Abjad Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⢠⣀⢀⡀⠀⠀⠀⠀⠀⣠⣄
⠀⢠⣶⣦⠀⠀⣤⣄⣸⣯⣹⣷⣤⣀⣠⢤⡀⣸⣿⡿⡻⠿⠿⡟⣿⡿⢷⣤⣴⣶⣦⣀⣹⣿⣄⡀⢀⠀⠀⠀⠀⠠⣶⣶
⠀⠈⠙⠁⠀⢀⡽⠟⣛⣛⣛⠻⢯⠕⠒⢈⡯⠵⣜⠕⠁⠀⠀⣇⣙⣁⠀⠀⢩⡭⠁⠀⠀⠨⣩⡭⠂⢻⣿⣿⡞⠀⣭⣅
⠀⢠⣶⣦⣰⢏⡔⠋⠀⠀⠀⠀⢸⠀⠀⠚⠁⠀⠀⢀⠀⠀⢰⠃⠀⡸⠁⠀⡏⠀⠀⢀⣄⡀⠀⠱⠀⠀⢻⣿⣮⣇⣛⣋⣀
⠀⣬⣿⣿⣿⠈⠀⠀⠀⣶⣶⣤⡀⠀⠀⣀⣀⠀⠐⡏⠠⢠⣏⠀⢰⡇⠀⠀⣷⣄⠀⠈⠻⣿⣆⠀⠀⠀⠠⢻⣿⣿⣿⣿⣿⠇
⢠⢶⣼⢿⢻⣎⢄⠀⠀⠙⠛⠟⠛⠛⠛⠉⠙⢧⠀⡅⠀⠺⠿⠀⠀⡸⠀⠘⠉⠀⠀⠹⠦⠀⠙⢲⣶⣶⠟⣼⣿⣿⣿⣿⣿⣶⡄
⠀⣾⣏⠻⣽⣸⣷⣝⢶⣶⣶⣶⣾⣿⠇⠀⠀⣸⠀⢳⣤⣤⣤⣤⡀⠘⠲⣶⠆⢰⠁⠀⣠⣤⣀⣼⠿⠿⢌⢻⣿⣿⣿⣿⣿⣏
⠀⢿⣿⡞⡇⢦⣹⡿⢣⠟⡥⢰⡿⠃⠀⠀⡴⠋⠀⠉⠁⠀⠈⠹⠿⠆⠀⡎⠀⢸⠆⠀⠈⠙⠛⠿⣖⠲⣀⢳⡹⣿⣿⣏⣿⣿⣧
⠀⢾⠏⣿⣿⣿⡟⡱⠋⠉⠀⠈⠀⠀⣠⠞⠁⠀⠀⠐⢋⣹⣄⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⣀⡀⠀⠈⠀⠀⠀⠱⡝⣷⣯⣿⣿⠃
⠀⠀⣰⣿⣿⢏⡞⠁⣀⣀⣠⣤⣤⠶⢿⡶⠶⠶⠒⢾⣿⣿⣿⠟⡶⣶⣾⣶⡶⠖⠶⢦⣤⣾⣿⣦⣀⣀⣀⡀⠀⢙⡌⣿⣆⡉
⠀⣰⣿⣿⣿⣶⣝⠿⣿⣉⡉⣀⣀⣤⠤⠿⠶⠒⠀⣚⣛⣩⣙⠛⠓⠛⣛⠛⠓⠒⠚⢋⡜⠿⢯⣤⣤⣈⣉⣉⡿⣫⣾⡟⠿⠃
⠀⢈⡉⠙⠿⠟⠿⣿⣮⣍⣭⣤⣶⣶⡖⠉⠹⢿⣿⣿⣿⡿⢛⣩⣻⣿⡿⠏⠉⠉⢿⣿⣿⣿⣶⣶⣶⣭⣭⣋⣼⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⡿⠟⠁⠀⠀⠀⠀⠀⠉⠁⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠉⠉⠘⠻⠿⠿⠟⠉⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⢀⡎⠉⠉⠀⢃⠀⠀⠀⠀⠀⡄⠐⠚⠒⠒⠒⠠⠤⡀⠀⠀⠀⠀⠀⣠⡴⠒⠒⠒⠒⠒⠀⡄⠀⠀⠀⢠⠚⠛⠋⠀⠒⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠤⢄⠀⠀⠈⢦⠀⠀⠀⢸⠏⠀⠀⠀⣀⣤⣄⢀⣾⠀⠀⠀⢸⠂⠀⢀⡤⢤⡄⡀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⢹⡀⠀⠀⠀⠃⠀⠀⠘⠒⠊⠀⠀⣀⣼⠇⠀⢀⡇⠀⠀⠀⡞⠁⠀⠀⠈⠉⠀⠀⠀⣾⠀⠀⢸⡇⠀⠉⢷⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠤⡆⠀⠀⢧⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠋⠛⢷⡀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⡿
⠀⠀⠀⠀⡼⠀⠀⠀⣀⣀⣀⠀⠀⠈⡇⠀⠀⡇⠀⠀⢘⡁⠈⡦⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠳⢄⣀⣀⣀⣠⠀⠀⢠⡟⠀⠀⢸⣀⣀⡤⠞⠀⠀⢀⡗
⠀⠀⠀⠀⠃⠀⠀⠜⠉⠉⠉⢆⠀⠀⠙⠀⠀⠃⠀⠀⠀⠈⠁⠀⠀⢀⡸⠃⠀⠀⠈⢲⡀⠀⠀⠀⠈⠉⠁⠘⠀⠀⢸⠇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠚⠶⠶⠖⠂⠀⠀⠀⠘⠒⠒⠒⠂⠀⠀⠒⠐⠒⠲⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⠦⠔⠐⠋⠀⠀⠈⠑⠒⠒⠒⠒⠲⠶⠚⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠉⢹⡆⠀⠀⠀⣿⠉⠉⣷⠀⠀⠀⢰⡏⠉⠉⠀⠀⠀⠀⣿⠉⢹⡆⠀⠀⠀⣾⠉⠉⠁⠀⠀⠀⢰⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⠛⢻⡇⠀⠀⠀⣿⠛⠻⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠛⠛⠛⠀⠀⠀⢸⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⠇⠀⠀⠀⢿⣶⡶⠋⠀⠀⠀⠘⠷⠶⠶⠀⠀⠀⠀⠿⡶⠾⠃⠀⠀⠀⠙⠶⡶⠦⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠆⠀⠀⠀⣶⠀⠀⣶⠀⠀⠀⠰⠶⣶⠶⠀⠀⠀⠀⠀⠶⢶⡆⠀⠀⠀⣶⠀⠀⣶⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⡀⠀⠀⠀⣿⣄⣠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣄⣠⡟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠁⠈⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠁⠈⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠛⠀⠀⠛⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠙⠀⠀⠛⠀⠀⠀⠘⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⣿⢷⢿⡇⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⢠⡞⠛⣷⠀⠀⠀⠀⣿⠛⢳⡄⠀⠀⠀⣴⠛⠛⣦⠀⠀⠀⢸⡟⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠻⣦⣿⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠶⠞⠁⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡷⠶⣟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠸⢧⣤⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣤⣤⡟⠀⠀⠀⢸⡇⠀⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⢠⡄⠀⣠⠀⠀⠀⠀⣄⠀⢠⡄⠀⠀⠀⣤⠀⠀⣤⠀⠀⠀⢠⡄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠸⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡾⢷⣿⠀⠀⠀⢠⡟⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠞⠁⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⠳⠶⠋⠀⠀⠀⠀⠙⠷⠟⠁⠀⠀⠀⠿⠀⠀⠿⠀⠀⠀⠸⠇⠀⠺⠂

⠀⠀⠀⠀⠀⠀⠀⣷⠀⢰⡆⠀⠀⠀⠺⠶⢶⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣤⡼⠃⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⢸⣿⣿⣿⣿⠇⠀⢀⣤⣶⣾⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣿⣿⣿⠟⠛⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⡀⠀⣸⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣦⣌⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢈⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠠⢾⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⠶⣤⣤⣤⡀⠀⠀⠀⠀⠹⣿⣿⣦⣶⣿⣿⣿⠇
⠀⠀⠀⣀⣀⣀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⢀⡴⠋⠁⠀⢼⡿⠀⠀⠈⠹⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⠿⠟⠋
⢀⣴⣿⣿⣿⣿⣿⣄⠀⣿⣿⡇⠀⠀⠀⠀⣾⠁⠀⠀⠀⣾⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿⣿⣧⡀
⣿⣿⣿⣿⣿⠋⠉⠟⠀⣿⣿⡅⠀⠀⠀⠸⡿⠃⠀⠀⠀⣿⡇⠀⣀⣠⠼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣦⡀
⢻⣿⣿⣿⣿⣦⣤⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠉⠁⠀⠈⢉⣿⣿⣿⣷⡀⠀⠀⠀⣠⣤⣴⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣶⣶
⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⣿⣿⣿⣿⣧⣄⣠⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⡿⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠙⢿⣿⣿⣧⡀⠀⠛⢿⣿⣿⣿⠿⠋
⠀⠀⢻⣿⣿⣿⣶⣷⠀⠀⠙⠻⠿⣿⠿⠉⠁⠀⣹⣿⣿⡟⠛⠛⠛⠉⠉⠀⢠⣾⣏⠀⢈⣿⣿⣿⣷
⠀⠀⠀⠙⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢀⣶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣀⠀⠀⠀⠀⣠⣤⣄⠀⣤⣶⣾⣿⣼⣧⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡀⠀⣿⣄⣀⡀⣼⡏⠉⠛⢸⣯⡀⢸⣿⢻⣇⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣾⣷⠖⢸⣏⠉⣿⠞⢷⣤⣾⠃⠙⣻⣟⠋⠀⠛⠛⢁⡀⣠⣤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣶⣿⡄⠈⠿⠟⠋⠀⠀⢠⡄⢀⡘⣿⠙⣷⣰⡿⣷⡿⣿⡟⢹⡇⣤
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣞⠃⠀⠀⠙⢋⡀⠀⠰⣿⣴⣶⡼⣷⣾⡏⠹⣧⣿⡟⠁⣿⡇⠿⠇⠸⣿⠟⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⣰⡟⢈⣿⢰⡿⠻⣧⣸⣧⣴⣤⢰⡆⢸⣯⣿⣿⣤⡀⠈⣿⢷⣦⠙⠁⣠⡶⠶⢶⣦⣴⡟⠁
⠀⠀⠀⠀⠀⠀⣿⣃⣾⣏⡘⢷⣶⢿⣿⣿⠁⢻⡿⣷⢸⣿⣿⡆⠉⢋⣀⠉⢠⣤⣄⠰⣿⣀⣤⣤⣼⠋
⠀⠀⠀⠀⠀⣤⣿⡿⢿⣍⢰⣆⠀⢈⣿⠉⠀⠘⠃⣉⣼⠇⢠⣴⣤⡛⠻⣧⣿⢁⣿⠆⣩⣭⡅⠀⣽⡇
⠀⠀⠀⠀⠀⠁⠘⣷⣤⡿⠀⠻⠷⠾⠋⠘⠛⠛⠛⠋⠁⢰⡿⢿⡍⣿⡀⠹⣿⡀⠀⠀⢿⣤⣤⡾⠋⢀⣴⠾⠟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣉⡁⢀⣴⣶⣦⣄⠀⣀⣺⣷⡿⣷⣼⡇⠈⠻⣿⣇⡀⠹⠇⢀⣀⡀⠀⠀⣶⡄⣿⡁⠀⠀⣿⠃
⠀⠀⠀⢠⡾⣷⢀⣾⢻⣷⣾⠏⠿⣦⣿⣿⠛⣿⣿⣤⡿⠛⢿⣦⡾⠏⠉⠋⢀⣴⠟⠛⣿⡄⠀⣿⣷⠈⠃⠀⣸⡏⠀⠀⣶⡀
⠀⠀⠀⠀⠀⣿⣿⠃⢸⣿⢿⣆⠀⠀⣸⡟⠀⣿⡏⠁⠀⠀⠀⣠⣶⠀⠀⠀⠉⣡⣤⡄⢸⡇⠀⣿⢻⣇⠀⢀⣿⠁⠀⠀⣸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⢸⣷⠌⠛⠷⠾⠛⠁⢀⣹⡁⠀⣤⡀⠀⣿⡄⣴⠟⠷⣾⡏⠘⣿⠈⠻⠾⠋⠀⢻⡆⣼⡇⣀⣴⠾⠋
⠀⠀⠀⠀⠘⠟⠀⠀⣈⣭⣤⠀⠀⠀⠀⣼⣟⣭⣄⠀⣿⢿⡄⢸⡟⠋⠀⣸⡟⠻⣦⣿⠀⣠⡶⠿⢷⣎⣿⠙⣛⣫⣥⡶⠾⠛⠁
⠀⠀⠀⢀⣠⣤⣶⣿⠋⠉⠶⠟⣿⡄⠀⣿⠈⠉⣿⣸⡟⠈⢿⣼⣷⠀⠀⠟⠁⠀⠀⢁⣾⠋⢠⡾⢠⣿⣿⡎⠋⠉
⠀⠀⠀⠈⠉⠀⢸⡇⣤⠀⠰⣷⠘⣷⢠⣿⠀⠀⢸⣿⡇⠀⠀⠻⡿⠀⠀⠀⠀⢀⡀⢸⡇⠀⠘⠻⠛⣡⡿
⠀⠀⠀⠀⠀⠀⢸⡇⢿⡇⠀⢹⣇⢹⣿⡏⠀⠀⠘⢿⠃⠀⠀⣀⣠⣤⣶⠾⠟⠛⠁⠘⢿⣦⣤⣤⡾⠛
⠀⠀⠀⠀⠀⠀⢸⡇⠸⣧⣀⣸⡟⠀⠻⠃⠀⣀⣠⣤⡶⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⣉⣠⣤⣶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠟⠛⠉⠁

⠀⠀⠀⠀⠀⢀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⡀⠀⠤⠄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣤
⠀⠀⠀⠀⠔⠁⠀⡇⠀⠈⢆⠀⡄⠈⢠⠀⠀⠐⠈⠀⠀⠴⠀⠀⠘⡆⠀⣠⣄⠀⠀⠈⠀⠀⡀⠀⠀⠆⠘⠁⢀⠤⠂⣀⡽⢀⡔⠀⠀⠀⠐
⠀⠀⠀⠈⠀⣴⠀⢻⡀⠀⢸⠀⢐⣃⠀⠁⠈⠀⢀⡎⠀⠀⠀⠠⠀⡇⠀⠻⠂⠀⡀⠀⠀⣈⠁⠂⠀⠀⠀⠀⢉⣰⠈⠁⣠⠋⠀⠀⡀⠲⢶⡀
⠀⠀⡀⠀⠀⡀⠀⣀⠑⠄⠘⠀⠘⠃⣠⠂⠠⠀⠀⠛⠒⠒⠀⠀⠀⡇⠀⢀⡠⠎⠀⢀⠀⠚⣀⣀⢀⠀⠐⡀⠙⢦⡀⠀⠙⠢⡄⠀⠉⠀⠀⡼
⠀⠀⣇⠠⠜⠘⠋⠉⠀⠀⠴⠤⠒⠁⠀⠀⠀⠈⠂⠀⠤⠤⠀⠀⠰⠷⠚⠉⠀⠀⠀⠴⠒⠉⠀⠀⠀⠀⠀⡷⠚⠉⠀⠀⠀⠀⠙⢦⠄⠀⠁
⠀⠀⢡⠀⠀⠠⠄⠀⠠⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠠⠄⢀⠂⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⡀⡆⠀⠀⠀⢠⠆⢀⡀⠠⡀⠀⠀⠀⠀⢀⠀⠀⡏
⠀⠀⠀⠇⠀⡥⠀⠀⠂⠀⠀⠀⠁⠸⠀⠀⢀⢠⠁⠀⠀⠉⠀⢠⠀⠀⠸⠁⠀⠀⠈⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠸⡄⠁⠀⠐⣼⠀⢸
⠀⠀⡜⠀⠀⣀⡀⠀⠂⠀⠀⢠⠀⠀⢃⠀⠀⠰⣄⠀⠸⡄⠀⠸⣇⠀⠀⠀⠚⠲⢤⣀⠀⠀⠰⣇⣀⠀⡆⠀⡀⠀⢀⠀⠀⠷⠀⠀⢠⡈⠀⡀
⠀⠀⠇⡀⢸⠁⠘⠦⠤⠤⠀⣇⠀⠀⢸⢠⠁⠀⠀⠀⠀⣸⠀⠀⡏⠀⢰⣆⠀⠀⡠⢁⠀⠀⠀⣀⣀⣀⡇⢀⣷⠀⣸⠗⠒⠁⠈⠦⡈⣇⠠⡇
⠀⠀⠘⠉⢉⠔⠒⠒⠠⡄⡀⠈⠀⣉⣤⠤⢬⡁⠀⠁⠈⣠⠄⠀⠄⠀⢈⡁⠵⠎⠠⠌⣀⠀⠀⠀⠀⠀⠁⠈⠙⠉⠀⡄⠀⠤⢀⣀⣤⠭⠤
⠀⠀⠀⡰⠋⠀⣀⠄⠀⡇⠈⠉⠉⠁⠀⠀⠀⠹⡄⣠⠞⠁⠀⠀⠀⠁⡻⠀⠀⢠⣄⠀⠀⢱⠀⠀⠀⠀⠀⣀⡤⠤⠚⠀⠀⠀⢀⠀⠀⣀⣀⣸
⠀⠀⢾⠀⠀⢸⡟⠀⠐⡇⠀⠀⠀⠀⣦⠀⠀⠰⣴⠋⠀⢴⣦⠀⠀⢠⢁⠀⠀⠘⠟⢀⡠⠊⠀⠀⡀⠀⣈⠉⠁⠉⢙⡆⠈⠉⣙⠀⣀⠁⠀⠁
⠀⠀⠘⣆⠀⠀⠀⠀⢀⠇⠀⡀⠀⠐⠉⢀⠐⠁⠁⠀⠀⠀⠀⣀⠐⠁⠈⠀⠀⠀⠈⠁⠰⢀⡀⣀⠉⠙⠙⢁⣠⡴⠋⠀⠀⢰⠃⠸⢿
⠀⠀⠀⠀⠀⠄⢀⠞⠁⢀⡜⠀⠀⠻⠀⠀⠀⠀⠐⠠⢴⣀⠤⠖⠀⠀⠰⠶⠒⠖⠑⠦⠚⠁⠠⠥⠶⠆⠀⠉⠉⠀⠀⠀⢠⠤⠴⠶⠾⠷
⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⢀⠀⠀⡠⠐⠆⠀⢀⠄⠠⢠⠄⠐⠒⠊⠉⣱
⠀⠀⢀⠀⡀⠀⠀⠀⢂⠀⠐⠄⠈⠀⠠⠂⠀⠀⠀⠤⡀⠱⢀⠠⡄⠰⠀⠀⠀⠡⠀⠈⠁⣀⡤⠖⠈⠀⠁⠀⢸⡴⠏⠀⠄⠞⠀⢀⣀⠀⣀⠏
⠀⠀⠀⠀⠻⠦⠴⠁⠀⠑⢄⠘⡀⠘⠁⡠⠊⠀⠀⠀⠐⠀⠏⠀⠁⠀⠡⠀⠈⠀⢀⡀⠀⠉⠢⢀⠀⠀⢹⡀⠀⣀⠀⡠⠂⠰⢊⠟⢁⢈⣀
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⡠⠊⠙⠦⡀⠀⠀⠀⠀⠀⠑⢈⠃⣰⠁⠀⡴⠃⠀⠀⠀⠀⡏
⠀⠀⠁⠀⣀⠀⢀⡀⠤⠂⠁⠀⠀⠈⠢⣇⠀⠀⠀⠀⠠⠤⠞⠉⠙⠛⠓⠒⠂⠉⠀⠀⠀⠈⠒⠤⠊⠀⣐⠡⠔⠒⠋⠀⠀⠗⠂⠉⠉⠉⠛⠆

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⡆⠀⠆⠀⠀⠀⢰⡆⠈⠃⠄⠀⠀⠌⠀⠀⠑⠁⠀⠀⠂⠀⠀⣠⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠉⡁
⠰⠁⢠⠠⠀⠀⠀⠘⠀⠐⠆⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠃⠀⠂⠋⠀⠀⠀⠀⠀⠉
⠞⠒⠀⠐⠀⠂⠀⠐⠃⠀⠐⠊⠀⠀⠀⠈⠂⠐⠂⠀⠀⠀⠀⠀⠒⠁⠀⠀⠊⠒⠒⠒⠀⠀⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠀⢀⡀⠀⠀⠀⢸⠀⠀⢨⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⠰⠀⢀⠄
⣎⠀⢠⠀⠀⠀⠀⢸⠀⠠⢤⠀⠀⠀⠈⢹⠃⠈⠁⠀⠀⠀⠁⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄
⠁⠀⠈⠉⢁⠀⠀⢸⠀⠀⢸⠀⠀⠀⢀⠘⠂⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠸⠀⠸⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠑⠈⠀⠀⠈⠉⠐⠐⠁⠀⠀⠛⠉⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠁
⢀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡉⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⢳⠀⠀⠀⡎⠀⠐⢤⠀⠀⠀⢀⠀⠈⠙⠀⠀⠀⠎⠀⠐⠂⠀⠀⠀⠘⠀⠀⠚
⢁⠀⠸⠀⢚⠀⠀⠀⡅⠀⢁⡀⠀⠀⠀⢃⠀⠀⠸⠀⠀⠀⠸⡀⠀⠒⠋⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⡆⠀⡆⠈
⢰⣤⠀⠀⢸⠤⠀⠀⡷⠀⠀⢴⠄⠀⠀⠐⠀⢀⠀⠔⠀⠀⢸⣥⠄⠀⠀⠀⠀⠀⠀⠀⠤⡦⡠⠀⠸⡧⠀⠘⢠

⢠⠀⢠⡀⠀⠀⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡔⠀⠀⠠⠀⠀⠰⠄⠀⢀⠂⠀⠀⢰
⠐⠄⠄⠉⠀⠀⠉⢸⠀⠈⠀⠀⠀⡃⠀⠀⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⡧⠀⠈⠀⡀⠀⠇
⠔⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠅⠀⠀⠁⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⡀⠀⠀⠡⡀
⠀⠀⠀⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠘⠚⠁⠀⠀⠀⠈⠁⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⡀
⠠⠀⠀⠁⠀⠀⠀⠁⡠⠀⠃⠀⠀⠀⠃⠀⡖
⠀⡐⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠄
⠴⠤⠀⠁⣀⡀⠀⠀⠀⣴⠀⠀⠀⢀⠂⠀⠀⢀⡠

⠀⠀⠀⠀⠀⠈⠉⠉⠳⢄⠀⠀⠀⠀⠀⠀⠉⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⣀⡀⠀⠀⡀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣤⣹⠇⠈⡁⠀⠀⠀⠀⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠄⠀⠀⡿⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢦⡀⠁⠀⠀⠀⢰⣆⣀⠀⣼⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡆
⠀⢀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠈⠙⠛⠛⠛⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇
⠀⠘⠀⠀⢀⣀⣨⡅⠀⣇⣀⣀⣀⣨⡇⠀⠀⢀⡀⠀⣀⣀⣀⣀⠴⠞⠁⠣⡀⠀⠀⠀⠀⣠⣄⣤⡿⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⣀⣠⠤⠴⠟
⠀⠀⠙⠋⠉⠁⡀⠀⠢⣄⠀⠀⠀⠉⠁⠀⠀⢀⠼⣏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠁⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢢⣤⠐⠈⠁⠀⠀⠈⠁⠒⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⢀⣀⠀⠒⠈⠁⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠾⢳⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢸⠇⠄⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠻⣍⠉⠉⠛⠁⠀⠀⠀⠀⠀⣠⡄⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⡾⠁
⠀⠠⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⠸⣆⠀⠀⠡⡀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠿⣘⡛⠛⠋⠐⡦⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⢸⡇
⠀⠐⢠⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠿⠀⠀⠀⢁⠀⠀⠀⠀⠀⢿⠁⠀⠀⢂⡀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⠉⠀⠀⠀⣸
⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠴⠤⠾⠃⠀⠀⠀⠉⠒⠶⢶⠶⠛⠃⢤⠠⠾⠃⠀⠐⠤⠶⠚⠋⠀⢩⡂⠉⠋
⠀⢀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠂⠀⢲⡄⠀⠀⠀⢸⡆⠀⠀⠈⠁⠐⢲⡄⠠⠀⠐⠂⠀⠀⢀⡟
⠀⠀⠀⠀⠀⣀⣀⣤⡶⢋⡀⠀⠀⠀⠀⠁⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡞⠀⠆⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠈⡉⠉⠀⠀⠀⠳⡄⠀⠀⠐⠤⠤⢄⡀⠀⠀⠀⣠⠴⠦⠴⠟⠀⠀⠀⠀⠀⠻⠂⠀⠀⢠⡾⢀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⣃⣀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⣸⡏⠉⠀⠂⠀⣀⡀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣀⣀⣠⡇⠀⢀⣀⣤⡴⠟⠒⠒⠶⠒⠤⢤⣀⣀⡀⠀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠐⡇⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠉⠁⠀⠒⢢⡄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠹⡆⠘⠀⠀⠀⠙⢀⠀⢁⠀⠀⠀⠀⣿⠀⠀⠄⠀⠀⠀⠀⠀⠸⠧⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠐⢶⠀⠀⠀⠀⡞⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠠⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠟⠀⣰⠀⠀⠀⢸⡇⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠘⡆⠀⠑⣀⠀⠀⠀⠈⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢼⠂⠀⣰⠟⠀⠀⠀⢈⡇⠀⠀⠀⠻⡀⠁⡀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⠇⠀⠀⠈⠆⠀⠀⠀⢰⡟⠛⠁
⠀⠀⣀⣠⣤⠿⠁⠚⠃⠀⠀⠀⠀⢘⠷⣤⠴⠶⠾⠃⠀⠀⢤⣄⠀⡼⠃⠀⠢⣀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠸⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠒⠀⠀⣼⠉⠉⠉⠉⠀⠀⠀⡀⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠰⣾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠒⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠂⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⣴⠒⠄⣀⡶
⠀⠀⠁⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢳⡜⠀⠀⠀⠀⠉⠀⠀⠠⠿⠡⣤⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠒⠠⣄⠀⠰⠤⠼⠃⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⣾⠀⠈⠁⠤⠤⠀⠘⠛⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠒⠀⠀⠀⠀⠘⣦⡁⠀⠀⠀⣿⠀⠂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆
⠀⠀⠀⠑⠲⠶⠶⠶⠛⠉⠲⠞⠁⠀⠀⠘⠶⠖⠚⠋⠉⢡⡴⠶⠶⠏⢀⠀⠀⠀⠀⠀⠉⠀⠤⣤⣴⡶⣍⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠘⠗⠂⠈⢳⡀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⡼⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⢸⡀⠀⠄⠳⡄⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠄⠂⠁⠀⢱⠀⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠉⠀⠀⠐⠂⣿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⡗⢲⡇⠀⠀⠉⠙⣏⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡼⠋
⠀⠀⠂⠀⠀⠀⠀⢰⡿⠂⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⠁⠀⠟⠀⠀⠀⠀⡏⠀⠀⠠⠀⠀⠀⠀⠀⢰⠋
⠀⢠⠀⠀⠀⠀⠀⣀⣴⣆⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣰⢆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀
⠀⠈⠂⣀⣠⣴⠞⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣤⣀⣤⠤⠞⠀⠀⠀⠠⣤⣤⣤⡟⠀⣄⣀⣀⣀⣼⠁⣀⣀⣀⣴⠋⠀⠀⠀⣠⡤⠞
⠀⠀⠀⠈⠉⠉⠈⣷⡀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢧⡀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠉⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣄
⠀⠀⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢸⡇⠀⠀⠘⠶⠛⢁⡤⠾⠋⠲⡄
⠀⢠⣀⣀⠀⠰⠚⠛⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⠋⠋⠈⠀⠀⠀⠐⢄
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⢠⡞

⠀⠀⠀⠀⠀⠀⢠⠤⠶⠶⠶⣶⠖⠆⠀⠀⠀⡠⠴⠶⠖⠒⠛⠩⠟⣁⠒⢄⠀⠀⠀⠀⠀⢀⡠⠴⠖⠒⠿⢍⡘⠲⢄
⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⢸⠀⢳⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠈⠆⠈⡄⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠘⢆⠘⡆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠘⡂⢸⠀⠀⠀⡇⠀⠀⢸⢀⡹⠂⠀⠀⡏⡰⠀⠀⠀⠀⠇⠀⠀⡰⢉⠏⢠⣀⠠⠼⠔⠃
⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⡇⢸⡀⠀⠀⡇⠀⠀⠈⠁⠀⢀⣠⣾⡯⢤⣀⠀⠀⢰⠀⠀⢠⡅⢸
⠀⠀⠀⠀⡸⠀⠀⡜⡄⠀⠀⠀⣁⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠳⡀⢸⠀⠀⢸⡀⢼
⠀⠀⠀⢀⡇⠀⢰⡡⡇⠀⠀⠀⢩⠀⢇⠀⠀⡇⠀⠀⢠⡒⢲⠲⡄⠀⠀⠀⢱⠀⠃⠘⡀⠀⠈⡆⠘⡆⠀⣠⡤⡤⣤⡀
⠀⠀⠀⡸⠀⠀⠈⠉⠁⠀⠀⠀⢸⠀⢻⠀⠀⡇⠀⠀⢸⢀⣸⣀⠜⠀⠀⠀⢸⠀⡇⠀⡇⠀⠀⠘⢆⣉⠖⠀⠉⢹⠁⡇
⠀⠀⢀⠇⠀⢰⠒⡖⢶⠀⠀⠀⢈⡆⢸⠀⠀⡇⠀⠀⠈⠉⠉⠁⠀⠀⠀⣠⣣⠎⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢠⢇⡜⠁
⠀⠀⠸⠀⠠⠯⠜⠀⠸⠄⠠⠠⠀⠧⠜⠀⠀⠧⠤⠄⠀⠀⠀⠠⠤⠤⠞⠋⠀⠀⠀⠀⠀⠈⠢⠤⠄⠠⠤⠶⠓⠉







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⢿⡿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠗⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠺⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠘⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠃⠀⠀⠀⠀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣤⠀⢀⣤⡄⠀⣤⡄⠀⠀⠀⣿⡇⠀⠀⠹⣿⡆⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⢠⣿⠟⠉⠉⠙⢿⣷⠀⠀⠀⢸⣿⠇⠀⠀⠀⠉⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⣿⡇⠀⠀⢀⣿⡇⠀⠀⠀⣾⡿⠋⠉⠉⠻⣿⡄
⠀⠀⠀⢺⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡗
⠀⠀⠀⢘⣿⣷⣤⣀⣤⣾⣿⠀⠀⠀⢸⣿⡄⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣷⣤⣀⣤⣾⣿⡃
⠀⠀⣰⣿⠟⠉⠛⠛⠋⠉⢻⣷⡄⠀⢸⣿⣿⡿⠋⠸⣿⣇⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⣿⡇⠀⢠⣾⡟⠉⠙⠛⠛⠉⠻⣿⣆
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠘⠿⠋⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣈⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⢀⣀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠏⣠⡗⠻⣍⡱⠀⡀⠀⠀⠀⢠⣧⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠
⠀⠀⠀⠀⠘⢈⡶⣦⣾⣗⠟⢉⡝⠀⠀⠎⢻⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠌⠀⢀⣿
⠀⠀⠀⠀⠀⠹⢆⣽⠉⠀⢦⣠⠀⠀⠀⠀⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠄⠁⢀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠈⠻⢶⠀⠈⠻⡄⠠⠁⠆⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠊⠀⢸⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠚⣧⠀⢀⣷⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠉⡇⠙⠻⠜⠉⠻⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⠀⣀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⣀⠀⢀⠀⣀⡀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠄⠀⠀⠀⣠⠲⠀⠀⠀⠄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⠀⡀
⠀⣴⣔⡱⣄⠘⣄⡹⢿⡛⠓⠓⠛⠛⡇⠀⢘⡀⢀⢤⣰⠞⠛⢧⠀⠠⠀⠀⡠⠀⢚⠀⠀⡀⠠⠻⠀⠀⠀⢘⠀⠀⠀⣸⡏⠀⡀
⠀⣿⣿⡟⢸⡆⣼⠙⠲⣝⠢⡀⠀⠀⢹⣾⢋⠐⠁⠆⢷⢠⣴⣶⣶⣦⡀⠀⣗⠀⠀⢡⠈⠀⠀⠘⣶⠁⠀⠀⢱⠠⣿⣿⠙⠑⢳
⠀⣿⣿⣧⣌⣀⡏⠀⠀⠈⡷⠇⠀⠀⠘⡿⣧⠀⠀⢸⠈⢺⣿⣿⣿⣿⡇⠀⡿⠀⠀⠀⣶⠻⡀⠀⡿⡋⠀⠀⡙⢸⣻⣿⡦⠄⠀⡇
⠀⢸⡿⠃⡀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣁⣠⣞⠀⠀⠙⠿⢿⣛⢀⡔⢻⡀⠐⢇⠀⢥⡀⠀⣴⠘⠒⠀⢠⠀⠀⠛⠛⢦⣼
⠀⠀⡧⣤⣭⠿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡭⠭⠭⣭⣽⡇⣼⡁⠀⠀⠀⠈⢧⠀⠉⠀⠈⡇⠀⠀⠈⠙⠀⡀⠀⠉⢰⡆
⠀⠐⠀⠀⢸⡄⢇⠀⠀⠀⠀⠀⠀⠀⢸⢯⣽⣿⡯⣛⣿⣿⠀⠀⠀⠘⣄⡴⠀⠀⠀⠀⣇⠀⠀⠀⠀⠄⠄⠀⠀⢞⡤⢀⠀⠀⠀⡄
⠀⠀⡀⠀⠈⠁⠰⠦⣤⣀⣀⣀⣠⠤⠚⣼⠀⢸⣿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠄⡠⠠⠀⣠⣀⣀⣴⠎⣀⠀⢀⠠⣤
⠀⠸⠤⣤⣤⡤⠂⠀⢨⡉⠀⠋⡅⠀⢠⣿⣦⣼⣿⣿⡿⠉⠏⠉⠉⠁⢿⡼⠦⣤⡴⡏⠀⠀⠃⠀⠀⠉⠈⠁⠀⠈⠉
⠀⠀⠀⣻⠀⣇⢀⡴⢾⣧⢰⣤⣇⠀⠈⠙⡟⡟⢻⠋⠁⠀⢁⠀⠇⠀⢰⢀⣀⢠⡤⠃⢀⠀⠀⢀⠀⠀⣀⣀⠀⣀⠀⠀⠀⠁
⠀⠀⠈⠿⠟⠚⠓⠀⠾⢿⣿⣟⠿⠿⠦⠀⣿⣿⣽⣀⠀⠀⢠⠀⡄⠀⢤⣄⡄⠸⢤⡀⢋⣿⣷⣬⣑⣢⠜⠳⠃⠻⠛⠘⠀⠪⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⢿⢊⡛⠚⡳⠄⠛⠖⢿⡤⠚⠉⠀⠀⠉
⠀⢀⠔⠁
⠔⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣯⠿⠿⣿⣿⡿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣺⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⣠⣴⣿⣿⡋⠀⠀⢀⣠⣴⣶⣤⣄⠀⢀⢀⣀⣀⣀⡀⠀⠀⠐⠷⣤⡶⠀⠀⠀⢀⣤⣄⡀⠀⣠⣶⣿⣿⣷⣦⡀⠀⢀⠔⡀
⠀⠀⠀⠀⠈⠙⢿⡿⣋⣀⡀⢠⣿⣿⣿⣿⣯⣿⣆⠸⡸⠟⣋⣀⣀⠀⠸⣦⡞⢿⣇⠀⠀⠀⠸⣿⣿⠇⢰⣿⣿⣿⣿⣿⣿⣷⠀⠊⠺⠿⢦⡀
⠀⢠⣾⢻⣟⡛⣮⠑⣿⣿⣿⠸⣿⠻⠿⣿⠯⢻⡿⠀⣰⣾⡟⢉⡻⣿⣦⠙⠓⠟⠛⠀⣀⣤⣤⣤⣄⡀⠘⣿⣿⣙⣉⣿⣿⡏⠀⣎⣤⢒⠀⠉
⠀⣿⣿⣼⡟⣽⣿⡇⢉⣉⣁⡀⠙⠿⣿⣿⡿⠟⠁⠀⣿⣿⣾⣿⣷⣿⣿⡆⢸⠷⢠⣾⣿⠿⣿⡿⢿⣿⣆⠈⠛⠿⠿⢛⡋⠀⠢⠯⣢⣏⠳⢀⣠
⠀⠘⢿⣿⣿⡿⢟⣴⡿⠿⠿⢿⣦⠀⠀⠐⢶⣠⡦⠀⠻⣋⣀⣉⣀⣉⡿⠀⣠⠄⣾⣿⠀⢀⠀⣀⠀⢸⣿⡆⠀⣰⡿⠿⠿⣷⡄⠚⠁⠀⠀⠸⣿
⠀⣠⣴⣦⣄⡀⢸⣷⡄⠀⠀⣰⣾⡇⠸⣦⡞⣿⡁⠀⠀⠈⠛⠛⠛⠉⠀⣿⣿⡇⢹⣿⠀⠈⠀⠈⠀⢸⣿⠁⠀⢿⣆⠀⠀⢸⡟⠀⣠⣶⠛⠓⣦
⣾⡟⠷⠶⢻⣷⠈⢿⣧⣿⣿⣿⡟⠁⠀⠙⠓⠛⠃⠀⠀⣠⣾⡿⣿⡿⣷⣮⡉⠀⠀⠙⠿⣿⣿⣿⡿⠟⣡⣴⠶⢾⣟⠿⠿⢛⣠⠀⣿⣸⠀⠀⣿
⢻⣇⣠⣄⣸⡿⠀⣀⡈⠉⠉⠁⣠⣾⣿⣿⡿⢦⡀⠀⣼⣿⡿⣷⠈⢰⣿⣿⣿⡄⠀⠀⣀⣀⣀⡀⠀⢰⣿⣤⣶⣦⣽⡇⢰⣿⣿⠇⠈⠛⠻⠛⠁
⠀⠉⠛⠛⠉⠀⣶⣿⣿⣶⡀⢰⣿⣿⡛⠉⣰⣿⣷⠀⣿⣿⣷⣌⠃⢈⣻⣿⣿⡇⢠⣾⣿⣿⣿⣿⣦⠈⢿⣁⣉⣈⡹⠃⠋⠛⠯
⠀⠀⠀⠀⠀⠀⠈⠛⢿⠟⠀⠈⢿⣧⣝⣾⣿⣿⠏⡀⠹⣿⣿⠛⠈⠛⣿⣿⡟⠀⢾⡿⣻⣿⣿⣻⣿⠀⢀⣬⣭⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⡛⠁⢼⡿⠂⠈⠙⠻⠿⠿⢛⠉⢀⡀⠈⠷⣶⣶⣶⡶⠏⠀⣿⡋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣧⠀⣠⣶⣾⣷⣶⣄⠀⢄⢸⢞⢣⢤⡀⢠⣤⣍⠁⢀⣰⡆⠙⠳⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⣸⡟⠉⠉⠉⠉⢿⡆⠀⢍⡷⢛⠆⠁⠻⣿⡿⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣅⣤⣄⣠⣤⣸⠃⣠⠀⡠⢀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⡄⠀⢸⣿⣎⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣧⠀⠈⠙⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠻⠿⣿⣿⣿⣿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⢸⣿⣿⣶⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣼⣄⣈⣉⣋⣉⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⠶⠟⠙⠶⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡀⢉⡉⠀⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢐⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⢲
⢰⠀⠀⢀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠑⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡞
⠈⢆⠀⠀⠈⢦⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⠛⠛⠁
⠀⠀⠑⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬



⠀⠀⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⣠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡧⠤⡧⢤⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⢳
⠀⠀⡀⢴⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣡⠤⠧⢤⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠒⠚⠦⢊
⠀⠀⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤
⠀⠀⠀⠀⣠⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣄⠀⠀⢀
⠀⠀⠀⠀⠉⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠁
⠀⢀⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⠀⠀⠣⣀⠜
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠙⠄⠀⠖⠉⠱
⠰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⢀⣀⣀⡀⠀⠊⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢜⠇⠀⠀⠀⠀⠉⠳⣬⣵⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠈⠀⠀⠀⣀⠀⠀⠀⠈⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢿⠃⠀⠀⠀⣤⣨⠷⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣶⠞⡟⠀⠈⡀⠀⠀⠀⠀⠁⣤⣠⠽⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠀⠀⠀⡤⠀⠃⠀⠀⠀⠀⢸⡢⠐⡂⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⢀⠊⢀⣤⣘⡄⢀⣼⡓⠚⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢁⠘⠋⠉⠀⠈⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠧⠂⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠜⠁⠀⠈⠠⣠⣠⡤⠤⠄⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⣀⣤⣤⣿⣿⡆⠀⠀⠀⠀⠀⢀⠄⠉⠃⠐⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠃⠀⠒⠈⠀⠀⠠⠈⠛⢷⣄⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣹⣑⠈⠉⠉⠙⠛⠒⠒⠶⠒⠒⠋⠁
⠀⠀⠀⠀⣀⠀⠈⠛⠛⠒⠂⠠⠤⠀⠀⠠⠤⠄⣈⡿⠛⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢤⡢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢤⣀⣀⣄⣀⡀⠀⠀⠀⠀⢀⣰⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣶⡶⠖⠋⠁


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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠙⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛⡛⠀⠀⢀⢀⣛⡛⠿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀⠤⠴⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿
⣋⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⢉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠋⠉⠉⠀⠀⠀⠀⠉⠉⠛⠛⠶⣤⣀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣰⣿⣄⣀⣀
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠈⠉⠉⠛⠷⢦⣄⡀
⠀⠀⠀⠀⢀⡾⠁⠀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠾⠛⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢀⣿⣥⡶⠛⠉⠀⠀⠈⠉⠉⣿⠛⠉⠉⠉⠉⠀⠘⠛⢛⡟⠛⠛⠛⢛⣿⠛⠛⠂⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠉⠛⢶⣤⣀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠛⢶⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⠲⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡅⢎⡇
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠛⠀⠒⠒⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢊⠴⠁⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠸⠃⠀⠈⡆⡔
⠀⠠⠀⠀⠀⠀⣰⣁⡍⢀⡴⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠓⠒⠒⠒⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠀⠀⠀⠀⠀⡠⠂⠉⠉⡇⠢⡀⠀⠀⠀⠀⠀⡇⡤
⠀⠀⠀⠙⠔⠉⠉⠉⠉⠁⡜⢣⠈⠉⠉⠉⠉⠑⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢘⠀⠀⢀⡴⢆⠀⢸⠀⠀⠀⠀⢀⠈⡀
⠀⠀⢠⠖⠉⠉⢹⠙⠢⡀⠑⠊⠀⢀⠔⠋⠉⠉⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠙⢦⡀⠀⠈⢹⠈⠁⠀⠀⠸⠛⠀⠀⢀⠔⠁⠀⢈
⠀⢀⠁⠀⠀⢀⠾⡀⠀⢡⠀⠀⢀⠃⠀⠀⢀⠼⣀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⠦⣠⡈⢆⡀⠀⣀⠞⢸⡤⠔⠁⠀⢀⠴⠁
⠀⠀⠙⠂⠉⠁⠀⠈⢙⠈⠀⠀⠈⠛⡆⠈⠁⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠉⠈⠉⠀⠁⠀⠀⢀⠔⠁
⠀⠀⠀⢆⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡔⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⡠⠒⠛⠂⠘⠓⠢⡀⠀⠀⠀⡤⠖⠛⠃⠘⠋⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁





⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠊⠙⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠈⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢣⠀⡴⣔⢉⢩⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡔⠒⢄⠀⠈⠁⠒⢄
⠀⠀⠰⠢⢄⠀⠀⡰⠛⢤⡣⠄⠃⠈⢣⠀⢀⠀⢀⡆⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠢⡊⠗⢄⠀⠀⠈
⠀⠀⢐⠀⠠⠃⠀⠑⠀⠲⡀⠁⡛⠀⠘⠀⠀⠀⡜⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠙⠦⠴⠃⡀⠜
⢀⠄⣈⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠑⡲⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡀⠑⠄⣀⡠⠎⢠⠒⠄
⠣⠠⠆⠀⠀⠀⠀⠀⡠⠊⠉⠉⠓⢦⠀⠀⠐⠒⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢬⣊⠀⠀⠀⠀⠀⠀⢈⡓⠅⢠⣄⡀
⠀⢠⠄⠤⡀⠀⠀⠠⣁⣀⡠⠚⠤⣀⡇⠀⠀⠀⡠⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢠⠀⠑⢄⠀⠀⠀⡰⠋⠀⠀⢠⠀⠉⢆
⠀⠸⡀⠀⠉⠢⡀⠀⢘⡀⠀⠀⠀⡇⠀⠀⡠⠊⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⠴⠋⠢⣀⣈⠀⠀⠀⣇⣀⣀⠤⠊⠢⢀⣈
⠀⠀⠈⠢⡀⠀⠈⠒⠤⠵⠦⠤⠾⠤⠐⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⢨⠈
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⣀⣠⠃⠀⠀⠀⠀⡇⠑⣄⣀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠉⢢⠀⠀⠀⠗⠉⠀⠀⠀⠀⠉⠲⡀
⣀⣀⣀⣀⣀⣀⣀⣘⣤⣄⣀⣤⣤⣤⣜⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣤⣤⣤⣤⣤⣤⣤⣃⣀⣈⣀⣀⣀⣠⣄⣤⣤⣤⣃
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠚⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠄⣀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⣉⡠⠒⠕⠂⠱⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⠀⠀⠀⠘⠀⠀⠤⠤⠤⢀
⠀⠀⠀⠆⢀⡤⠄⠁⠁⠠⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠻⠿⠛⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰
⠀⠈⠇⠤⠀⠀⠀⢰⠄⠀⠀⢱⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⢸⠀⠀⠉⠀⠀⡡⠅⠈⢸
⡂⢀⡜⠀⠈⡰⠦⠜⠀⠈⡃⠤⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⢰⡀⢐⢸⠉⣃⣀⠈⠉⡑⡀⢀⠀⡀
⣇⣎⠃⠀⡰⠀⠀⠀⠀⡴⣁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠘⠀⠉⠁⠀⠭⠤⠤⠬⠭⠠⠈⠀⠀⠃
⠨⡹⠀⠊⠈⠁⠀⠀⠀⢤⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣀⠠⠇
⠀⠘⢦⡘⠀⢠⣀⡰⠌⣀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠉
⠀⢀⠐⠀⠉⠙⠃⠙⠉⠁⠂⠁
⠀⠀⠀⠀⠒⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⣂⠠⠤⢀⣄⣂⠀⠀⠉⠐⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⢌⠐⠒⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⠀⢌⢆⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠹⡄⠀⠀⠀⠀⡃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠦⠀⠈⠇⠀⠐⡀⠀⠀⠀⡃⠀⠀⠀⠀⡠⢈⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠐⠈⠲⡄⠀⠀⠑⠀⠂⠈⠀⠀⠀⠀⢀⣀⡀⠀⠄⠀⡀⡜⠀⠂⠐⠀⠀⠀⠀⡇⢀⢀⠀⡀⠀⢀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠄⠀⠀⢀⠌⠀⠀⠀⡄⠈⠀⠄⠀⠀⠀⠀⠨⡭⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠀⠂⠠⠐⠒⠀⠂⠂
⠀⠀⠀⠀⠀⠀⢠⢎⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠃⠐⢄⠀⠀⢀⠄⠀⠀⠀⠠⠤⠠⢄⠀⠀⢃⠄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠁⠁⠠⠀⠀⠁⠅
⠀⠀⠀⠀⢀⡴⠃⠀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⠄⠈⠄⠀⠀⠀⠒⠐⠂⠀⠁⠀⠀⠀⠀⠑⠃⠂
⠀⠀⠀⣠⠊⠑⠄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠌⠁⠁
⠀⢀⠾⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠤⠤⠤⠄⠐⠊⠁
⠀⠈⠢⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⡅⢢⡔⠀⠀⠀⠀⠀⠀⠀⠆⠈⠢⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⢀⠔⣡⠞⢉⠔⠉⡀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠄⢀⠊⠀⠀⡐
⠀⠀⠀⢀⠔⢁⠔⢁⡼⠋⡠⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⡠⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣠⢁⠀⢀⠐
⠀⢀⡐⢡⣔⣁⣴⠋⠀⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠘⢑⠞⠓⠅⠀⠀⡀
⢀⠘⠁⠀⠀⠀⠁⠜⡇⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⡐⠁⠀⠠⢈⠀⠀⠢⠐
⠉⠀⠀⠀⠀⠀⠃⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⠉⠀⠀⠀⠀⠀⢕⠄⠀⢁
⠐⠒⠒⠒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠀⠉⠛⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣲⣶⠶⠂⠀⠀⠀⠀⠀⢹⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⣰⠋⠠⠙⠃⠀⠀⠀⠀⠀⠛⣅⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠛⢹⠐⠀⠀⠀⠀⠀⢠⡙⠲⢀⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢻⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⡴⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⢻⡄⠀⠀⢳⡀⠀⠀⢠⠀⠀⠀⠀⢀⠀⢀⡀⠇
⠀⠀⠀⠀⠀⠀⠘⠁⢠⣀⠀⠀⠀⣷⠀⠀⠀⢳⡀⠀⡈⢦⡀⠀⠀⠼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢸⡀⠀⠀⠈⣧⠞⢃⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢠⡟⠙⢣⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣾⣀⣠⠚⠇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⣿⠂⠀⢤⡄⠀⢸⡆⠀⠀⠀⠀⢠⠀⠀⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣿⠀⠀⡠⣣⠊⠁⠀⠀⢀⣀⣸⣇⠀⠀⣀⠤⠬⠷⢔⣄⡀⠀⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠚⠒⠛⠛⠛⠛⠛⠚⠋⠉⠉⢉⠀⢻⠁⠀⠀⠀⠈⠉⢛⠛⢦⡀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠁⢸⡇⠀⠀⠀⠀⠀⠤⣍⣲⢽⣆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣯⣤⣤⠞⠓⠲⠶⠶⢤⡭⠶⠋⠁⠀⠨⠇⢁⣠⠔⠂
⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠶⠶⠶⠶⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⣇⡶⣼⣠⣴⢴⠢⣶⡖⢲⠂⠀⢴⢲⡦⠶⢰


⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡤⠀⠀⢤⡄⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠮⡀⣠⠇⠀⠀⠈⣰⣆⠀⠀⠀⠀⠀⡐⢂⡀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠂⡠⠁⠈⠢⡄⠀⠀⢀⠞⢻⠏
⠀⠀⠀⢠⡄⠀⠠⠋⠀⠀⠀⣌⠆⠡⣱⠀⠀⡠⠎⣰⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠰⠀⠀⠚⡩⠀⠀⢏⡠⠂
⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠑⠒⠒⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠈

⠀⠀⠀⢰⠀⠀⠐⠒⡆⠀⠀⠀⢀⠦⡄⠀⢠⠦⠖⠴⠤⠆⠀⠀⡔⠒⠒⠒⠂⠀⠀⠀⣴⣦⠀⠀⢀⠀⠤⢀⡒⠀⢀
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡒⠇⢴⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢱⢈⠈⠠⡁⠀⠀⠰⠩⠭⠆⠀⠀⠑⠠⠤⠄⠒⠉⡄
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣮⠃⠈⠀⠀⢘⠀⠀⠉⣠⠇⠀⠀⡇⠈⠁⡀⠁⠀⠀⡱⠀⠀⢊⡀⠀⠸⡀⠀⠀⢐⠒⠗
⠀⠀⠀⠈⠓⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢠⡶⠒⢦⡀⠀⢠⠢⠴⢦⡒⡄⠀⠀⠀⢀⠄⠂⠀⠀⠰⠀⡆⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠀⡀⠰⣒⢤
⠀⠀⠀⠀⢸⣄⠀⣠⠇⠀⢸⠨⠉⠩⠁⡇⠀⠀⢠⠃⡠⠃⠀⡠⠊⠀⠉⢢⠀⠀⢰⠋⠉⢉⠒⠀⠀⢸⠰⡸⢀⢎⠆
⠀⠀⠀⢀⢎⡟⠉⠁⠀⠀⢸⢀⠀⠈⢀⠃⠀⠊⠉⠒⠁⠀⠀⢏⠀⠑⡈⢩⠃⠀⢸⠐⠈⠐⢸⠀⠀⣨⠳⠤⠢⣟⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠈⠑⠒⠒⠁⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠒⠀⡨⠋⢵⣶⣶⣝⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⣶⣭⣵⡌⢙⣆⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠞⠛⣿⣿⣿⣿⣿⡁⢰⣮⡅⠀⠛⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠙⠂⠀⠀⠀⠀⠐⢆⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⣶⣦⣄⡀⠀⠀⠀⠀⠈⠉⢹⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠛⠛⠛⠋⠤⠀⢒⣀⡉⠀⠈⠀⠀⠈⣀⡒⠂⠤⠄⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⡩⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣁⠒⠀⠠
⠀⠀⠀⠀⠀⠀⣠⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢒⡀⠉⠀⠀⠀⠀⠀⠀⠈⡅⣒⠐⠌⠤
⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠩⠤⠐⠂⡀⠀⠀⠀⠀⠀⡐⢒⣰⣸⣀⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⣒⣉⠭⠄⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠠⠄⠒⣒⠈⠉⠀⠀⠀⠀⠁⠉⣐⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⣀⣀⣀⠐⠈⠉⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢹⣿⣿⣿⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣆⡤⠖⠚⠛⢳⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠾⠛⠁⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠋⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⢠⣤⣶⣶⣾⡋⠉⠉⢉⡽⣿⣶⣄⠀⠀⠙⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠃⠀⢀⣼⡵⠋⠹⠿⢿⠀⢠⡏⠀⠛⢛⡟⣇⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡾⢹⠁⠀⠀⣠⠞⠀⠸⠷⣤⣠⡞⠀⢹⡄⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⡶⠀⠀⢀⡞⠁⠘⠷⠶⠚⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣤⣶⠟⠀⠀⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠀⣾⠀⠀⠀⣠⠄⠀⠀⠀⠈⠉⠉⠉⠁⣴⣤⡀⣿⠟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠛⢲⡄⠀⠈⢻⣄⣿⠀⠀⠚⠉⠳⢦⣀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢡⠖⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⣽⣇⠀⢀⡏⡙⠻⠀⠀⠀⠀⠀⠀⠉⠛⠒⢀⣀⠜⠁⣀⣤⣤⣩⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣠⣿⠀⠀⣧⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣁⣀⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡤⣶⣿⠀⠀⠘⢷⣄⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⠽⠛⠛⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⣿⢸⡇⢀⣤⠤⠄⠀⠿⠿⠧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⡶⠚⠓⠀⣿⠙⠛⠛⠛⠛⠒⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⢸⡇⣸⠀⠀⠀⠀⠀⠀⣀⠠⠿⣦⡄⠀⠀⢀⣶⡛⣯⣤⡶⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⢻⢸⡇⣿⠀⠀⠀⠀⣠⠞⠁⠀⠸⣿⡁⠀⠀⢸⣿⠛⣾⠁⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣸⡇⣿⣠⡴⠖⠒⡯⠀⠀⠀⠀⠈⠛⠒⠚⠛⠋⠀⠹⣶⠟⠁⣸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣇⢸⣿⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠞⠋⠈⢷⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢻⣿⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠻⣾⡟⠈⣿⠀⢰⠃⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢳⣄⠀⠀⣿⡇⢀⡿⠀⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⢹⡇⠀⠙⣶⣾⢿⣿⡏⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⠁
⠐⠛⠛⠓⠲⠶⣾⡏⠸⡇⠀⢷⡀⠀⣸⣿⠷⣿⡿⠶⠿⢤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣤⣶⡿⠃⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠙⠷⠞⠻⢦⣼⠿⣶⡿⠛⣿⣿⠛⠲⠶⠤⣤⣄⣀⣉⣉⣉⣉⡉⠉⠉⠛⠛⠒⠒⠶⠶⠶⠤⠴⠿⠿⠧⠶⠤⠤⠤⢤⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠏
⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠉⠛⠛⠛⠓⠲⠶⠦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣦⠀⣀⣠⣤⡤⠄⠀⠉⠀⠀⠀⠀⠀⠠⠐⡧⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡁⠀⢀⠀⠀⠀⠀⠀⠠⠖⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⣀⢀⣀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⢑⡤⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀⠤⠤⠐⠂⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠑⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡈⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠠⠄⠀⠄
⠀⠀⠀⠐⠀⠀⠀⢀⠀⠁⠈⠀⣄⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡁
⠀⠐⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⠟⢀⣀⣠
⠀⠀⡇⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠹⣄⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢌⠉⠀⣶⠁⠀⠄⠄
⠀⠈⠂⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⡀⠀⡂⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡌⡄⠀⢹⣧⣔⡢⠂⠑⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⣃⣉⣀⣵⣘⡦⠀⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢻⣷⣿⠀⠈⣿⣷⡀⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣻⠁⠀⠩⠃⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⡆⠌⠙⢠⠦⠤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⡇⠂⠀⠀⠀⠙⠀⠀⠰⢤⡴⠋⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⣄⠀⠀⡰⡀⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢠⡆⠀⠀⠀⠀⠀⠀⠇⠈⢀⠀⠙⠷⠄⠂⡅
⠀⠀⠀⠀⠂⠀⠘⠋⠘⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣼⠴⠛⠉
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠒⠋⠀⠐⠦
⠀⠀⠄⡴⠁⠀⢀⣘⠀⠀⠀⡰⠃⠀⡇⠀⠀⠀⠀⠀⠀⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⣠⣴⡾⠛⠉⢁⣀⣀⣤⡤⣐⡴⡀
⠀⠀⠀⠓⠂⠀⠰⠰⠀⢴⡾⠥⠤⠴⠇⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⡀⠀⠁⠀⠁⠀⠀⠀⠚⠒⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⢉⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡵⣾⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠾⠱⠿⠏⢺⣿⣏⣼⠋⢹⣯⡉⣯⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⢀⠴⠒⠿⠛⢁⣽⣯⠀⠀⠀⡛⠟⠚⢆⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡼⣶⢁⠀⠄⡤⡸⠈⣻⣦⡀⢄⠹⠆⣀⣀⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠿⡀⢻⠀⢶⢋⣽⡿⠯⢭⣟⠿⠖⡺⢿⡝⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⣿⣿⣤⠾⣸⠏⠀⠐⡭⠛⠛⠋⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣔⡐⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁
⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⠐⠂⠀⠀⠈⠂⢤
⠀⠀⠀⠀⡴⠡⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀
⠀⠀⢀⠎⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢀⠔⠀⠀⠂
⠀⠀⡎⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠰⠃⠐⠀⠀⠀⠀⣠⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠓⢠⠀⠀⠀⠀⠀⠀⠀⠐⡀⡄⠘⠀⠀⠀⠀⠐⠀⢀⠔⠁
⠀⡆⡠⠀⠀⠀⠀⠀⠀⠠⠼⠀⠈⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠢⠤⠄⠀⠀⠀⠈⢁⠂⠀⠀⠀⠴⢀⡔⠁
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠠⠁⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⠘⠂⡀⠁⢦⣀⠴⠤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠨⠡⠀⠀⠀⠀⢀
⡄⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⡀⠕⡊⠁⠁⠀⠀⠀⢼⠀⠀⠁⠀⠀⠂⠀⠉⠁⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⢤
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠘⠒⠀⠀⠄⠀⠀⡀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠲⠤⠄⢀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⣀⣠⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⢤⣄⡠⠄⠀⡤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣵⣿⡿⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⣫⠟⣵⣌⣛⡟⠁⠀⠀⠉⠓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢫⡀⠀⣠⠞⣡⣾⣿⣿⣿⢠⡞⣠⠆⠀⠀⠀⠀⠀⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣀⣧⡞⣡⣾⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀
⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⠞⢃⣴⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀
⠀⠀⠀⠀⠀⢠⠏⢠⣄⡴⢃⠴⠋⠀⠘⣜⣆⠀⠀⠀⠀⠀⢀⢄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠃⣾⣷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⡞⠀⢀⡏⠐⠣⡀⠀⠀⠀⢈⣨⣤⣶⣶⣶⣿⣿⡼⢟⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⡸⢁⡴⣯⣀⣠⣐⣁⣤⣶⣾⣿⣿⣿⡿⣿⡏⢹⣿⣿⣷⣄⡀⠙⠲⢦⣤⣀⠀⠀⠀⠀⣠⡆⠐⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱
⠀⠀⠀⠀⢣⣞⣵⠟⢹⣿⠛⠛⠻⣿⢿⣿⣫⣿⣾⣿⣷⢘⣿⣿⣿⣿⣿⣷⣶⣦⣤⣭⣶⣦⣴⡾⢻⣿⠇⠀⢸⣿⣿⣿⡁⠟⣿⢹⣿⣿⠸⡸
⠀⠀⠀⣰⣿⠟⠁⠀⠈⠻⢶⡀⠢⡘⣷⠾⢿⣿⡿⠣⠬⣉⠛⢦⣌⠁⡹⣿⣿⣿⡿⣿⡿⠿⣟⢹⣿⡟⠀⠀⣿⣿⣿⣿⣷⣤⡇⣾⣿⡏⠀⡃
⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠙⠦⠴⣯⠀⠀⠙⢯⣀⠀⢀⡵⠀⠉⠛⠶⠶⣭⣭⡭⠿⠟⠲⠶⠤⢽⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢄⡀⣸⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⣿⣿⡷

⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢀⡤⢠⣀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⣷⡀⠀⠀⠀⠀⠀⡨⠟⠓⢤⣰⣶⠀⢰⠁⠀⠀⠈⢃⠀⠀⠀⢀⠄⠠⡀⢈⠀⠁⠀⠀⠠⠀⠀⠢⡑⡀⠀⠈⢂⢀⠐⡄
⠀⠀⢿⠹⣆⠀⠀⠀⡜⢀⡀⡈⠀⢹⠉⠀⠘⣄⠀⠀⢀⡆⠀⠀⠀⣵⣶⣶⣶⠃⠀⠐⠀⡀⠀⠐⠀⠀⠑⡘⢄⠀⠨⠈⠀⠐⠄
⠀⠀⢸⡄⠘⢿⠀⠀⣹⣄⠀⠀⢀⡜⠀⠀⠀⠈⠉⠉⠁⠹⣷⣄⠀⠙⡿⢿⣯⣿⣿⣿⣾⠀⠘⠀⠀⠀⠀⠈⢄⠒⠁⡄⠀⠀⢈
⠀⠀⠸⠇⠀⠀⠰⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⡄⢠⡶⠀⠀⠈⠛⠃⠀⠀⠀⠂⠉⠉⠉⢣⣄⠀⠀⠀⠀⠀⠀⠀⠢⡀⠡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⢀⣀⣼⣥⣤⠀⠀⢀⣴⣶⣶⣦⣤⠄⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⢀⣀⠀⠀⠀⠀⠀⣼⠋⠙⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠰⢿⣿⣷⣿⣿⡁⠀⡀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠘⢾⣿⣿⣶⣲⠀⠘⠳⢾⡷⠾⢶⣄⠀⠈⠻⠿⠿⠋⠀⠀⢰⣿⣿⣿⠿⠗⠀⠧⠰⡷⠀⠀⠰⠆⠀⠀⠠⠊⠀⠀⠀⠀⠑
⠀⠀⠀⡽⠉⠉⠀⠀⠀⠀⠸⣇⡀⣠⡟⠀⠀⢀⠀⠖⡦⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠁
⠀⢠⣴⣧⠀⠀⣤⠴⢶⡀⠀⠉⠛⠉⠀⢠⣾⣦⣤⡀⠀⠐⢳⡀⢀⠠⢀⣸⠀⣆⡀⠤⡀⠀⠀⠀⠠⢢⠀⢃⠀⠀⠀⠂⠢⢀⠆
⠀⠀⠀⠉⠀⠀⠿⣤⡼⢋⡀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢠⣴⡀⡇⠀⠑⢤⣼⣿⣧⣤⠊⠀⠀⠠⠀⠀⠀⠀⠀⠁⠂⠄⠠⠐⠁
⠀⢤⣦⡀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠈⢄⠙⢿⡄⠀⡿⡱⠁⠀⣊⠀⠼⠓⡧⣤⣑⠄⠀⠁⠀⠸⠁⠀⠀⠀⢀⣴⣤⡀
⠀⠈⠻⡟⠀⠀⠀⢲⣿⣿⡇⠀⠀⠀⢀⠀⠀⠉⠦⢦⡔⠊⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠂⠀⡠⠤⠀⠀⠀⠀⠉⠛⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠶⠷⠒⠀⠀⠶⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠂⠂⠁⠀⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢠⣆⠀⢀⡖⣶⠆⣦⡀⠀⠀⠀⠀⠀⠀⣤⠀⣀⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⠉⠛
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠯⠽⠀⠒⠀⠀⠀⠀⠀⠰⢿⡟⢩⠧⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⡞⠛⠛⠛⠛⠛⠛⠉⠛⣷
⠀⠀⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⠠⠀⢁⡀⠠⡄⠀⠀⠀⠀⠀⠦⣤⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣼⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠘⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣛⣻⣟⣛⠛⠛⠋
⠀⠀⠀⠉⠉⠙⠓⠒⠦⠤⢄⣼⠁⠀⠀⡒⠉⠙⣶⣄⠀⣤⠘⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣌⠉⠉⢉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣼⣿⡖⠁⠙⠟⢣⠀⠀⠀⣴⠟⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢀⡴⠋⣹⠆
⠀⠀⠀⠀⡠⠄⠀⢀⡀⢰⠡⠀⠀⢇⡘⠉⠑⣤⣤⡄⡘⠀⢰⠟⠀⠀⠀⠀⠀⠶⠆⠀⠀⣾⣿⡧⠀⠀⠄⠐⣏⣠⠞⡡⣪⣶⣄
⠀⠀⠀⠀⠠⣰⡀⠘⠀⠀⠀⡀⠂⠈⠻⣦⠀⠛⡿⠋⠀⠀⠀⠀⠀⠠⡶⢠⡜⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⢻⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣮⣵⣾⣯⣵⣶⣦⣄⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠤⣄⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠄⠀⠄⠀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠁⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠀⠀⠂⢐⡶⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣧⡀⠀⢀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢿⣿⣷⣦⡄⠀⠴⠄⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠈⠣⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠉⠘⠂⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡷⠶⣤⡀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠈⠁⠀⠐⠧⠄⣀⡀⠀⠈⠛⠛⣛⠋⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⣀⠋⠈⣩⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣇
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣆
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢧⡀
⠀⠀⠀⠀⢸⣇⣀⣀⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡹⠆
⠀⠀⠀⠀⠀⣹⠟⠛⠛⠿⢷⣦⣀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠶⡾⠉
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡹⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡀
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠐⠚⠆⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⣇
⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠈⠱⠦⣀⠀⠀⠀⠀⠀⢛⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙
⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⠎⠀⠁⠀⠀⠀⢢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠐⠊⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠈⠁⠉⢹⠀⠀⠀⠀⠀⠒⠒⠒⢶⠚⠃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠓⠤⢄⠀⠀⠐⠒⡶⢋⠻⠇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠉⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠂

⠀⠀⠀⠀⠄⠒⠒⢒⠒⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⢀⡠⢁⠀⠀⠰⠂⠁⢸⣿⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣷⣗⠀⠀⠀⠀⠀⢀⢘⠚⡉⠉⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⡘⠠⡤⠫⠚⠛⠘⣃⣠⡇⠀⣿⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡯⣿⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡂⢠⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⡀⠸⠀⠀⠀⠈⣿⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠇
⠀⠀⠀⠀⢠⡥⣤⣤⣤⣿⣿⠀⠀⠀⠀⠈⠶⠶⠻⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢐⢘⠂⠀⠀⢀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⢵⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⣍⢹⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠘⠘⠀⠀⠃⡞⠀⠀⠀⠀⠀⢀⠀⠛⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⢸⡍⢹⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⠠⠜
⠀⠀⠀⠀⢸⡓⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⣴⠀⠀⣀⣀⣘⣉⣀⣘⣻
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡆⠀⠀⠀⡇⡇⠀⠀⠀⠈⠀⠂⠈⡄⢀⡀⠀⠀⠀⠀⠻⠉⠓⠒⠺⠿⠒⠛⠻⠃
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢲⡀⠔⡜⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⢸⢰⡆⠀⠀⠀⡤⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡇⠇⠈⢆⠀⠣⠀⠀⠀⠀⠀⠞⣰⠃⡨⢄
⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⡇⢾
⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠑⠀⠐⠀⠀⠀⠀⠤⠎⠀⠀⠀⡈
⠀⠀⠀⠀⢸⠾⢻⠀⠀⠀⠀⢸⠤⠄⠀⠀⠀⠘⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⠶⠶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣾⡧⠀⠀⠀⢸⣿⣿⣉⣉⣉⣀⣉⡉⣉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⣾⡎⢿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠿⠿⠿⠿⣿⣿⡿⢃⠀⠀⠀⢸⣿⣿⣿⡙⣿⣿⣿⢃⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠘⠛⠛⠘⣿⣿⣿⡇⠀⠀⠀⡟⣴⣿⣿⣿⣷⣶⣶⣶⡜⠃⠀⠀⢸⣿⣿⣿⣷⡙⣿⢃⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣰⣿⣿⣿⣷⠹⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡿⢋⣤⡛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⣿⣿⣿⣤⣾⣿⣿⣿⣷⣬⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣦⣝⣛⣡⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠛⠓⠶⣤⡀⠀⠀⠀⢀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣸⢃⣠⠖⠶⠶⠶⠖⠛⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠙⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠈⠙⢻⣿⠉⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠛⠛⠛⠚⠛⠛⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⢠⡄⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣸⠇⠀⠀⣿⠀⠀⢸⡇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠃⠀⠀⣿⠀⠀⢸⣇⣀⡟
⠀⠄⠀⠀⠀⠀⠈⠉⢹⠀⠀⠀⣿⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⣿⠀⠀⢸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣿⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠿⠤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠲⣯⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⣤⠀⠀⠀⠀⠀⠀⠀⠈⢦⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⡶⣾⠉⠀⢀⡠⠒⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢿⣯⣿⣠⢳⠁⠀⠀⠀⠀⡤⠀⠐⠈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⣾⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣿⣥⠀⠉⢹⣛⣁⡠⠀⢠⣷⣲⣚⣛⣩⡐⠂⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣫⣶⠀⠀⣾⡈⠁⠀⠐⠋⠉⠉⠉⢉⠉⢁⡀⢀⡀⡠⠟⠀⠀⠀⠈⢰⡆⠀⠀⠀⠀⠀⠈⠋⠙⡛⠉⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⡿⠷⠠⠤⠤⠤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣥⣝⢆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣹⣇⠀⡉⠛⠻⢷⣤⡄⠈⠣⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠄⠐⠉⢴⠿⠛⠻⢿⠀⡀⠀⠀⠈⠉⠳⢤⡙
⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⣾⣄⠀⠀⠀⠀⠛⢷⣆⡆⣀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠙⢿⡓⠦⣄⡀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣟⠀⠀⠀⠱⣦⣄⠀⠀⠀⠈⠓⠺⢿⣦⣀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⡙⡛⠿⠿⣆⣠⡁⠙⢻⠶⣷⣂⡀⠀⢨⠟⢻⣟⠁
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣽⣄⡻⣿⣧⣀⠀⠘⠿⣿⣦⣦⣔⣾⣿⣿⣿⣿⡶⠶⠛⢷⣄
⠀⠀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣴⣤⣌⣏⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠈⠑⠚⠓⠚⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣤⣤⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣀
⣿⣯⣤⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⢀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡄⢠⡍⡄⠀⠀⠄⠀⢀⠀⠀⠀⠀⡀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡄⢀⠀⠀⠀⠣⡔⠈⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠈⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠐⣤⣁⣀⠔⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄⡄⠀⣠⣀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠸⠙⠞⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠟⠙⠻⠸⡊⠠⡀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠜⣔⠀⡀⠀⣰⣥⣠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠈⠀⠂⠀⠀⠀⠡⠐⠒⢫⡆⠀⠀⠀⠀⠀⠀⠀⠉⠱⠶⠚⢉⡉⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠠⠀⢴⠘⢇⠀⠀⠀⠤⠀⠴⠾⠷⠄⠀⠠⠾⠶⠱⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠠⢀⠣⣀⠘⠀⠠⠀⠄⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⢉⣠⡆⠀⠀⠀⠀⠀⠁⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣃⣈⣀⣀⣀⣓⣤⡀⠇⠀⠀⠀⠀⠀⠈⠡⠤⠤⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠄⠀⠀⠃⠠⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠆⠀⠤⠸⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢃⠀⠤⠀⠀⠀⠘⠀⣀⠐⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠊⡀⠠⡀⠀⡠⢘⠇⠀⠄⠂⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠈⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⢠⠀⠀⠶⠥⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⣀⠁⠂⠍⢈⡉⡐⢄⠀⠁
⠀⠀⠀⠀⠀⢀⠐⢎⣪⢗⡋⢉⡱⠂⢄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠉⠉⠈⠉⠈⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⠀⡠⠊⠡⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠒⠂⠂⢡⠀⠈⠁⠀⠀⠀⠈⠁⠁⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠒⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠤⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠃⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⣀⠀⠀⠀⠀⡠⠒⢄⡀⠄⠒⠄⡀⣀⠠⠀⠄⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⢴⠃⡠⠊⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢄⠀⠰⠢
⠀⠀⠀⠀⠀⠀⠀⡈⣨⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⣆⠆
⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⣀⣀⣀⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣀⣀⣀⡀
⠀⠀⠀⠓⠚⠉⠛⠛⠛⠿⠷⠶⠶⢶⣦⣤⣤⣤⣀⣀⣀⡀⢀⣀⣀⣠⣤⣤⣤⣴⣶⠶⠶⠾⠿⠛⠛⠛⠉⠁⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠀⠀⠉⡏⠉
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡐⠈⠐⠃⢁⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠙⠃⠁
⠇⠀⠀⠀⠀⠠⠴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⠄
⠘⢄⠀⠀⠀⠐⣚⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣓⠂⠀⠀⠀⡠
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠠⠄⠨⠁⣈⣁⡀⠥⠠⠄⠀⠒⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⠶⠦⠳⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠛⠁⣰⢶⣾⠊⢈⢈⣤⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣧⡀⢛⣉⠉⢨⡁⠛⠚⢺⡏⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⠉⠉⠛⠻⢧⠆⣄⠀⡅⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡖⠀⠀⠀⠀⢀⠷⢧⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢈⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⣠⠞⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⢫⠀⠀⠀⣠⠟⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⣰⠏⠀⠀⢂⠈⠓⢲⠎⠀⠀⠀⠈⠑⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⢀⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⡾⢫⠀⠀⠄⠈⢀⠀⠠⠁⢀⠀⢈⡀⠉⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⣠⣜⣹⠟⡉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠎⠀⠀⠀⠀⠀⠐⢀⠀⠀⡀⠈⠀⠀⠀⢀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⣀⠤⠒⠈⣩⠿⠃⠢⡀⣠⡏⠝⠉⠛⠛⠓⠒⠀⠀⣤⡟⢀⡇⠀⠀⢀⠁⠀⠀⠀⠀⢀⠀⠰⣄⠀⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢞⠱⣅⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⣀⡀⠀⠁⠀⠀⠂⠀⠀⡶⠀⠀⡁⠀⠀⠀⢀⠀⠀⠀⠐⢀⠟⠳⣄⠀⠄⠀⠠⠀⢳
⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠉⠓⠶⣀⠄⠈⣀⣼⠃⠀⠀⠀⠄⠂⠀⠀⠄⠀⠈⠀⡜⠀⠀⠈⠳⣄⠀⠀⠄
⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠊⠉⠣⡈⠢⡀⠀⠀⠀⠀⡀⠰⡅⠀⠀⠀⢈⣱⡿⢛⡿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐
⠀⢸⡟⠻⣦⣄⠀⠀⠀⠀⢀⠀⠀⠀⠳⡀⠀⠙⣆⢹⣦⣠⠖⣉⠤⠚⠁⢀⣤⡶⠛⠁⣠⡞⠁⠉⠀⠀⠈⠐⠀⠈⠀⠀⠤⣴⠀⠀⠀⠀⠀⢀⡟
⠀⢸⡇⠀⠈⠛⢷⣄⡀⠀⢸⠘⡄⠀⠀⠹⣄⠀⠀⣡⠤⠒⠋⠁⣀⣴⠾⠛⠛⠒⠛⠉⠉⠳⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⡼
⠀⢸⡇⠀⠀⠀⠀⠉⠻⣦⡀⠁⢱⡄⠀⠀⠈⠲⠋⠀⢀⣠⣴⠟⠋⠁⠀⠀⠀⠀⢀⣤⠖⠀⠀⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣴⠋⠀⠀⠁⣠⠞⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠐⢰⡾⢧⡔⢃⣀⠈⠉⣧⠰⠞⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣠⣴⠾⢻⡇⠀⠀⠀⠀⣈⣢⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⢻⠖⠁⠀⡼⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⠁⠀⠀⢀⣀⣴⠛⠦⠤⠚⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣀⠢⣤⡤⠖⢺⣿⠋⠉⠛⠛⠛⠛⣿⠋⠉⣿⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢻⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣇
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⢀⡿⣆⠀⠀⠀⠀⠀⠈⢧⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡏
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠹⣆⠀⠀⠀⠀⠀⠘⡇⢸⡿⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣷
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⠀⠀⠹⣆⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿
⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣀⡀⣀⣀⣼⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⣿⣀⣤⡶⠟⠋⠉⠉⠉⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣿⠉⠀⠀⢀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⢀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠉⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢰⡟⠋⠁
⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣶⡾⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠛⠛⠛⠛⢿⣷⠀⠀⠀⠀⠀⠐⠔⣤⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠓⠞⠋⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡀⠀⢀⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣅⣈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⢉⣉⣉⣉⡁⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠤⠤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⠟⠛⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⢠⢂⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⢧⣀
⠀⠀⠐⢀⠴⠠⠒⠈⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠢⠠⠾⢧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠉⠃⠀⠀⠀⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡂⡄⠀⣀⡀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⢠⠖⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀
⠒⢀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠐⢨⡼⣉⠑⠶⠤⠤⠄⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠭⠏⠀⠀⠀⠀⠀⠀⠈⠒⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣞⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠠⠀⠈⠈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡘⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢠⠀⠠⠗⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠖⠂⠀⠴⠷⠚⠉⠈⠉⠀⠀⠀⠀⠀⠀⢀⣤⡶⠼⢴⡞⠀⠀⠀⠀⡠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠉⠙⠟⠀⠀⠁⠀⠀⢠⢀⡷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⠋⢇⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⠀⠀⠀⠀⢀⡤⠄⠀⢀⣀⢀⠀⠐⠒⠠⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⢀⠠⠀⠔⠂⠀⠉⠈⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠴⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄
⠁⠉⠀⠀⠐⠓⠀⠤⠀⠀⠀⠀⠀⠀⢀⡌⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⢤⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⢋⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⡁⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠲⠄⠀⠀⠀⠁⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠂⠠⣀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡘⠳⠈⠻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⢀⣤⠄⠀⢀⣀⣀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⢘⠉⡉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠤⠜⣀⠈⠙⠀⠀⠀⢀⣀⣀⡀⠀⠒⠀⣀⣀⠀⠀⠀⠀⢠⠤⣀⠠⠤⠀⡀⠐⠀⠀⠀⠀⠀⠈⠙⢁⡠⠶⠀⠀⠰⠆
⠀⠀⠀⡀⡀⢠⡄⠀⠀⣠⠄⠁⠀⠀⠀⠈⢁⠀⠀⠀⠀⡀⠈⠭⢀⠃⠀⠀⠈⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⣘⠇⠀⠀⢀
⠀⡀⠀⣻⡇⠀⠀⠤⠴⠅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢡⠈⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⢠⠀⠀⣰⡟⠛
⠈⠁⠊⠉⠁⠀⠠⣤⢴⠆⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⣦⠤⣬⣴⠅⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠐⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠁⠙⠀⠀⠀⠀⠋⠀⠀⠉⠛⡀⠀⠀⠂⠀⠀⠐⠋⠀⡖⠉⠀⣀⠀⠠⠀⠀⠀⠀⠆⠀⠁⡾⠉⠁⠀⠀⠠⠄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⣀
⠀⠀⠀⠀⠐⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠂⢀⡀⠀⠀⠐⠂⢂⡒⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠁⠀⠠
⠀⠀⠀⢰⠞⠓⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠉⠃⡴⢠⠀⠀⠜⠁⠀⠀⠈⠁⠈⠀⣀⠀⡀⢠⠠⡀⠀⠀⠀⠀⢀⢤⣀⢀⡄
⠀⢀⠄⢸⣆⣀⠀⠈⠙⠲⠆⢤⠀⠀⠰⣀⠰⠀⢁⡈⠘⡆⢀⡀⠀⠀⢀⠐⠒⡃⠉⠉⠀⢳⡌⠁⣀⠀⠀⠀⠈⢂⠙⠈⠉⠁
⠒⠀⠰⠛⠉⢉⡃⠠⡆⠀⡛⠀⠀⠀⠀⠉⠀⠀⠀⠒⢾⠀⠈⢵⠆⠀⠉⠉⠉⠃⠄⠀⠀⠸⠀⡤⠀⠀⠀⢸⠎⢘⢿⠀⠀⠀⢀⣶⠰⣶⡀
⠉⠓⠀⡂⠀⠄⠀⣀⡀⠀⡁⠀⠀⠀⠀⢀⠀⢈⡁⣈⡏⠀⠀⠀⡰⡄⠀⡀⠀⢠⣈⣉⣤⠀⠀⠀⠀⠀⠀⠀⠀⡞⣦⠀⠀⠀⣹⢿⠀⠉⢳⡀
⠈⠀⠰⠇⢀⠘⠓⠎⠲⠀⠶⠀⠀⠀⠀⠼⠛⠈⠛⠰⠃⠀⠰⠆⠰⠂⠀⠟⠲⠎⠩⠀⠴⠀⠀⠀⠀⠀⠀⢀⣤⡟⢫⡈⡹⠃⠟⠸⡀⠀⠘⡋
⣀⣀⣀⣀⣈⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣆⣈⣀⣀⣀⣀⣈⣀⣙⣁⣀⣀⣀⣰⣄⣀⣀⣀⣁⣀
⣿⠿⠿⠿⠿⠿⠿⢛⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣿⣻⣿⣿⣛⣛⣟⣻⣿⣿⣛⣿⣟⣻⣛⠿⠻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢧⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⣰⠋⠑⠢⣄
⠀⠀⠀⠀⡔⢋⣉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡆⠀⠀⠀⡏⠀⠸⠀⠀⡴⠃⠀⠀⠀⡜
⠀⠀⠀⠀⡄⠸⡀⠱⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⢄⡀⠀⡆⠀⠸⡀⠀⣸⠀⠀⡇⠀⡼⠁⠀⠀⢀⠞⠀⣠⠔⢾
⠀⠀⠀⠀⠘⢄⠑⢄⢱⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢶⢫⡱⡀⠹⣤⠶⡇⠀⣷⠦⣤⢁⡞⠀⠀⠀⢀⠎⢀⡜⡝⡳⡼
⠀⠀⠀⠀⠀⠈⠳⣄⠙⢧⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠳⡱⡘⣄⢹⡀⢻⢀⡏⢠⣇⠞⠀⠀⠀⢠⠋⢀⢎⠜⡜⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢴⠉⠙⡦⣤⠤⢤⡀⢀⣀⣀⣀⣀⣳⣱⣜⣌⣆⣷⣀⣿⣁⣼⣏⣀⣀⣀⣠⠇⠠⠯⠮⠾⠼⢤⣐⣒⠢⠭⢽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠊⠁⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠧⠝⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠚⠀⠀⠀⠀⠀⢴⣰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⣔⢲⠀⠀⠀⠀⠓⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⣄⠀⠑⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠚⠀⠀⠀⠀⠀⠀⠺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠂⠀⠀⠀⢯⡹⠀⠀⠀⠀⠰⠽⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⢸⣿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⣿⣄⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⣹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⣤⡄⠀⠀⣿⡿⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⠀⠍⢻⣧⠀⠀⣤⣄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠙⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣌⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢣⣭⡸⣿⣶⣿⣣⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣭⣭⣿⢟⣫⣽⣶⣤⣄⡀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢳⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣩⣿⣽⣿⣿⣿⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⡹⣿⣿⡿⣿⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡇⣿⢸⣿⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣾⣿⠀⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠼⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠁

⠀⠀⠀⠀⠠⠐⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠑⠂⠰⠀⠐⠒⠉⢀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⣀⣀⣄⣀⣠⣀⠀⠐⠂⠂⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀⠀⠀⢈⠔⠒⠃⠈
⠀⠀⠀⠀⢀⠁⠀⡰⠀⠀⠀⣠⡆⣀⣒⢀⠄⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠀⠀⠀⡀⠠⡐⠀⠀⠀⠈⠄⠀⠀⠤⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠂⠀⢈⢠⠟⠀⠀⠉⠉⠓⠺⡄⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠔⠅⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠼⠀⢀⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠐⠀⡼⠴⠀⠠⢬⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠀⠉⠀⠀⠈⠉⠁⡤⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠴⠦⠆⠀⠔⠋⠁⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠠⠄⠀⡆⠠⢸⡀⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⢄⡀⠀⠀⡈⠀⡠⠂⢀⡀⠀⠀⠀⠀⠀⠙⢄⡁⠂⠀⣀⡄⢁⠀⡀⠳⣄⠈⠀⠁⡠⡞⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠢⢄⣀⢥⠚⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠀⠀⠀⠆⠙⠒⠊⣩⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣁⠀⠁⠂⣤⠐⠈⢀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣤⠒⠓⢤⡀⠀⡠⠓⣥⠤⣇⠸
⠀⠀⠀⠀⠀⡄⠒⠉⠀⠀⠀⠙⠒⠚⠑⠙⠒⠉⠀⠀⠀⠉⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠁⠂⠤⠤⠅⠀⠈⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⡇⠀⠒⠀⢰⠀⠀⡖⡆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡀⡠⠂⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠁⠊⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣀⠀⣄⣀⣈⡀⠀⠁⠀⠈⠀⠀⠀⣈⣀⡤⡰⠂⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠈⠳⢦⣤⣭⣍⣛⣢⡄⠀⣐⣙⣥⡍⣴⠚⠁⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠑⠀⠀⠉⠀⠈⠁⠈⠳⠋⠉⠁⠀⠀⠀⠙⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡀⠀⠁⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⠀⠀⠀⠀⠀⢀⡀⣀⠀⢼⡀⠀⡀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠠⠡⡀⠠⡏⠠⢄⡿⠚⢿⠈⡄⠑⡄⢀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠚⠦⣌⠊⠴⢓⢴⣛⠡⣀⠿⢿⣶⠚⡁⠁⢠⢈⡮⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠒⠶⢖⡛⢷⣾⣷⣄⠀⡈⠳⡤⠤⡤⠠⠄⠉⠓⠤⠤⠤⠤⣚⢃⣡⠿⠖⠂⠊⣁⠤⠓⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣨⠉⠓⠓⠤⠍⣈⠉⠉⠓⠒⣶⣦⡠⠶⣷⠷⠟⢛⡿⣿⠥⠶⠒⢊⡉⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠐⣚⣭⡍⠀⠀⠀⠀⠀⠀⠀⠉⠉⠺⢭⣀⣁⣁⣠⠐⢉⡡⠁⠀⠀⠀⠀⠀⢛⠒⠂⠠⠀⠁
⠀⠀⠀⡔⠀⢐⡩⢴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢍⡐⠒⠆⠀⠂
⠀⠀⠀⠈⠄⢡⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠉⠂⠈
⠀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠤⠴⢒⡟⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠙⢤⡀⠀⠁⠐⠚⢄⡀⣠⠴⠐⠈⠀⠀⣠⠴⠭⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣭⣮⢐⣦⣄⢀⢀⣀⠀⡀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠗⠹⠕⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠻⢽⡟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⣀⣤⡴⠟⠋⠀⠰⠁⠀⠀⠀⣀⡴⠚⠉⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠀⠀⠀⠠⠄⣀⣘⣦⡶⠟⠛⢡⡶⠂⠀⡆⢀⠀⣠⡴⠛⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣴⠾⠛⢰⣿⡀⢠⠇⡎⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡀⢀⡀⠀⠤⠒⠂⠀⠀⣀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠁⠐⠒⠒⠒⠒⠀⢠⠿⠞⠋⢁⣴⣾⣞⡇⢿⢸⢠⣱⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⡷⠛⠃⠉⠀⠀⠀⠀⠀⢀⣀⣀⠟
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣇⢀⣴⣾⢿⠋⢘⠈⠁⠛⠛⠘⢻⡶⠛⠛⠉⠁⠀⢠⠀⠀⢀⣇⣤⣤⡤⠤⠶⠶⠟⠛⠋⠁⠒⠒⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠚⡿⠋⢁⣼⣿⣿⠀⠀⠀⠀⠀⣾⣧⣄⣠⣤⣤⠶⠃⠀⠀⣼⣿⣿⢂⣀⣀⣀⣀⣀⣘⣂⣀⣀⣐⣐⣺⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠄⠠⠄⠀⠀⣀⠀⠀⢧⣴⠿⠋⣠⠴⠀⠀⠀⠀⠀⣿⠀⠉⠉⠁⠀⠀⠀⣠⠾⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣬⡆⠀⠀⠀⢀⣿⠤⠤⠀⠠⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⢀⣼⠿⠋⠁⠀⠀⠀⠾⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠚⠇⠄⠛⢒⣶⣌⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠂⠀⠀⠀⠀⠀⠉⠉⠛⢆⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢎⢔⡞⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢿⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⢛⡍⣼⠇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣴⣿⣿⠏⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⡀⠀⠀⢀⣐⣶⣿⡿⠟⣁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⣠⡾⠒⠀⠀⠀⠀⠀⠈⠀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⠻⠻⠻⠟⠛⢙⣋⡴⠊
⠀⠀⠰⣤⣤⣤⣤⣦⣤⣰⣼⢀⡾⣋⠤⠤⠄⠀⠀⠀⠀⠀⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠤⠓⠂
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣿⣿⣿⣷⠆⢀⣐⣠⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠘⣷⣤⣄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠛⠛⠉⠉⠉⠉⠁

⣿⠿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠓⠶⣄⡀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⣠⣀⣀⣀⣠⠴⠚⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⡤⠖⠛⠛⠲⣼⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠛⠻⢿⣷⡖⠋⠉⠙⠳⣄
⠀⠀⣾⠁⠀⠀⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢸⡆
⠀⠀⢿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠈⠳⢤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠞⠁
⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⢠⠄
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⢠⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢠⠀⠀⢸
⠳⣤⣾⠀⠀⢸⠀⠀⠀⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⡇⠀⠀⢸⠀⠀⢸⡦⠴
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠹⣄⠀⢸⡀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣼⣀⣀⡼⠁
⣶⣶⠶⠾⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣶⣶⣶⣶

⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡏⠙⣿⢋
⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⢷⡤⢸⡾⠿⠿⠿⠿⠿⠿⠿⠿⠮⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠶⠼⠧⠤⠿⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠉
⠀⠀⠀⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⡇⢀⠂
⠀⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⡁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⠀⡀⢀⠀⢀⠀⡀⠀⡄⢀⠀⢀⠀⡀⠀⡀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣸⣿⢈⡀⢡⣌⣠⠌⣤⢁⣄⣠⡌⣠⣈⣤⣀⣄⢑⣿⣦⠀⡀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿
⣿⣿⡿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⣀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢀⢈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠥⠂⠈⠁⠐⠰⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡔⠂⢸⠞
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢠⠀⠈⣿⣷⠆⠀⠈⠻⠟⠁⠘⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣦⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣄⠀⠄⣤⠄⠠⣀⠀⠀⠀⠀⢀⠀⡼⡄⠀⠀⠀⠀⠀⢰⠒⣲⡄⠀⠀⠀⠀⠀⡟⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⡀⠑⢄⡀⠨⠤⠀⠀⠀⠈⢀⠀⠘⠀⣰⣆⠀⠀⢹⠛⢛⡆⠀⠀⠀⠀⠀⡇⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠫⣁⣄⣠⡀⠀⠀⡀⠀⠀⠀⡰⠧⠼⡄⠀⠀⠉⠉⠀⠀⣀⣀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣷⣬⣦⣝⠩⠒⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⣴⠋⠁⠀⠀⢰⡇⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠥⣀⣨⠉⠐⠂⢈⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⠤⠄⢸⡇⢸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠴⠐⠂⢀⠀⠐⠂⠀⣁⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣖⡀⣀⠀⠒⠀⣈⢀⣐⣢⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠃
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⢈⣉⠋⠋⠙⠙⠉⢉⠁⠀⢀⢈⡉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠁⣧
⠀⠀⠂⠀⠁⠀⠃⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣡⠀⠀⠀⠻⠀⠁⠖⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣬⣥⣾⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠴⣶⣄⣀⣀⣀⣠⡄⢀⣠⠞⠁⢴⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⠛⠛⠉⠁⠚⠉⠀⠀⠀⠺⣧⠀⠀⠀⢠⣤⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢆⣿⠟⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠨⠋⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠶⢄⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡴⡇⠀⠀⠀⠐⠲⠖⠋⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣧⡀⠀⠀⠀⠀⣰⠁⢐⠢⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠟⣿⣿⠋⠀⠀⠀⢀⡴⠃⢀⣾⣇⢀⡀⠉⠉⠉⠛⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡎⢧⡀⠀⠀⠀⣀⡴⠋⢀⣴⣿⣿⣿⣿⣗⣴⣦⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣦⣉⠓⠒⠋⠁⠴⠾⠛⠛⠛⠋⠉⠙⣿⣿⣯⣌⡆⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⣀⣠⣤⣴⣶⣷⣾⢿⣿⣿⣿⣿⣶⣆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠻⡿⠿⢿⣿⡿⠟⠉⢀⣀⣤⣶⣶⣿⠿⠿⠛⠉⡉⠡⠿⢗⣿⣿⣿⣿⣿⡷⠃⣠⠀⠘⢆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⢎⡉⠑⣸⣿⣿⣿⠟⢋⠉⠀⠀⠀⠈⠁⠀⠀⠉⠁⠸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⣛⠛⠛⠛⠛⠋⠙⠈⣿⣿⡟⠘⣿⣿⣯⡿⢷⣾⣯⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠴⠭⠯⣛⣉⡁⠀⠀⠀⠈⢿⣿⣿⡁⢹⣿⣿⣿⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠙⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⣀⣠⡼⢖⠀⠀⠀⢸⠏⠻⣇⠠⢿⣿⡿⢛⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣀⣀⣀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢀⣠⡯⠗⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡄⠄⠐⢢
⠈⡆⠀⠌⠀⣀⠒⠀⠀⠀⠀⣼⣿⣟⣛⣛⣛⣛⣿⣿⡄⢀⠀⠠⡠⠂⠀⠀⠁⠐⠁⠀⠀⠠⠀⢀⢀⠁
⠀⢱⡀⠀⠀⠰⡀⠤⢀⠒⠀⣏⣟⠻⠻⢫⡟⠛⢻⢹⡇⠘⠀⠀⠀⠀⡀⠀⠀⠐⠘⠁⠐⠂⠀⠀⠸⠐⠒
⠀⠸⢷⠀⠀⡄⡄⠀⢡⢀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸
⠀⡆⠁⠁⡄⠀⡋⠀⠉⠂⠀⠀⢈⡉⠙⠛⠛⠉⢉⡀⠀⠁⠀⠀⠈⠀⢀⡀⠀⠀⠀⠘⡀⠀⠀⠀⢨
⠀⠡⡀⠀⠀⠐⠡⠀⠀⠈⠀⠀⠀⠁⠀⠤⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠈⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠒⠠⠀⠀⠄⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢐⠆
⠀⠄⠀⠐⠀⠃⠁⠀⠀⠈⢺⠅⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⡀⡀⠚⠁⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠉⠀⠀⠀⡄⠀⠀⠀⠀⠐⢶⠃⠴
⠰⠆⠀⠀⠲⠀⠀⠄⡄⠀⠀⠡⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⠁⠀⠀⠀⠉⠐⠚⠘⠓
⠀⠀⠀⠀⠀⢀⢀⡪⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠐⠐⠀⠀⠁
⠀⢠⠤⠤⠤⠄⠀⠀⠄⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⠂⠠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠐⡄⢠⡀⠤⠦⠖⠀⣼⠿⢿⣿⣷
⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡠⠀⠈⠀⠀⠀⠘⡄⠀⢠⠀⠀⠀⣉⢐⣄⢨⡋
⠀⠀⠈⠁⠉⠁⠈⠃⠀⠠⠠⠀⠀⠠⠄⠀⠠⢄⠄⠀⠁⢀⡄⠀⠐⠇⠀⣷⣄⠀⣀⠘⠀⠈⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⢀⠠⠤⠀⠀⠀⢀⠀⠐⠒⠗⢆⠀⡽⢄⠈⠀⠀⠁⠀⠀⠀⠂
⠀⠈⠒⠂⠒⠒⠐⠐⠂⠀⠀⠀⠄⠀⠀⠈⠁⠀⠁⢸⠀⠀⠀⠀⠀⠀⡉⡆⠀⠀⠐⠀⣠⠀⠀⠀⠀⡄
⠀⠨⠁⠀⠐⠀⣐⣤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⡰⠀⣌⠀⠀⠀⢠⠀⠀⠠⠠⡆
⠀⠀⠠⠤⠤⠤⠤⠀⠠⠤⠠⠄⠤⠄⠀⠀⠀⠀⡀⢸⠀⠀⠘⠷⠔⠊⠀⠈⠈⠀⠀⡀⠀⠀⠀⠀⢀⠡⢤
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠽⠖

⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⠀⢸⠟⠛⠛⠛⠛⢻⡇⠀⠀⠀⣠⠴⣖⣷⠦⣀⠀⠀⠀⠀⠀⢤⠀⢀⣀⣀
⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⢻⢫⠝⡟⢹⠀⠀⠀⠀⠀⢿⠀⢀⣿⣽⡗
⠀⠀⠀⣧⣤⣤⣼⡇⠀⠀⠀⠘⠛⢛⣿⣿⡛⠛⠃⠀⠀⠀⠈⠛⢼⡤⠗⠊⠀⠀⠀⠀⠀⠉⠀⠀⠈⠗
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⣠⣾⣫⣟⣷⣄⠀⠀⠀⠀⠤⢒⣉⣉⡒⠤⠀⠀⠀⠀⠀⢘⣧⡴⢒⣆⠀⠀⠀⢰⠒⠒⡒⠒⣶⣶⡆
⠀⠀⡧⡧⠴⡧⢾⢾⠂⠀⠀⠀⠀⠡⢒⣒⠌⠁⠀⠀⠀⠀⢰⣫⣤⣿⣿⠏⠀⠀⠀⢸⠹⡇⡇⢦⣬⠍⡇
⠀⠀⠙⢿⣾⣷⣻⠟⠀⠀⠀⠀⠀⠀⢱⡦⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⡀⠀⠀⠀⠸⠤⠤⠥⠥⠶⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⣤⠀⠀⠀⠀⠠⢲⢶⣀⣶⡲⡄⠀⠀⢠⠒⠉⠀⠉⠉⠐⡄
⠀⠀⠀⣾⣿⣿⣷⡄⠀⠀⠀⢠⢀⠵⠤⠤⢎⠙⠀⠀⠀⢰⣟⠋⣾⣿⡦⢏⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡏⣿⣿⡿⠁⠀⠀⠀⠈⠛⠒⠒⠒⠒⠛⠀⠀⠀⠈⠹⡶⠾⠿⠷⡾⠀⠀⠀⠀⠉⠒⢦⠔⠀⠉
⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⡀⢀⢄
⠀⡔⠀⣲⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⢸⠄⢠⠀⠀⠀⠀⣦⣼⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠑⠠⠿⢁⠔⡠⠤⣄⠀⠀⠀⡄⠀⠉⠉⠀⢸⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠮⠥
⠀⠀⠀⠀⠃⠚⢇⡀⠿⠀⠀⠀⡇⠀⠀⠀⢠⠞⠀⠀⠀⠀⣼⣛⣿⣟⣟⡿⠀⠀⠀⠀⠀⢰⢲⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠘⠈⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦
⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠠⣶⠶⣶⠟⠃⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⢠⣤⣤⣿⣤⣤⡀⣿⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣸⣿⣀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⠟⣿⠙⠿⠀⣿⠀⠀⢸⣯⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⡆⠀⠀⠙⠋⠀⣿⠀⠀⠐⣿⣤⣤⣼⣯⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠛⠛⠛⠛⣿⡄
⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠿⠀⠀⠈⠛⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠙⢿⣦⣤⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢹⣿⡆⠀⠀⠀⠀⣠⡴⠒⠲⣶⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢠⣿⢃⣠⣾⠟⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢻⣿⡀⠀⠀⠀⠻⠋⠀⠀⣸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠰⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⠛⢿⣷⠀⠀⠀⣠⡶⠚⠉⢹⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠘⣿⣧⡀⢸⣿⡇⠀⢀⣼⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠘⠛⠛⠛⠛⠀⠙⠛⠛⠉⠈⠛⠛⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠠⣤⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠄





⠀⡉⠉⠁

⠀⠀⠀⠀⠁⠿⠛⠉⠀⠀⠀⠀⠀⣨⡀⠈⠀⠀⠀⡀⠀⠰⣔⠒⠼⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠩⣝⠢⣄⡀⡲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠠⠚⡃⠀⠀⠀⠀⠦⠀⠰⣘⢫⡟⢨⡓⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣑⣱⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣖⣤⠆⠀⢠
⣀⣤⣆⣼⣴⣄⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡁⠀⠀⢸⡀⠀⣀
⠉⠙⠊⠉⠀⠈⠉⠀⠈⠀⠀⠀⣠⠔⠛⠁⠀⠐⠃⠀⠀⠀⠀⠀⠘⠉⣉⠉⠉⠉⢉⡛⠀⠠⠈⠀⠄⠀⠀⠀⠏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠤⠀⠀⠤⠀⢢⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⡈⠨⣮⡏⣹⠋⠀⠀⠀⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠄⢜⠲⢏⠅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀
⣷⢮⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡇⠀⠀⡎⠉⡖⠉⠉⣧⠀⠀⠈⠈⠉⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣦⣥⣽⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⡷⣟⣾⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠁⠀⠀⠠⡦⠀⠀⡀
⠔⠀⠀⠀⠀⠀⢼⡤⢀⡀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂⠓⡀⢠⠂⢀⠀⢠⢺⠿⠟⠛
⡾⠇⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣇⣀⡾⢠⠏⠀⠸⢶⣶⠶⠶
⠐⠛⠄⠀⠀⠀⠀⡇⠀⡇⠀⠀⢠⣤⡄⠀⠀⠐⠋⠀⠀⠀⢰⣿⠛⣧⠀⢢⠀⠀⠈⣧⠘⣆⣷⠃⠀⠀⢸⠷⠁⠚⠛
⠀⠀⠀⠀⠀⠀⠀⣇⣠⠁⠀⠀⠈⡈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠈⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂
⢐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤
⠘⠀⠀⠀⠀⡀⢀⣀⡀⠀⢠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠸⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢚⠥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢈⡁⡐⢄
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠁⠘
⠠⠀⡶⠉⢫⠑⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡚⠛⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⢼⣉⠀⠀⢖
⡄⢻⡤⠔⠚⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠴⠊
⠘⢦⣈⣓⣂⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⣜⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠠



⠀⠀⢠⠖⢦⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠄
⠀⠀⢸⣄⣬⡀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠒⡂⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⡆
⠀⠀⠸⣿⣇⠇⠀⠀⠀⠀⠀⠀⢧⣀⣈⣉⡁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠳⡅⠀⠜⢀
⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠘⠛⣿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⠄



⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡍⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡘⢢⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⠄⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⢔⠂⢹
⠀⠀⠧⠤⠭⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣒⣒⣒⣲⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣞⠡⠨⠤⢌⣳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣐⡦⠾⠖⣷⠈⠉⠉⠃⡾⠻⡿⣻⠿⠡⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣵⣤⣀⡉⠛⠶⢿⠸⠠⡀⢠⣿⢽⠯⣒⠕⠋⣠⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⡉⠉⠡⠤⠤⠴⠈⠀⠰⠄⠭⠈⠤⠤⠬⠁⠐⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠡⠐⠂⣀⢊⣈⣀⠀⠀⠄⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣨⡤⣥⡄⠀⠀⡀⣁⠙⠀⠀⠈⢡⣀⠐⢖⣢⣶⣷⣾⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⠁⡠⣒⣥⣶⡛⡇⠚⡁⠘⠸⡏⠑⢤⡈⠑⠟⠫⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡭⠶⠿⠿⠿⢶⣶⣢⣕⠿⠍⠿⠳⡿⠶⠇⢦⡥⠤⠧⠷⠷⠿⠛⠂⠁
⠀⠀⠀⠀⠀⠀⢶⠋⡔⠁⠀⢀⡤⣠⣀⠀⠈⠙⢝⢽⢦⠀⣄⠀⠰⠎⢀⡀
⠀⠀⠀⠀⠀⣼⠏⠘⢀⡼⢟⡩⠚⠁⠙⢷⣦⣇⠈⠆⢲⡇⠀⠈⡩⢂⠤⠊
⠀⠀⠀⠀⢠⣿⠠⠧⠔⠚⠁⠀⠀⠀⠀⠀⠉⠛⢤⢼⣀⡿⠀⠘⢢⠌⣒⠄
⠀⠀⠀⠀⣸⠃⠀⣆⠀⠠⣀⡀⠀⠀⢀⡀⣀⠀⢸⡄⠀⢱⡄⠖⠓⠊⠁
⠀⠀⠀⠀⠙⢔⠰⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⡇⠔⡜⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠄⡀⠠⠔⠁⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⢲⢄⣀⣀⣀⡴⡿⢦⢄⡀
⠀⠀⠀⠀⠀⢀⠔⠡⠤⠀⢸⣄⣀⠑⠁⣰⡏⠐⠁⡈⠲⢄
⠀⠀⠀⠀⡰⠁⡀⢁⠀⠐⢽⡝⠂⠀⠐⢚⡯⢐⠠⡂⠄⠀⠣⡀
⠀⠀⠀⠐⠀⠄⡠⢀⠀⡀⣸⡇⠀⠀⠀⢰⡪⢐⠨⢂⠅⡂⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠐⠈⠈⠉⠈

⢀⠀⠈⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠀⠀⠉⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⢀
⣀⣐⣒⣒⣒⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣼⢷⠀⠀⢸⣭⣗⠀⢠⡟⠉⠀⠀⣿⠙⣦⠀⢸⣯⣭⠁⠀⢸⣏⡉⠀⢰⠋⣙⡂⠀⢸⣤⣼⠀⠀⣷
⠀⠀⠸⠟⠛⠇⠀⠸⠧⠞⠁⠘⠷⠶⠂⠀⠿⠶⠋⠀⠸⠷⠶⠆⠀⠸⠁⠀⠀⠘⠷⠿⠃⠀⠸⠀⠸⠀⠀⠿

⠀⠀⠀⣷⠀⢰⣦⠞⠀⠀⢸⠀⠀⠀⢰⣦⣴⣷⠀⢰⣷⡀⡗⠀⣰⠖⢦⡀⠀⡟⢻⡆⠀⡴⠛⣦⠀⢰⡟⣳⡄
⠀⢠⣤⡟⠀⢸⡟⢷⠄⠀⢸⣧⣤⠀⢸⡏⠉⣿⠀⢸⡏⠻⡇⠀⠻⣤⡾⠁⠀⡟⠉⠁⠀⢧⣴⣿⠀⢸⡟⢻⡄

⠀⠀⣠⣤⡄⠀⢠⣤⣴⠄⠀⢠⡄⠀⡄⠀⢠⡄⠀⣤⠀⢠⡀⠀⠀⢠⠀⠀⣤⣀⡄⠀⢤⡀⣠⠀⢠⣤⣤⡤
⠀⠀⡙⢶⣄⠀⠀⢸⡇⠀⠀⢸⣇⢠⡇⠀⠈⢿⣼⠃⠀⠘⣧⡾⣦⡟⠀⠀⢨⣿⡀⠀⠈⣿⠁⠀⢀⣴⠏
⠀⠀⠙⠛⠁⠀⠀⠈⠁⠀⠀⠀⠙⠋⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠈⠁⠀⠀⠉⠀⠉⠀⠀⠉⠀⠀⠙⠛⠛⠁
⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⣀⣀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠀⣀⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⢹⡇⠀⠘⢉⡗⠀⠘⢩⣗⠀⣠⣿⣇⠀⠸⣯⣭⡄⠀⣾⣯⡄⠀⠉⣽⠃⠀⣸⢿⡇⠀⢺⣍⣿⢀⣿⠙⣇
⠀⠀⠸⠇⠀⠴⠿⠦⠀⠲⠴⠟⠀⠉⠹⠏⠀⠀⠶⠾⠃⠀⠻⠶⠏⠀⠰⠃⠀⠀⠻⠶⠇⠀⠀⠴⠋⠀⠻⠾⠃

⠀⢀⡾⠀⠹⡆⠀⠀⠀⠀⠀⣤⡀⠀⢀⣤⠄⠰⣄⡀⠀⣀⣀⡀⠀⢠⡄⣴⠆⠀⠀⣴⠇⠺⣧⠀⠀⣀⣶⣰⡄
⠀⠸⣧⠀⢀⡇⠘⠛⠃⠀⠛⢿⠛⠀⠚⢧⡀⠀⣼⠋⠀⠴⠶⠄⠀⣠⡾⢡⡄⠀⣰⡏⠀⠀⠹⣧⠀⢽⡿⣿⠅
⠀⠀⠙⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⢠⠴⠶⣤⠀⠀⢀⣶⡄⠀⠀⣠⢦⠀⠀⢀⡀⠀⢀⡀⠀⠀⣀⣄⡀⠀⠀⠦⡦⠀⢰⠆⠀⣴⠀⢀⡴⢦⡀
⠀⠀⣿⢾⣽⣿⠇⠀⢘⣿⣦⠀⢀⡿⣯⡤⠀⢀⡅⠀⢠⡀⠀⠰⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⡟⠁
⠀⠀⠈⠛⠒⠋⠀⠀⠉⠛⠋⠀⠈⠙⠋⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠉⠉⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣆⣨⣿⣿⣿⣿⣿⣿⠟⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣠⣾⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠋⠛⠛⠿⠿⠿⣿⣿⣿⠿⠿⠿⠛⠛⠉⣀⣤⣶⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣴⣶⣾⣉⣉⣉⠉⣉⣁⣀⣉⣉⠉⢉⣉⣉⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⡿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠋⢁⣠⣶⣿⣶⣄⡈⠙⠻⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⡴⢶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢶⣾⣿⣿⠋⠀⡄⢠⠸⡌⢸⡆
⠀⠀⠀⠀⠀⠀⢀⡾⢁⢔⣾⣿⣿⣧⠆⣰⢁⠎⣰⣿⣮⠃
⠀⠀⠀⠀⠀⠀⡾⢠⢣⣾⣿⣿⣿⣫⣞⣵⣫⣞⠻⠟⠁
⠀⠀⠀⠀⠀⢰⠇⡏⣾⣿⣽⣿⣿⡏⠉⠀⡷⠆⢲⠂
⠀⠀⠀⠀⠀⢸⢸⢰⣧⡇⣿⣿⠛⠁⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⣿⢸⢸⢸⡇⣿⣿⣀⠀⠀⠀⠀⠀⠲⢺⠋⠀⠀⠀⠀⠀⢀⢤⣀
⠀⠀⠀⠀⠀⣏⢺⠸⡈⡇⠹⡝⣿⣀⠀⣴⣦⣤⡤⢠⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠢⠄⡀
⠀⠀⠀⠀⠀⢿⠈⠆⢃⠸⣆⠡⠀⣹⡷⠸⣿⠏⢀⠞⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⡀
⠀⠀⠀⠀⠀⠈⠷⣄⣈⣦⣽⣶⡿⠋⠀⠀⣀⠴⠋⠀⠀⠀⠀⢀⠏⢀⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠛⠰⢇⡄⠀⠀⠀⠀⠀⠀⠀⣰⢷⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠘⢇⡀⠀⠀⠀⢾⣀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠠⠿⡤⣄⣀⠘⠰⢲⢤⡄⠀⣰⢣⣾⠃
⠀⠀⠀⢀⣠⡴⢟⣽⣦⣀⠈⠐⠀⠀⠊⢸⠳⣶⣤⡀⢀⡌⠀⠀⠀⠀⠀⠀⠈⠉⠘⠷⡆⠀⠈⠁⣰⢣⣿⠃
⠀⢀⡴⠛⢻⢿⣾⣿⣿⣟⢯⡀⠀⠀⠒⠛⣇⢿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⣿⠏
⠀⣼⢁⠞⣤⡡⢽⣿⣿⣏⡎⢷⠀⠀⠀⠀⢻⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣷⠏
⠀⡏⣼⢤⣷⣿⠃⣿⣿⣿⣿⠘⡇⠀⠀⠀⠸⡇⢹⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣰⣏⢺⠇
⠈⣷⣿⡸⠿⣿⢼⢹⣿⣿⣿⣀⢳⠀⠀⠀⠀⣧⠼⠗⢚⣿⠳⣦⣄⡀⠀⡤⠒⣯⠹⡏⢷⡏⢠⠏
⠀⢻⣿⣦⣻⡖⡶⣸⣿⣹⣿⣼⣿⡆⠀⠀⢰⠃⠀⠐⠛⠛⢋⠡⣿⠙⢶⣆⢃⠘⠀⠁⠈⣇⠊
⠀⣾⢻⣿⣿⡀⣤⣿⣿⣿⢟⢞⣥⣷⡔⠲⡃⠀⠀⠀⠀⣉⠥⢊⣽⣿⣶⡿⠀⠀⠀⠀⠀⡟
⠀⣿⢹⠿⢾⢇⣴⣿⣿⡿⠛⠛⠁⠀⠙⡆⠱⠀⠀⠀⠠⢐⣪⡿⢿⡯⢨⡷⣀⠀⠀⣀⡼⠁
⠀⠘⣷⣶⡰⣿⣿⡿⠋⠀⠀⠀⠀⣀⣀⢸⡀⡶⠚⢛⢻⣿⣿⡇⢖⠪⡤⠳⣤⡭⠝⠁
⠀⠀⢿⢿⣷⣾⣿⣤⣤⣴⣶⣻⣿⣿⠿⣸⡿⣧⠀⠘⠘⣿⠻⠷⡴⠶⠶⠋
⠀⠀⠈⠇⠙⠿⣿⣿⣿⣩⣿⣿⡿⠷⠿⣿⢱⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⠟⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⡆⠀⠀⠀⠀⢀⡴⠖⠒⠾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢒⡒⠶⣇⠀⠀⠀⢠⢿⣀⣀⣄⣀⣸⠀⠀⠀⠀⠀⢘⠀⢸⠋⠉⠉⠉⠉⡏⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⢒⣒⣋⣿⠀⠀⠀⢸⡌⣿⠀⠀⠈⡏⠀⠀⠀⠀⠀⢘⠀⢸⠀⠀⠀⠀⠀⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠈⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⡇⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⢸⣿⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡗⠀⢸⠀⠀⠀⠀⠀⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠸⡞⡇⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠱⠅⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠁⠈⠹⡆⠀⢻⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣹⠀⠀⠀⠀⠀⡧⠀⢸⡀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⣴⠃⠈⠲⢄⡀⢀⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢉⡞⠁⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠋⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢸⡆⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⣾⠀⠀⠙⠢⢄⡴⠋⠀⠀⠀⠀⢸⣇⡤⠤⢼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠹⣦⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡗⠀⠀⡇⢀⣀⣀⣀⣇⣀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡇⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⣾⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠚⢌⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠈⠀⠁⠀⠀⠄⠀⢀⠔⡠⠀⡴⢿⡟⠁
⠀⠀⠀⠀⠀⠀⡄⡒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢁⠈⣰⠎⡠⠋
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠄⠤⠠⠤⠀⠒⠊⠁⠀⠀⠀⠠⠈⠀⢁⡴⢃⠜⠁
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠋⠈⠉⠁⢀⣀⣀⠠⠄⠀⠐⠂⠀⠀⠀⠔⠁⢊⡠⠃⣠⠋
⠀⠀⠀⠀⠀⠀⠙⠀⠐⠀⠀⠒⠂⠁⠁⠀⢀⣀⣀⡀⡀⠤⠒⡰⠀⠔⣠⢟⢀⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠒⠂⠊⠁⠀⠀⠀⠀⠀⢀⠀⠠⢲⡴⣏⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠤⠤⠤⠀⠂⠉⠁⠀⢂⠀⢠⡎⣠⠯⠤⠄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠤⠤⠄⠐⠂⠸⠣⣀⡴⣧⠞⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠠⠤⠀⠐⡆⠀⡠⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⠀⠀⠤⠤⠴⠟⠡⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⢰⠖⠒⠚⠻⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⡀⠀⠀⠀⣀⣀⠤⠔⠒⢛⣋⣉⣩⣥⣥⣤⣶⠾⡿⠽⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣝⣒⣪⡭⠤⠖⢒⠚⠋⠭⢍⣀⣀⣠⣤⣤⣔⣶⣶⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠛⢉⣐⣉⠠⠎⠁⠚⠋⠏⠋⠀⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠄⠄⠤⠄⠀⠀⠀⠀⠀⠄⠔⠔⠐⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠐⠆⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⢀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡋⠉
⠀⠀⠀⠀⠀⢸⡡⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⠦⠼⠂⠒⠀⠀⠀⠀⠀⠜⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⡿⣣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤⢄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡘⢃⡞⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠌⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠔⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠈

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

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠈⠂⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠙⠛⠿⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⢀⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡛⠁⠀⠀⠀⠀⠀⠛⣿⣟⠋
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠐⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆



⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣦⡀
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢣⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣧
⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣭⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⠎⣀⣀⣀⠤⠤⠶⣚⡉⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠛⠛⠉⠽⣶⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⢉⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⢖⣒⡢⠤⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣥⣶⠯⢃⣁⣄⠳⡄⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠒⠈⠀⠀⠉⠀⠐⠒⠒⠂⢄
⠀⠀⠀⣀⠞⠙⠲⠖⠢⡀⠀⠒⠨⡳⡀⠄⠠⠀⠀⠀⠀⠀⠀⠱⠽⠿⠟⠒⠉⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⣠⢀⡀⣠⠠⠀⡀⠠⢀⣀⡄⣀⠉⠘
⠀⠀⠄⠘⣁⠦⡀⠀⠀⢹⠂⢀⡠⠘⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⡄⠃⠀⠃⣇⢀⡀⠁⢀⢠⡿⠀⠘⠀⠀⡄
⠀⢨⠂⣠⠃⠀⢀⠛⠶⢎⠀⠘⡁⠦⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⡇⢧⣀⡇⣇⣠⠧⠄⢀⣀⠿⣄⣸⠰⠀⡇
⠀⠸⣄⣍⠐⢀⣆⠀⠀⠀⢀⠞⡤⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢀⠃
⠀⠀⠣⡻⠉⠁⠈⠀⠀⠀⣀⠦⡀⢀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢀⣀⠀⠤⠘⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⡹⢤⡉⠂⢴⣈⠒⢡⣀⠴⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⣠⠁⠀⠡⠍⠉⠩⠍⠐⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠀⣢⠤⠤⠄⣦⣸⠀⡐⠁⠉⢢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠤⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣌⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠉⠲⡔⠢⢱⡀⠀⠀⠀⠀⠀⠁⡖⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢼⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡧⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠈⠂⠀⠋⠀⠀⢠⠄⠀⠀⠀⠀⠀⠔⠄⠀⠛⠀⠐⡁⠀⠀⠀⠀⠀⠉⠡⠈⠀⠁⠉⠩⢸⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠐⠊⠂⡀⠀⠀⠊⠀⠀⠀⠀⠀⡀⠀⠀⡀⣀⠄⠀⠀⢀⢤⠀⠀⠀⢡⠀⠀⠀⠀⠀⡀⢰⢐⠀⠀⠂⢐⢰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⢄⠀⠀⢀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠒⠂⠐⠉⠀⠐⠰⢠⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢄⠂⠀⢀⡠⠄⠀⠀⠀⠀⠀⠤⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠄⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠜⠤⢰⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡅⠤⢀⠂⠀⠀⠀⠆⠓⠊⠈⠒⠀⠑⠚⠈⠒⠂⠆
⠀⠀⠀⠀⠀⡰⠋⠢⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡠⠋⠈
⠀⠀⠀⡠⢎⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠄⠀⠀⠀⠀⠤⠕⠊⠁
⠀⠀⠀⠳⢄⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣏⠲⣈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⠼⢻⡽⠋⡉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡈⠂⠀⢠⠊⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠔⢁⡴⢙⡵⠋⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⢂⢔⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⣱⡁⠈⠀⠔
⠀⠀⠀⠀⠔⢁⡴⡙⡴⠊⢀⠀⠁⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠐⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡑⠞⢳⠷⢖⣁⣀⡀
⠀⠀⢀⠞⠉⠉⠉⠉⠁⠶⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠀⠐⡆⡰⠀⠐⠀⠔⠀⠀⠍⠢⡀
⠀⠰⠃⠀⠀⠀⠀⠐⡆⢀⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣀⢼⠍⠀⠀⠀⠈⠺⡄⡀⢀⠀⠅
⠀⠀⠤⠤⠤⠤⠤⠤⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠤⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠒⠁⠀⠀⠀⠀⠀⠀⠉⠂⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢴⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠝⢻⡍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠄⠀⠠⠀⣠⡿⠤⠀⡀⠀⠀⠀⠀⠀⠈⢆⠀⠋⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠉⣁⣀⡀⠀⠀⢠⡋⠀⠀⠀⠉⡀⢤⣤⡄⠀⠀⠈⠁⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡏⠀⠉⣦⣾⠁⠀⢹⡆⠀⣼⣿⣿⣿⣷⣶⡗⠘⠛⠁⠀⠒⠒⠂⠀⠀⠀⠙⢷⠄⢷⠇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠤⠶⠁⠘⠦⠴⠾⠄⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠓⢦⣄⠀⠀⣆⢠⠄⢦⢠⠄⠂⠀⠀⣠⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣲⡒⣰⠆⠀⠀⠀⠀⠈⠉⣿⣿⣿⣧⣰⡋⢉⠶⡉⢉⡆⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠙⣷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⣤⣏⠀⠀⠀⠀⠀⠀⢀⣨⣭⠉⠉⠉⠁⠀⠀⠀⠈⢁⣀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⠉⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⣤⣤⠹⡆⠀⡈⠛⠁⠀⠀⢿⣻⡆⠀⠀⠀⠀⠀⢀⣶⣾⣅⠀⠀⢹⡆⢠⣴⠀⢀⣴⠟⠉⣠⣾⡁⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⢦⣀⣀⠀⠀⢺⣿⣿⣿⣿⣿⠹⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠘⣿⠀⠉⣴⡟⠁⠀⠀⠻⠟⠡⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠘⠋⠀⢠⡞⣀⣉⢳⡀⠠⣾⣿⣿⣿⣿⡇⢻⣿⡇⠀⢿⠇⠀⠀⠈⡄⠀⡤⠀⠠⣿⠀⣸⡟⠀⣤⣤⡄⠀⠀⠀⡰⠟⠁⠀⠙⠷
⠀⠀⠀⡀⠀⢠⣤⡄⠀⠈⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⢉⠁⠈⢉⣁⣀⡀⠀⠀⠰⠆⠀⠀⠀⠶⢸⣿⢀⣿⠃⠀⣿⣿⡇⠀⢰⡖⠀⠀⠀⠀⠀⠀⢰
⠀⢀⡞⠀⠀⠈⣿⠅⡀⢠⡄⢀⠀⠀⠀⠙⢶⡀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⡆⠀⠆⠀⣼⡏⣸⡿⠀⠀⠻⠿⠇⢰⣦⠈⢆⠀⠀⠀⠀⠠⠊
⠀⠙⠛⢻⡶⠀⠠⢄⠙⠀⠁⠈⠠⠆⠀⠀⢸⡇⠀⣘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢰⣿⢃⣿⡇⠀⠀⠺⣷⣿⣞⣿⡆⠀⠿⠂⠀⠺⠇
⠀⠀⢀⡞⠁⠀⠒⠂⠀⠀⠀⠀⠀⠚⠁⠀⢰⡇⣸⣿⣿⣿⣆⠀⠈⠐⠆⡀⠀⠀⢻⣷⠀⣠⣿⡏⣼⣿⢀⣦⠀⠈⠛⠛⠛⠙⠃⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠈⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣙⣀⠀⢸⡇⠈⠉⠉⠉⣁⡀⠀⠂⠀⠀⠀⠀⢸⣿⣾⣿⣿⣼⣿⠇⣼⠿⢶⣁⠄⠀⠀⠚⠻⠿⠿⠿⠿⠛⢉⡅
⠀⢠⣶⠿⠀⣬⣐⡀⠀⣿⣾⠇⠀⢡⡞⠁⣾⡇⠰⣶⢿⣿⣿⣿⣿⣶⣤⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠀⣀⣀⡼⢣⣆⠀⠀⠐⠒⠂⠀⠤⠐⠊⠁
⠀⡘⠁⠀⠀⠻⣿⡇⠀⠈⠉⠀⣠⡈⠀⠀⢻⣇⠀⠀⠸⢿⣿⡿⠏⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⢨⣿⣦⠈⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠾⣿⣦⠀⠛⠁⠀⠀⠀⢠⣿⣶⡖⡆⠘⣿⣦⡀⠀⠀⠀⣴⣾⡀⠀⠀⣰⣿⣿⠟⠉⣠⠔⠀⠄⠀⠀⠀⡤⠀⠐⠀⠀⠤⠀⣉⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠀⢠⡟⠀⠀⠈⠻⣿⣷⣤⣄⡙⠛⠀⢀⣼⣿⡿⠁⡀⡀⢀⠀⣀⡀⠀⢰⣿⡇⠀⠀⠀⡀⠐⡀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠉⣿⣯⡀⠀⠀⠀⠂⠀⡙⢿⣿⣿⣷⣤⣾⣿⡟⢀⡄⠀⡰⠀⢀⡔⠁⢠⠀⠉⠀⢤⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠉⠉⠁⡴⠄⠀⠀⢠⠁⠀⠈⢿⣿⣿⣿⣿⡇⠢⠤⢴⡤⠤⠋⠀⠀⣼⡆⠀⠀⣰⣄⠀⠀⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⢠⣿⣿⣷⠀⠀⠀⢸⡄⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀⠚⠓⠀⠀⠀⣠⡿⠀⠶⠁⠀⠀⠑⠖⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⠶⠶⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠖⣰⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣤⡤⠶⠶⠒⠒⠛⠲⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢠⡞⢁⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠹⣆
⠀⠀⠀⠀⣠⣿⣞⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠛⠳⢦⣼⢀⣠⣴⢖⣛⣋⣉⣁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣉⣛⣶⣿⣆
⠀⠀⠀⢠⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠲⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡄
⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠱⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠶⠀⠼⠁⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢧⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡋⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡆⠀⠀⣏⣀⡀⠀⠀⠀⣠⡴⠿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉⢩⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⣒⣚⣯⣷⢶⠶⠞⣻⣿⣟⡉⠉⠁⠀⠈⡄
⠀⠀⠀⣀⣤⣠⢄⣀⠀⢳⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⡀⠀⣀⣴⣁
⠀⠀⠈⠀⠈⠐⠋⠚⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡋⣙⣰⡿⠋⠉⠁⠀⠀⠙⠉⠓⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠉⠉
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⢤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠧⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⣀⣠⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡆⠐⠀⠘⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⢿⡟⠡⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⣴⣂⠀⠀⠀⠀⢿⣿⣇⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⣄⢸⡇⢀⡀⠀⠀⠁⢀⢽⠇⠀⠀⠀⢘⣿⣦⣄⠀⢀⣠⣀⠀⠀⠥⠀⣴⣿⣿⠟⠁⣀⠀⠀⣿⣿⡇⠀⠀⢠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⡇⠀⣀⣴⠀⠀⢠⣀⡆⠀⠀⠀⢰⣮⣟⡯⡱⠟⠉⣰⡀⠀⠀⢰⣿⣿⠃⢠⣶⠤⠀⠀⢿⣿⡇⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡷⣿⡇⣿⡿⣿⠀⠀⢸⣿⡇⠀⠀⠀⣼⡇⠨⣿⢠⠀⢐⣿⣿⡇⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⠻⢿⡇⠉⠀⣿⠀⠀⢸⣿⡇⠀⠀⠀⡝⠋⠐⢿⠈⡀⢐⣿⣿⡇⠀⠀⠀⠀⢤⣾⣷⣤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⣿⣸⣷⣾⡇⣾⣿⣿⠀⠀⠀⠉⡀⠀⠀⠀⣿⣷⠀⠀⠀⡂⠠⣿⣿⡇⠀⠸⢦⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠈⠠⠃⣿⢙⠻⢿⡇⠁⠀⣿⠀⣠⠰⠃⠑⠀⠀⠒⣿⣿⠀⠀⠀⣤⡾⣿⣿⡇⠀⠀⠀⡀⠔⠚⡃⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣷⣾⡇⣶⣿⣿⣾⣿⡷⠉⠀⠀⠀⠈⣿⣿⠀⠀⠊⠀⠀⠙⡿⡇⠀⠀⠀⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⠙⢻⣋⠉⠉⢤⣿⣿⡟⠀⣄⡀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢹⣿⣿⠀⢸⣿⣿⠀⠘⠻⡇⠠⣦⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡅⠿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣦⡤⠈⠀⢸⣿⣿⠀⢸⣿⡇⠀⠰⣿⣶⠖⠀⠀⠀⠈⠁⠀⠀⠀⢰⠈⣿⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⡇⠀⠀⠀⠙⠿⠀⠈⠙⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣤⡞
⠀⢠⣄⠀⠀⠀⠀⢀⣀⢰⣿⡇⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⢴⣾⡿⠛⢹⣿⡇⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⣿⡇⠄⠂
⠀⢸⣿⡇⠀⠉⠁⣀⣤⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠐⠋⠁
⠀⢸⣿⡇⠀⣴⣿⠟⠋⠉⠉⠓
⠀⢸⣿⡇⠀⠈
⠀⠈⠻⠇

⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⠩⠀⠠⠑⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣾⣷⡆⠀⠀⠀⠀⠀⢠⣤⠶⡶⢶⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠐⠂⡒⠲
⠀⠀⠀⠀⡐⡄⣦⡄⠀⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⡇⠀⠀⠀⠀⠀⠈⢩⣿⠩⡯⣻⣎⠉⢱⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⠀⢸
⠀⠀⠀⠀⠡⠁⠈⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢀⡇⠀⠀⠀⠀⠀⠀⠿⠿⠷⠾⠿⠿⠖⠃⠀⠀⠀⠀⠀⠀⡸⠅⠤⠤⠼⣀⠌
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣶⣾⣿⢶⣤⢀⠀⠀⠀⠀⠀⠀⢰⠶⡐⠂⠒⢂⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡍⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⢿⣿⣭⣿⣽⣿⠃⢱⠀⠀⠀⠀⠀⢸⠀⠈⠲⠞⠁⣠⣾⣎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⣀⣭⣯⣄
⠀⠀⠀⠀⠀⠿⠟⠫⣡⠒⠁⠀⠀⠀⠀⠀⠘⠏⠀⠠⢀⡸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡸⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠆⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃



⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⡄⣠⣦⡀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠠⠐⠒⣦⡀⠀⠀⠀⠀⠀⠀⡖⠂⠒⣀⠂⠒⢲
⠀⠀⠀⠀⣿⣿⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣘⣟⣁⠀⢃⣙⣟⣁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⣽⡇⠀⠀⠀⠀⠀⢀⡥⡄⠠⠿⠄⠀⢸
⠀⠀⠀⠀⣍⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠺⠿⠿⠿⠂⠀⠀⠀⠀⠀⠿⠷⠶⢤⡤⠤⢼⠅⠀⠀⠀⠀⠀⠸⣿⠟⡿⢿⠿⠟⠛



⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠰⡶⠀⠼⠧⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⡛⢍⠉⠉⣉⠝⡇
⠀⠀⠀⠈⠉⠀⣈⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡘⡐⢛⡘⢰⠀⠀⠀⠀⠀⠀⠀⠃⡀⠑⠚⢡⢖⡲⡄
⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣭⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠀⠂⡛⠛⣰⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠂⢣⣛⡓⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠄⠢⡄⠀⠀⠠⣀⡤⠒⠂⢄⣠⠄⠀⠀⣠⠄⠐⠦⣄⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⡀
⠀⢸⠁⠈⠹⣷⡀⠀⠀⠀⠀⠀⣿⢳⣤⠇⠀⠀⣰⡏⠀⠀⠀⠈⠉⠀⠀⠀⣿⠀⠀⠀⠘⣷⠀⠀⢸⣇⡀⢀⡀⠀⠀⠈⣿⠀⠀⠉
⠀⠘⣗⡶⠀⣿⣷⠀⠀⠀⠀⠀⣿⡼⠋⣷⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡿⠀⠀⢸⡏⠀⠘⠁⠀⠀⠀⣿⠖⢦⠄
⠀⠀⠉⠀⢸⠏⣿⣇⠀⠀⠀⠀⠿⠀⠀⠛⠀⠀⠈⠻⢦⣀⣀⠤⠂⠄⠀⠀⠾⠆⠀⠴⠛⠁⠀⠀⠸⠇⠀⠠⠄⠀⠀⠠⠿
⠀⠀⠀⢀⡏⠀⠸⣿⡀
⠀⠀⠀⣼⠥⠤⠤⢽⣷⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠉⠀⠀⠘⡏
⠀⠀⢠⠇⠀⠀⠀⠀⢿⣇⠀⠀⠸⣇⠀⠀⢲⠀⠀⢀⡧⢠⠶⠼⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠐⢆⠀⠀⠀⠀⡅⠀⠐
⠀⢠⣿⠀⠀⠀⠀⠀⠸⠿⣧⠀⠀⠈⣱⡆⠸⠀⠀⢸⣧⠀⠀⠀⢇⠀⠀⠀⢠⡀⠀⠀⣦⠐⠁⠀⠀⢸⡇⠀⠘⠦⠀⠀⠀⠃⠀⠬⠃
⠀⠚⠚⠀⠀⠀⠀⠀⠈⠛⠉⠳
⠀⠀⡀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⢠⡦⠀⢠⢤⡆⠀⠀⠀⠀⣀⠄⠀⠐⠦⣄⠀⠀⠀⠰⣶⠖⠒⢦⡀⠀⠀⣠⠖⠀⠉⠑⠢⣀
⠀⠠⠗⠀⠀⠀⠀⠰⣿⡄⠀⠀⠀⠀⢈⣿⡄⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⣿⣠⣀⣸⠇⠀⣼⡏⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢸⣯⠻⣄⢸⡇⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⠃⠉⠁⠀⠀⢹⣇⠀⠀⠀⠀⠀⣼⠇
⠀⢀⣀⣇⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⢠⣿⠀⠈⠿⠇⠀⠀⠀⠈⠓⢄⣀⠀⠠⠘⠁⠀⠀⠰⠿⠄⠀⠸⠁⠀⠀⠈⠂⠀⠀⠐⠺⠥

⠀⠘⣿⡏⠉⠹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⣶⠶⠒⠀⠀⠀⠀⠐⠉⡲⠂⠀⠀⠈⣿⠀⠀⠈⢿⡄⠀⠀⠀⢸⠋
⠀⠀⣿⡇⠀⢀⣷⠇⠀⠀⠀⠀⠀⠀⢸⣂⣀⠀⠀⠀⠀⠀⣴⡟⠀⢠⣦⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿⡀⠀⢠⠃
⠀⠀⣿⡇⠚⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣦⠀⠀⠀⠰⣿⡀⠀⢿⠻⠐⠄⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠹⣧⠠⠎
⠀⠀⡿⡇⠀⠀⠣⣦⣀⢰⡀⠀⠀⣦⡀⠀⢀⡟⠀⠀⠀⠀⠛⢧⣀⠀⡀⡠⠆⠀⠀⠘⢿⣦⣀⣀⡀⢀⣿⡀⠀⠀⠀⠀⢻⡇
⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⡴⣤⡤⡤⡴⠦⣄⣤⠄⠀⢶⢀⡆⠀⠀⢶⣲⡆⠀⠀⠀⣴⠶⠀⠀⠀⠀⡒⢦⣄⠀⠀⠀⠰⡆⡄⠀⠀⠦⠀⠐⠶⠤⠤⢤⣲⠆
⠀⠀⠁⠀⡶⠀⠀⠀⣰⠃⠀⠀⠸⣦⡇⠀⠀⠀⠹⣿⣄⠀⣠⠄⠀⠀⠀⠀⣰⠇⠸⣿⡆⠀⠀⠀⣿⡇⠀⠀⠀⠐⠂⠀⠀⣰⣿⠃
⠀⠀⠀⣾⡇⠀⠀⢰⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⢟⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡰⡿⠃
⠀⠀⠘⣿⡆⠀⠀⢿⣧⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⡼⠣⣿⣄⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⣀⡴⣿⡇⠀⠀⠀⠀⠀⣰⡼⠁
⠀⠀⠀⠹⢵⣄⣀⣈⡿⣦⣀⣀⣠⣟⡇⠀⠠⢴⠄⣘⡁⠀⠙⣿⢦⡀⠀⠀⣤⣄⠀⠀⠀⠉⠉⠀⡿⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠁⠉⠈⠁⠈⠀⠀⠀⠚⠓⠁⠀⠀⠘⠛⠛⠀⠀⠉⠋⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠙⠚⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠈⠙⠂⠉⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠟⠋⠀⠀⠘⠛⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠉⢀⡀⠀⠀⢦⡔⠀⢉⣼⠏⠀⠀⠀⠀⠹⣧⡁⠀⢢⡵⠀⠀⢀⡀⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⠷⠀⣀⡄⠁⣠⣾⣿⡀⠀⠀⠀⠀⠀⠈⣓⣄⠈⠀⡀⠀⠾⠊⡰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⡤⠀⠐⠚⠁⠈⣿⠧⡀⠀⠀⢀⠔⠁⠀⠈⠐⠂⠀⢤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⣉⡳⣄⠀⠀⠟⠀⠀⠀⠀⣀⢀⡈⠀⢁⠀⠀⡘⠀⢀⡀⣀⠀⠀⠀⠀⠡⠀⠀⣠⢞⣩⣻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⠉⢻⠾⣷⣎⣤⣂⠨⠭⠒⡞⡿⠓⢀⢘⠀⠀⡁⡤⠚⢽⢓⢶⡭⣄⣀⣤⣁⣼⠿⠛⢻⣡⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⣇⠞⡕⢿⣿⠙⠓⠲⠒⠶⡓⢧⣀⣜⡸⠀⠀⠇⣢⣀⡼⠘⠉⠀⠚⢴⡋⣿⡿⡰⠒⢸⠃⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡻⠸⠸⣿⡆⢀⠀⠀⢀⠶⠁⡇⠀⢠⠀⠀⡄⠀⢸⠸⢁⡀⡀⢀⣈⢱⣿⡇⡘⠌⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣷⣶⣿⣷⣂⣤⣵⣶⣾⣿⣿⣶⠌⠀⠀⠡⣶⣿⣿⣶⣶⣦⣭⣌⣸⣿⣴⣾⣉⠁
⠀⠀⠀⠀⠀⠀⠍⠢⣀⡀⡤⠐⠊⠹⣿⣿⠿⠿⠿⠛⠿⣿⡿⠿⣿⠇⠀⠀⠀⠀⠘⣿⠿⠿⣿⠿⠛⠿⠿⠿⣿⣿⡏⠁⠂⢤⢄⣀⠔⠹
⠀⠀⠀⠀⠀⠀⠈⡄⠀⣀⠴⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡉⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠦⢀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣵⣟⡓⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠐⠂⢁⠜⣡⡾⠍⠉⠉⠑⠀⠀⠉⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠛⠛⣿⠟⢿⣿⠿⡿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⡠⠠⠐⠂⢉⠴⣡⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣄⢀⢠⠀⠀⢩⠀⢘⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣠⠞⠁⠀⠀⢀⡴⣢⡾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣼⣿⠉⠁⠀⠈⢹⡞⠀⠀⠠⠀⡆⣞⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡼⠁⠀⠀⣤⡴⢋⣴⣯⣷⣇⠂⠐⠀⢀⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⣀⠀⢃⡄⣿⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣞⡵⠋⠀⠀⢀⡼⢋⣴⣿⣿⣿⣿⣿⠿⡿⣶⣿⣿⣴⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⠀⠎⡇⣏⢹⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⢠⣤⠞⣵⣿⡿⠿⣏⣧⣾⣯⣴⣵⣩⠥⣿⣿⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣤⡷⣿⢸⣿⢧
⠀⠀⠀⠀⠀⢠⡏⠀⢀⣠⣾⢞⣵⠞⣛⠛⠿⠛⡛⢿⡯⢍⣙⡛⠿⢾⣿⣿⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⣧⠀⣯⢱⡟⣿⢿⢸
⠀⠀⠀⠀⢠⣏⠀⠀⢀⡿⢫⣿⠁⠀⠀⣹⠁⢿⠋⠁⠈⠂⠉⠉⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡠⢤⠀⠀⢸⣿⣦⣽⡈⣧⣿⣾⡇
⠀⠀⠀⣠⠟⡘⠀⢀⣾⣵⠏⠸⣦⣖⡒⡛⠀⢟⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠣⠜⠀⠀⠸⣸⡿⣿⣇⣿⣿⡿⠅
⠀⠀⠀⢧⣊⣤⣶⡿⣿⣿⠁⠀⠙⢿⡙⠛⣿⣿⣿⣾⡅⠀⠒⠓⠒⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⢤⣦⣼⠀⠀⠀⠀⢠⣟⣿⣿⣾⣿⣷⡿⣳
⠀⠀⠀⣠⠟⣩⣎⣴⡿⠃⠀⠀⠀⠀⠉⠳⣬⣉⣿⣿⣷⣶⣶⣶⣴⣶⣶⣦⣽⣿⣿⣿⣮⣶⣶⣶⣾⣿⣿⣦⠤⡄⣄⠉⣉⣙⠛⣛⠿⢾⣾⣿⣽⣿⣯⣿⠾⠋
⠀⢀⣴⣷⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⣿⢿⡿⠧⠬⠉⠭⠿⠽⠏⠛⠛⣿⠛⠛⠛⠿⠉⠉
⢀⣾⠟⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⡀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠚⣿⠃⢀⡴⠾⢉⣋⣉⡻⠲⣄⠀⣀⣄⠰⣿⠆⠀⣼⠁⠀⠲⡌⢳⡄⣴⣶⣾⡓⣶⣤⡼⢧⡼⠃⠀⣠⡴⠒⠚⠳⢬⣍⠳⣦
⠀⠀⠀⠀⠀⣰⠏⣣⠞⠉⠡⠈⠙⢳⡌⠛⢉⢹⡄⢀⣤⠀⢿⠀⠀⠀⢡⢨⡇⠈⠉⠛⠛⢋⡉⢻⡛⣷⢠⡞⠁⠛⠋⢻⠀⠀⣸⢷⡈⢷
⠀⠀⠀⠐⠀⣿⠃⣏⠀⠉⣠⡴⠚⢉⣀⣦⠞⠋⢷⡛⠈⣳⠌⢧⡀⠀⠀⡼⠁⣀⠀⢰⣆⢸⡿⣮⡉⠁⣾⡴⠶⠶⠦⠾⠃⢸⡅⠈⡇⢸⡇
⠀⠀⠀⢾⣷⠘⣏⠹⠶⠋⣁⣰⡶⠚⠉⠰⣶⠆⠸⠟⠳⠧⢀⣀⠙⠳⣿⡇⠀⣿⢷⣿⣩⣿⡷⣟⢧⠀⢹⡷⠛⣩⠷⣴⡄⠘⢓⣻⠇⣸⠁
⠀⠀⠀⠠⠀⣶⢋⡀⣰⠶⢋⣡⣦⢀⣤⠶⠶⣤⡴⠖⠚⢋⠉⠙⣶⢶⡀⢻⠀⣿⢻⡹⡜⣎⢧⢹⡌⢧⠀⠳⣄⣹⡄⠙⠁⣰⡿⢋⡴⠃
⠀⠀⠀⢶⣶⠹⠶⠋⠁⣴⡋⣹⢃⣞⣠⣤⣿⡎⡷⣖⢛⣙⡇⠀⢹⡈⣧⠸⣆⠸⡎⢧⢻⡸⡜⣇⢳⡘⣧⠠⠀⠉⣻⣿⣯⡭⠖⠋⠀⣀
⠀⠀⠀⠀⠀⠠⠀⢀⡞⣡⣟⡽⠃⣯⡛⠉⣀⡼⠃⠉⣉⣡⡤⠀⠈⣧⢹⡄⠘⡇⢹⡜⣇⢷⣳⡘⣆⣷⠾⣆⢺⣉⠟⠓⣆⠸⡯⣽⠆⣭
⠀⠀⠀⠠⣶⡄⠀⡼⠛⠁⣠⠞⢙⡯⠉⢻⡉⠤⠀⠛⠉⣀⣠⠀⠀⠸⡆⢳⡀⢧⡀⢳⣸⡾⣿⠋⢹⣄⡤⣿⠀⠉⠙⣉⡁⠀⡇⣿⠰⠦
⠀⠀⠀⢀⣨⠴⠶⡆⢰⡞⢁⡴⠟⠀⠀⠈⣇⠀⠀⠒⠋⢉⣀⣤⠀⠀⢻⠈⢧⠈⣷⠈⢧⣠⢾⡿⠽⠋⠉⢡⣦⠀⣾⠽⢣⠞⠁⠘⢧⡀
⠀⠀⠀⠘⢶⡖⢾⠁⠀⠙⠋⠀⠀⡿⣆⠀⢹⡀⠒⠀⠘⠉⠁⣀⡄⠀⠈⣧⠘⡆⠘⠂⠈⠙⠉⢀⡴⢚⡦⢈⡵⣤⠀⣰⢿⣋⡽⠟⠉⠳⡄
⠀⠀⠀⠀⢈⡇⠘⣧⣀⠀⠈⠀⢸⣇⠹⡄⠈⣧⠀⢁⠀⠚⠋⣉⣀⣤⠤⢾⣠⡽⢀⣤⡶⢺⠃⠙⠋⠉⠀⡼⠧⣇⠸⠧⠤⠤⠤⠶⠶⠶⠟
⠀⠀⠀⢠⡟⢁⡀⣠⠼⣷⠀⠀⣾⡀⠀⢻⡄⠸⣆⣤⠴⠖⣋⣩⡤⠖⢛⡉⠀⢀⡟⠈⣹⠏⠀⡟⠛⣛⣿⣓⠒⠛⠲⠶⡄⠀⡶⢻⡛⠓⣆
⠀⠀⠀⠘⣷⠋⠉⠛⠚⣻⠀⢠⣏⠀⣤⠀⢻⡄⠀⠙⠖⠛⣉⡀⠦⡿⠿⢃⡴⠋⣹⠋⣡⡴⢠⣇⣰⡿⠒⢾⣇⣤⡀⠀⡇⠀⡇⢸⣥⣄⣿
⠀⠀⠀⠀⠈⠳⠶⠶⠚⠁⠀⣼⡍⢰⡟⣇⠀⢷⡀⢠⡴⣿⣿⣷⠀⢀⡴⢯⣠⠞⠁⢀⣷⠀⢸⣏⣁⣀⣀⠀⠙⠀⠙⢺⡇⠀⡇⢺⡉⠋⣿
⠀⠀⠀⠈⢀⣾⣆⣴⡟⠀⢠⣯⠀⣼⠀⠸⡆⠈⢷⠀⠙⢯⡿⠁⣰⠋⢀⡴⠃⣠⡞⣿⠀⠀⣼⠉⠉⣉⡽⠏⢿⠙⠛⣻⠀⠀⡇⢼⠃⠀⣿
⠀⠀⠀⠀⢸⡇⠋⣾⠀⠀⣾⠅⠀⠧⣤⣤⣿⠀⠘⣧⠀⠄⢀⡞⣡⠖⢋⡴⠛⢯⣿⠁⣀⢀⣿⠖⠋⠁⠀⣠⠞⠀⠀⡿⠀⠀⡇⣸⠇⠀⡏
⠀⠀⠀⠀⠘⢧⠀⢿⠀⠸⣧⣤⣤⣄⣀⣀⣀⡀⠀⢹⡆⠀⠚⠋⠁⣠⠞⣵⠛⢶⡟⢸⣋⠉⠉⠛⠛⠓⠒⠻⠶⠦⠤⣧⣄⠀⣷⡛⠒⢺⡇
⠀⠀⠀⠀⣴⠚⠓⠚⠳⠦⣤⡀⠠⠀⢈⣉⣉⣉⡉⠛⠋⠀⣤⠀⡴⢯⣄⡉⣳⠏⢀⣤⡉⢩⠟⢛⡟⠓⠒⣶⠶⣤⢤⣤⡟⠀⠌⠉⠉⠉
⠀⠀⠀⠀⡟⠐⠒⠛⠓⠶⣤⠙⡶⣋⣭⣭⣭⣍⣉⠓⣦⠀⡟⢦⡙⠲⣬⣙⣏⡷⠈⠋⢠⡟⢠⠟⠀⠒⡀⢿⠀⡇⠀⣤⢶⣶⣶⣒⣲⡶⣦
⠀⠀⠀⠀⡇⠐⠋⠉⠛⠲⠆⢸⢳⣇⣀⣀⣀⣠⠟⢰⠇⠀⠳⣄⡷⢀⡤⡍⣭⣤⣄⢠⡟⢠⠏⠀⣴⣀⡀⢸⠀⡇⠀⣿⣿⡿⢏⣉⣉⡇⣿
⠀⠀⠀⠀⡇⠐⠋⠉⠙⠳⠀⡟⢨⠭⠤⠤⣭⡉⢀⡟⢀⢠⡶⠶⠦⡄⠙⠁⣿⠒⠛⠘⠓⢋⣀⣠⡟⠛⠁⢸⣀⡇⠀⣿⢨⢉⡉⡍⢥⠀⡏
⠀⠀⠀⠘⢧⡵⠶⠶⢤⣄⢸⣇⣀⣠⣄⣀⠀⠀⡾⠀⢈⣸⡏⠉⢛⡇⢠⠶⡏⢀⣴⡆⣴⠋⠉⠙⠛⢳⠀⣬⣭⡁⠀⢻⠰⠀⠂⢲⡟⡇⡇
⠀⠀⠀⠠⠀⠛⠛⠛⠛⠛⠻⠛⠓⠶⢤⣨⠟⠾⠃⠀⢯⡽⠀⢾⣹⠇⠈⠛⠁⣾⢹⠇⠻⣄⠤⢀⣠⠞⣴⣌⢧⣙⡇⢸⡈⠁⠁⠁⠙⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠉⠉⠁⠀⠉⠁⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠒⠒⠒⠒⠂⠰⠷⣭⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⢀⠤⠟⠀⡠⠞⠉⠦⡀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠷⠾⢎⣡⠶⢶⡉⠀⠀⠀⢀⣈⠶⢼⡏⠲⠶⡦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠘⠀⠠⠐⣀⡀⠀⠀⠀⢠⡴⠆⠠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⣰⠇⠀⢠⣿⣿⣿⠀⠀⠀⢸⣿⣿⣦⠀⠀⢿⡋⠈⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣽⠀⠀⠀⠙⠛⠁⠠⠀⠠⠀⠙⠛⠁⠀⠀⢸⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠔⠷⠄⢠⡄⠀⠀⠀⠰⣦⠴⠂⠂⢠⡷⠀⠀⠀⠀⣴⠀⠴⠿⠴⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠘⠾⡉⢩⠗⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠤⠤⠤⠤⢤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡴⠶⠆⠀⠶⠆⠀⠙⠛⠁⢦⡴⠘⠛⠃⠀⠲⠦⠀⠰⠖⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⠉⠈⠉⠉⠁⠀⠒⠒⠶⠶⠶⠶⢶⠖⠒⠀⠀⠈⠉⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠤⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠰⠒⠒⠺⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣎
⠀⠀⠀⢀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡀⣀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀
⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠂⠀⠀⠞⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⡀
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠤⢤⣤⢤⡤⠤⣤⣤⣤⢠⣤⣀⣀⣠⣤⠤⠤⠤⠤⠤⠄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠠⠤⠤⠤⠤⠤⣤⣄⣀⣀⣤⢠⣤⣤⠤⠀⣤⢤⡤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣅⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⡆⠀⠀⠀⠀⠀⢸⠉⠁⠉⠀⠀⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠀⣀⣀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣀⣀⣀⠀⢤⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣴⡆⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣦⣀⣴⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢉⡙⠏⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠻⣏⡉⠷⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⢀⡴⢉⠀⢺⡟⡰⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⢆⠹⡗⠀⡈⢦⡀⠀⠀⠀⣧⣤⠀⠀⡇
⠀⠀⠀⠀⠀⡀⠐⠂⠀⠁⠀⠀⠀⠀⢠⡍⠀⠀⠑⠊⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⠊⠀⠀⠉⡄⠀⠠⠀⠠⡇⠀⡃
⠀⠀⠀⠀⠀⠟⠛⠆⠀⠉⠀⠁⠀⠀⠘⢇⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡠⠃⠀⠈⠂⠘⠁⢀⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡅
⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠⠀⠀⠀⠀⡆⠀⠀⢸⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⣌⣉⣉⣉⣉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⡸⠀⢸⡁⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠟⠛⠛⠻⠛⠇⠀⠀⠀⠀⠀⠀⡀⠘⠃⠀⢱⡇
⠀⠀⠀⠀⠠⠂⢠⡖⠒⠲⡄⠀⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠃⠐⡠⢃⡄⠀⠀⠀⠀⠰⠪⢿⣄⣀⣴⠟
⠀⠀⠀⠀⠠⡀⢀⠻⠻⢟⠃⣀⠄⠀⠀⠀⣧⣀⣀⣀⣠⣄⣀⣀⣀⣠⡇⠀⠀⠀⠛⠛⢏⠔⠩⠬⠤⡄⠀⠀⢀⣤⣤⣤⣭⣥⣤⡀
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣶⣶⣶⣀⣀⣨⣶⣶⡆⠀⠀⠀⠀⠁⠀⣤⣶⣶⣦⡀⠂⠀⠀⠀⢀⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠉⠉⢻⣄
⠀⠀⠀⠀⠩⡭⡭⡭⡭⠭⠭⠭⠁⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⡷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠘⠟⢂⣠⣤⣶⣦⣐⠚⠟
⠀⠀⠀⠀⢀⣃⣓⡓⣓⣒⣒⣒⠀⠀⠀⠀⠀⢀⠈⢻⢸⡟⡼⠃⠀⠀⠀⠀⠀⢣⡀⠀⡐⠀⢀⡠⠀⠀⠀⠀⡏⢌⡟⠛⠛⠛⣿⠩⡃
⠀⠀⠀⠀⠠⠆⠦⠆⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠷⠷⠇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠔⠃⠀⠀⠀⠀⣛⣚⠛⣛⣛⣛⢛⣓⡳
⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠒⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠊⠛⠗⠀⠠⠀⠀⠀⠀⠀⠀⡠⠀⡴⢁⠀⠲⠄⢤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢰⣾⠖⠚⠛⠓⢾⣶⡆
⠀⠀⠀⠀⠀⢁⠀⠠⠠⠄⢀⠀⠀⠀⠀⠀⠘⣇⠀⡏⠀⢢⡀⠀⢀⠏⠀⠀⠀⠀⠀⠲⣶⣶⠆⠀⠀⠀⠀⠀⢨⠃⠀⠀⣀⡤⠂⢹⡀
⠀⠀⠀⠀⠀⣀⣤⣀⣀⣠⣆⠀⠀⠀⠀⠀⢠⡜⠓⣧⡙⠛⡡⠔⠋⣆⠀⠀⠀⠀⠀⠀⠈⠁⢄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠁⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠒⠛⠛⠛⠛⠓⢐⡄⠀⠀⠀⠀⠙⠒⢻⡉⠉⠓⠃⠜⠁⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⢘⡦⢤⣤⠤⢾⠁
⠀⠀⠀⠀⠀⠃⠙⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⣶⠿⠛⠛⠿⣷⣄⠀⠀⠀⢰⠿⠟⠃⠀⠙⠿⢷⡆
⠀⠀⠀⠠⠤⣶⣶⣿⣿⣿⣿⣶⣶⠤⠄⠀⠀⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⡙⢿⣵⢆⡀⠀⠀⠘⣿⡆⠀⠀⢸⠀⣤⣤⣤⡄⠀⢸⡇
⠀⠀⠀⢀⠀⣿⣶⣮⣭⣭⣵⣶⣿⠀⠀⠀⠀⣿⡇⠐⠂⣃⡀⣠⡄⠀⠀⠀⠡⠐⢝⢿⣵⣆⡀⢀⣿⠇⠀⠀⢸⠀⠶⠶⠶⠂⠶⢸⡇
⠀⠀⠀⣸⠀⠻⠿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠿⠧⠿⢧⠀⠀⠀⠀⠈⠢⡁⢝⢿⣯⡾⠋⠀⠀⠀⢸⠀⣏⣉⣉⡁⣋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠥⠙⠟⠁⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠼⠃

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⢠⡄⠃⠀⠀⠀⣿⡟⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠟⠀⠀⣰⡳⠲⣘⡆
⠀⠀⠀⠀⠀⡈⡀⠀⠐⠀⠀⠀⣿⣧⣠⣿⠃⠀⠀⠀⡆⠀⠀⠁⠀⠀⣿⡇⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⡀⠀⢠⣳⠁⣀⣙⣃
⠀⠀⠀⠀⢀⡃⠉⠉⡀⡆⠀⠀⣿⣿⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠃⠀⠰⢻⡀⠓⣦⠞
⠀⠀⠀⠀⢈⣰⠀⠀⢁⠰⠀⠀⣿⣿⣶⡿⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠣⢡⢪⠝
⠀⠀⠀⠀⣴⡄⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⣦⠀⣠⣤⠀⠀⠐⠐⠀⠀⠀⠀⢰⣶⣦⠀⢀⣤⣤⡄
⠀⠀⠀⠀⣯⡇⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⣐⣻⠃⠀⠀⠀⠰⠀⠀⠀⠀⢸⣿⣿⡀⢸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⢿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘⣾⣾⡁⠀⠀⠀⢐⢰⠀⠀⠀⠀⢸⣿⢷⣧⣾⣿⣿⡇
⠀⠀⠀⠀⡷⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⣀⠀⠀⢨⠿⢫⡵⡄⠀⠀⠠⠠⠀⠄⠀⠀⢸⣿⠘⣿⣿⠩⣟⡇
⠀⠀⠀⠀⠛⠃⠀⠛⠃⠀⠀⠀⠀⢀⣀⣀⠀⠂⠐⠀⠀⠀⢈⡋⠀⠛⠙⠀⠀⠈⠂⠀⠀⠀⠀⠈⠛⢀⣉⠉⠈⠛⠁⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡬⠀⠺⠁⠀⠀⠀⣿⣿⠻⣿⣆⠀⠀⠀⣾⣿⢿⣷⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣾⡟⢻⣷⠀⠀⠀⠸⠿⣿⡿⠟
⠀⠀⠀⠀⠀⠠⣭⠀⠀⠅⠅⠀⠀⣿⣿⢀⣿⡟⠀⠀⢸⣿⠁⠀⣿⡇⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠹⣷⣌⡉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠨⡼⠀⠀⠄⠅⠀⠀⣿⣿⠿⠛⠁⠀⠀⠘⣿⣤⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡌⠹⣽⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠬⠀⠸⠄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣺⡽⠁⠀⠀⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣤⡀⠀⣤⡄⠀⠀⡄⠆⠀⣀⢀⠀⠄⠤⠀⠀⡤⣦⠀⢰⡄⠀⠠⣤⡄⠀⣰⣶⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠸⡟⡇⢀⣿⠇⠀⠀⠅⠀⠀⠀⠀⠄⠅⠄⠀⠀⠐⣟⣰⢸⠇⠀⠀⠹⣿⣠⣿⠃⠀⠀⠈⠉⠉⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⣿⣇⢸⣿⠀⠀⠀⢀⠀⠌⠈⠃⠘⠀⠂⠀⠀⠀⡭⢼⢨⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠰⢁
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠆⠀⠀⠀⢸⣿⢻⠇⠀⠀⠀⠸⠀⠀⠃⠠⠀⢰⠀⠀⠀⣐⣟⠘⣸⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠌⢀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠒⠐⠀⠈⠒⠊⠀⠀⠀⠁⠋⠀⠘⠂⠀⠀⠀⠘⠛⠃⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢄⣀⢀⠠⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠙⠀⠈⠈⠀⠀⠀⠁⠀⠀⠈⠈⠀⠉⠀⠀⠁⠈⠀⠀⠉⠀⠁⠈⠀⠀⠉⠀⠁