⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣵⣭⠭⠉⠛⠛⡿⡿⡿⢫⠿⡿⣫⣷⣞⣛⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠀⠀⠀⠀
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠿⠭⢁⣾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣛⡿⠿⢿⣛⣻⡿⣯⣭⣭⣽⠀⡄⡀⣅
⡿⠿⠿⢿⡿⡿⡿⠿⢯⣭⡭⠭⢭⣭⣭⣭⣥⣭⣭⣭⡿⡿⡿⡿⡿⡿⡿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠹⡿⡿⡿⡿⡿⣶⣶⣾⡿⡿⡿⡿⡿⡿⡿⡿⡇⣦⡇⣯
⣝⣩⡿⣷⣶⣶⣶⡿⡿⡿⡿⡿⢟⣭⠿⠯⢟⣻⡿⡿⡿⠿⡿⡿⠭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠻⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠆⠳⠆⠹⠿
⣾⣽⡿⣟⣛⣛⡿⠿⠻⠭⢭⣛⠿⠾⡿⡿⡿⡿⣾⣶⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⢾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣾⡿
⡿⡿⢿⡿⡿⠶⢖⣊⠾⠷⣾⠿⢿⡿⡿⢿⡿⣯⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠲⠀⠀⠉⠉⢙⣻⡿⡿⡿⡿⡿⡿⡿
⣤⣷⣶⣶⣶⣶⣶⡿⡿⡿⡿⡿⡿⡿⡿⣷⡿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⡻⠿⢿⡿⡿
⣷⣶⣟⣛⣛⣛⣋⣭⡭⡿⣭⣽⢿⢿⡿⡿⡿⠃⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢿⢿⡿⣷⣾
⣽⡿⡿⡿⡿⣳⣥⣶⣦⣤⣬⣬⣷⣶⣶⡾⠇⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠌⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡇⢸⠀⠀⠀⠀⠀⠀⣀⣰⡿⡿⠀⠀⣠⠞⢀⣴⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡘⣇⠀⠀⠀⣠⣾⡿⣟⡻⣄⣤⠞⣁⡴⠿⡿⡿⡿⣧⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡝⣯⢿⡿⡿⡿⢻⡿⣟⡿⡿⢰⡄⢮⠍⠉⠉⠹⡿⡿⣷⡿⡿⡗⠛⠛⠛⠛⠿⢿⣦⠀⠀⢀⣴⡿⠛⡿⣆⠀⠀⠀⠀⠀ ⡧⡿⡿⡿⡿⡿⡿
⡿⡿⣟⣟⢿⣷⣭⡿⡿⡿⣼⡿⡿⡿⡿⣵⡿⡿⡿⡿⡄⡇⣼⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣶⣶⣶⣶⣶⣬⣯⣾⣷⡾⠋⠀⡈⢻⡿⡆⠀⠀⠀⠀⠀⢣⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡆⡿⡿⡿⡿⡿⡿⢿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡷⢨⣦⣾⣾⠟⠀⠀⠀ ⠀⢸⣷⢻⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣧⢻⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡏⡿⡿⡿⡿⡿⡿⣶⡿⡿⠟⠁⠀⠀⠀⠀ ⠀⣼⡿⢸⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣯⡻⡿⡿⡿⠿⢿⡿⡿⡿⡿⡿⡿⣷⣵⡿⡿⡟⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣷⢌⣫⡾⢛⣷⡿⡿⡿⡿⡿⡿⡿⠿⠛⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⡿⡿⡿⡿⡿⡿
⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣸⡿⣩⣶⣍⠛⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⣐⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿
⢣⡿⠟⣽⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⢿⡿⢇⡿⢡⡿⠟⠛⠓⠶⠖⠉⠀⠰⣶⣶⣾⣶⣾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿
⡿⣱⡇⣫⣶⡿⠿⢻⡿⡿⡿⡿⠿⡿⡿⢿⡿⡿⡏⡴⣒⣶⢲⡶⣶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿
⣶⡿⣷⡿⡿⣷⣾⡿⣾⡿⣵⣾⡿⡿⣾⡿⡿⡿⢇⡿⡿⣯⣬⡅⡿⠶⢅⠭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿
⡽⠛⠻⠿⡿⣻⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡟⣡⣦⡭⣛⡿⡿⡿⢋⣯⣒⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿
⢲⣶⣭⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠃⣋⣀⣭⡫⣾⡏⡚⠿⠟⠿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿
⡻⢿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣋⣛⠃⢶⣭⣍⡙⣻⢏⣬⣙⡻⠶⢦⣼⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿
⣘⣛⡋⠿⠿⠿⡿⡿⡿⡿⢫⣾⡿⡿⡿⡿⣃⣥⣴⣶⣶⣶⣷⣝⠻⡿⡿⡿⡿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿
⠛⠛⢛⣛⣓⣶⣦⣭⣭⢡⡿⡿⡿⡿⡟⣽⡿⡿⡿⡿⡿⡿⡿⡿⡿⣌⠻⡿⡿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿
⣭⣽⡿⡿⡿⡿⡿⡿⢇⣾⡿⡿⡿⡿⢸⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣧⡘⢿⡿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿
⠻⡿⡿⡿⡿⡿⡿⡟⣸⡿⡿⡿⡿⠃⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⣷⣄⠹⡿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿