀⢀⠌
⡀⠀⡀⠀⠀⢔⢦⠓⠁⠀⢁⠀⠀⠂⢀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠊⠤⡤⠀⠀⠀⠀⡃⠀⠀⠀⠀⡠⠂⠀⠠⠂
⠗⠈⠱⠀⠀⠀⠢⡑⢄⠀⠀⠄⠀⢈⡎⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⡠⢀⠔⠁⠀⠀⠉⠐⠂⠀⠀⡠⠊⠀⢀⠔⠁
⠀⠀⠀⠱⡀⠀⠀⠈⠐⠬⠀⠈⠗⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⠀⠥⠒⠁⠀⠀⠀⠌⠀⠀⢀⠠⠊⠀⢀⠀⠁
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠠⠄⠊⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣀⣀⡤⢤⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠙⢋⡀⡙⠃⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣩⣻⡆⠀⠀⣀⣀⣠⠤⠷⣄⡘⢧⣐⣛⣦⣼⡵⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢇⡬⠖⠚⠉⠉⠀⠀⠀⠈⢻⣙⡞⠃⢹⠞⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣦⠽⡶⠒⠒⠚⢛⡽⣿⠀⠀⠉⠀⠉⠉⣇⠀⠀⠰⡏⢭⡉⠉⠉⠉⢹⡛⠾⠟⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠊⢻⣦⠘⡇⠀⡔⠲⠋⢠⠇⠀⠀⠀⠀⡠⣄⢻⠀⠀⠀⢻⡀⠹⣄⠀⢀⣼⠇⠀⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⢸⣿⠀⣧⢸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠓⠊⢸⠀⠀⠀⠀⢷⠀⠘⡆⣏⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡿⡏⠀⡏⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⣷⢹⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⣿⠇⠰⣇⡼⠀⠀⣼⠀⠀⠀⠀⠀⠀⢯⡽⠀⡇⠀⠀⠀⠀⠸⡄⠘⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⣄⣀⣀⣀⣀⣤⣤⠴⠶⠶⡶⠶⠶⠶⡶⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⡄⠀⠀⠘⡇⡴⢡⠜⠛⠛⠛⢻⠀⠀⢰⠋⠉⠉⠙⢳⠀⠀⠀⠀⠀⠀⠀⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⠀⠀⢰⣧⡄⠀⢸⠃⡇⠈⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠘⠿⠁⠀⠸⣴⠃⠀⡟⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢧⡼⠒⠒⠛⠛⠃⠘⠛⠛⠛⡟⠀⠀⠀⣠⠋⠉⠉⠹⣄⣀⠀⠀⠈⢯⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣭⣝⣛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⣀⣀⣠⠖⠒⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡲⠉⠉⠉⠑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⣀⣤⢴⣤⣤⣀⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠋⠀⠀⠀⠈⢻⡕⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠇⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⢷⣄⣀⣠⣴⠟⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠈⠉⠉⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⡀⠀⠸⠷⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⣔⠒⠚⠛⠭⠉⠀⠀⢀⣀⣀⠀⠀⠀⠊⠉⠉⠛⠓⠲⠤⠤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⡏⠉⠀⠉⠉⠉⠉⠑⠒⠶⠀⣀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠤⢀⣀⡴⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠙⠧⣄⡠⠦⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠦⠶⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⢀⡽⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⣀⣤⣶⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⡾⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣶⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠠
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⢿⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡇⠀⠐
⠀⠀⠀⠀⠀⠈⣷⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⠇
⢀⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀
⢸⠉⠲⡃⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠛⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠾⡿⠃⠀⠀⣠⠖⠉
⢸⠀⠀⠁⠘⢶⣤⡈⢿⡿⠛⠉⠀⠀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠁⠀⠀⠀⠀⠀⠀⢀⡴⢀⣠⣶⠟⠁
⠈⡰⠀⢹⣦⣈⠻⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣠⣾⡗⣿⣿⣃⣴⡟⠀⢆
⠀⢣⢧⡄⢻⣟⢷⣮⠉⠟⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀⠀⣠⠾⠛⠛⠓⣭⡟⣿⡟⢠⡸⡜
⠀⠈⢎⢿⣷⠙⢦⡉⠳⣦⣀⠀⠈⠻⢦⣄⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡷⠚⠁⠀⣀⠄⠟⢁⡼⠛⣾⡿⢱⠁
⠀⠀⠘⣾⣿⠀⠀⠻⣦⡀⠉⠛⠶⣦⣤⣬⣽⣿⢍⢤⣤⣀⣀⣀⣀⣀⣨⣿⡿⣿⢿⣯⣥⡤⠴⠶⢛⠁⢀⣴⠟⠁⠀⡿⣧⠃
⠀⠀⠀⠈⠧⣵⠀⠀⠈⠙⢶⣄⡀⠀⠀⠉⠉⠉⠀⠀⠂⠄⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠤⢚⣡⡶⠛⠁⠀⠀⣬⠼⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢂⣥⠶⠋⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⠠⡀⠀⢀⠀⠀⠀⢀⣠⠔⢋⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⡓⢼⣦⣠⡴⠋⣡⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠋⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣷⣞⣩⣯⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⣀⣠⣴⣶⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠹⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠋



⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⠿⠿⠿⠿⠿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣩⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⡟⣋⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠹⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢹⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣀⣀⣠⣤⣤⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣤⣤⣄⣀⣀⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠻⠶⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠶⠟⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣴⣷⣮⣙⠿⣿⣿⣿⠿⠛⠛⠛⠙⠛⠻⠿⣿⣿⣿⠿⣋⣵⣿⣦⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣤⣝⠻⣿⣿⣷⡮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢵⣾⣿⣿⠟⣫⣦⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣦⣝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣫⣴⣿⣿⣿⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⠟⣫⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣝⡻⣿⣿⣿⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠻⣋⣵⣿⣿⡿⢗⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡺⢿⣿⣿⣦⣝⠛⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠻⣿⢟⣫⣶⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣷⣍⡻⢿⠟⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣴⠶⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠶⣦⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣭⡛⢶⣄⣠⠾⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢿⣿⣿⠶⠋⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⡾⠃⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⢷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⡿⠛⠋⠀⣠⣏⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣱⣾⣯⣭⣭⣤⣴⠟⠉⠀⣠⣤⣶⣿⣯⣭⣭⣭⣭⣛⣶⣿⣿⣌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⢿⣿⣿⡿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⠁⢠⡞⢹⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠰⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣿⣿⣿⣿⣿⡷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠙⢲⡄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣇⠀⢷⡀⠀⠀⠀⠀⢀⣤⠞⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠈⢓⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⡆⠀⣷⠀⣀⣤⣾⡛⢁⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡧⠀⢸⠀⠈⠉⢉⣽⣿⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡷⠀⢸⠂⢀⣴⣾⣿⠟⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢦⣀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⡇⠀⠀⠀⣰⠃⠀⣼⠖⣻⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣌⠳⢤⣠⠞⠋⠉⡉⠉⠙⠛⠿⠷⢤⠴⠞⠁⢀⣼⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣉⠓⠾⣏⣻⣿⣷⣶⣤⣤⣠⣤⣤⣶⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⠛⠁⣠⡼⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠦⠶⠛⠉⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠉⠕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⡢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⠈⡄⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠜⠒⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠑⠒⠒⠢⡤⠒⠚⠀⢀⠂⠄⠔⡠⡠⢃⢊⠎⠀⠀⠀⠀⠀⠀⡄⢣
⠀⠀⠀⡠⠄⠠⢼⠀⠀⠀⢀⢀⠄⡠⢀⢀⢀⠄⢄⣄⣐⣆⣐⣀⣀⡀⣠⣠⡥⠚⠘⠺⡴⠋⠁⠳⡎⠀⠀⠀⠀⠀⠀⠀⠄⠸
⠀⠀⡜⠀⢀⢤⢀⢄⠔⡀⠡⢂⠜⡴⠥⠆⠚⠈⣩⠜⢋⢩⠉⠉⠙⠩⢍⣉⠒⠲⢤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠑⠤⠤⠤⠤⠀⠂⣒⠶⠂⠁⠀⠀⢀⡤⠊⠀⠀⠀⠂⢣⠀⠀⠈⠐⠀⢙⠢⣕⠀⡨⢉⠐⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠈⡆⢁⠄⠀⠀⠂⠠⠈⠓⢄⠑⡡⢂⠄⢉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠋⠐⠄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡐⢍⡀⠀⠀⠈⠒⠤⠀⠑⢄⠕⡨⠐⡨⢐⣌⣲⣄⠀⠀⠀⠀⠀⠀⠓⠢⡀
⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢀⠜⠀⠁⠀⠀⢀⣀⣀⣀⣀⣀⠠⠀⠇⠀⡂⠤⠄⠒⠒⠒⠀⠠⢈⣢⣀⠕⠊⢁⠀⠄⠈⢀⠂⠄⡀⠠⠀⠀⠀⡅
⠀⠀⠀⠉⠉⠉⠁⠒⠠⢁⡬⠔⠒⠈⢉⠄⠍⠀⠀⠀⠀⢿⠁⠁⠚⠁⠀⠀⠀⢠⠀⠀⡠⢀⠀⠌⡙⡰⠡⠂⠌⡰⢠⠂⠎⡐⠡⢂⢂⠂⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⣀⣀⣻⣏⣐⣁⣊⡐⠀⠁⠂⠈⠀⠀⣁⣊⣈⣀⣀⣁⣈⣀⣁⣁⣈⣐⣀⣁⣀⣈⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⡤⠀⣠⠀⠀⠴⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⠄⠀⢀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣜⠇⢀⡀⢸⡃⠀⠀⠸⠁⢰⡌⠀⠰⠊⠀⠀⣢⠆⠀⢰⡁⠀⠀⠗⠀⠀⠗⢠⠃⠰⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢀⡀⠁⢰⡥⠀⠸⢀⠀⢠⠚⠀⠀⠀⠰⠂⡜⠁⠀⢀⠀⠀⢀⠴⠀⣀⡒⠀⢀⡶⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡀⠀⠀⢈⡸⠀⠘⠃⠀⠀⠸⠊⠀⠀⠀⢀⡭⠀⠀⠘⠃⠀⠉⡀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⢸⢻⡀⢀⡀⢀⠴⠀⠀⣀⠀⢀⠄⢀⣈⠁⢀⠀⠀⠼⠃⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⡀⠂⠈⠁⠀⢰⠄⠀⠛⠀⠈⠁⢀⡪⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⡀⠀⠠⢀⠀⡀⠀⢀⠀⡀⠀⠀⢀⠀⠀⢀⠀⡠⠀⠀⡀⢀⠀⡠⠀⡀⠀⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠉⠂⠁⠊⠔⠨⠊⠔⠄⠈⠔⠡⠊⠔⡡⢂⠅⢊⠔⠡⢊⠄⡥⢊⠔⠨⠔⡡⡪⢂⠁⢊⠔⡡⢊⢔⠡⢊⠔⡥⢊⠂⠕⠊⠠⢊⠄⠔⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣤⣤⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⢹⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠲⠖⠋⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⢶⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⡀⣀⣸⡇⢸⣇⣀⢀⣀⣴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣀⣀⣠⣭⣭⣍⣹⡇⢸⡏⣉⣭⣭⣅⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢹⡇⢸⡏⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄
⠀⠀⠀⠀⠀⢀⡎⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠸⡄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢷
⠀⠀⠀⠀⢀⡟⠀⠀⢄⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⢀⡄⠘⣧⡴⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⣴⠏⠀⠀⠘⡇
⠀⠀⠀⠀⢸⣧⠞⣧⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣸⠓⢦⡇
⠀⠀⠀⠀⠈⠀⠀⠘⣧⡀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⣰⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⠁⠀⠀⠀⣧⣤⡴⠶⠾⠛⠋⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⡀⠀⠀⠀⡞⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣥⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣶⣾⣿⣿⣶⣶⣶⣶⣾⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠉⠙⠇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣖⣢⣤⠤⠶⠲⢶⣾⣿⣋⠀⠀⠜⢠
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠟⠟⢿⣿⣿⣶⠦⠀⠀⠀⠀⠹⣏⠋
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠤⢤⣤⣄⠈⠗⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣗⣤⢀⣼⣿⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⢸⣧⠇⢠⡶⠶⠾⠿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠶⠤⣀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⡃⠀⣤⣤⣶⡶⣿⣿⣿⡋⢙⠓⡀⠀⠀⠀⠀⠀⠉⣉⣩⣿⣽⣥⣦⣄⡀⠈⠁⠀⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠙⢷⡤⠑⠐⠁⠀⠀⠁⣿⡄⠀⠀⠀⠀⠀⠈⠈⢿⡥⢋⣠⠟⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⣠⣤⣠⣤⣄⡀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⣤⣄⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣶⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣈⣿⣤⣤⣀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠏⠈⠉⠙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣾⣿⣿⣿⣿⣿⣿⡿⣋⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣛⡛⠿⠛⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣟⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⣆⠀⠀⣿⠏⠀⣴⣶⠶⠶⠖⠾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣷⡶⠁⠀⣼⣄⠤⡤⠤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⢀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠻⠿⣋⠀⣤⠄⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠙⠈⠉
⠀⠀⠀⠀⠠⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⣀⡀⠠⡄⠀⠀⠉⠀⠀⠈⠉⣩⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠌⢷⠤⣇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⢘⢐⣂⣽⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⣷
⠀⠀⠀⠀⠈⠛⣿⡛⠛⠟⢿⣿⣇⠀⠀⠀⠀⠀⣸⣾⣿⣿⠿⢷⣄⣠⣴⣶⣶⣿⣿⣿⣿⡏⠀⡠
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⣿⡿⠁⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠳⠽⠿⠟⠉⠉⠙⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠉⠉⠓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣞⢻⡝⢦⡀⣤⡄⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⢠⡼⣦⡙⠈⠻⠀⡇⠀⡼⠁⠀⠀⠔⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣤⡀⣠⢶⠄
⠀⠀⠀⠀⠀⠀⣱⠦⠀⠀⠀⠀⣿⢠⣇⣀⠀⣀⣈⡀⣀⡀⣀⣒⣂⣄⡀⠀⠀⠀⠀⠀⢷⠀⠀⡞⠐⠟⡵⠛⡹⠃
⠀⠀⠀⠀⠀⠘⠓⠒⠙⢢⡀⠀⠘⣿⡇⠀⠀⠈⠀⠈⠀⠀⠁⠉⠑⠉⠑⠀⠇⠉⠀⠂⢾⣀⡼⠁⠀⠀⠀⣛⣲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⡇⢀⡠⢤⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⡥⠊⠀⡼⠋⠀⠀⢀⣠⠤⠨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠃⡀⡀⠀⠀⣀⡀⠀⡀⣀⠁⠀⠈⠃⡀⠀⡠⠊⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢚⠈⠈⠀⢁⠀⠀⠀⠀⠀⡸⠀⠓⠑⡡⠊⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠑⠠⢀⠀⠁⠀⠀⠒⠉⢀⡀⢤⠎⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠠⠤⠄⠀⢀⢀⣀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⢀⢤⣾⣷⣦⣀⣀⣀⣀⣀⣀⣀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⣹⣿⠯⠃⠀⠀⠀⠀⠀⢡⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⡄⢃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⠄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠘⡘⣇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⡀⠀⣀⡴⠋⠁⠀⠙⣆⠀⠀⠀⠀⠀⠀⠃⢁⢻
⣖⠻⠻⠲⡴⠛⠁⠀⠀⠀⣀⡴⠋⠉⠛⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡀⠄⠘⢺⡛⠁
⠹⣆⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⣇⠀⠀⠀⠈⣧
⠀⠘⢦⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⡆
⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠈⠓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⣤⣤⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡏⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣴⢋⣵⣾⣿⣷⡀⠀⠀⢠⡞⣭⣶⣿⣿⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⣇⣿⣿⣿⣿⣿⡟⠉⠉⣻⣸⣿⣿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠻⣿⣿⣿⣿⠟⠁⠀⠀⠘⢿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠧⠀⠀⠀⠉⠉⠁⠀⠀⡀⢀⡀⠀⠈⠉⠉⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡆⠀⠀⠀⠀⣀⣴⣶⣶⣦⣄⠀⠀⠀⠀⡆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠄⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⢀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠜⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢡⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⡀
⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣦⣤⣀⣀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣤⠤⣤⠤⠴⠖⠒⠛⠓⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠛⠉⠛⢲⡉⠋⠀⠻⣔⣀⡤⠤⣴⣒⣓⣲⡚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣆⣀⣈⣡⠴⠚⠉⠁⠀⠈⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⢰⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠮⣭⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡇⢀⣀⣀
⠀⠀⠀⢰⣒⡦⠀⣀⣤⣤⣄⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⣀⣴⣶⠿⠚⠀⠻⠶⠟
⠀⠀⠀⠀⠉⢀⣀⣓⣶⡤⠾⠃⠀⠀⢳⣤⣀⠀⠀⢀⠀⠀⢀⡴⠋⠉⣀⣤⡘⠮⠶⠭⡖⠃⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⢰⠋⠉⠁⠈⠙⠲⠤⠤⢤⣀⣈⠛⠛⠛⠛⠛⢫⠟⠒⠒⠚⠁⢰⠃⠀⢾⡭⠽⣀⣠⣤⡀⠘⠓⠒⠋
⠀⠀⠀⠀⠈⠳⣕⠤⣀⣀⡀⠀⣀⣤⣤⣭⡿⠀⠀⠀⠀⠘⠷⠶⢦⣄⣠⢿⡖⠛⠛⠒⠛⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠋⠁⢶⣛⣒⣶⠿⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⠗⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣷⣦⠀⠀⠀⠀⡠⠔⣒⠤⠤⢠
⠀⠀⣀⣤⣶⣶⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣪⣶⣿⣿⣿⣷⣮⣳⣄
⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⢞⣵⣿⣿⣿⣿⣿⣿⣷⡽⣿⡆
⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠻⠿⢟⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠈⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢙⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⢞⣵⣾⣷⣄⣏⠉⠙⠛⠛⠛⠋⠋⠉⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠤⠀⠀⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣿⣿⣿⣿⣿⣿⡆⡀⠀⣀⣒⣒⣈⣩⣭⣭⣤⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣾⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⢿⣿⡻⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⠁⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢽⣿⣷⣿⡿⠋⠀⠀⠀⠻⢿⣿⣿⡿⠏⠀⠀⠀⠁⠛⠻⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⢂⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⣀⣠⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⠸⠀⠉⠁⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣹⣿⣿⣿⣿⣿⣿⣾⡏⡰⠂⠀⣰⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣰⠁⠀⠀⢹⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⣿⣿⣿⣿⣿⡟⠁⠛⠀⠀⠀⠀⢿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⡿⠫⠊⠀⠀⠀⠀⠀⠀⠀⢻⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠛⠛⠿⢿⣿⣛⡛⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠢⢶⣤⢀⢄⡀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠑⣇⣚⢡⡞⡥⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠬⢢⠃⠙⠙⢇⡇⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⣸⠀⠀⠠⢀⡷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠉⠉⠁⠓⠀⠁⠸⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠰⠁⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⡱⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠇⢠⠁⠀⠀⠀⣨⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⣄⡁⠀⣀⡤⠄⠗⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠗⠉⠀⠂⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣨⠀⠀⠀⠈⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠐⠠⠰⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠂⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣧⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⡘⢀⠢⠃⠀⠀⢀⠄⠃⠀⢀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠉⠉⠛⠀⠀⢀⡇⠀⠀⠀⠀⡠⠈⠀⢼⣄⣀⢀⠔⠁⠰⠀⡸⡊⢰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⠁⠀⠀⠀⠀⢃⠀⢀⠊⠀⠙⠊⠀⢀⡶⢂⢫⡑⢄
⠀⠀⠀⠀⠀⠈⠒⠀⠀⡀⡀⠀⢀⣦⡴⠋⠠⢔⣶⣶⠒⣲⠗⠀⠀⠀⠀⣀⣀⠴⢏⣠⣈⣄⠝⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡁⢤⣤⡤⢎⣉⣀⠿⠉⠓⠲⡦⢀⠀⠀⠀⠀⠀⠻⣭⣹⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠼⠿⠇⠼⢿⣏⣉⣶⡆⠐⡏⠀⠙⠛⠛⠛⠙⠻⠿⠀⠿⠧⠼⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠄⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢉⣩⣿⣶⣶⠐⡆⢲⣶⣿⣍⡉⠉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣴⣾⣿⣿⣿⣿⣿⠂⡗⢸⣿⣿⣿⣿⣷⣦⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠠⣇⣼⣿⣿⣿⣿⣿⣿⣿⣦⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣭⣭⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⢻⣿⣿⣿⣿⣿⣿⣿⡶⢲⠒⣶⣿⣿⣿⣿⣿⣿⣿⡿⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⠻⣿⣿⣿⣿⣿⡇⢸⠀⣿⣿⣿⣿⣿⣿⠟⠋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣭⣿⡿⠿⣧⣸⣄⣿⠿⣿⣿⣭⣤⡴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⣉⡻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠛⠃⠀⠚⠃⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⠰⠶⢂⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏⠉⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⢤⣞⢹⣿⣦⣤⣾⣿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣼⣥⠼⣶⣶⣬⣻⣿⣿⣿⣿⣿⠧⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀⠙⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢿⡇⠀⠀⠀⠈⣿⣿⣟⣿⣿⣿⣧⠀⡼⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣧⠀⠀⠀⢀⡸⢏⣾⣿⣿⣿⣿⣿⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢰⠋⠛⢿⣿⠿⠛⢹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠗⠀⡇⠀⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⠛⣿⣿⡿⣿⣿⣿⠟⣿⣟⠛⠛⠛⠻⣿⣿⣿⡿⠋⣛⡿⠋⢻⡇
⠀⠀⠀⠀⠀⢸⣯⡀⠙⠻⣿⠀⢿⣿⠀⢻⣿⡿⢠⢿⣿⣦⣄⠀⠀⠈⠹⢿⣦⣸⡿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⢿⣶⡄⢿⡀⢸⣿⡇⠘⢛⣁⣠⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣾⡇
⠀⠀⠀⠀⠀⢸⣿⣆⢻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡏⠁⠀⠀⠀⠈⠉⠙⠛⢿⣿⣛⣛⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢻⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠙⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣯⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠉⠻⢿⣿⣿⣶⣿⣾⠟⠻⣿⣿⣿⣷⡀⠀⠀⠀⢀⡠⠔⣠⣿⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣯⣄⠀⠀⠙⣿⡿⠋⠁⢤⣤⠬⢻⣿⣿⣿⣶⣦⣼⣷⣶⣾⡿⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⢠⣿⣇⠀⠀⢤⣐⠲⠤⠙⠻⠿⣿⢿⣟⣣⣼⣿⠟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⣤⣴⣾⣿⣿⣿⣦⡀⠀⠈⠁⠀⠀⣀⣄⠀⣴⣿⣽⣟⡿⣶⠄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡟⠉⠉⠙⠛⠉⠁⣈⣭⣤⣤⣾⣷⡵⣝⢿⣿⣮⣝⢿⣭⣻⣷⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⣠⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣽⣿⣿⣷⣽⣿⣿⣿⣤⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⡠⠒⢛⡉⠛⠒⢦⣀⠀⠀⠀⠀⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠔⡡⣫⡟⢀⡤⠛⢦⡀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⣾⠫⠞⣵⣹⡏⢰⣿⣆⡇⠀⢰⠀⢷⣄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⡞⠁⠀⠣⣭⠽⠳⢤⣭⠞⠁⠀⢸⠀⢸⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⣰⠏⣠⠴⠒⠚⠋⠉⠉⠛⢲⡄⠀⠀⢸⠀⠈⣇⢸⣤⠖⠒⠒⠲⢤⣀⠀⠀⠈
⡏⠀⢧⣀⠀⠀⠀⢀⣀⣤⠾⠁⠀⠀⢸⠀⠀⢻⠘⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠐
⠻⡄⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠙⢦⣄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣏⠛⢦⣄⠀⠈⠢⠄⣤⠘⣆⣸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⡟⠀⠀⢸⡟⠶⣤⣀⣠⣴⠏⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠸⡄
⠀⠀⢠⡇⠀⠀⡼⠁⠀⠀⠈⠁⣯⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⣀⡀⠀⠒⢮⡁⢚⠄⢣
⠀⠀⠀⠳⠶⠚⠁⠀⠀⠀⠀⠀⠘⣾⢦⣤⠴⠞⠁⢀⡠⠖⠋⠉⠉⣧⡤⠤⢷⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠻⡄⡖⠒⠚⠉⠀⠀⢀⣀⣼⠁⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢤⠇⡇⠀⠀⠀⠀⡞⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⠃⡇⠀⠀⠀⠀⠙⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡗⢀⡇⠀⢀⣀⣀⠀⠀⠉⠓⢤⡀⠈⢦⡀⠀⡐⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠘⠣⡀⣇⠀⢌⠟⠉⠉⢁⣒⣛⡂⠒⠛⠢⠈⠓⢦⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣇⣀⡇⠀⠀⡇⠈⠑⢾⣀⡄⣞⠀⣫⠈⠉⠉⠙⠓⠒⠦⠾⠀⠳⣌⡑⠒⠠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡶⠃⠀⠀⠀⠉⠀⠾⠋⠃⠀⢠⡄⠀⠙⡛⠀⠉⠀⣼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠇⠀⢰⣦⡀⠀⠀⢀⣤⠆⠀⠀⠀⠐⠦⠁⠀⠀⣄⠈⠛⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⠀⡀⠀⢻⡿⡦⠀⠉⠉⣴⠆⠀⠀⣰⣦⣧⣄⠀⠈⢳⡆⢐⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣇⠀⠈⢠⣤⣅⣄⠂⠀⣸⡟⠻⠿⠴⠟⠉⠉⠻⢿⣶⣴⡞⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡛⣷⠴⠛⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢾⡄⠀⠴⠟⠛⠷⢶⡄⠀⠀⠀⠀⠀⠈⣋⣥⣼⣿⣿⡇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢼⡇⠀⠀⠀⣀⣠⣠⣀⠀⠀⠀⠀⡴⣻⣿⣿⡿⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣧⠀⠙⢻⣿⣿⡏⠙⡹⠀⠀⠸⡇⠙⠻⠿⠧⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⣿⡞⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣇⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣤⡀⠀⢠⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠈⢄⠀⠀⠀⠀⠸⢿⡿⣿⣿⠟⠀⠘⣿⣿⣭⣽⣿⠛⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣴⠆⠀⠀⠣⣄⠀⠀⠀⠀⠙⠋⠉⠀⣴⣾⣿⣿⣿⣿⣿⡗⠸⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⢿⣦⣤⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⡏⢿⣻⣏⢿⣿⣷⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠷⣬⣯⣤⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀
⠀⠀⠀⠀⠀⣠⠔⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣦⣄⡀
⠀⠀⠀⠀⢠⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠛⣷⣄
⠀⠀⠀⠀⠃⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⣿⣆
⠀⠀⠀⢈⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢻⣿
⠀⠀⠀⡌⠀⠀⠀⢀⣿⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⡇⠀⢀⡴⣿⣿⡿⠋⠀⣠⣾⣿⣿⡟⠛⢶⣶⣶⣶⠶⠖⢶⣶⣶⣶⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠁⠀⡞⣼⣿⡟⠁⢀⣾⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣷⡄⠀⢹⣿⣿⣿⣦⡈⠑⣤⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢐⣇⣿⡟⠀⣠⣿⣿⣿⣿⠟⠀⠀⣾⡆⠈⢿⣿⣿⣿⡄⠉⠙⣿⣿⣿⣷⠒⢿⣿⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⡀⠀⣿⡿⠀⢰⣿⣿⣿⣿⠏⠀⠀⣼⣿⣿⡄⠈⢿⣿⣿⣷⡄⠀⠹⣿⣿⣿⡀⢸⣿⣿⡀⢀⣿⡟⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⡇⠰⡇⣹⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣇⢸⠀⠀⠀⠀⡇⠀⠷⢣⣏⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⢦⡑⠿⢸⠀⠀⠀⠀⣇⡴⠲⢤⠞⠲⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡤⠾⡄⣀⣀⡔⠻⡇⠀⠸⡄⠀⠘⢦⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⢀⡔⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⠀⠀⡴⠛⢾⠁⠀⣿⠁⢸⡀⠀⢳⠀⠀⠹⡄⠀⠈⠳⢶⡛⠋⠉⠙⠻⢄⠀⠀⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠷⣸⠃⠀⡏⠀⠀⡇⠀⢸⢧⠀⠀⢧⠀⠀⠈⢦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠳⡄⠘⢯⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⡽⠋⣹⠀⠀⡇⠀⠀⢻⠀⠘⡎⢧⡀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠹⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⣿⡀⠀⢻⡀⠀⠈⢇⠀⠘⢆⠙⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠀⢸⡍⠲⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⢏⢧⠀⠀⠱⣄⠀⠈⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⢧⢀⡘⢿⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡳⢟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡇⠀⠀⢸⣸⡏⢳⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠤⠚⢧⠜⠁⢹⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⢀⡉⠀⠀⠀⠀⣧⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡼⠀⠀⠀⠉⠙⠒⢲⠒⠒⠋⠁⠀⠀⠀⠘⡟⡟⠉⠉⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠛⠛⠷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣀⣀⣀⡀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠂⢠⡞⠉⠉⠉⠛⣦⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⢸⠀⣿⡀⢀⣀⣀⡀⣸⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⣤⡾⢿⣋⣿⣉⣿⠟⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠋⣷⡾⢟⠉⠉⠀⠀⣀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣿⣿⠀⠧⠀⠀⠀⣹⣿⣯⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢇⣼⣃⣿⣀⣋⣠⣀⣀⣹⣇⣹⣿⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣾⡟⢤⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣧⠀⢹⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡟⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣷⣿⣇⢺⣇⠀⢀⣀⣀⣀⣤⣄⣀⠀⠀⣿⠀⢸⡇⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣍⠽⣧⣼⣿⣿⣿⣿⣿⣭⣤⣤⡟⠀⣼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡞⣻⣿⡟⠋⠙⠟⢹⠅⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣴⠛⣿⣦⣄⣺⡅
⠀⠀⠀⢀⡾⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡿⣷⣴⣋⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⣆
⠀⠀⢀⣾⠃⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡅⢈⠉⠻⣶⡊⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢹⣆
⠀⠀⣼⠃⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⢸⣿⡎⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡀⡇⠀⢻⡄
⠀⣸⣿⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣿⠀⠈⣷
⢠⣿⠋⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⢀⠀⠀⢺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⢿⠀⠀⠸⣇
⣼⠃⠀⠀⠀⠀⠀⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⡄⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡀⠀⠀⠀⠀⠀⢻
⣿⡀⠀⠀⠀⠀⢠⠇⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠀⠄⠰⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢃⠀⣨⠀⠀⠀⣸
⠈⢷⣆⠀⠀⡄⢸⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢉⣷⣿⢀⣄⠘⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠀⡇⠀⢠⣶⠋
⠀⠀⣿⡀⠀⢳⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠈⣿⠃⣿⢀⡄⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⠁⠀⣸⠇
⠀⠀⠸⣧⠀⠈⣆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢻⡇⢠⡟⠀⠀⠠⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠏⠠⢠⡟
⠀⠀⠀⠹⣧⠀⠘⢆⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣹⣷⣼⣃⣘⣆⣀⣀⣀⣠⣿⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣰⠋⢀⠎⠀⢠⡟⠁
⠀⠀⠀⠀⠘⢷⡀⠈⠣⡀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣦⣋⣉⣟⣉⡟⣉⣟⣉⣼⣭⣠⣿⣤⣟⣉⣹⠿⣦⠀⢀⣴⠟⠁⡰⠋⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠛⣦⡀⠈⠢⣄⠉⠛⠶⣤⣄⣀⣀⣀⣤⠾⢋⣽⡿⠋⢛⡿⣋⠉⠉⠙⠉⠻⢦⣄⣉⣉⣻⣦⡾⠟⠋⢀⡤⠊⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠉⠒⣤⢀⡉⠉⠉⠉⠀⠐⠋⠻⠛⢈⡼⠁⠸⣆⡑⠀⠀⠀⠀⠈⠉⠉⢉⣀⣠⠔⠊⢁⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣌⣉⠒⠒⠒⠒⠶⡶⠶⢂⣁⠀⠀⠀⢈⣉⠲⠶⠶⠖⠂⠚⠒⢈⣁⣤⣴⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢦⣄⡀⠀⠀⠲⣬⠳⠄⡴⢋⡴⠂⠀⠀⣠⣤⠶⠟⠋⢩⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠈⠁⣾⠁⠈⢀⣤⠶⠛⠉⠀⠀⠀⢀⡾⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆⣘⣠⡾⠋⠁⠀⠀⠀⠀⠀⢠⡿⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⢠⡿⣀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿
⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣶⣶⡾⠿⠿⠿⠿⣶⣶⣦⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⠿⣷⣄
⠀⠀⠀⠀⠀⢠⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣧
⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⡿⠛⠛⠛⠛⠛⠛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠛⠛⠛⠛⠛⠻⣿⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠈⢿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠟⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣔⣉⡥⠤⠤⠤⢄⣀⡉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠺⣮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣯⣼⣿⣿⠋⣡⢤⡉⢻⣷⠀⡀⠀⢀⠀⣠⣾⣿⢿⣿⣿⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢡⡎⠹⢿⣿⣿⠀⠧⡴⠇⢠⣿⣇⣑⣒⡋⣰⣿⢋⡔⠲⣌⠹⣿⣿⣿⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⡟⠀⠀⠀⠙⠻⣷⣦⣤⣶⣿⠟⠁⠀⠀⠈⠙⢿⣌⠳⠾⠟⣰⣿⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠀⢸⠀⠀⠀⠀⠀⠀⠈⢛⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣾⣿⡿⠟⠋⠉⠙⡆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠋⠁⠀⠀⠀⠀⠐⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡇⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢱⠀⠀⠀⣀⣤⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⢨⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⢹⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⡤⢞⣿⣿⣿⣿⣶⣄⠀⠀⠀⣬⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠙⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⠉⠉⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⢁⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⠈⢦⣻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠻⣬⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠃⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠱⣀⠀⠈⠙⢿⢻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣯⡵⠞⠉⠀⡠⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡙⡏⠀⠀⠀⠁⢹⣅⡈⠁⠒⢲⣶⠒⠒⢒⡩⡿⠋⠀⠀⢤⡤⠊⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣦⡛⠂⠀⠀⠀⠀⢸⠀⠈⠉⠒⡏⢹⠒⠉⠁⠀⣿⠀⠀⠀⣮⡄⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⢸⠀⠀⠀⠀⢹⡀⠀⠀⠀⠷⣋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⢨⡏⠀⠀⣷⠦⠀⠺⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⠛⠛⣧⠀⠀⡟⡛⠋⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⣿⠉⢹⠋⠁⠀⠀⢙⣿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⢲⣝⣷⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣽⣻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣦⣚⣛⣛⣛⣛⡯⠭⠗⠀⠀⠀⠈⠩⣛⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉

⣿⢿⠿⠿⡿⡟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣿⣿⣟⣿⣿⣿⣟⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠂⠀⠀⠡⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠘⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠄⠀⠀⠀⠤⠀⢠⠀⠀⠀⠈⢄⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⣠⠤⠊⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠤⠰⠄⠂⠀⡄⠀⠀⣠⣀⣀⡀⠉⠙⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠐⠒⠂⢼⢛⠉⠉⠈⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠃⠀⠛⠁⢼⠀⠀⠀⠀⠀⠀⠐⠄⠐
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⡘⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⡠⠳⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⡈⠢⠁⠀⠤⠀⠀⠤⠄⡄⠀⠐⠀⠀⠎⠰⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⠘⠛⠿⠤⢰⡖⢲⠇⠀⠚⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠒⠀⠀⠠⡄⠀⠀⡀⡀⠀⠐⢀⠀⠁⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠁⠀⠡⢒⡄⣁⣛⠄⠁⠀⠃⠂⠈⢄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⡀⠀⠀⠀⠩⠁⠀⡫⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠉⠉⠃⠈⣋⠁⠈⠉⠉⠘⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠀⠀⠉⠁⡀⠤⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⢐⡒⠂⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣶⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣏⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢹⠟⢿⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣴⣟⣃⣾⣿⢃⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠯⠛⠛⣛⣈⣧⣤⣷⡶⠀⠀⠀⠀⠀⠁⠈⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣤⣿⣦⣶⣶⣾⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣭⡛⠉⢿⣿⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠀⢸⣿⣇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠊⣿⣿⠄⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⢀⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠶⠀⠐⠃⠀⠀⠀⠀⠀⠀⠿⣻⣷⡾⣝⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⡀
⠀⠀⠀⠀⠀⠠⠄⠀⠡⠒⠀⠀⣿⣇⠀⠠⠀⠀⠄⠀⠀⠀⠀⢸⡟⢣⡔⢀⣤⠀⠀⠀⠀⠀⠀⠀⠺⠓⠻⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣝⢣⡀⠀⠀⠰⠆⠀⠀⠀⠐⠠⠡⣄⣴⣷⡠⠆⠒⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⢹⢀⠀⠀⠀⠀⠀⠀⣀⣷⣴⣿⡁⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⢻⡾⠷⠀⠀⠀⢀⣰⡟⠉⣿⣿⣧⠀⢹⡄⠀⠀⠀⠀⠀⠀⢠⢯⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠿⣆⠀⠀⠀⠀⠀⢬⡗⠀⠀⠹⣿⣿⡆⠀⢣⡀⠀⠀⠀⠀⠠⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠁⠀⠹⣧⡀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣷⡀⣀⢡⣀⢀⡠⢈⣠⣼⠏
⠀⠀⠀⠀⠀⢤⣤⢀⠞⣏⢹⡅⠀⠀⠀⠀⠙⢿⣤⡀⠀⢹⣿⠀⠀⠀⣿⣿⣿⡇⠛⠀⣹⢍⣂⣴⣿⠏
⠀⠀⠀⠀⠀⠘⠛⠈⢃⣹⠘⢳⡄⠀⠀⠀⠀⠈⠹⢿⣶⣄⣉⠒⠀⠒⢿⣴⡿⣿⡄⣴⣴⣿⣿⡿⠁⠀⠀⠴⠶⠖⠀⠀⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣿⣿⢷⣶⣶⡿⣿⣿⣷⣾⣿⣼⠋⠀⠀⠀⠀⡠⠄⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣿⡿⠷⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⢶⡶⣠⣤⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠐⢛⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠎⠀⠀⠈⣿⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡖⡚⣿⡙⢧⣢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢙⣧⣿⣿⣿⣜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣄⣇⣀⣠⣀⣠⣽⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣄⣤⣤⣿⣿⣧⣤⣤⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣏⢋⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⣿⣽⡏⠉⠉⠙⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠖⡀⠀⠀⠀⠀⠀⡰⡱⢻⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⡇⠙⠦⠀⠀⠀⡐⡱⠁⢸⠀⡟⣿⠀⠀⠀⠀⠀⢀⣤⡞⢸⡇⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⢷⣰⣄⠚⡁⠰⣰⠁⠀⢸⠀⡇⢸⠀⠀⠀⠀⠀⣹⣾⣗⣾⠁⠀⠀⠈⣿⣮⡲⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢴⣾⣿⡏
⠀⠀⠀⠈⠋⠈⠻⣦⣙⠛⠤⣤⡾⢠⡇⠘⢤⠤⠀⣲⣿⠿⠋⠘⠃⠀⠀⠀⠀⠹⠟⢿⣦⣄⡀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⣀⣤⣾⠟⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣦⣄⡤⣾⣿⣤⣦⣶⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣟⣿⣶⣿⣿⣿⣿⣿⣽⣶⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡙⠻⣮⣵⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣭⣫⣤⣍⣽⣉⣼⣏⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣤⣤⣴⣶⡶⠶⠟⠛⠛⠛⠛⠲⢦⣀
⣿⣿⣿⣿⣿⣿⣿⣭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡄
⣿⣿⣿⣿⣿⣿⣿⣯⣟⢿⣷⣦⣶⣶⣤⣤⣤⣤⣤⣬⣿⣿⣂⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠟⠋⠀⢸⡇
⢸⡏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣷⢰⣶⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠸⠟
⠈⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠘⣧⠻⣿⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⠘⠛⠉⠁
⠀⠸⣧⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢹⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠳⠭⣟⣻⣿⣿⠿⠋⠀⠀⠀⠀⠻⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣝⡻⢿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠠⣤⣾⣿⣿⣿⡄⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣡⣢⠊⠉⠙⠻⠿⡟⠹⠀⠔⠊⠀⣀⠤⠐⠖⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⠒⠂⠈⠉⠉⠙⠄⠀⠀⠀⠀⠀⢸⡆⠀⠔⠈⠀⡠⠊⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣀⠔⠂⠺⣿⢷⢶⣄⡀⠀⠀⠀⠀⠳⣀⣀⠔⠈⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠉⠐⠠⠾⠄⢀⠻⢿⣦⠔⠀⠀⠀⠐⡀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⢻⡏⠿⢛⠀⠀⠀⠀⠀⠰⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⠀⠈⢀⣿⣧⡀⠀⠀⠀⠀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣼⣿⣿⣿⣄⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠇⠰⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠙⠲⣦⣤⣤⣤⣤⣤⣤⣴⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠻⡿⠋⠁⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⠶⣶⣶⣶⠖⣺⠟⢛⣿⣿⣷⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⢒⣿⡟⢉⣿⣷⡄⢀⣀⡀⣿⡿⢣⡾⠋⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠟⣠⡿⠋⣠⣾⣿⣿⡟⠉⠀⠉⠻⣴⠟⢁⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡿⢡⣾⠟⢀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⠦⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠁⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣛⣷⣿⣿⣿⣟⣲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣋⡼⠿⣿⣿⣿⣿⣿⣿⡿⠷⣌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢁⡾⠉⠀⠀⠹⣿⣿⣿⣿⡟⠀⠀⠈⠻⣍⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣸⣿⣄⡀⠀⢠⡴⠻⠛⠛⠿⠳⣄⠀⢀⣠⣼⣷⡀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⠟⠋⠻⣄⣀⡀⠀⣀⣀⡼⠋⠛⠿⣿⣿⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠻⣄⠀⠀⠀⢈⣿⣿⣿⣿⣏⠀⠀⠀⢀⡾⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣷⣄⣠⣾⣿⣿⣿⣿⣿⣆⣀⡴⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠛⠿⠿⣿⣿⡿⠿⠟⠋⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⡿⠿⠓⠦⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢒⣒⣛⣛⣳⣶⣶⣾⠷⠶⠶⠾⠿⣿⣯⡭⢭⣍⣙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡭⠖⠚⢉⣩⣥⡶⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣄⡉⠳⣄⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠋⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⢦⡘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠁⢠⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡏⡴⢃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠁⠂⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠉⠉⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡄⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⢀⣀⡴⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⠓⠒⠛⠋⠉⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⡼⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⡀⠹⣄⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⡾⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣳⡀⠈⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣳⠦⣄⣈⣙⡛⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠋⣠⣲⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠭⠭⠿⠿⠿⠿⠿⠟⠿⣿⠿⠋⠉⠙⠛⠛⠛⠛⠋

⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⢤⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⠤
⠀⠀⠀⠀⣟⣴⣿⣿⣿⡿⢸⣡⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠻⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜

⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢻⡿⠋⠀⠀⠀⢀⣀⠀⠀⠀⠉⢻⡿⠁⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢶⢶⣶⣶⣶⡶⢲⡶⣶⣶⣶⣶⠂⠀⠀⠀⠀⣿⣿⣿⣿⣶⣄⠀⣠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣾⣿⣿⣿⠇⠈⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠓⠿⠿⠟⠋⠀⠈⠓⠿⠿⠛⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣤⡶⢂⣶⣦⣤⡀⠀⠀⣠⡤⢰⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠘⠿⣡⣾⣿⣿⣿⡿⠗⠺⣏⣠⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠈⠛⠋⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⢠⡄⠀⠀⣠⡀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⢠⡇⠀⠀⣰⡀
⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠸⣿⠿⠿⡿⠇⠀⠀⢹⣿⣷⣾⣿⠇⠀⠀⠸⣿⠄⢰⣿⠇⠀⠀⠻⣿⠿⠿⣿⠇⠀⠀⠻⣿⡦⣼⣿⠇
⠀⠀⠀⢈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏
⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠿⣿⣿⣿⡿⠟⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢴⣾⣿⣿⣶⡤⠀⠀⠤⣤⣤⣤⣤⠄⠀⠀⣤⣤⣤⣤⣤⡤⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠛⠛⠿⠟⠛⠛⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠉⠻⠟⠉

⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⢀⣾⠀⠀⣧
⠀⠄⠀⢴⣶⣆⣸⣶⡆⠀⠀⢰⣶⣿⣷⣶⡆⠀⠀⢰⣷⡀⣠⣿⡀⠀⠀⢼⣧⡀⣠⣾⡆⠀⠀⢼⣿⣿⣿⣿⡆⠀⠀⢸⣿⡄⣠⣿⡇
⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠈⠉⢱⠉⠉⠀⠀⠀⠘⠿⠿⠿⠿⠁⠀⠀⠀⠉⠙⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣄⣀⣀⣀⣀⣄⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⣀⣀⣼⣧⣀⣀⠀⠀⣀⡀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠛⢿⡿⠋⠙⠀⠀⠈⠙⢿⡿⠋⠀⠀⠀⠈⠙⢿⡿⠋⠁⠀⠀⠈⠙⢿⡿⠋⠁⠀⠀⠛⠿⣿⣿⠿⠛⠀⠐⠈⠛⢶⡶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠋⠉⠉⠉⠉⠉⠙⠛⠒⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣋⢁⠠⠤⠐⠒⠀⠀⠀⠀⠈⠉⠉⠀⢀⡐⡢⣼⠟⠦⣤⡀
⠀⠀⠀⠀⠀⠀⣴⠋⡠⣎⡸⠀⠀⠀⠀⢀⠠⠄⠒⠈⠁⠈⠁⠀⠀⢀⣴⡟⢢⠖⣄⠙⠶⣄
⠀⠀⠀⠀⢠⡞⣡⠊⠀⠀⠀⢀⠤⠐⠈⠀⠀⠀⠀⣄⠀⠀⠀⢀⣴⢿⡇⠙⢄⠉⠈⠳⡄⠈⢷⡀
⠀⠀⠀⣰⠏⡐⠁⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠘⠘⢀⣠⡴⠋⠀⠘⣇⠀⠀⠱⣄⠀⠘⢦⠀⢻⡄
⠀⠀⢰⠏⡔⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁⠐⠒⠢⣄⠈⠳⣄⡀⠈⢆⠀⠀⠳⡀⢻⡀
⠀⠀⡟⢰⠁⠀⡜⠀⠀⠀⣀⣠⡴⣶⠟⠛⠛⠦⡄⢠⠒⠉⠉⠑⢄⣀⠄⠀⠀⠙⢦⠈⢆⠀⠀⢱⠘⣧
⠀⢸⠇⡆⠀⠸⢴⡶⢾⡋⠉⠴⢶⠁⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢘⠋⠀⠀⠀⠰⢎⣧⠘⡀⠀⠈⡇⢹⡀
⠀⣾⢰⠀⠀⠇⢸⡇⠧⠟⠀⠀⠸⡄⠀⠀⠀⠀⢹⢯⡀⠀⠀⣀⠜⠀⠀⠀⠀⠓⠊⣿⠀⠇⠀⢠⣹⢸⡇
⠀⣿⠶⡀⢸⠀⢸⡇⠀⠀⣨⣃⠀⠈⠒⠒⠒⢚⠥⠤⠬⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠃⢸⡇
⠀⡟⡶⠃⢸⠀⠘⣇⠀⠉⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡿⠀⠇⠀⠀⠀⢸⡇
⠀⡇⠁⠀⢸⠀⠀⢿⠙⠶⣤⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠞⡛⠁⢰⡇⢠⠀⠀⢸⠀⢸⡇
⠀⡇⠀⠀⢸⠀⠀⠸⡆⠀⠸⠉⠉⠙⢋⣿⣿⡛⠻⢿⡿⠟⠋⣿⠳⣄⠀⢌⣻⠀⣸⠃⡈⠀⢎⡿⠀⢸⠇
⠀⣷⢸⠀⠈⣤⡄⠀⣷⠀⡄⠀⢀⣴⠋⢸⣿⠇⠀⠀⠀⠀⠀⢸⡄⠈⢳⣄⠇⠀⣿⠀⠇⠀⠀⠇⠀⣿
⠀⣿⢸⠀⠀⠷⠃⠀⢸⡄⠇⢀⣾⡁⠀⢸⠏⠀⠀⠀⠀⠀⠀⠈⣧⣤⢾⡏⠓⢶⡏⡘⠀⠀⠰⠀⢠⡏
⠀⣿⠀⡀⠀⠈⡇⠀⠘⣷⠞⠋⢹⡟⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢳⠀⠸⣧⡧⠦⣤⣧⣄⣸⠇
⠀⠸⣦⣧⠤⢤⣧⣤⡴⠏⡠⡀⣾⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠸⡇⠀⠀⠀⢠⢲⡄⠈⠉
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠓⠉⢷⡀⠻⠶⣤⡤⠤⢤⣤⡤⠴⢾⡟⠋⢀⡼⠃⠀⠀⠀⠀⠉
⠀⠀⠐⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠟⠀⠀⣀⣉⣁⠀⠀⠹⣶⠋⠀⢜⠇
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⢿⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠲⡀
⠀⠀⠀⠀⠀⠀⠛⠜⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡦⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡶⠶⡶⣶⣤⣀⣿⣀⡤⠶⠒⠛⠚⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠏⠓⠀⠀⠀⠀⠀⠙⢿⠋⠀⠀⠀⠀⠀⠀⣄⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡻⠛⠷⠤⣤⣄⣀⣀⣀⣀⣼⣦⣤⣤⣤⠴⠶⢞⣛⣭⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠶⠦⠭⢭⣭⣼⠷⠴⠶⠶⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⣛⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢁⣴⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣿⡟⠉⠀⠀⠙⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣇⠀⠀⠀⠀⣿⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⣿⣿⡷⣤⣴⠾⢋⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣠⣶⣾⣿⡶⠶⠶⠶⠶⠶⣿⠀⣿⣿⣿⡷⠶⠶⠶⠶⢶⣾⠋⣤⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠉⠉⠉⠉⠉⢙⣿⠀⣿⣿⣿⡏⠉⠉⠉⠉⠉⠙⠿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿
⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄
⠀⢰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧
⠀⣼⠃⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⣿⣿⣿⡄
⢠⡿⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⣿⣿⣿⣧
⣼⣧⣤⣼⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠷⣶⣿⣿⣿⣿⣿
⠉⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠈
⠀⠀⠀⢻⣿⣿⣿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣿⣿⣿⠃
⠀⠀⠀⠈⢿⣿⣿⣿⣮⣙⠻⠶⢦⣤⣤⣄⣀⣀⣀⣸⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣤⣤⣤⠶⠾⢛⣩⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣦⣤⣀⣈⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠋⠉⢉⣁⣠⣤⣶⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠠⣿⣿⡿⢛⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢆⣖⡾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠻⠛⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠅⠀⠀⣄⠀⠀⣸⠀⠀⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠄⠰⣆⡰⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡤⢄⡢⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠔⠆⠀⠀⠀⢌⢢⠀⠀⠀⠀⠀⠄⠀⠓⠀⠀⡠⢌⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡄⠀⢀⢀⠀⠃⠄⠀⢢⠀⠀⡠⠀⢀⠤⡀⠀⠀⠑⠊⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠣⡀⠇⠀⠀⠀⠠⠇⠼⣅⠤⠈⠂⠊⠀⢀⠄⢄⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⠀⠊⠁


⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠤⡉⠉⠐⠒⡆⠀⢠⠄⠀⠀⠀⠒⠀⠀⣠⠭⢄⠀⠀⡖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⠒⠁⠀⠀⠀⠙⠒⠊⠀⠀⢀⣀⡀⠀⠀⠑⠀⠚⠀⣀⡨⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⣀⠀⠀⠀⠀⠀⠘⠢⠃⠀⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡔⠒⡄⠀⠀⠀⢰⠉⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡔⠃⢀⡀⠀⠈⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠇⠜⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁