Tracking Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠟⠛⢷⣆⠀⠀⠀⠉⠉⠉⠉⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⢶⣶⠾⣿⡀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠁⠀⠀⠀⠀⠀⣸⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡉⣹⡇⠀⠀⠀⠀⢐⣿⣩⣿⣉⣙⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣩⡿⢻⡇⠀⠀⠀⠀⣼⡏⠉⠉⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠃⠀⠀⢰⣿⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⠛⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢰⡿⠙⢷⣄⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢿⡇⠀⠀⢹⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢻⡿⠁⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⣼⠏⢠⡿⠁⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠿⣶⡿⠀⠀⠀⠀⠀⠸⠷⠾⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣼⠏



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⢀⠀⠄⠀⠀⠀⢂⠀⠀⠀⠄⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣉⡉⠉⣉⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⣿
⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠛⠃⠀⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠃⣠⠶⠲⣦⡈⢻⡄⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠟⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⡀⠀⣸⠇⢸⡇⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠉⢠⡟⠁⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡀⠘⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠿⠛⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡟⠀⣾⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⣿
⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⣿
⣿⣿⠀⠻⠿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⣿
⣿⣿⠷⢶⣶⡶⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⢶⣿⠆
⣿⣿⠀⠘⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⠟⠁
⣿⣿⠀⡄⠸⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠋
⣿⣿⠀⣿⡄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡷⠋
⣿⣿⣴⣿⣷⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⡰⠶⠶⠶⠶⠆⣶⣶⣶⠶⠄⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣛⣋⣭⣵⣶⡿⠇⠀⠀⣰⡿⣫⣵⡖⡲⣶⣭⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢟⣛⣭⣵⣶⡾⠿⢟⡻⣿⡅⣶⣾⡇⠀⢸⡟⣼⡟⣭⣶⣶⣮⡻⣷⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢟⣛⣯⣭⡶⠾⠿⠿⣧⣿⣷⢹⣿⡇⠀⢿⡇⡿⢘⣛⣛⣛⣛⣓⢹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣫⣵⣾⠿⠿⢿⣶⣝⢿⡎⣿⡇⠀⠘⣷⡹⣶⣿⣿⣿⣿⣷⠞⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣱⣿⡟⡴⣫⣝⢲⡹⣿⣧⢻⣸⡇⠀⠀⠘⢿⣮⣝⣛⣛⣋⣵⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡏⣧⠻⠿⣹⢇⣿⣿⢸⣧⠃⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡸⣿⣿⣎⢿⡿⣣⣿⣿⡟⣼⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⡻⢿⣷⣴⡿⠟⣫⣾⣧⢻⡇⠀⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣶⣶⢰⣿⣿⣿⣿⡜⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣛⣛⣭⣽⡇⣿⣿⢺⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢟⣛⣭⣽⣿⣦⡱⢿⡿⣿⣿⣿⣿⠇⠀⣀⣀⣀⡀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠶⠶⠆⠀⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡴⠚⢹⡏⠓⢦⡀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠙⡏⠉⠀⠀⠀⠀⠉⣹⠋⠉⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢦⣀⣰⡆⣀⡴⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⢹⡏⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠞⢧⠀⠀⠀⢀⡾⠱⠶⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⣀⣤⠴⠶⠒⠊⢳⡄⣠⠞⠐⠒⠶⠦⣤⣀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠐⢧⣀⡀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢀⣀⡼⠂⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣈⡉⠙⠛⠛⠒⠒⠒⠒⠛⠛⠋⢉⣁⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⢀⣠⣴⠶⠿⠛⠛⠻⠷⢶⣦⣄
⠀⠀⢀⣴⠟⠉⢀⣠⣤⣤⣶⣤⣤⣀⠀⠙⠿⣦⡀
⠀⣠⡟⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠙⠳⣦⠀⠙⢷⡄
⢰⡟⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠈⣿⡀
⣿⠃⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢹⡇
⣿⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⢹⣇⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣾⠃
⠈⢿⣄⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣼⠏
⠀⠀⠻⣧⡀⠀⠈⠙⠛⠿⠶⠿⠛⠋⠀⠀⣠⡾⠋
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠿⠿⠿⠷⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⣀⣀⣀⣀⣀⡀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⣠⡶⠟⠋⠉⠉⠉⠉⠛⠷⣦⡀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠖⠠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣶⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠈⠛⠷⢶⣦⣤⣤⣶⠾⠛⠉⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⢠⣤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠛⠐⠶⠶⠆⢠⣄⡈⠻⣦⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢼⡟⠋
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣄⠀⠀⣀⣠⣤⣶⣶⣶⣦⣤⣀⠀⠀⣠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢋⣴⣾⡿⢛⣋⣭⡉⣭⣉⡛⠿⣿⣦⡙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣰⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣬⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⢰⣿⠏⣼⣿⣿⣿⣿⣿⣿⡿⢋⠅⣸⣿⣷⡘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⡇⣾⣿⠸⢿⣿⣿⣿⣿⠟⣡⡾⢋⣾⣿⣿⣿⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢃⣿⡇⣿⣿⢰⣶⣿⣿⣿⣿⣦⣉⣵⣿⣿⣿⣿⣷⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠠⣶⣶⣶⣶⣶⣶⣶⣶⣦⡐⣶⣾⣿⣿⣧⢹⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣆⠻⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣡⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣶⣴⣤⣦⣴⣦⣴⣶⣶⣦⣴⣦⣤⣬⡙⣿⣧⡙⢿⣷⣮⣙⡛⠿⠀⠿⠛⣋⣥⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣶⣌⡛⠻⠿⣿⣿⣿⠿⠿⢛⣩⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣭⣭⣭⣭⣭⡙⢿⣷⣶⣶⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣉⣉⣉⣉⣉⣉⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⣠⣶⠿⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⣼⡟⠁⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠶⠶⢦⡀⢸⡇
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠈⡷⢸⡇
⠀⠀⢻⣧⡀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣤⣤⠞⠁⢸⡇
⠀⠀⠀⠙⠻⣷⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⠀⠀⠘⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⣛⣛⣿⣛⣛⣿⣛⣻⣿⣛⡃⠀⠀⠀⠀⠀⣿⣤⣤⡤⢤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠿⠿⠿⠷⠾⠿⠿⠿⠃

⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣚⣓
⣶⠓⠓⠛⠚⠛⡻⡟⠛⠚⠛⠛⢻⡆⠀⠀⠀⣿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⣫
⣿⠀⠀⠀⠀⠘⣄⡜⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⣠⡴⠶⣦⣄⠀⠀⠀⠀⣠⣴⠶⢦⣄⠀⠀⠀⠀⠀⠘⠃
⣿⠀⣠⠞⠀⠀⢸⡀⠀⠈⢦⡀⢸⡇⠀⠀⢻⣭⡿⠰⠂⠦⣀⣼⠉⠀⠀⠀⢹⡇⠀⠀⢰⡏⣠⣶⣶⠘⣧⠀⠀⠀⠀⢘⡁
⣿⣾⣥⣤⣤⣤⡾⣧⣤⣤⣤⣽⣾⡇⠀⠀⠀⠀⢀⡀⣄⠴⠉⢻⣄⠀⠀⠀⣸⠇⠀⠀⠸⣇⠸⠿⠿⣠⡟⢀⡤⠶⠰⠊
⠿⠿⠿⠿⢿⣿⣦⣾⣿⠿⠿⠿⠿⠇⠀⠀⠀⣒⠊⠁⠀⠀⠀⠀⠙⢻⣶⡟⠉⠀⠀⠀⠀⠈⠻⣶⡟⠋⠀⠀⠓⠶⠰⠆⣄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠠⠆⠤⠠⠄⠤⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⠡⠄⠤⠠⠄⠤⢠⠄⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣒⠲⡄⠀⠀⡰⠒⠲⡀⠀⢠⠒⠒⡄⠀⢠⠖⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣛⣡⠇⠀⠀⠑⢤⠞⠀⠀⠘⢦⡔⠁⠀⠈⠳⡴⠃⠀⠀⢀⡴⠶⠶⣦⡀⠀⠀⠀⠀⣶⣶⡶
⠀⣠⣤⣦⣤⡀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⢠⠄⠀⠀⠀⠠⡄⠀⠀⠀⣾⠁⠀⠀⠈⡷⠀⠀⠀⠀⣿⠛⠛
⣼⢋⣤⣤⣌⢻⡆⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠰⠂⠀⠀⠀⠐⡇⠀⠀⠀⠘⠷⣤⣤⠾⠃⠀⠀⠀⢀⣿⡀
⢿⡘⠿⠿⠿⣸⠇⢠⡤⠆⠶⠉⠀⠀⠀⠀⠀⠘⣤⢀⣀⡞⠉⠉⢳⢀⡀⣬⠃⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⢿⣭⡟
⠀⠙⢷⣶⠞⠋⠀⠰⠆⠦⠴⢄⡀⠀⠀⠀⠀⠀⠀⠈⠈⢧⣀⣀⡼⠈⠁⠀⠀⠀⠀⠀⠀⠀⠴⠦⠐⠐⠂⠒⠐⠠⠶⠆
⠀⠀⠈⡟⣤⣀⣄⣠⣀⣄⣤⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⣮⣿⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⢸⠿⣇⠀⢸⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⡿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣽⣟⡙
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⣿⡿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣟⣿⣟⣿⣯⣯⣿⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣿⣿⣿⣻⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣷⣿⣿⢿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠷⠦⠸⠿⠾⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡶⢶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣰⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣖⣖⣶⣶⢼⣿⣿⣿⣻⣿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⣿⣿⣷⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣟⣿⠿⡻⢿⣇⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣾⡿⣿⣿⣿⣿⣿⣷⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣽⣽⣿⣿⣿⣿⣿⣿⣟⡟⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣯⣯⣿⣏⣿⣿⣯⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⣿⣿⡟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣄⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛



⣿⣿⣿⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣛⣛⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣠⡴⠋⠁⠀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠈⠉⠓⢦⣀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣠⠶⠋⠁⠀⠀⠀⣀⣠⣤⡤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⠞⠁⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠈⠳⣄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣠⠞⠉⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠙⢶⡄⠀⠀⠘⢦⡀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⡼⢃⡀⠀⠀⠀⠀⠀⠙⠛⠓⠶⢤⡉⠛⢦⡀⠉⠙⢦⠀⠀⠙⢦⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡞⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣀⣈⣧⣤⣤⣼⣇⠀⠀⠈⢷⡀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣾⠁⡟⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⢉⡽⠋⠀⠀⣠⠴⠛⠗⣿⠀⠀⠀⠈⣧⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢰⡇⠀⠁⠀⠀⠀⣀⣴⣚⣁⣀⣠⣴⣯⡤⠤⢴⢺⠵⠛⠁⠀⢻⠀⠀⠀⠀⢸⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⢠⡇⠀⠀⠀⡏⣭⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⢸⡇⠀⠀⠀⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠀⠀⠀⠀⢸⠇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣧⠀⢷⠀⠀⠀⢹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⡾⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠸⣆⠈⢧⡀⠀⢸⡄⠃⠀⠀⢀⣀⣀⣀⣀⣀⣷⠊⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⣆⠀⠹⣆⡈⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣰⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⣄⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣴⠃⣼⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠳⣄⠀⠀⠈⠳⢦⣀⠈⠉⠓⠲⠖⠀⠀⠶⠖⠂⠀⠀⣠⡴⠛⠁⠀⠀⣠⠞⣧⠀⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢷⡀⠀⠙⠳⣄⠀⠀⠀⠈⠙⠓⠶⠤⢤⣤⣤⠤⠤⠶⠚⠋⠁⠀⠀⢀⣠⠞⠁⢀⡟⠀⢿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⡀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⣠⠾⢇⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠳⠄⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠶⠶⠶⠒⠛⠉⠙⠲⠶⠶⢶⡚⠁⠀⠈⢳⡀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⢧⡀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡌⠳⡄⠹⣄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⢧⡀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⡉⢉⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⢋⡴⢦⡙⣧⣀⣀
⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠉⠉⠉⠈⠻⠟⠁⠉⠉⠉⣿⣀⣀⣀⡀
⣿⣿⣉⣁⣈⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠉⠉⠉⢹⡆
⣿⣿⠋⢉⣉⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⡄⢸⡇
⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣧⢸⡇
⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣠⠞⢋⣉⣉⠙⢷⡄⠀⠀⠀⠀⣿⢸⡇
⣿⣿⣄⣈⣉⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢠⡏⢠⡟⠉⠉⣷⠀⣿⠀⠀⠀⠀⣿⢸⡇
⣿⣿⠋⣉⣉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠈⢷⡈⠻⢦⡴⠟⢠⡿⠀⠀⠀⠀⣿⢸⡇
⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠈⢷⡄⠀⠀⣠⠟⠀⠀⠀⠀⠀⣿⢸⡇
⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠻⣆⣰⠏⠀⠀⠀⠀⠀⠀⣿⢸⡇
⣿⣿⣄⣉⣉⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⣿⡟⠉⢻⣿⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿⢸⡇
⣿⡇⠀⠀⢿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣿⢸⡇
⣿⡇⠈⣧⠈⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠓⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠾⠃⢸⡇
⣿⣯⣠⣿⣆⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣴⣿⣿⠿⠟⠻⢿⣿⣿⣦⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠘⣿⣿⣧⢠⠒⠚⢿⡇
⡰⠒⠓⠒⠤⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⠀⠀⠈⢧⡀
⢧⠀⠀⠀⠀⣿⣿⠀⠀⢻⣿⣿⣄⡀⠀⠀⣀⣴⣿⣿⡏⠀⢧⠀⠀⠀⠉⠲⢄⡀
⠀⠉⡲⠦⢤⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⢣⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠀⢸⡀⠀⠀⠀⠉⠑⢢⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠉⢒⣦⣤⣀⣀⡼⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢰⠁⠀⠀⠉⠑⠢⡀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⣳⠤⣤⣀⡀⣠⠇⠀⠀⠀⠙⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡀⠀⠀⠈⠉⢢⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀
⠀⠀⠀⠉⠒⣦⣤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⠧⠄⣀⣀⣀⣀⠤⠴⢤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⡀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣻⡻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢀⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠚⠇⡀⠀⠀⠀⠀⠀⠈⢉⡩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡅⢄⠜⠉⠉⡀⡀⠀⠀⠠⡠⠙⠓⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠩⡢⠀⠀⠀⠔⠑⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠢⡤⠀⠀⠈⡂⠲⠙⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠚⢆⠀⠀⠄⠺⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⣀⢀⠀⠄⠃⠀⠀⠀⣀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⢀⢼⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⣰⠓⠅⠀⠈⠆⡀⠀⠀⠀⠀⢀⢱⣿⣿⣿⣧⠃⠀⠀⠀⢠⡞⠉⢻⡆⠁⠄⡀⠀⢀⢄⠎⠂⠁⢸⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠢⠂⠡⠂⠀⠀⠀⠢⠀⠀⠀⠀⢈⠜⣿⣿⣿⢟⠄⠀⠀⠀⠈⢿⣶⣾⠃⠀⢨⠎⢪⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠋⡆⠀⠀⡌⠀⠀⠀⠀⠐⢄⡀⠔⠐⠁⠁⠐⠈⠉⡀⡀⠀⠀⠀⠘⣿⡏⡠⠑⠁⠀⠈⠑⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⣀⣤⠾⠛⠁⠀⠀⢀⡠⠀⠁⠂⠢⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⣔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⡁⠀⢀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠢⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠢⠈⠀⠪⣠⡀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⠀⠫⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠄⠠⠖⠀⠢⠂⠀⠀⠀⢸⣷⣄⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⠀⠀⠀⠀⠀⠀⢀⢀⠤⠋⢸⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⢇⠀⠀⠐⠄⠀⠀⣼⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠌⠂⠢⠀⠀⢀⢤⠢⠀⢅⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⢀⠀⠀⠀⠃⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⡠⠊⠃⠀⠀⠀⣈⠆⠊⠀⠀⠀⠀⠁⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠡⠀⠀⠀⠈⠂⢤⢀⠀⣿⠁⠢⡀⢀⠈⠢⣀⡀⡐⠔⠉⠀⠀⠀⠠⡠⠐⠴⡀⠀⠀⠀⠀⠀⠀⠀⢢⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠂⠠⠠⠤⠄⠐⠷⠿⠤⠠⠄⠵⠮⠲⠶⠾⠤⠤⠤⠤⠖⠷⠠⠠⠤⠄⠾⠤⠠⠤⠤⠤⠤⠐⢈⠔⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠔⠁





⠀⠀⣀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢀
⣿⡟⣉⣻⠟⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢨⡁⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⣶⣶⡆⠀⠀⠀⢴⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⡀⢀⣀⣀⣀⢀⡀⠀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⢀⢀⣀⣀⢀⣀⢀⣀⡀⣀⡀⣀⢀⡀⢀⣀⣀⣀
⣿⣛⣶⣿⢑⣻⣿⣿⡏⡜⣷⢰⣿⡇⠙⣸⡏⡇⡓⣽⢘⢪⡣⣶⢹⢘⢪⡇⣚⡯⣶⢜⣿⢹⢳⣶⣟⢴⡎⡇⡙⢸⣕⡺⣿⣶⣛
⠛⠛⠒⠛⠙⠛⠃⠘⠘⠛⠙⠚⠛⠋⠃⠛⠛⠛⠛⠙⠛⠋⠛⠑⠛⠘⠃⠓⠀⠛⠀⠚⠛⠛⠓⠑⠛⠂⠚⠃⠛⠘⠃⠘⠛⠒⠛
⠀⠀⢤⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠙⠒⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠘⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⠛⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⢸⡃⠈⡷⠴⡏⠀⢹⠀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⠀⠙⠛⠁⠀⠉⠛⠉⢀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⡀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠈⡟⠒⠶⠶⠶⠚⡏⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣻⠇⠀⢻⠉⣻⠿⡏⢹⠃⠀⢿⡳⠤⣄⣀⡤⠖⠚⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢴⡃⠀⠀⠈⣇⢳⣶⢋⡏⠀⠀⠀⣹⠄⣰⠋⠳⡄⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⢦⣀⠀⢹⡞⠘⣿⠀⠀⣠⠞⠁⢠⡇⣾⠁⢿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⢷⢰⢇⡴⠋⠁⠀⠀⠘⡇⠉⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠇⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣤⣤⠴⠞⠙⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⢠⣴⣶⣄⣴⣶⡄⠀⠀⠀⠀⢠⠶⣾⣷⠶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠸⣿⡽⣻⣿⣿⠇⠀⠀⠀⠀⢸⠀⠂⠐⠀⡥⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣠⠤⣀⡴⠊
⠀⠀⠀⠘⢷⣿⡿⠋⠀⠀⠀⠀⠀⢸⠀⠁⣾⣷⣿⡇⠀⠀⠀⠀⠀⠀⢿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⣷⡖⣶⡇⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⠒⢲⣦⠀⠀⠀⠀⠀⠀⠀⠀⣐⣧⣵⠀⠀⠀⠀⠀⠀⠐⠄⡐⢒⣤⡀
⠀⠀⠀⠀⠿⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣁⣸⠏⠀⠀⠀⠀⠀⠀⣷⣤⣸⠟⠛⠿
⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠈⠧⣿⠿⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁


⠀⠀⠀⠀⠀⠰⣷⣶⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤
⠀⠀⠀⠀⡐⠁⠫⠉⠀⠀⠀⠀⠀⠀⢸⡉⠀⠈⡍⠀⠀⠀⠀⠀⠀⢸⠖⢫⣗⢾⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⣸⠀⠀⠀⠀⢀⣤⣦⣀⣀⣶⣤
⠀⠀⠀⡐⢁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡀⠈⠻⣿⠀⠀⠀⠀⠀⢀⡈⠁⣀⣀⣀⣺⠀⠀⠀⠀⠀⠛⠛⠉⠉⠛⠛
⠀⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣴⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣾⠂⠀⠀⠀⠀⠀⠠⠀⠂⠐⠀⠄
⠀⠀⠘⢿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡋⠛⠒⠀⠀⠀⠀⠀⠀⣀⣽⠄⣶⠆⠀⠀⠀⠀⢀⠤⣼⣷⢐⠿⠤⡀⠀⠀⠀⣦⣶⣶⣶⣶⣶⣦⡔
⠀⠀⠀⠀⠈⠙⠻⠿⠅⠀⠀⠀⠀⠰⠶⠞⠁⣽⠀⠀⠀⠀⠀⠀⠘⠉⠓⠉⠑⠋⠙⠀⠀⠀⠀⠡⢈⠜⠛⠘⠄⡠⠃⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⣼⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⢺⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⣷⣶⣿⣶⣼⣿⡶⠿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣶⣿⣶⣿⢾⠇⣭⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⢩⣿⣿⣿⣿⣭⢿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡳⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣹⣿⣿⣷⣿⣿⣾⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣿⣿⣏⡉⢸⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣻⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣽⣿⣿⣺⣿⣿⣿⣿⣿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡿⡟⢻⣿⣿⣿⣿⣿⣿⡟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣽⣿⣿⣿⡽⣿⡷⡵⣻⠧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⣷⣿⣿⣿⣿⣿⣿⣿⣟⡟⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣻⣿⣿⣿⣋⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣯⣿⢿⣷⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢻⣿⣿⡟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣯⣠⣾⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃



⡖⠒⢲⠖⠶⠶⠶⠶⡖⠶⠶⠶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣶⡶⣶⡶⠶⡶⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⣀⣀⢀⠀⡀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠰⡄⠇⡰⢄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡿⠁⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠊⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠠⡀⡆⢠⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈⠀⠘⡶⠁⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠇⡠⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡀⡇⢠⡀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢰⠂⠐⠂⠁⠬⠐⠀⠁⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⠂⠀⠱⣶⠃⠈⠂⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠂⠀⠀⡨⠠⠞⠀⠆⠇⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠦⠀⠅⠀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠈⡌⡔⠀⡤⠤⠤⢤⣀⠀⠀⠈⠀⢳⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣃⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠭⠭⣙⣒⠀⠸⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠭⢝⣒⣂⠀⠰⠿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣊⣩⣍⣙⣓⣒⠦⠥⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣛⣛⣒⣒⣒⠭⠭⣓⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣒⣒⣒⣒⣒⡦⠭⢭⣒⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠙⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⣉⣀⣉⣉⣉⣉⣓⣒⣤⣼⣤⣤⣐⣀⣀⣀⣀⣀⣀⣀⣈⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⠊⠐⢲⡖⠂⠂⠐⠀⠑⠲⣀⠖⢖⠊⢙⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠦⡈⢢⡠⠚⠁⠑⢄⣀⡀⢀⠴⠊⠙⢦⡤⠓⠉⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⣄⠽⡊⠑⢄⠀⠀⢼⠁⠈⡇⠀⠰⠉⠆⠱⣄⠴⠊⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠈⢣⠴⠋⠑⠙⢦⠀⢀⣠⠖⠊⢉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⣇⡠⡖⠁⠀⠀⠀⢀⣠⠷⣋⣀⠤⠚⠁⠀⠑⢄
⠀⠀⠀⠀⠠⠀⠀⣸⡴⢯⠀⠈⣦⣀⡤⠞⠉⠀⠀⠈⢣⡀⠀⠀⢀⡠⠜⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠑⢤⡇⠙⢄⠀⠀⢀⡠⠖⠉⢑⡤⠒⠉⢣⠀⠀⠀⠀⠀⣏⡳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣰⣼⣏⣓⣤⣷⣔⣉⣀⣤⣊⣹⣄⣀⣀⣀⠑⠀⠀⠂




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

⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡿⢟⣛⣛⣛⠿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⣝⢿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⢸⣿⡿⣿⣿⡿⣋⣵⣿⡇⠀⠀⢸⣿⣿⡇⣶⣦⣶⣶⡆⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠟⢑⣒⠋⢵⣿⣿⡇
⠀⠀⢸⣿⡇⠁⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⣿⡇⢸⣏⣴⣶⣬⣾⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠈⠉⠉⠉⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠏⠀⠿⠏⣰⣿⣿⣿⡇
⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⣿⡇⠸⠿⠿⠿⠿⠿⠿⢿⣿⡇⠀⠀⢸⣿⣿⣿⣄⣀⣀⣀⣼⣿⣿⣿⠀⠀⠀⣿⣿⣿⣶⣄⡀⣴⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⢸⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⣿⠀⠀⠀⣿⣿⡿⠛⠛⠛⠛⠛⠛⢿⣿⡇⠀⠀⢸⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡏⠀⢀⠄⠁⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠺⠿⠿⠂⠀⢸⣿⡇⠀⠀⢸⣿⣿⣧⠀⢠⣿⠿⢿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠏⠀⠈⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣆⠈⣼⠃⠀⠀⣼⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⠀⢸⣏⠀⢀⣿⣿⣿⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣷⡄⠀⣠⣾⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⠀⠀⠀⣿⣿⣿⡘⣇⠀⠀⠀⣸⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣷⣬⣭⣤⣴⣿⣿⣿⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡟⡛⠛⣤⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⢏⣶⣶⣶⣶⢸⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡆⢀⣤⣍⣻⣿⣿⠀⠀⠀⣿⣿⣿⣿⡿⠄⢿⠛⢻⣿⣿⡇⠀⠀⢸⣿⡁⠀⠈⣛⣛⡋⠀⠀⢹⣿⠀⠀⠀⣿⣿⣿⡏⣼⣿⣿⣿⣿⢸⣿⡇
⠀⠀⢸⣿⣿⣛⣛⣰⣦⢈⣿⣿⣿⣿⠀⠀⠀⣿⣿⣫⣭⣒⣭⣝⣫⣭⣻⣿⡇⠀⠀⢸⣿⣷⣦⣼⣿⣿⣿⣴⣴⣿⣿⠀⠀⠀⣿⣿⠟⣼⣿⠿⠿⠿⠿⢸⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣶⣿⣿⣶⣷⣾⣿⣿⣿⡇
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⢰⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢸⣿⣿⣿⢰⣿⣿⣷⠈⣿⣿⣿⠀⠀⠀⣿⣿⣿⡿⠃⢀⠀⢻⣿⣿⣿⡇⠀⠀⢸⣿⣿⡿⣿⡧⠀⣿⡿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⢠⣶⣂⠸⢿⣿⣿⡇⠀⠀⢸⣿⣿⡷⢠⣶⡖⠢⡐⣿⣿⣿⠀⠀⠀⣿⣿⡧⠀⠀⠉⠉⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⠸⠿⠿⠿⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡗⠀⠻⠁⠸⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⢿⣿⣧⣀⠇⣿⣿⣿⠀⠀⠀⣿⣿⣿⣶⣤⣀⠄⣈⣙⣿⣿⡇
⠀⠀⢸⣿⣿⣿⡀⠘⠛⠀⣠⣿⣿⣿⠀⠀⠀⣿⣿⣿⣷⡆⠀⠀⣾⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣦⣉⣉⣡⣾⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⡇
⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠢⢈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠛⢄⠀⠀⠈⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⢴⡁⠀⠀⠀⠈⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠑⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠤⠄⠠⠄⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠁⡠⠐⠢⡀⠙⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢃⠀⢠⡀⣀⠄⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠢⢀⣈⣁⡠⠊⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠐⠠⣤⠀⠀⠤⠔⠚⠣⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣙⠳⣤⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠄⠤⠄⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣭⠆⠀⠈⢩⠋⠝⣋⡛⢍⢫⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⢁⢠⠸⡘⢅⠸⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⢀⠔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡜⢠⣤⡄⠊⠀⡈⢆⠢⢍⣒⣒⡡⠊⠳⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢄⠁
⠀⠀⠀⠀⠀⠀⡜⠠⠁⠀⠀⢀⠀⠘⡌⢆⠀⠀⠉⠢⡀⠀⠈⠢⡀⠀⢀⠊⠀⠀⠀⢠⠊⠉⠑⡄⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡼⠠⠁⠀⠀⠀⠑⠃⠀⠘⡌⢆⠀⠀⠀⠈⠦⡀⠀⠈⢦⡌⠀⠀⠀⠀⠐⢄⣀⡠⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⡰⢡⠃⠀⢠⡆⠀⠀⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠈⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣦⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⣀⡠⠤⠿⠐⠒⠺⠄
⠀⠀⡰⢁⠂⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⠀⠀⠱⡘⣄⠀⣀⣀⡀⠤⢤⣗⠒⠦⠭⠙⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢰⢃⠂⠀⢠⢢⠀⠀⠀⠀⠈⠛⠁⠀⡠⠠⡀⠱⡘⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⢠⢃⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠁⠀⠡⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⣣⣤⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣍⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⡀⠀⢀⠐⠀⠂
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⠇⠀⠰⣀⠀⠀⢀⣴⡷
⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢀⣿⣿⠄⠒⠀⠀⠀⣾⣿⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⢀⣿⡟⠓⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣀⠠⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⡠⠂⠀⠀⠀⡀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⢀⠼⣿⡇⠀⢸⣿⡇⢠⡶⠋⢠⡀⢻⣿⠀⠔⠈⠀⠀⠀⣠⣌⠁⠀⣼⡿⠀⠀⠀⠀⠀⠀⠤⠃
⠀⠀⠀⢀⠐⠁⠀⣿⡇⠀⠸⣿⡇⠸⠷⣶⡟⠁⢸⣿⠀⡀⠒⣶⡤⢸⡿⠁⠀⠀⣿⠃
⠀⠀⢠⠁⠀⠀⠀⣿⡇⠀⠀⣿⣷⠀⢠⡟⠀⢀⠘⣿⡈⠀⢀⢿⡇⢸⡇⢀⠄⠰⣿⠀⠀⠀⠀⡄
⠀⠀⢠⠀⠀⠀⢀⡿⠀⠀⠀⠘⣿⡆⠘⣁⡠⠁⠀⣿⠁⢠⠁⣼⠃⠀⠉⠀⠀⠀⣿⠀⠀⠀⢠
⠀⠀⠀⠑⠀⠐⠈⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⠀⠈⠚⠋⠀⠀⠀⠀⠀⠀⠘⠧⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⣀⡀⡀⢠⡄⠀⣀⣀⡀
⠀⠀⠀⢾⠷⠂⠀⠐⠒⠀⢹⡇⢸⣟⠄⠀⡎⣿⡄⢾⡇⡀⣿⣗⠀⢸⡇⠀⣿⣅⠁⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠋⠈⠀⠁⠉⠁⠈⠉⠀⠈⠁⠁⠈⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠤⠤⠶⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠻⢷⣶⣤⣴⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣤⣦⣠⣤⣤⣤⣬⣭⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠑⠂⠀⠀⣸
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠒⠒⠲⠶⣤⣤⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢻⣿⣿⣿⣿⡟⠩⠐⠆⢻⣿⣿⠇⠀⠀⠀⠐⠛⠻⢷⣤⣄⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⣆⣴⠀⠸⣿⣿⠀⠀⠀⠀⠀⠲⠆⠀⢸⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⢸⣿⣿⣿⣿⡆⠸⠇⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠙⠻⢿⣿⣿⣿⡿⠠⡄⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⠆⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠲⠄⠀⠀⠀⠀⠀⠀⣈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⠀⠉⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠓

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

⠀⠀⢀⠔⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⡉⠉⠉⠉⠁⠢⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠐
⠀⢸⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⡇
⠀⠘⠀⠀⠐⠠⠊⢓⢄⠀⠀⠀⠀⠀⡈⢈⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠐⡢⠂⠉⠒⠀⠀⢀⢠⠶⠋⠑⠄⠂⠀⠀⠃
⠀⢰⠀⠀⠀⣶⢄⠀⠑⠤⡀⢀⢔⠔⠁⠀⠑⢠⡀⠀⠀⠀⠀⠀⢀⠠⠲⠃⠉⠪⢂⠀⡀⢕⠍⠂⠀⠀⠀⠀⢰⠀⠀⠀⡇
⢀⢼⠀⠀⠀⠇⠑⠥⠀⢨⡊⢊⠀⠀⠀⠀⠀⠀⢪⡂⠲⠂⡠⡰⠁⠁⠀⠀⣠⣤⡐⢝⠌⠀⠀⠀⠀⠀⠠⠢⠻⠀⠀⠀⡧
⡇⢸⠀⠀⠀⢦⣀⡄⡄⠀⠀⠐⢥⡀⠀⠀⠀⠀⢑⠀⠀⠀⠠⡆⠀⠀⠀⢸⡇⢀⣿⠀⠑⠢⡀⢄⠎⠀⠀⠀⢠⠀⠀⠀⡇
⡇⢸⠀⠀⠀⣧⠈⠀⠘⠅⠀⠀⠀⠩⣂⠀⠀⡠⡢⠄⠄⠀⡪⡁⠀⠀⠀⠈⢿⣿⠏⡀⡀⠔⠪⢄⠀⠀⠀⠀⢸⠀⠀⠀⡇
⡇⢀⠀⠀⠀⡄⣴⠀⠀⠀⠀⠀⠀⠀⢈⢅⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠓⠁⠀⠀⡀⠔⢕⠀⠀⠀⢸⠀⠀⠀⡀
⡇⢸⠀⠀⠀⡅⠁⠀⠀⠀⠀⠀⡠⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⡶⠋⠁⠀⠀⣠⡀⠐⠈⠀⠀⠨⡢⡀⢸⠀⠀⠀⡇
⡇⢸⠀⠀⠀⡇⠀⠀⠀⠠⢔⠞⠪⡢⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠩⡢⠀⠆⠂⠁⠀⠀⠀⠀⠀⠀⠈⠒⢬⠀⠀⠀⡇
⠑⢼⠀⠀⠀⡇⢀⡠⡢⠔⠀⠀⠀⠈⣷⣄⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠈⢓⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡰⢹⠀⠀⠀⡧
⠀⠘⠀⠀⠀⣗⠥⢂⠀⠈⠑⢄⠀⠀⣿⠙⠷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠣⠡⡀⠀⠀⠀⢀⢂⠇⠁⠀⢸⠀⠀⠀⠇
⠀⢰⠀⠀⠀⡇⠀⠑⢅⢀⠀⠀⠲⢠⣏⠀⠀⠨⡢⠀⠀⠀⠀⠀⢀⢄⠮⠃⠁⠀⠈⡢⡒⠄⠂⠀⠀⠩⣂⠀⢸⠀⠀⠀⡆
⠀⢸⠀⠀⠄⠁⠀⠀⠀⠑⠕⡄⡀⢸⡗⠡⢠⢀⠈⢰⢄⢀⢠⠮⠊⠀⠀⢀⠀⡐⠡⣏⠀⠀⠀⠀⠀⠀⠐⢅⡌⠠⠀⠀⡇
⠀⠀⠄⠀⠈⠢⢁⠀⠤⠤⠤⠬⠺⠾⠧⠤⠤⠤⠿⠲⠵⠴⠤⠤⠤⠤⠶⠷⠤⠤⠤⠵⠦⠤⠤⠤⠤⠤⠀⡈⠔⠁⠀⠠
⠀⠀⠈⠂⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠐⠁
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠉⠙⠉⠉⠠⠦⠄⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠈⠉⠙⠉⠛⡀
⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠰⠧⠤⠄⣀
⠀⠀⢀⣠⡄⠒⠛⠓⠒⠒⠒⠒⠒⠂⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠑⢢
⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠛⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣌⠳⠆⠈⠉⠉⠉⠉⠠⠾⢋⡴⢆⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠴⠖⠉⠁
⠀⠀⠀⠀⣿⠛⡟⠀⠠⠤⠤⠤⠤⢀⡴⣛⡾⠁⣀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠠⠴⠶⢌⡷⡄⠚⠛⠋⠁⠈⠻⢄⣘⡷
⠀⠀⠀⡌⢿⠏⠀⠀⠀⠀⠀⠀⢀⢮⡙⠁⠀⠀⠀⠀⠀⢰⠄⠀⢴⠄⠀⠀⠀⠀⠀⠈⠳⣡⡄⠀⠀⠀⠀⠀⠀⠹⠇⣴
⠀⠀⣴⠃⠘⠀⠀⠀⠀⠀⠀⢠⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠋⡸⠂⠀⠀⠀⠀⠀⠀⢸⠉⡆
⠀⠀⣅⢠⡆⠀⠀⠀⠀⠀⠀⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣴⠀⠀⠀⠀⠀⠀⢸⠀⡘
⠀⠀⠈⠲⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠟⠁
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠻⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⢰⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢴⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠃⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⢾⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⠓⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣀⠀⠀⠀⠀⠙⠿⣦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⣴⠷⠋⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⡀⠀⠀⠀⠈⠛⠛⢷⡾⠷⠾⠟⠛⠉⠀⠀⠀⠀⢀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠂⢤⣤⡄⠀⢸⡂⠀⠀⣿⠂⢠⣤⡤⠰⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢹⠃⠀⠀⣟⠀⠀⠀⠀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⡁⠀⠀⠉⠉⠉⢹⡇⠀⠀⣿⣉⡉⠉⠉⠀⠙⣧⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⠘⣇⠀⠀⠟⠈⢡⠀⢀⡴⠛⠋⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡌⠀⠀⠈⢳⠄⢀⡜⠛⠳⠤⠀⠀⠈⠾⠯⠤⢀⣸⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣼⣧⣤⡤⠰⠛⠲⠞⠙⠲⠀⠀⠀⠀⠸⠀⠀⠀⠈⠉⠑⠒⢠⣄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠷⠶⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠤⠤⠀⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠈⢤⠤⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⡀⠀⡀⠀⠀⣇⣀⣀⣀⡈⠉⠿⢂⠒⠒⠀⢤⣤⣄⣀⡀⡀⢀⡀⢀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⣟⠉⠉⢻⠋⠹⠟⠛⢩⣽⠛⠏⣭⡅⠴⡉⢹⠖⠒⠐⡟⠈⢿⡁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠒⠋⢉⠉⠹⢇⠿⠲⠶⢶⡄⠀⠀⣰⠴⠶⢧⣸⠇⠀⠈⠙⠆⠛⢃⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⣄⣠⣾⡦⢾⣿⣦⡀⠀⠀⠀⣠⡟⢹⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠠⣿⡟⠛⠿⠀⠙⠁⣠⡛⠀⠱⠀⠀⠀⡛⠁⡾⢷⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣥⠄⠒⠒⠈⢀⣍⠉⠀⢿⠀⠀⣠⠃⢸⠀⠀⠳⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠲⠂⠈⠉⣹⠏⠉⢹⣿⠀⢠⡋⠀⠿⢢⡄⠀⢣⣀⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠛⠉⠠⠷⠤⠰⠾⠛⠳⡄⠙⠾⠆⠾⠇⠀⠈⠁⠖⠁⠶⠶⠄⠀⠀⠀⠀⠠⠶⣷
⠀⠀⠀⠀⠀⠀⢰⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠
⠀⠀⠀⠀⠀⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡄
⠀⠀⠀⠀⠀⡌⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⡀
⠀⠀⠀⠀⠀⠏⠀⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠸⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠧⠤⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⡀⠐⠀⣠⣄⣠⣀⣀⣀⣀⣀⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⢞⣛⡿⢿⠿⣛⣛⣫⣿⣬⡁⣿⡏⣨⣿⣯⣛⣛⣛⠿⠿⢿⣛⠢⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⠶⢂⣀⣀⣀⣀⡰⠶⠬⠓⠉⠘⠫⡴⠖⣀⣀⣀⣀⣀⠶⢦⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⣀⡀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠤⠤⠤⠀⠀⢀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠩⠉⢉⣁⣀⠀⠠⢼⡯⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠉⠐⢄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣒⡒⠒⠆⠀⠀⡜⠧⡀⠰⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠄⠀⠠⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠀⠤⠭⠭⢀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠁⠀⠀⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠉⠉⢁⣐⡒⠢⠠⠭⣁⣺⢀⣀⠀⠀⠀⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣒⡒⠒⠢⠬⠍⣉⣒⠒⠼⣿⠉⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡠⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠤⠤⠤⠭⠍⣁⣒⠂⠠⠬⢹⠿⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠐⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠙⠒⠂⠤⢤⡨⣄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠋⠉⠛⡇⠀⢸⡏⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠋⢻⠀⠀⣿⠙⠛⠋⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢧⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⢼⡇⠀⢸⠀⠀⠀⠀⣠⢾⠀⠀⢸⠀⢀⠀⠀⣠⢾⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠈⠳⠔⠋⢸⡇⠀⢸⠀⠈⠳⠞⠁⢸⠀⠀⢸⠀⠈⠢⠞⠁⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣄⣀⣀⣀⣀⣸⠇⠀⢸⣀⣀⣀⣀⣀⣸⠀⠀⢸⣀⣀⣀⣀⣀⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠤⠤⠤⠤⠤⢤⡄⠀⢠⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡜⢧⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠸⣁⣈⠆⢸⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠦⠤⠬⠥⠤⠼⠃⠀⠸⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋


⠀⠀⠀⠀⠀⠀⣖⣦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⢀⣀⠀⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⢸⠀⡁⠇⢸⠀⡾⡄⡧⢇⠀⠀⡇⠀⠘⠧⡀⡇⢸⢼⢰⠁⢱⣾⢎⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠉⠁⠀⠉⠀⠁⠀⠀⠀⠉⠁⠀⠈⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⡉⠭⠍⣁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠊⠁⠀⠀⠀⠀⠉⢢⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⣂⠉⠉⠉⠉⠉⠉⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡑⢌⠢⢄⣀⣀⠤⢊⠜⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣁⠂⠀⠀⢂⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠉⠉⠉⠢⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⠉⡉⠉⢹⡁⠀⣀⠀⠀⠀⠀⢸⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢤⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⠘⠋⠀⠀⠈⠁⠢⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠂⢀⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠱⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠢⣀⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡎⢐⠄⢀⠠⡀⠀⠀⠀⠘⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⢀⢀⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠃⠠⡄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠰⠒⠉⠑⠂⠀⠁⢠⡍⠉⠒⠊⠉⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⢎⠈⡳⠸⠏⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠋⡀⢸⠀⠀⠀⠀⠀⠀⠀⡠⠋⠑⢌⣉⡥⠚⠀⠤⢄⡀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢄⠀⠀⠀⠀⠁⠀⡀⠀⠀⠘⠤⢂⢌⠔⠀⢸⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢀⠌⠀⠀⠀⠀⠀⠈⠑⢠⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠈⠢⣑⠤⣀⠀⠀⢎⡰⠀⢀⡠⢐⠥⠊⠀⠀⢸⠀⠀⠀⠀⢠⣎⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠙⡀
⠀⠀⠀⠀⠀⠘⡤⠤⠤⠤⣬⠃⠀⠀⠀⠁⠒⠨⠭⠬⠭⠭⠐⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠪⣓⢦⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠱
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠇⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠈⢁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀
⠀⠀⠀⠀⠀⡰⠡⢤⠬⠥⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠂⡶⡰⣒⠂⠲⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⡜
⠀⠀⠀⠀⡰⠱⠁⠀⠠⡄⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠃⡣⡘⣢⡀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠤⣀⠀⢀⠔⠁⢀⠜
⠀⠀⠀⠰⠡⠃⢀⡀⠀⠀⠀⠐⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠛⢊⡁⠈⠓⠤⣀⠜⠁⠀⠀⠀⠀⠀⠀⠑⡁⠀⡠⠊
⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠲⢄⡀⠸⠀⠀⠀⠔⠁⢑⠀⠀⠀⢰⠈
⠀⢀⢂⠂⠀⠀⠀⠀⠰⣉⡁⠀⠀⠑⡐⡤⠠⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠸⠤⠤⠀⠤⠄⢤⠀⠀⠀⢙⠀⠀⠀⠈⠐⠈⠀⠀⠀⢸
⢀⢂⠂⠀⠘⠃⠀⠀⠀⠀⠀⠰⠉⠆⠱⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣆⣘⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣁⣵⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⣠⣾⠿⣛⣻⣛⡻⣿⣦⠀⠀⠀⢀⣴⣿⢟⣻⣿⣛⢿⣷⡄⠀⠀⠀⢠⣶⣿⣿⠇⢿⣿⣷⣦⠀⠀⠀⠀⣴⣿⢟⣿⣿⣟⡿⣷⣄
⠀⢰⣿⢣⣾⣿⣿⣿⣿⣮⢻⣧⠀⠀⣾⡟⣵⣟⠋⠉⢛⣷⡝⣿⡆⠀⢰⣿⣿⣻⣾⣷⣿⣾⡻⣿⣷⠀⠀⣼⡿⣽⡿⣟⣛⣿⢿⣞⣿⡆
⠀⢺⣿⢺⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⣿⡿⣿⠀⠙⡎⠁⢸⡗⣿⡇⠀⢸⣭⣅⣽⣿⣿⣿⣿⡅⣭⣽⠀⠀⣿⡇⣿⣿⣗⣷⣾⣿⡿⣿⡇
⠀⠘⣿⣮⡻⣿⣿⣿⠿⣣⣿⠏⠀⠀⠹⣷⣝⢷⣦⣧⣶⢟⣵⡿⠁⠀⠈⢿⣿⣾⣻⠟⢿⣻⣾⣿⠟⠀⠀⠹⣿⣝⢿⣿⣿⣿⢟⣵⡿⠁
⠀⠀⠈⢿⣿⣷⣶⣶⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣶⣶⣾⣿⡟⠁⠀⠀⠀⠈⢻⣿⣿⣇⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣿⣶⣶⣾⣿⡟⠁
⠀⠀⠀⠀⠹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠩⠅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠛⠤⠰⠾⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠯⣄⠀⠐⢶⡔⡿⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠍⡀⠀⠀⠀⠀⠉⠁⠠⡀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡴⠁⠀⠀⣑⠢⡄⠠⠆⠉⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢤⠘⠀⠀⠀⠀⠀⢀⠂⠀⢣⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢀⠐⣀⠀⠀⠂⡼⠁⠀⠀⠂⠀⡐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠀⡰⠂⡀⠈⠂⠀⠀⠀⠀⠄⢤⢀⡎⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠢⠤⢴⠁⠀⠀⠀⠀⠀⢁⠀⠀⠉⠉⠀⠢⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢛⠣⡀⠶⢴⠁⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⢀⣀⠳⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡦⢬⡂⠈⢅⠀⠀⢀⠀⠀⠀⠀⠈⠙⠶⡬⠖⠁⣠⠃⠐⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠈⠀⢘⠀⠑⠀⠀⠀⠀⠀⠉⠲⠽⣞⠕⠁⠀⠠⠀⠁⠒⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢰⢄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠀⠀⠀⠀⠀⡰⢧⡌⠉⠂⠌⡒⠄⠀⠀⠁⠀⠀⠚⠀⠀⠉⠁⢀⡤⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⢸⠉⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⠂⣁⠀⠀⠠⡄⠀⠀⠀⠐⠂⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠀⢀⠈⠣⣀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢄⠀⠀⠀⡼⠀⠀⢸⠀⠈⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⠁⠀⢰⠃⠀⠀⠈⠁⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⠒⠐⠀⣠⣀⢘⠀⠀⠀⠀⠊⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣠⡦⢀⠠⣤⣤⣬⡏⠤⠌⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠷⣚⣧⠴⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣺⣭⠿⠷⠶⠶⠾⠯⣿⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡫⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠔⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⣯⢧
⠀⠀⠀⠀⠀⠀⢀⡴⣞⣯⣾⣷⠶⠶⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣄⢸⡾⡆
⠀⠀⠀⠀⠀⢀⣏⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⡁⠀⠀⢻⡿⢻⣿⢣⠇
⠀⠀⠀⠀⠀⠘⣎⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠛⠀⠀⠈⣿⡾⣿⣘⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠈⠑⠲⡯⣿⠀⠀⠀⠀⠀⠀⠀⠒⠛⢡⣿⡅⠀⠀⠀⠀⢸⣿⡿⡡⢀⢹⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣿⡇⣴⣿⣿⡶⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣿⡿⠈⣼⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⡇⠈⠁⢸⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠃⠀⣼⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⣆⡇⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡼⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⡇⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣷⠀⠀⠀⡤⠘⠃⠂⠐⠛⠉⢙⠢⡀⠀⠀⠀⢀⡀⣷⣬⣭⣭⣟⢦
⠀⠀⠀⠀⣠⢖⣻⣭⣽⣗⢿⢻⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢆⠙⣤⠄⢲⡀⠠⠤⠤⠄⠀⣿⣸
⠀⠀⠀⡼⡷⢩⠋⠀⠂⡍⢷⡤⡽⣦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢦⠈⠓⠸⡄⠀⠀⠀⠀⢠⡟⣿
⠀⠀⠐⣷⡇⢠⠀⠀⠀⠐⢸⡇⡿⢮⡳⣤⡀⠀⠀⠀⠘⢧⠀⠀⢘⠳⣄⡀⠙⠀⠀⠀⢀⠞⢳⡞⡆
⠀⠀⠀⢳⡳⣄⠑⢦⠶⣣⡾⣳⠃⣰⢣⣿⣿⣶⣤⣀⣀⣀⣳⡀⠈⣆⠀⠉⠐⠛⠓⠛⠁⡴⠻⣞⢧
⠀⠀⠀⠀⣹⢞⣹⡧⣾⢻⣜⡇⠀⠈⠓⠮⣽⢛⣿⣿⣿⣿⡏⡁⠀⣏⠁⠀⠀⠀⠀⠀⢀⡆⠀⠘⣯⢣
⠀⠀⠀⢸⡷⣏⣡⡕⢸⠈⢧⡳⣤⢤⣖⣫⣶⣿⣿⣿⣿⣿⣟⣇⠀⠹⡦⠀⠀⠀⠀⠀⢨⢳⡀⠀⠘⣯⢧
⠀⠀⠀⠐⡗⣯⡤⢮⠸⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣏⠠⠀⠙⠦⣄⡀⠀⠀⠀⠀⡅⠀⠀⢸⡎⡆
⠀⠀⠀⠀⢯⢻⡄⢛⣶⠀⠀⠈⠉⠛⠟⠀⠈⠛⠻⠿⠛⠉⢰⠘⢄⣀⡠⠀⡀⠉⠉⠒⠒⠶⡆⠀⠀⣼⣿⣸⡀
⠀⠀⠀⠀⠀⠳⣽⣟⢻⠁⠙⠺⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⡼⠃⠀⡰⢻⣿⣧⢧
⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⡜⠀⠀⠀⠀⢠⢞⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠁⠒⠛⠀⠖⠋⠀⣿⣿⣿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢯⡳⠾⠶⣶⣶⣶⠒⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣿⣿⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢟⣾⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠴⣺⣵⣾⣿⣿⡟⣠⠁⠀⠀⠋⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣎⢿⣿⣿⡿⢟⣉⣏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⣿⣿⣿⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⠭⠭⠖⠉⠳⣝⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⣿⣿⣿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠯⣽⣟⣲⡶⠦⣤⣤⣬⣥⣤⣴⣦⣭⣤⠤⢶⡖⣿⣿⡿⣣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠒⠒⠒⠛⠛⠋⠉⠙⢾⣫⠞⠁