Rum Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣩⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⢿⡛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣼⣿⣠⣤⣵⠘⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠉⢩⠀⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠀⠀⢸⠀⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣿⣿⣷⣶⣾⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢲⣛⣤⠀⠀⡳⠖⠛⠛⠙⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣠⣴⣾⣿⣿⣿⡏⠁⠀⠠⡀⠀⠀⠀⠀⠈⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣋⣁⠀⠀⠀⠑⠤⠀⣀⡀⠠⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⡄⢀⣤⠜⢁⠀⠀⠀⠀⠀⠀⠰⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⠀⠀⠀⠀⠀⠀⣸⢷⠿⡔⢿⠉⠀⠀⠄⠀⠀⠀⣀⢠⡇⢸⠉⣿⣯⡍⠉⠉⠙⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠤⠉⠝⠶⠴⠞⠀⠀⠀⠀⠀⠀⠀⣧⣾⠇⢸⠀⣿⢼⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠰⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⠀⢸⡿⣿⣿⡚⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢠⡄⡆⠀⠀⠁⠦⠥⡄⠀⠀⠀⢰⣾⡟⠀⢸⠐⣿⡏⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⢠⣤⣠⡄⡄⣤⢀⡄⠀⠀⠀⠀⣘⣿⡇⠀⢸⣤⣏⠀⠒⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠿⠀⠇⠂⠘⠳⠇⠀⠀⠀⢀⡇⣿⠁⠀⢸⣎⣿⣟⢀⡈⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣴⣶⣒⡀⠀⠐⠒⠐⠂⣄⣃⣍⣠⡿⠀⠀⢸⠟⣿⣿⠿⠛⠿⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣝⣛⣛⣛⠻⠿⠿⠿⠿⠿⠖⠖⢒⣛⣩⠽⠃⠀⠀⢸⣷⣿⣿⡄⣀⡀⢰⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠤⡶⠀⠃⠀⠀⠀⠊⠀⢔⠜⣥⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣗⠚⠗⠛⣀⡠⢶⣿⣂⡴⢫⡾⠁⢀⡴⠃⠀⠀⢀⢄⣂⣂⡀⢄
⠀⠀⠀⠀⢀⣤⠄⠀⠀⢿⣮⡙⣿⣿⣿⣿⡥⢿⣬⣭⡴⠻⠟⣡⣾⣥⣤⣤⣮⠖⠋⠉⠉⠉⠑⢄
⠀⠀⠀⢠⡟⠁⠀⠀⣠⢴⠾⠟⠉⣙⡋⡿⣿⠀⠌⠉⢿⠏⣼⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⣾⠇⠀⠀⠀⡟⣧⣄⣀⣴⠿⠧⣧⣿⣄⡀⠀⡘⢰⡏⠑⡘⣷⡀⠐⠉⠙⢣⠀⠀⠀⠀⠀⠣⠀⠠
⠀⠀⠀⠘⡂⠀⠀⠀⠈⠀⠀⢠⣴⡆⢰⣶⡤⠈⠙⢾⣷⡘⣿⣶⡇⣿⡇⢸⡦⢀⡜
⠀⠀⠀⠀⠘⢦⣄⣤⣤⣤⣶⠿⠋⠀⠈⡏⣷⣀⣦⡈⢿⣷⣿⣿⣠⣿⣿⢞⣵⣩⡦⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣀⠀⠑⢌⠻⣿⣿⣶⣿⣿⣯⣿⣻⣿⣾⠻⠷⠞⡭⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠍⠿⣷⣦⣿⣿⣿⣱⣮⢻⣷⣭⣼⣿⣿⣓⣒⡶⠭⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢌⣛⣛⢩⣥⠖⠢⠉⢳⣷⣾⣿⣿⣿⡿⣿⣏⡉⣟⡛⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡿⠛⢴⣢⠈⠆⣿⣿⡿⡟⣯⠻⡟⢿⣿⣎⠻⠿⠓⠒⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣋⣕⡏⠈⣠⠔⢃⠜⢠⠿⣿⠹⠘⠈⠂⠘⠀⠈⢻⣧⠐⡰⠷⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢘⢡⣠⠎⡠⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠋⠲⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡞⢀⡠⠠⠜⢧⠀⠀⠀⠀⠀⠀⠀⣼⠃⣀⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠷⠆⠅⠈⠳⣤⣀⠀⢀⣀⡴⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠉⠉⠉⠉⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢵⣦⢤⢛⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢑⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⣀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣧⠀⣿⣿⡄⠀⣿⠉⣿⡆⠉⣿⡏⠉⢹⣇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠑⠒⠒⠛⠛⠛⡟⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⡟⢸⡏⢹⡇⠀⣿⣤⣿⠃⠀⣿⡇⠀⠈⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠉⠉⠉⠿⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠀⣾⣧⣼⣷⠀⣿⠀⣻⡇⠀⣿⡇⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠿⠁⠈⠿⠀⠿⠀⠹⠇⠀⠻⠇⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠈⠑⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣦⣶⣶⠀⣴⡄⢠⣦⣦⠀⠀⣴⣶⡄⢠⣶⣶⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠉⠀⣿⡇⢸⣿⣿⡄⢀⣿⣿⡇⢸⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢿⡇⢸⣿⣿⡇⢸⣿⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⣠⣶⣶⣶⣆⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⢸⣿⣼⡇⣿⡇⢸⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁⠀⠀⠀⠀⢠⣯⣤⣈⣑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⠈⣿⣿⠀⣿⡇⢸⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠂⠀⠀⠐⠋⠓⠒⠈⠂⠀⠉⠁⠂⠀⡈⠑⢦⡀⠀⠀⠀⠀⠛⠃⠀⠀⠛⠃⠘⠛⠀⠛⠛⠀⠛⠃⠘⠛⠛⠛⠛
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢱⡄
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⡀⣈⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⢰⠂⠁
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⠜⠛⠀⠀⠀⠦⠀⠀⠀⡇⠀⠀⠰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠘⣦⠄⠀⠀⢀⡤⠄⢠⡤⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇⠀⠀⠀⠐⠠⡀⠐⠁⠀⠀⡶⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣾⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⢧⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣀⣀⠀⡴⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠁⠀⠀⠠⠀⠄⢠⠠⠄⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠋⠈⣖⣟⣶⣄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢈⣡⣿⣿⠄⣸⡟⠁⠀⠈⠹⡆⠀⠀⠀⠀⠀⣮⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠿⠿⠋⢠⣿⡇⠀⠀⠀⠈⣿⠀⠀⠀⢀⣠⢾⠋⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣠⡾⠋⠀⢸⡆⠀⢠⠇⣀⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡏⢠⡿⠀⠀⠀⢸⡇⠀⣯⡞⠁⠀⠀⠀⢣⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠀⠀⠀⢠⣿⠁⢸⡇⠀⠀⠀⢸⡇⢀⣾⡀⠀⠀⠀⠀⡜⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⠜⢿⣷⡀⠀⠀⣼⠇⠀⢺⡇⠀⠀⣀⣘⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⡀⠀⠀⠀⢀⠔⠋⠉⠉⠙⢿⣧⡀⠈⢿⣿⣄⢸⡿⠀⠀⣾⣿⢀⡼⢻⣿⣱⡿⠻⣄
⣿⣿⣿⣶⣶⣾⣤⣄⣀⣀⣦⣤⣽⣿⣶⣾⣿⣿⢸⣷⣦⣤⣿⢋⣾⣱⣿⣿⣿⣁⡀⠈⢳⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣠⣴
⣿⣿⣿⣿⣿⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢃⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣲⣶⣶⣯⣵⣾⣿⣿⣿⣿⣷
⠷⠾⠿⢻⡿⠃⠀⠻⢿⡟⠛⠻⢟⢛⣿⣏⢉⣿⣏⡛⠿⠇⣼⠃⢩⣿⣿⣿⣿⣿⣿⣿⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠄⣀⡴⠉⣤⣤⣤⣠⡴⢻⣦⣤⣬⣉⣫⣟⣉⣉⣭⣍⣶⣶⣿⡀⢨⣾⣿⣿⣿⣿⣷⡅⣀⣿⣿⣿⣉⣭⣉⣉⣻⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⣀⣤⣤⣤⣤⣀⠀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢉⢹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⡒⣾⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⢩⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠀⣻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡼⠃⠙⣿⣿⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡍⠀⠂⠀⠀⠀⠀⠀⠀⠬⣭⣽⣶⠬⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⢀⠀⠤⣼⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠐⠀⢀⢀⣼⣭⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⢿⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠽⢿⣶⣤⠀⠀⠀⠘⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡱⢻⠟⠁⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠉⠖⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⡆⢻⠀⢰⢰⡄⣴⠂⠀⣤⡅⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠃⠣⠘⠶⠂⠒⠛⠘⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠃⠀⠹⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⢀⣀⡀⣈⣉⣉⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⣂⡴⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠉⠉⠙⢻⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣶⣶⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠁⠀⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠂




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⢠⣾⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠤⠤⠤⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⡿⡿⠀⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠐⠂⠀⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⣤⣤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⡇⣿⡏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣟⣿⣿⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⢻⣧⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⡉⠉⠉⠉⠉⠉⠉⠉⠁⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣷⢸⡇⢸⡇⣿⣧⣼⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠏⢸⣇⢸⡇⣿⡏⠉⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠛⠛⠧⠘⠿⠿⠃⠿⠃⠀⠛⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣾⣿⣿⡿⠿⠿⠿⠿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⠟⠛⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄
⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⢀⣤⡶⠶⠶⠷⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⣠⣤⣴⣶⢶⣦⣀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣤⣤⣶⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢸
⣿⣇⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣶⠶⣶⣼
⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⣿⡇⠀⠀⠀⠀⢺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⢹⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠈⣿⡆⠀⠀⠀⠀⣿⠀⠀⣰⡾⠋⠉⠁⠀⠈⠉⠻⣦⠀⣰⡶⠶⣶⠀⣴⡶⠶⠶⠾⣆⠀⠀⣠⣤⣄⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⢹⣧⠀⠀⠀⠀⢹⡇⠀⢻⡆⠀⢀⣤⡀⠀⠀⠐⢿⠆⣿⠇⠀⣿⠀⣿⡇⠀⠀⢸⣿⠀⣿⡏⠉⣿⡆⢸⡿⠁⢽⣗⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠈⣿⡆⠀⠀⠀⠸⣧⠀⠈⢿⡄⠻⣿⠟⠀⠀⣀⠀⠀⢉⠀⠀⠈⠀⠙⠀⠀⠀⢸⣿⠀⣿⠇⠀⠘⣿⣿⠇⠀⢸⣿⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢻⡆⠀⠸⡇⠀⠀⠀⠐⠿⣿⠁⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠟⠐⠿⠀⠀⠀⠛⠋⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠘⣷⠀⠀⢿⠀⢠⣴⣦⡀⠸⣶⡄⢰⣶⠀⠀⠀⠀⠀⠀⠀⣾⡆⢰⡶⠀⢀⣄⠀⣀⡀⠀⠈⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣿⡄⠀⠻⡀⢸⣇⠘⣧⣀⣼⠇⠀⢻⣆⡀⠀⠀⠀⠀⣠⡟⠀⣼⡃⢀⣼⠿⣦⡞⢿⡀⠀⣿⠀⠀⣼⡇⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠸⣷⠀⠀⠻⠿⠋⠀⠈⠛⠋⠀⠀⠀⠙⠻⠶⣶⡶⠾⠋⠀⠈⠛⠟⠛⠋⠀⠀⠀⠸⣷⠶⠟⠀⠀⣿⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠘⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠋⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⡼⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠁⣠⠹⡤⢄⠀⠀⠀⠀⡀⠁⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠃⠀⠸⠆⢀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⠁⠀⠈⠉⢹⡁
⠀⠀⠀⠄⠀⢠⠀⠸⠀⣿⣃⣸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢸⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠁⠘⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀⡅⠀⢸
⠀⠀⠀⠟⠄⠒⣄⡀⠀⣇⣠⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠬⠁⠿⠒⠀⠀⠀⠀⠿⠔⠀⠐⠤⠄⠀⠀⠈⠧⢀⡀⣤⡤⣤⡄⡠⠾⠁⠀⠸⠀⠀⣶⠠⠬⠟
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠀⠀⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⡇
⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠠⡇
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⢘⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠟⠲⠦
⠀⠀⠀⢀⡾⠀⠀⠱⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⡄⠀⣴⠂
⠀⠀⠀⠈⠁⠀⠀⠠⣤⡄⠀⠀⢴⠚⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠀⠀⠀⣸⠀⠀⠀⠀⠠⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠀⢸⣏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⢈⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡏⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⣛⠀⠀⠀⠰⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠣⠤⡴⠦⠶⠾⠟⠀⠘⠟⠀⠀⢤⣤⣀⣀⠸⠀⠀⠈⠐⠂⣴⠄⠒⠀⠀⠛⠀⠸⠀⡀⣀⡀⠀⠀⣀⣈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠉⣿⡇⠁⠀⠀⠀⠀⠀⣠⠀⢠⣤⣄⡀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡆⠀⠀⠀⠀⣿⣆⣀⠀⠀⣯⣥⠀⣿⡷⢀⡀⠀⠀⣀⣼⣿⣀⠸⠿⠟⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⠄⠀⠙⢿⣿⡿⠀⠜⢷⣿⣾⣿⣿⣿⡷⠃⠀⣽⣿⡿⠛⠁⠀⢰⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⢠⣤⠀⢼⣿⣇⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⣸⣿⣷⣄⣀⣠⣴⣿⣄⣨⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠀⣾⣿⣿⣦⣦⠸⣿⣿⣿⣿⣧⡄⢰⣤⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠐⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⢿⡿⢻⠛⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⢸⠀⠀⠻⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠘⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⣿⣿⣿⣿⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠐⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣀⣠⣼⣿⣿⠗⠈⠀⠀⠀⠀⠀⠀⠀⠸⣦⠑⠆⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠉⠨⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡝⠄⠀⠻⠟⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠁⠀⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡦⠢⠄⠒⠙⣄⠀⢠⣀⣴⠂⠀⠀⠀⠀⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⠄⠀⠐⠂⠙⣧⠈⠃⠁⠧⠀⠀⠁⠀⠘⠂⠀⢀⡀⠀⠀⠦⠀⠀⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡿⢘⣷⣶⣶⠄⠠⡑⢄⠀⠀⠐⠀⠀⠀⣤⡀⠸⢿⠞⡃⠀⢠⠄⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠀⢀⠻⣿⡿⣧⡀⢑⠠⢦⠀⠀⠀⠀⠀⠀⠙⠀⠐⠚⠧⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠆⠰⣶⠶⠉⣍⣱⠈⡤⠐⢃⠀⠀⠀⠀⡀⠀⠀⠀⢈⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠡⠄⠈⣤⠾⢿⡁⠀⢁⠘⢹⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣴⡟⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸⡔⠘⠃⠀⠐⡀⠀⠀⣀⠇⠀⠀⢀⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⠟⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣥⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠂⠀⣞⠉⠀⠀⠀⠀⢇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⣶⣶⣶⠆⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣼⠀⠈⢿⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠀⠀⠀⠀⢂⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠸⡆⠀⢸⠲⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠙⡀⠸⠀⠀⠀⡑⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠘⢠⣦⡄⢸⠓⠊⠳⢤⣀⠀⠀⠀⠀⠀⢠⠅⠀⠠⢄⡀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⢌⠉⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠒⠒⠋⠙⠠⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠙⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠚⠓⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣧⣜⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡟⡛⠛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⡿⠻⠟⣓⢤⡤⣤⣄⣴⣶⣾⣯⡇⠁⣿⣷⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠿⠀⠡⢉⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣄⢠⣥⣤⠘⢁⣋⣴⢻⡟⠈⠛⡿⢿⠒⢀⠿⠿⠁⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣥⠀⠈⠒⠋⠀⣇⣀
⠀⠀⠀⠀⠀⠀⡼⣷⣿⠍⢻⠛⢻⠀⣠⣿⢹⣬⣿⣬⣤⣤⡧⠼⣯⣤⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⡏⠙⢢⣤⠶⢶⠻⣿
⠀⠀⠀⠀⠀⡘⢿⢾⣿⣦⣿⡟⡏⣹⣿⣿⣫⣿⣿⡿⢻⣿⡐⣷⠰⡞⢻⣿⠷⠙⠓⠀⠀⠀⠀⠀⠀⠀⢀⣶⣡⡄⣿⣇⠀⢠⢠⣤⣤⣆⢹⣧
⠀⠀⠀⠀⠀⠁⠈⢿⣿⡶⣿⠁⡟⣿⣿⣷⣾⡯⢥⡶⠻⣿⣿⠁⠙⣡⣿⡿⣆⡀⠀⢄⠀⠀⠀⠀⠀⢀⡋⠉⠻⢛⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠻⢳⠁⣠⢹⣿⡿⠉⣉⠛⡿⠠⠚⠙⣷⡤⠴⠏⠛⢿⡏⠹⡆⢿⡄⠀⠀⠀⠀⠀⢿⡝⠒⣹⣽⡿⠋⠘⣸⣿⣿⣧⢹⡀⠀⠉
⠀⠀⠀⠀⡀⢀⣰⣋⡠⠾⢡⡿⣆⠨⣿⣿⣭⡇⠠⢂⣾⡉⠃⠀⠀⠀⢰⡈⡇⠀⢀⠀⠀⠀⠀⠀⠀⠢⢤⣿⠤⣽⡟⢆⡀⡀⣿⣏⠉⢉⡸⣧⣀
⠀⠀⠀⠀⠀⡈⠁⣿⣿⣶⠾⠃⡿⣦⡿⡿⣿⣿⣷⠼⣷⠓⠀⠐⠛⢆⠈⠀⠉⠐⠊⠁⠀⢂⠀⠀⠀⠀⠈⠑⢄⣈⣷⢦⣿⡿⣧⡿⢷⡞⢧⣉⠀⠁
⠀⠀⠀⠘⠳⣿⡀⢻⣿⣿⡿⢎⣻⢏⡞⣹⢧⣿⣿⠀⡟⠀⠀⠀⠀⠈⣦⢦⡄⠀⡀⠀⢂⣹⠗⠀⠀⠀⠀⠀⠀⣿⠒⠀⠘⢣⠏⠀⠀⠀⢸⢿⣾
⠀⠀⠀⢀⠀⢿⣿⣿⣿⡜⠛⣺⢿⡿⣾⡇⣮⢹⣿⢠⠇⢸⡄⠀⠀⠀⢸⠇⣥⢀⣜⣆⠈⠉⠀⠀⠀⠀⠀⠀⡆⣿⡇⠀⢘⡦⠂⠀⠀⠀⢀⡟⢸⣀
⠀⠀⣰⣿⣧⡈⣿⣿⡎⠷⡴⣻⣮⢘⣿⣷⡟⣼⡇⢸⠄⠀⠐⠀⠀⠀⢈⣼⡇⢹⢻⣿⠱⡀⠀⠀⠀⠀⠀⠀⣤⣿⠇⠀⢰⡧⡇⣄⠀⠀⡸⠀⠈⡏⢇
⠀⠀⠻⠟⣿⣷⡿⣿⣷⣤⣦⡿⠙⣿⣿⣿⣿⣿⣿⠘⠀⡀⠀⠀⠀⠀⠘⠈⠁⡘⢸⢷⡁⠃⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢸⣿⡇⣿⡒⠄⠃⠀⠀⡏⢺
⠀⠀⠀⣴⠙⠻⣿⢿⡏⠀⠀⡇⠀⢹⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇⢸⡄⠁⠀⠁⠀⡀⠀⠀⠀⢸⣿⠀⠄⠀⣭⢿⠱⡉⠠⣀⠀⠀⣣⣿⡀
⠀⠀⠀⠀⠀⢀⡋⢸⡇⠀⠀⠀⠀⢸⣿⡟⢹⠋⡿⡆⡄⠀⠀⠀⠤⠄⢰⡇⠐⠃⢸⢷⠀⠀⢸⠄⣄⠀⠀⠀⠸⣿⠀⠀⠀⢿⣷⣷⡜⢷⣈⠃⠀⢘⣿⡇
⠀⠀⠀⠀⠀⠉⠀⢸⠁⠀⠀⠤⠀⢸⣿⣿⠘⢰⠐⡇⠢⡄⠀⠀⠀⠀⠀⠋⢸⠇⣼⡆⣇⠀⠈⡿⠃⠀⠸⡆⢸⣿⠂⢀⢶⡀⡏⣿⡸⣦⠻⣧⣠⣾⣿⡇
⠀⠀⣶⣿⣏⡀⠀⠢⡀⣁⡀⠀⠀⣾⣿⣿⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⢀⡆⣾⡄⢸⡆⠨⠀⠀⢢⢀⠀⠀⠃⢸⣿⡇⠁⠈⠠⡇⠈⡿⠈⢂⣼⡟⣿⣿⡇⡀
⠀⠀⠘⠿⣏⣠⣗⣤⣦⠟⠻⠿⣷⣿⣿⣿⣂⠈⡻⠿⠿⠆⠀⠀⠀⠀⢰⢡⡿⡇⠈⡗⠀⠀⠀⢸⡋⠀⠈⠓⢸⣿⣧⠀⠹⠇⠳⠲⣶⠊⠀⠀⡄⣿⣿⣿⡇
⠀⠀⠀⠒⠯⠅⠀⠉⠀⠀⠀⠀⠀⠈⠙⠶⣶⣸⣟⡑⠚⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣅⣀⡀⢀⣼⡋⠀⠶⣤⣿⣽⡆⠀⠸⠁⠀⠀⢿⡀⠀⠠⢀⣽⣿⣟⠁
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠛⠛⠛⠓⠚⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠒⠚⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠴⣺⠵⠚⠘⠋⠉⠉⠓⠓⠯⣓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣶⣦⡀
⠀⠀⠀⠀⠀⢀⡞⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦
⠀⠀⠀⠀⢀⠧⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣹⡀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⡞⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢳⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⢐⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠐⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣸⠃⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⢳⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢗⡏⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⢳⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠎⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢭⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢜⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⠀⠀⠀⠀⢀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠭⣙⣂⡲⡴⢖⣒⣻⠽⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡆⢀⡗⢈⡴⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣧⠊⠿⡉⢫⡑⣏⢹⠳⣠⡊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠾⠃⢛⡁⣉⡁⡛⠋⠴⠆
⠀⠀⠀⠀⠀⢀⡈⢱⡞⢓⠆⠉⠀⠁⠀⠀⠀⠈⠐⢇⡱⢯⣁⡢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⢃⡡⠌⠛⠊⠙⠈⠁⠛⠸⢆⡌⠛⣁⡀
⠀⠀⠀⠀⠀⣀⢹⠯⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⣱⡌⡆⠀⠀⠀⠀⠀⠀⢠⡙⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢇⡈⢥⡀
⠀⠀⠀⠀⢈⡈⡝⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⡷⠤⠀⠀⠀⠀⠀⢰⡌⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠐⠦
⠀⠀⠀⠀⢀⡉⣟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣞⠲⠀⠀⠀⠀⠀⢠⡅⣨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳
⠀⠀⠀⠀⠈⡉⢯⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢚⠞⢦⠇⠀⠀⠀⠀⢠⣅⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⠁⠻⠆
⠀⠀⠀⠀⠀⠍⡙⣦⡌⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡉⡟⢢⠄⠀⠀⠀⠀⠀⠀⢤⣄⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠍⡸⡇
⠀⠀⠀⠀⠀⠀⠣⢁⣳⢃⢠⠦⡀⣀⢀⡀⡀⠤⡐⢳⣔⠋⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦⠋⢼⢆⡀⠀⠀⠀⠀⠀⢠⣔⠓⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠤⠛⡲⠷⣼⠬⡦⠽⡲⢺⡏⡘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢃⣬⠁⠓⠺⠞⠷⠙⣃⢠⡆⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠚⠅⠊⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠰⠛⠘⠋

⠀⠀⠀⠀⢤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⢲⡄
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣧⣿⣿⣿⣇⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣟⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣔⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠶⠦⣄⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢹⣿⣷⣄⠀⠉⠉⠒⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠻⣿⠛⠛⠿⣿⣿⣿⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣴⣿⣶⣶⣀⣿⣿⣿⣷⡀⠀⠀⠈⢣⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠱⣄⠀⠀⢸⡇
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢦⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡏⠀⠀⠀⠀⠀⠈⠳⣼⡇
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⠇⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠛⢿⣿⣿⠇⠀⠀⠈⢿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⢸⣿⡏⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⢻⣿⠀⣀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣦⣤⣿⣿⡿⣿⣶⣭⣛⣿⣶⣄⠀⠀⠀⠀⠀⠈⠓⠶⠦⣄⠀⢸⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠋⠀⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⠻⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁




⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠙⢿⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣸⣿⢡⣞⣿⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣿⡟⣀⢻⣷⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠀⣿⣷⣿⣦⣻⣦⠀⣼⡏⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣸⣿⣂⠘⣿⣏⠻⣿⣿⣿⣿⣷⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣼⣧⣾⣿⣿⣿⣿⣴⢀⢀⣀⢹⣿⡟⠛⠻⠿⠿⠻⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠿⣿⡇⣸⣿⡏⠀⢹⡇⠻⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⠟⠀⠈⣸⣷⣿⡞⣿⠀⠀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠁⠀⢀⣶⠿⣿⣟⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⠋⠀⠀⣸⣿⠿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⡴⠛⠉⠁⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠢⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠉⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢚⠂
⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠨⡭⠀⠀⠀⠀⠀⡲⢖⠀⠀⠀⠀⠀⣩⣅
⠀⠀⠀⠀⠀⠀⣗⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢽⣻⠅⠀⠀⠀⠀⡮⣽⡂⠀⠀⠀⠀⠶⠦
⠀⠀⠀⠀⠀⢐⣶⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢽⣾⠅⠀⠀⠀⠀⣽⣻⠄⠀⠀⠀⢀⣛⣛
⠀⠀⠀⠀⠀⢐⣿⣗⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠨⣿⣾⡅⠀⠀⠀⠠⣽⣯
⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⠐⣾⡷⠂
⠀⠀⠀⠀⠀⢸⣿⡯⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠰⣿⣿⠇⠀⠀⠀⣘⣿⣟⡁
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣒⡂⠀⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢐⣲⣂⠀⠀⠀⠀⢬⡪
⠀⠀⠀⠀⠀⢸⣿⡂⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢰⠯⣖⠀⠀⠀⠀⢝⣺⠄
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣗⠀⠀⠀⠀⠀⣺⠭⣗⠀⠀⠀⠀⣗⣚⡅
⠀⠀⠀⠀⠀⣸⢿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⢭⣿⠀⠀⠀⠀⣗⣖⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣸⣿⡇⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⢐⣿⢽⣇
⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⣾⣿⡇⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⢸⡯⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣤⣬⣵⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⢠⡟⠿⠚⣤⢈⣴⣥⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠷⠲⢀⠽⢦⡀⢰⣆⠟⣠⠖⠢⠌⡰⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢒⣡⡴⠞⠻⢉⠉⢁⡀⣾⢁⡄⢸⣦⣴⡿⠲⢟⠉⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡴⠛⠉⠀⣀⠤⠲⣀⠚⣁⣾⡊⠉⠉⢡⠈⠀⠓⢨⣇⣀⣀⠀⠛⢦⡀⠦⡀
⠀⠀⠀⢀⣒⣒⣀⣐⣺⣎⣴⠏⠀⣠⠢⠗⠋⠁⢀⣀⣈⣉⣭⣭⣥⣟⣩⣤⡖⢚⣋⠈⠉⠋⠳⣄⠀⠙⢦⣹⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢹⠋⢯⣽⡟⠛⠁⠠⣺⠋⢀⡀⠀⠛⠉⣩⣍⣀⢀⣀⣈⣉⣉⣉⠛⠛⠻⠶⣧⠐⠠⠀⣷⡄⠈⠿⠾⣿⠿⠿⢿⠋
⠀⠀⠀⠀⣌⠙⠢⢀⡟⠛⢛⡈⢁⣴⣛⡡⠆⠐⠁⢛⣘⣫⣭⣭⣭⣭⣭⣭⣙⡛⠳⠦⠄⠀⢰⣦⣌⠛⠀⠰⠶⠆⡐⢶⡼⠃
⠀⡖⠻⠓⣛⣃⡠⢞⣴⠇⠈⠁⠈⢿⡿⢓⣦⠾⠓⡉⠉⠀⠀⠀⠀⠀⠀⢈⣉⠉⠛⠲⢤⣉⠻⣯⠉⠰⠲⠶⢂⠀⠁⠀⢁⣠⢤⡄⡀
⡀⠈⢀⣼⢀⣭⡶⠟⠉⠀⠀⣀⣾⣧⣴⠟⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⢤⣉⠳⣌⣓⣒⢂⣴⡌⠻⢶⣤⠀⠡⠟⠈⣷
⠃⠀⠨⣥⢸⡇⠀⢀⣤⡴⠞⣉⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣉⡉⠹⣦⣝⣦⡄⡄⢰⡇⢀⡤⠻
⠐⠡⡀⢿⠸⡇⢰⠈⣿⠀⠊⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⢿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⡇⢸⡇⢠⣀⣶
⠀⠁⢈⣿⡘⠇⢸⠘⣿⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⣿⣿⣿⣷⣿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠆⢸⡏⣿⡇⢸⡇⡾⣾⠃
⠀⠰⠂⢸⠇⠀⠈⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠁⢩⣿⣀⣀⠤⣤⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⢸⡇⢣⡾
⠀⠀⠰⡆⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⡷⣶⠀⠸⣿⠄⠀⠀⣿⣿⣯⣤⣈⣸⣍⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠁⢸⣷⡏
⠀⠀⠀⡇⢀⠀⢸⢰⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⠀⠀⠀⠀⠀⣸⣿⣿⡏⣿⣿⣯⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢠⣿⡇
⠀⠀⠀⣿⢸⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠀⣾⢿⡇
⠀⠀⠀⣿⠘⠀⢠⠈⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠁⠀⠀⠀⠻⣿⣾⣿⣿⣿⣏⡽⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣟⠀⣷⢸⡇
⠀⠀⠀⣿⢠⡀⢸⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣇⠀⠀⠀⠀⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⣿⢸⡇
⠀⠀⠀⣿⢸⡇⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⡏⢸⡇
⠀⠀⠀⡿⠘⠀⢸⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⡤⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⣿⠀⡇⢸⡇
⠀⠀⠀⡇⣴⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠤⠀⣤⣀⣀⡀⠋⠀⠀⠀⢸⡁⠉⠉⠉⠁⠈⠙⠀⢸⠀⣿⠀⠀⣸⡁
⠀⠀⢀⡇⢸⠀⢸⣿⣿⢠⣀⣀⣠⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠐⠀⠁⠴⠀⢸⠀⡏⠀⢀⣿⡇
⠀⠀⢸⡇⣼⠀⠘⣿⣿⢼⣁⠀⡀⣀⠈⠁⠘⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⠄⠀⠀⢀⠀⢸⠀⠇⠀⠘⢿⡇
⠀⠀⠀⡇⢾⠀⠀⣿⣿⢸⠃⠀⠃⠀⠀⠀⡄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠈⠹⠄⢸⠀⢀⡀⠀⢸⡇
⠀⠀⠀⡇⢸⡆⠀⣿⣿⠘⠀⠀⠃⠀⢀⡄⠹⣆⠳⠀⢻⣆⠀⠀⠀⣀⣀⣤⣄⣠⣤⡤⢾⡇⠀⠀⠄⠀⠀⡀⢸⠀⣿⡇⠀⠸⡇
⠀⠀⠀⠉⣿⡆⠀⣿⣿⠀⠀⢀⡀⠀⠀⠒⣀⠀⠄⠀⡀⢈⡏⠉⠉⠉⠉⣁⠀⠀⡐⠘⣿⣧⣤⣶⣦⡀⣁⡇⢿⠀⣧⠁⢰⠀⢳⡄
⠀⠀⡀⢿⣿⠁⠀⣿⣿⠀⣤⣤⠀⠀⣷⡀⠀⣿⣤⣶⣿⣦⣁⣈⠕⠶⠖⠋⣈⣉⠁⣈⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⣼⠀⠉⠀⢸⠇
⠀⣰⠏⣼⣿⡄⠀⢻⣿⠀⢿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣶⣾⣿⣶⣿⣿⠿⣿⢩⣿⣿⣿⣿⠉⣭⠇⢿⢀⣿⠂⠀⠁⢸⡆
⢀⢫⡷⡍⠸⠁⢀⣼⠻⢄⡈⠋⠛⠛⠿⠛⢿⠿⣿⣿⣿⣿⣿⡙⠟⣉⢠⣴⡬⠧⠰⠷⢾⣿⣿⠋⠻⠜⢋⡴⠚⣨⡿⠀⢘⢤⡀⢹⡀
⠘⣿⠖⣋⢰⡚⢦⠈⠙⣦⡹⣦⣤⣴⣶⠶⠶⢶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⢶⣶⣶⣦⣤⣴⣶⣶⠖⠉⡴⠟⠃⠈⢂⠘⣧⡙⣸⠇
⠀⣡⠟⡉⠈⠙⠞⢳⣄⡀⠱⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠛⠛⢋⣙⣻⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣦⠄⢀⡄⠀⡠⠤⣙⡛⣡
⠀⠀⢳⣠⣤⡄⠀⠀⠉⠀⠠⠤⣤⣴⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣤⣤⣤⣤⡄⠀⠀⠠⠔⠛⠀⠂⢰⢆⣸⠟⠉
⠀⠀⠀⠀⢰⣠⡴⠇⢀⠒⢉⡁⠀⢌⠉⠉⢁⠙⠷⢦⣄⠘⣀⠀⠀⠀⠀⢀⣀⣴⠟⠋⠀⠀⠉⡀⣠⣐⡂⠑⢤⠀⢄⣠⠏
⠀⠀⠀⠀⠀⠱⢦⣦⠀⣠⠟⢩⣀⣸⠀⢴⡏⠠⠇⠠⢤⣤⣤⣤⣤⣤⡴⠶⠴⠤⠼⠄⢀⣡⢀⠀⢱⠋⢯⣀⣼⣥⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⠾⠗⠰⠦⣀⣠⣤⣤⣤⣤⣬⣭⣭⣤⣶⠶⠞⠛⠳⠛⠉⠉⠀⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣿⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣦⣶⣾⣶⣿⣿⣦⣤⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠆⡖⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣠⡆⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣾⣿⠇⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣻⠀⢀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣿⣿⣿⡟⠉⢀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣿⣤⡈⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣟⣡⣶⣾⣷⣿⣿⢦⣀⠀⠀⠀⠀⠀⠈⠙⠓⡇
⠀⠀⠀⠀⣀⠀⠀⠀⡽⣏⢤⡀⣿⢿⣶⣶⣌⣂⠀⢀⠀⠀⢀⣛⣉⣛⣿⣟⡿⣿⣿⣿⣿⢷⣾⣿⣶⠀⠀⠀⠀⢰⣀⣴⡇
⠀⠀⠀⠀⠀⠀⢳⠜⣿⣏⣀⠐⠋⠸⠿⣿⣿⣟⣿⣿⣻⣯⢂⠀⣠⣀⣿⣉⣹⢿⣮⡙⢿⣯⢿⣿⡿⠴⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⣿⣦⣠⣘⣿⠀⠀⢀⣀⡴⠤⠛⠻⠿⠯⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠘⣿⣻⡷⠻⣾⣼⣧⣴⣿⣿⣿⣷⣯⣀⡀
⠀⣤⣥⣿⣿⣿⣿⣛⣿⣤⣤⣽⣿⣗⣶⣤⣤⣴⡤⠻⠍⠿⠗⠛⣙⣿⠿⠿⠿⠀⠹⠛⠟⠚⠛⠉⢛⣛⠛⠿⠿⢛⣛⣿⣟⡛⠚
⠀⠈⠉⠛⠛⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣶⣤⣤⣬⣉⣉⡀⠀⠀⠈⠁⠉⠀⠀⠉⠉⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠛⠛⠛⠉⠀⠉⠩⠿⠅⠀⠲⠶⠒⠲⠶⠂⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢀⡻⠛⠀⢈⣁⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⣿⠿⢿⠿⣿⣶⣿⠿⣿⣿⣷⠀⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⢀⣠⡷⡄⠃⠘⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⢽⣿⣷⣦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣁⠶⠂⣿⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⡃⠀⢺⡯⠟⠙⠒⠉⢿⡿⣿⣿⣷⣶⣤⣶⡤⠐⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠸⢛⣧⡀⠀⠀⠀⠘⡅⢻⣿⣿⣿⣽⣿⠃⢰⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠠⠀⠀⡠⠋⢾⣿⠀⠀⡀⠀⢣⠈⢿⣿⣿⣿⢿⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢮⠹⣷⡀⡴⠄⠸⡇⠘⣿⣿⣿⣿⠀⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠰⣾⠃⠀⠘⠉⡇⢀⣻⣿⣿⣿⠀⢀⡿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⢀⣠⡟⠇⠀⠀⠀⢀⣿⢸⡧⣿⣿⣿⠀⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢩⡭⠅⠉⠁⢻⢶⠀⠀⠗⠹⢿⡘⣇⢸⣿⣿⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⣈⣥⠴⢄⠀⠠⣾⠷⠆⠀⠀⢹⡇⠁⠈⣿⣿⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠈⣿⡇⠈⣽⣧⡗⠁⠢⠘⠃⠐⢊⡅⠀⠁⢻⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⡼⠀⢸⣿⣷⡌⠉⠁⠀⠀⣼⣶⣦⣀⣼⡇⢠⠀⠘⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⠀⢀⣼⣿⣿⣇⠀⠀⢀⣀⣻⣿⣯⣿⣿⣷⣾⣷⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡈⣿⣿⣿⡄⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⡀⠁⢀⣿⣿⣿⡻⠄⠀⠀⢨⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⠙⠂⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⡄⠀⠀⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢤⣄⢀⡄⡀⢠⡀⣿⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣤⣤⣦⣴⡤⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⡄⠀⠸⠟⣥⠀⠚⠛⠻⠷⠖⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⡀⠁⠀⣀⠀⠀⠀⠀⠀⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠂⠀⠉⠃⠄⣠⣤⣴⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⢀⣀⣀⠀⠀⠀⡴⠊⠆⠀⢀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠹⠧⠀⠀⠙⠛⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⠉⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡍⢛⣦⣤⡶⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠱⠁⣰⣫⡽⣾⡁⠈⠻⣿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣁⣸⣠⣏⡁⠀⢻⡙⠃⠀⡅⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⢙⣿⣿⣧⢀⣠⣙⠃⢠⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢰⠀⠀⠞⠛⠿⣿⣿⣿⣿⣦⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡄⠀⠀⠀⠒⠀⠉⢉⣻⡏⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢇⠀⠒⠀⢀⠴⣋⠍⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠇⢐⠃⠀⠄⠁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣾⠁⠀⠀⠰⢿⣤⠶⠶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⡄⠸⠇⠀⠺⠏⠀⠀⠀⠳⣄⠰⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠗⠀⠀⠈⠁⠾⣣⠄⠀⠛⠇⠀⠀⠹⠆⢀⠈⠂⠈⠂⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢁⢋⣼⡹⠃⢆⠀⠀⠀⠃⠘⣧⠀⠙⢦⡀⠐⠄⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⠘⢆⣉⣠⡋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢻⠿⠓⠀⠆⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠘⣄⡀⠑⠀⠀⠀⠀⠀⠀⢀⠶⠉⡀
⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⣷⠀⣴⡇⠘⠙⢦⡀⠀⠀⠀⣀⡰⢃⠀⠜⡅
⠀⠀⠀⠀⠀⡿⢃⣠⠀⠀⠀⠀⠀⠀⠀⠸⢇⠈⠟⠀⠹⠁⢴⠀⠀⠉⠒⠒⠈⠀⠀⠺⠃⠀⠃
⠀⠀⠀⠀⠀⠘⠛⡧⠖⠒⠀⠀⠀⠠⢰⣶⣌⣃⢠⡄⢃⠴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⢀⡀⣠⠿⣷⣾⣷⣄⣠⡆⠀⠀⠀⣴⣧⣤⠿⣾⣿⠟⣷⣞⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⣀⡀⢻⣿⣶⣿⢻⡇⣻⡿⠷⣤⣀⡜⠉⡋⡿⢷⣼⣷⠚⠷⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠘⢻⣿⣿⣿⣿⢻⣶⡟⠀⣠⡿⣿⡁⠔⠀⠘⠗⢻⣿⠛⢃⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⣀
⠀⠀⠹⢾⣿⣿⣿⣿⡇⣰⡿⣥⣿⣿⡦⠀⡆⠀⢸⡇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠯⡀
⠀⢀⣶⣎⢻⣿⣿⡿⢔⣽⠟⣉⠿⠋⠀⢀⠃⠀⡘⣀⠀⠀⠀⢣⠀⠀⠀⠀⠐⠄
⠀⠀⠆⠀⠈⢹⣿⣿⡟⠧⠚⠀⠀⠀⠀⠈⠀⠀⠱⢛⡀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠠⠀⠀⠤⠀⣾⡦
⠀⠀⠀⠀⠀⢁⣽⡏⠀⠊⠀⠀⠀⠀⣠⠀⠀⠀⢣⡾⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠻⠗
⠀⠀⠀⠀⠀⠈⠉⠟⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⡅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⠀⢠⣧⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠘⢠⡟⠁⣷⠈⣧⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⢸⣇⣸⡇⢀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⢻⡄
⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠈⠀⠀⠀⠀⡈⣀⠀⢁⡉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡄
⠀⠀⠀⠀⢠⠁⠀⢠⠞⠁⠀⠀⠀⠀⠰⢿⠟⠀⢻⠇⠀⠸⣷⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆
⠀⠀⠀⠀⠈⣠⠞⠁⠀⠀⠀⠀⠀⢠⠀⡸⠀⠀⢸⡄⠀⠀⠈⠇⠀⠂
⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠆⢰⡇⠀⠀⠆⠡⡄⠀⠀⠘⡀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣿⠁⢠⡄⠀⠀⣴⠀⠀⠀⢹⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠎⠀⠈⣿⠀⠘⣇⠀⢸⡏⠀⢀⡇⠀⢻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠌⠀⡰⠀⡏⠀⠀⠈⣄⡿⠁⠀⠈⡇⠀⠀⠻⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⠀⠀⠀⠀⢠⠎⠀⣼⠃⢰⡀⠀⠀⠀⢹⠇⠀⠀⠀⢹⠀⣄⠀⠹⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢘⠀⠀⠀⠀⡠⠁⢀⡼⢉⡆⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠹⡆⠀⠈⢧⠈⢢⡀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠈⢳⡀⠀⠜⠁⢠⡾⢁⣾⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡆⠀⠀⢀⠀⠈⠣⠀⠙⢦⠀⠀⠀⣠⠾⠁
⠀⠀⠀⠀⠙⢮⣀⡀⠋⢀⠞⣿⠀⠀⠀⠀⠀⠰⠃⢠⡀⠀⠀⠀⠗⠀⡄⠈⢆⡀⠀⠱⣄⣠⡷⠟⠻⣄⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠉⠐⡶⠯⣀⣏⠀⢀⠀⠀⢸⡃⠀⠈⠻⠀⠀⠀⠆⠀⠇⠀⠀⠙⢢⡴⠋⠁⠀⠀⠀⠈⠷⠀⣁
⠀⠀⠀⠀⠀⠀⠠⠾⡁⣠⠌⠻⢦⡈⡀⠀⠈⣧⢀⡀⠁⠀⠀⠀⠂⢀⠂⣀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠶⠖⠉⠁⠀⠀⠀⠉⠛⠶⠄⣹⣼⣿⣤⡀⠠⠾⠶⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢏⠉⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠈⠁⠀⢄⠙⢦⡀
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢷
⠀⠀⠀⠀⢰⣏⡁⠀⠀⠐⠴⠆⢀⣴⡾⣃⣠⠆⠀⢸
⠀⠀⠀⠀⢀⣿⣟⣀⣾⣿⣷⣦⣿⡟⠉⠁⠊⠑⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠸⣦⣿⣿⠉⠛⠛⢋⣸⡿⠶⣚⣻⣴⣷⠇⠀⠀⠀⠀⢀⡤⠞⠋⢉⣉⠉⠙⠶⣄⠀⠀⠀⠀⠰⡳⡄
⠀⠀⠀⠀⣠⠟⢀⣄⠀⣴⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⡤⠞⠉⠀⢀⣨⡴⠶⠯⣶⡀⠈⢣⡀⠀⠀⠀⢱⢸
⠀⢀⡴⠋⣡⠏⡜⠉⢠⣿⡏⢻⠇⡄⢯⢷⡘⠿⠿⠛⠛⠉⢀⣠⣤⣶⠟⠁⠀⢠⢤⣀⠙⢦⡀⠙⢦⣀⡤⢏⡼
⠀⣼⠁⣰⠃⠰⠁⣰⣿⠏⢰⠀⠀⣿⠀⠀⠉⠛⠻⠯⠭⠉⠉⠉⠻⡅⠀⠀⠀⠀⠑⢮⡳⣄⠙⠲⠦⠤⠶⠋⠁
⠀⢿⠀⡏⠀⠀⢠⣿⠁⠰⣾⠀⠀⢹⣦⣀⠤⠤⠤⣤⣤⣤⣀⢀⠀⢻⠉⠛⣦⠀⠀⠀⢳⠈⡇
⠀⠈⠳⣧⢠⡀⠈⢻⠀⠸⣽⢸⡄⣠⠟⠛⠛⠛⢯⣉⠁⣀⣨⣷⣧⠈⢧⣄⡘⢦⡀⠀⣼⢀⡏⠀⢀⡤⠖⠚⠓⠒⢦⡄
⠀⠀⠀⠘⣏⢿⡆⠈⠳⣤⣌⠷⠋⢀⣰⣾⣿⣷⣶⣌⢿⣭⣴⣾⣿⣅⡀⠙⠓⠮⠛⠛⢁⣼⡷⠚⠉⣴⣾⡿⠿⠿⣦⡙⡆
⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⣀⡴⠿⢭⣤⣤⠟⢿⣿⡆⣯⠀⠀⠈⠛⠯⢿⣶⣶⣶⡾⠯⠤⠤⠶⠛⠛⠁⠀⠀⠀⢈⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⢧⣄⡀⠀⢀⣀⡴⠟⣿⡇⣿⠀⠀⠀⠀⠀⠀⠈⢿⡄⢻⡄⠀⠀⠀⢀⣤⡀⠀⠀⠀⢸⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⣠⡿⣡⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠹⢦⣀⣠⢞⡼⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⡴⠞⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡈⢡⣿⡀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⣶⡈⢳⠖⠀⠀⠀⠀⠺⠀⠸⣹
⠀⠀⠀⠻⢧⡀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠿⠻⠦⠤⢀⣀⡀⠠⠈⠸⣿⣀
⠀⠀⠀⠀⠀⠃⠛⠂⠆⠀⠀⠀⠀⠀⠀⣠⣶⣾⣋⣤⠄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⢐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠸⣿⠛⠛⠁⠀⠀⣀⠴⢾⣿⡯⠀⣤⣄⠀⠀⠀⠀⠀⠀⢰⢾⡏
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣴⡶⢦⠀⣁⣤⣿⠿⡃⠰⣄⠀⣿⠉⣾⡿⡗⣸⣷⣿⣤⣤⠀⠀⢠⣤⣴⣿⣿⣿⣦⣀
⠀⠀⢠⡿⠀⢀⣤⣔⣶⣶⡴⢿⣷⣿⣦⣿⣿⣿⣶⡿⣶⣿⣧⡴⠆⢘⡶⢼⣟⣿⣿⣿⣴⣦⣿⣿⠟⣟⣿⣿⣿⣄⣉⠀⠠⠀⠀⡄⣠⣼⠷
⠀⠀⠴⠀⠀⠀⠛⠻⣿⣿⠃⢈⡿⠋⢿⣿⣿⣿⡿⠁⠀⣿⣿⡧⠤⣉⠁⢄⣿⣽⣿⣭⣿⣶⣀⣟⣹⠻⢿⣿⣿⣿⣿⣦⣤⡤⢠⣯⣥⡄⢠
⢀⣷⡀⠀⠀⡨⠁⠀⢛⣿⣶⣿⣷⠀⠈⣹⣿⠟⠁⠀⣴⣿⡏⠀⢠⠴⣷⣦⣼⣿⢿⣿⡏⢻⣿⣟⣿⡷⣾⣿⣿⣿⣿⠿⠻⡑⠋⡇⢨⣵⣾
⠛⠋⠁⠀⢀⡀⣰⣿⣿⣿⣿⣿⣿⠦⡶⠿⣿⣧⠤⠒⠻⢿⡇⠀⢈⢦⣿⣿⣿⢁⣾⡽⣡⠘⢏⣿⣮⣟⣿⣿⣿⣿⡅⠐⡞⣿⣧⣧⣿⣿⣯
⣶⣦⣸⣿⣜⢿⣟⣽⣿⣟⣿⣿⣯⣷⣽⣰⠌⣡⠖⠀⠀⠨⢿⣠⣤⢀⣿⣿⣿⣿⣏⡼⣫⣴⣶⣿⡏⣙⣿⣿⣿⣿⡧⢀⣿⣿⣿⣿⣿⢻⣟
⠙⣿⡿⠿⣷⡟⡟⠲⠨⠿⢟⣿⣿⡷⠽⠟⠈⠁⠀⣶⣦⡤⢼⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⠟⢁⣽⣷⣿⣿⣿⣿⠧⣤⣾⣿⡿⢷⡿⠿⣿⣿
⠨⠉⠀⢉⠩⠹⣧⣆⢀⣀⣿⣿⣿⣅⡀⣠⣄⣀⣼⣿⢧⣠⣼⣿⣿⣿⣿⣿⣿⣭⣭⣭⣑⣈⣿⢯⡽⣿⠿⣿⣿⣮⡋⡂⣉⠆⢸⡇⣀⣻⣿
⢀⣀⣞⣷⣴⣾⣷⣿⣿⣿⢿⣿⣿⣯⣤⣿⣿⡿⣿⣿⣴⡻⠿⢟⢿⣿⡙⠿⣿⣿⣿⣿⣿⣯⢹⣯⣘⣷⣯⣀⣟⣿⣿⣤⡓⠀⡊⡙⢧⣦⡼
⣿⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⡗⢻⣿⣿⠃⠀⢀⡈⢿⣷⣀⣤⣠⣦⣙⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣼⣿⣿
⠻⣏⣩⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣶⣞⣛⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢈⡟⡁
⠈⠉⠛⠺⢿⠏⠿⠿⣿⠿⠿⠿⠏⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡶⣛⣯⡿⠟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠙⠙⠋⠁
⣶⣶⠶⠶⠿⢾⣾⣿⣿⣷⣶⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣶⣄⠈⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⣴⡿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠈⠑⢦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣤⢋⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⡀⢠⣤⠤⣤⣀⡀⠈⠰⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣼⣯⡉⢻⣿⣤⣶⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣾⣽⣂⡄⠀⠀⠀⠀⠀⠀⢀⣾⠘⠳⠿⠏⢣⣴⣤⣆⡙⢾⣿⣟⣶⣿⡟⣡⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠄⠈⠆⠀⠀⠀⡞⠂⠘⠁⣁⠈⠿⣩⣽⣿⣷⠈⠏⠀⠈⢻⣷⣶⣿⣿⣿⢟⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢠⣤⡞⠁⠠⢒⣠⣀⢩⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⠀⠙⠛⢻⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣇⢉⡈⢠⣾⣯⣛⣾⣿⣿⣿⣿⣿⡿⣄⠀⠀⠀⣿⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢋⣸⣾⣷⣾⣿⣅⣿⣿⣿⣿⣿⣿⣀⡙⢏⠁⣴⠞⠁⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣄⡴⢎⢤⣼⣿⣿⣿⣿⣿⣟⣿⣿⣬⣁⣿⠿⢿⣷⣞⠋⠀⠀⣸⠎⠁⠀⠀⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⡿⣛⢰⣾⣿⢻⣯⣿⣿⣿⣿⣟⣯⣿⣷⢾⣿⡄⠀⠻⠃⠀⠀⢠⢶⣾⣬⣏⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⣸⠋⣰⠗⣿⡿⠛⠉⠉⡙⠛⣿⣧⡌⢿⣀⣽⠧⠀⠛⢀⠀⣼⡇⢸⣾⠋⠛⣷⣾⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⢀⠚⠁⢸⣿⠀⣰⣾⣾⣿⣇⠈⠻⠗⠛⣡⡄⠀⠀⠀⢨⣿⡿⡷⠿⠃⠀⠀⠀⢺⡟⡷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠁⠀⣶⣿⠟⠁⠘⣯⣿⣿⣿⠇⠈⢱⣾⣯⠙⠂⠾⠖⡁⣾⡔⠀⠀⠀⠀⠀⠀⣾⣟⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⣴⠟⠁⠀⠀⣠⡾⢡⣿⠋⠀⠀⠈⢿⣿⠾⣷⣾⡇⠀⠸⣷⣆⠀⣀⠀⣠⣸⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⡟⠁⠄⠀⠀⢀⣤⣿⡟⠁⠀⠀⠀⠀⠘⢿⠆⠈⠫⣹⡀⠀⠙⢿⣷⣷⣿⣛⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣇⣴⣶⣾⣸⣿⣿⡿⣇⠀⠀⠀⠀⢀⣤⣾⣶⡶⠂⠈⠙⣄⡀⢀⠉⠈⠀⠁⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠿⣏⣿⢹⣿⠿⣿⣛⠻⠷⣾⣒⣤⡠⠔⢋⡛⣧⣿⢧⡄⠀⠀⢉⠱⡄⠆⠀⠀⠀⣼⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⠙⢯⡶⡈⢡⣾⠋⠁⠀⠻⣄⠀⠀⠰⠀⡴⠀⠀⠀⠻⠴⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡀⠀⠀⣰⠟⠙⠻⡦⠀⣸⠧⠟⠛⠁⠀⠀⠀⣀⣙⣉⣄⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣁⣤⣤⣴⣦⣾⣏⡀⢠⠞⢁⣼⠟⠀⠀⠀⠀⢀⡾⠃⠉⠉⠉⠻⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠟⠉⠘⠁⢿⠤⠟⠁⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠈⠻⠶⠶⠤⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣠⡤⠶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠄⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⡀⠀⠹⣿⡄⠀⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠇⠀⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢄⣀⠀⠠⢰⢠⣟⢀
⠀⠀⠀⠀⠄⠰⠂⠀⠀⠒⠒⠒⠒⠐⠒⠀⠀⠀⠒⠀⠚⠉⠁⠘⠁⠀⠐⠐⠂⠘⠛⠀⠈⠁⠈⠃⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢤⣠⠊⠁⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⢰⡆⢀⠄⠂⠀⠀⠆⠠⡖
⠀⠀⠀⠀⠀⠀⣷⢀⡤⠀⢸⣿⠀⢠⡄⠀⠀⡤⢶⠀⠀⠐⡇⠀⠀⣿⠸⠀⠀⠀⣦⡈⢠⡇⠀⡖⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⠀⣻⡇⠀⠀⡇⠘⡆⠀⠀⠄⠀⠀⣿⠠⠀⠀⠀⣿⠳⡀⠁⡸⢠⠏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢺⣷⠀⠸⡇⠀⠀⠀⣤⣼⣷⣤⣄⣀⢀⣛⣁⡀⠠⠴⣿⠖⣿⠚⡕⠁⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠎⠉⠀⠘⠀⢸⣿⡄⠃⣆⠀⠀⠀⠈⣿⣿⣿⣿⡽⡿⢿⠁⢁⣴⠾⠋⠉⠈⠘⠁⠀⠀⠀⢀⠆⢀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⢸⠀⢠⡀⠀⠀⠀⣿⣿⣤⠺⣦⣀⠀⠀⠈⠉⠛⠻⣷⡛⣎⣾⣿⢋⣥⡖⠁⠀⠀⠀⠀⠀⠀⠈⡀⠀⠸⣴⣿⣆⢸⡏⢠
⠀⠀⠀⠀⢹⠀⠘⡇⠀⠀⠀⣿⣤⣹⣄⠘⠋⠉⠀⠀⠀⠀⠀⠀⠈⣽⣿⣷⢻⣿⡇⠀⠀⠀⢰⡀⠀⠀⣼⠉⠀⠀⠀⠸⣿⣿⣿⣌⣐⡀
⠀⠀⠀⠀⢸⢀⣤⠀⠀⠀⠀⢸⣆⠀⠘⠒⠂⢌⣓⠲⡶⠋⠀⠀⠀⣿⣻⡏⣿⣿⡇⠀⠀⠀⠀⠙⢦⣠⣿⡶⡤⠄⠀⠰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢸⡿⠑⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⣯⣤⡄⠀⠀⢀⣿⢾⣧⣿⣿⠁⠀⠀⠀⠀⠀⠀⢙⣿⡇⠁⡄⠀⠀⢻⣿⣿⡗
⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⢠⢸⣿⣿⣰⡄⠀⠀⠰⡼⣯⣀⡀⠀⣾⣿⣸⣿⡸⣿⣷⡆⣤⠀⠀⢀⠀⢸⣿⠃⢰⠁⠀⠀⣾⣿⣿⣟
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⢸⡿⣿⣿⡇⢴⡄⢆⢻⣿⠿⢀⢌⣼⣿⣿⣿⣷⣹⣿⣧⢸⡆⠀⠘⣆⢸⣿⠀⠀⠻⢂⡼⣿⣿⣿⣷⣄⢀
⠀⠀⠀⠀⠀⣼⡇⠀⡇⠀⢸⠈⣿⣿⣿⣧⣸⣷⣾⠀⠻⣿⣿⣿⣻⣿⣿⣿⣿⢷⣽⣿⣿⣿⣄⣄⢸⣼⣿⠀⠀⠀⠋⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⡆⡇⢀⠐⡄⠻⣿⣿⣿⣿⣿⣟⣛⣓⣚⣉⣿⣿⠿⠿⢿⣍⡛⢻⡿⢻⣛⢻⠯⠞⣸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠓
⠀⠀⠀⠀⠸⢿⣿⡇⣀⣸⡀⠧⠠⠌⡉⠿⠏⢠⣭⡥⢴⠎⠙⠛⠿⢷⣾⣿⣟⣻⣧⣝⡲⢬⣍⣛⠻⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠛⠓⠀⠀⠀⠈⠀⠁⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠻⠿⣷⣾⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠷⠤⢀⣠⣄⠀⠤⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣤⣠⣤⣄⣐⣏⣡⣁⠠⢀⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠘⠻⠿⠿⠿⠿⠿⠿⠿⠞⠾⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣷⡦⠞⠛⠛⠙⠻⢿⣿⣯⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢈⣿⣿⠉⣥⣶⣿⢆⣀⡼⢟⣿⡿⣿⣴⠶⢙⣿⣿⣷⢈⠿⢋⣼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢉⣩⣴⣿⣿⢻⠜⠻⠊⠀⡀⣄⣀⢤⣨⣽⣿⣿⣶⣿⠿⠟⢁⠀⣼⣟⡻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡠⠻⠿⠿⠿⠈⠁⢀⣤⣴⣿⣇⡾⠿⣿⠃⠀⠋⠀⠀⢐⣠⣴⣿⣷⣭⣥⣴⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⣿⣿⣿⡿⠿⠂⠀⠀⣀⣠⡴⠒⠚⢿⢙⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⢟⣋⣸⣷⣿⣿⡿⣿⣿⡶⠁⠀⢈⣴⣿⣿⣿⡀⠀⠈⣎⢹⣿⣿⡟⡻⢛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣡⣶⣿⣾⣿⣿⣿⡿⣛⠽⣾⣏⡈⠑⠁⢠⣿⣿⣿⣿⣿⣷⠀⠀⠸⡜⣿⣿⣿⢤⡆⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠑⠈⠀⣀⣤⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿⢿⡆⠀⠀⢿⢹⣗⣤⡀⠥⡘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠝⠀⣠⠖⣿⣿⣿⣿⣿⡆⠀⠀⢌⠻⣿⡿⢿⡝⢱⠀⠀⠸⡏⣿⣏⠙⡔⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠰⠻⣿⣿⣿⣿⣿⣿⡿⣄⠀⠀⠀⠈⠳⡏⠁⠈⡆⠀⠀⢃⢿⡛⠛⠛⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠸⣶⣿⣿⣿⣿⣿⡿⠣⢎⢣⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⡘⣧⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣎⠀⡀⠈⠓⠚⠻⠿⢧⣀⡀⠀⠳⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣮⡂⠀⠀⠀⠀⠀⠈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣶⣶⣶⣿⡿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣟⢻⣿⡋⠉⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠉⠁⠀⠀⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠹⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⠿⣿⣿⠟⠀⠀⠀⠀⠈⣷⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡾⣿⣿⣿⣿⣿⠁⠀⢸⣿⣶⣄⣀⣀⣀⣰⣿⡿⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠙⠻⣿⣿⣧⡀⠀⠻⣧⣈⣭⡍⠉⣻⣿⡇⠀⢸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⡄⠀⢠⣄⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠈⣿⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣼⣧⠀⠀⣿⣦⠀⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣴⣿⣿⡀⠀⣿⣿⣧⠀⠹⣿⣿⣤⠀⠀⠀⠀⠀⣿⣿⣇⠀⣿⠻⡿⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣼⠋⠙⣿⡇⠀⢸⣿⣿⣧⠀⠹⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⠀⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⣠⣾⠃⠀⠈⢻⣿⠀⢸⣿⣿⣿⣦⠀⢹⣿⣿⡆⠀⠀⠀⣿⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣴⣿⣷⡄⠀⠀⢹⣿⡇⠈⢿⣿⣿⣿⣦⠀⢿⣿⣿⣄⠀⢀⣿⣿⣿⠀⢺⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡁⠄⢀⣾⣿⡇⠀⠀⠻⣿⣿⣿⣧⠘⣷⠙⣿⣦⠀⢻⣿⣿⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠙⣿⣿⣿⣧⣿⣄⠈⠿⣧⡀⢻⣿⠁⣹⣿⣅⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠉⠙⢿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⢻⣷⠘⡟⢠⣿⣿⣿⠟⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢿⣿⡧⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⣽⣿⣄⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠀⠈⠻⣷⠀⠀⣰⣿⣿⠿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⣿⣿⣿⣿⣦⣀⠀⠈⢠⣼⣿⣿⣿⣶⣟⣿⣿⣿⣿⡏⢻⠟⡏⢻⡟⢿⠆⠈⢿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣷⢻⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⡿⢿⣿⡅⢰⣿⣿⣯⠀⠇⢸⡇⢸⠀⠀⠀⠉⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⢸⣿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠈⠟⠋⠁⠀⠀⠀⠀⠀⠀⠙⠐⠇⣸⡇⠈⠀⠀⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷⠘⣿⣿⣿⣿⠀⠘⣿⣆⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⡆⠙⣇⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣿⡿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⢿⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠇⠹⠀⢸⣿⣿⠋⠉⠉⠙⠛⢿⣿⣿⡿⠛⢿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⢠⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⠃⢸⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠸⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢰⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣼⠁⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇⠀⠀⡿⠀⠀⡟⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣾⠃⠀⢸⡇⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣰⠀⠀⠀⢰⡇⠀⣿⠀⣸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡿⠀⠀⣿⠁⠀⠰⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⡇⠀⠀⠀⣸⠇⠀⣷⠀⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣾⣿⣤⣾⣿⣄⣠⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⣸⠇⠀⠀⠀⣿⠀⠀⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⣿⠀⠀⠀⢸⡿⠀⢰⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⢠⣿⠀⠀⠀⣾⡇⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣦⣀⣤⠀⢀⣠⣾⣿⡟⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⡿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣿⡿⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⣾⡏⠀⠀⠀⣿⡇⠀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣸⣿⠃⣾⣿⣿⣿⣿⣿⣇⠀⢸⣿⡿⠃⠀⠿⠀⠀⢀⣿⠇⠀⠀⣸⣿⠃⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣿⡟⣼⣿⣉⣙⣿⣿⣿⣿⣦⣀⣉⣠⣤⣀⠀⠀⠀⢸⣏⠀⠀⠀⣿⣿⣰⣿⣿⣿⡇⢠⡆
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣾⣿⣾⣿⣿⠿⠿⠛⢋⣹⣿⣿⠟⠛⠛⠛⠛⠛⠃⣠⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⠛⠸⠁
⠀⠀⠀⠀⣶⣆⠈⠉⠀⠈⣉⡉⠛⢁⣀⠤⡶⠾⠟⠛⠁⠀⠀⠀⢀⣠⣤⣴⣾⡿⣿⣷⠆⢠⣿⣿⣿⣿⡿⠛⠿⠆⠀⢸⣷⠄
⠀⠀⠀⠀⠈⠛⠷⠶⠾⠋⠙⠿⣷⣬⣭⣂⣀⣤⣤⣄⣰⣦⣴⣿⣿⣿⣿⣿⣿⣧⣈⣁⣴⣿⣿⣿⣿⣿⣷⣦⣤⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠛⠿⠿⠿⠿⠟⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠀⠀⢄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⡀⠀⠆⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⠁⠀⠀⢐⠀⠃⠙⠁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⠀⠀⠀⠀⠈⠌⠁⡄⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⠀⠀⠉⠀⠑⠀⠈⠀⢀⠈⠁⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠟⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣀⠀⠠⣤⢤⠖⠋⢀⡄⡤⡬⠁⠸⠁⠀⠀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠨⣀⡰⢾⣷⡀⡄⣠⣸⡅⡀⠀⠠⠄⠀⠀⠁⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢋⣹⣅⠀⠀⠀⠀⠀⠀⠉⠉⢬⣆⠤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠊⠙⣿⡀⠄⠀⢄⢙⡀⠖⠂⠤⠤⠒⡞⠠⠀⠤⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠒⠈⠀⢆⠀⠀⠒⠀⠀⠀⠀⠀⠐⠡⡀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠂⢸⡀⢒⠀⠀⠂⠤⠎⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠈⠐⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠻⡆
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣀⣀⣀⣺⣀⣀⠔⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠘⣷⡀⢀⣤⣴⣤⣤⡀⣠⣶⠟⠋⠀⢀⣀⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡤⢯⣗⣦⡄⠀⠀⠈⢻⣿⣁⡄⣀⠙⣿⠿⢏⣠⠔⣋⣤⣶⣾⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡾⠛⣿⠉⢳⣿⢤⣶⣿⠿⢿⣷⠯⡿⡕⢿⡿⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⢻⡵⣰⣻⢻⡟⠁⠀⣼⣿⠠⣋⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡿⣽⡄⣤⣴⣻⡍⣶⣽⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⢀⡖⠀⠀⢰⣿⣿⡟⠋⠀⢸⣿⣿⠐⢣⣼⡞⠉⣠⣿⣿⣿⣧⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⡤⠶⠋⠀⠀⠀⣿⣿⣿⡅⠀⠀⠸⣿⣿⣇⣹⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠿⠛⠛⠉⣠⡟⠀⠀⣀⡤⢤⣤⣤⣄⡀
⣾⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣶⡿⡿⣾⡿⢖⣯⣶⡿⠟⠛⠻⣿⣿
⠹⣷⣄⡀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣰⡻⢁⣤⣶⣽⣾⣿⣿⡇⠀⠀⠀⠀⠈⣿
⠀⠈⠙⠵⣲⣄⡀⠀⠀⠀⢀⡀⢀⡀⠙⠿⢛⣩⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⠟⠉⠈⣿⣿⠀⠀⠀⠀⢀⢿
⠀⠀⠀⠀⠀⠙⢻⡷⣂⣭⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠛⠋⠁⠀⠀⢰⣿⣿⠀⠀⠀⡰⣎⠟
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠛⢿⢯⣉⠉⠁⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣛⣆⠀⠀⢀⣠⣿⣿⣿⣴⡮⠿⠛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⢻⣫⡄⠀⠀⠀⢀⣀⣀⣀⠀⠙⣿⡟⣿⣿⡿⠛⠛⠿⣿⣦⡍⠛⡛⠻⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠵⡷⠀⠀⠈⠁⠀⠀⠉⠻⣆⢸⣿⢹⣿⠀⠀⢠⡠⡾⡲⣗⣱⣗⣳⢗⢢⣟⢁⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠙⣿⣿⣗⠤⢀⣤⣼⣟⠂⠀⣠⡴⠶⠖⠒⠒⠚⠃⠀⢿⡆⢿⣿⣇⡽⠞⠛⠉⠉⠉⠉⠉⠉⠻⣶⣟⢤⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠿⠟⠋⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡞⠴⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⣠⢶⡽⠋⠈⠻⣦⣙⣿⣦⣄⢀⣤⠶⠶⠶⠶⣾⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠾⠟⠛⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡶⠶⠶⣛⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡛⠻⠿⠿⠟⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣀⣡⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⣀⣉⣳⡎⣿⢀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣬⡿⢧⠬⠭⢿⣛⣻⣭⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠚⠛⠟⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠰⠦⠄⠈⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣼⢯⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣥⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢠⡀⠀⠀⠀⠙⠻⡿⣛⡿⢿⣿⣷⣶⣄⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⡀⣇⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠙⣿⣷⢨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⡀⠹⣿⡀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⢸⣿⣦⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣟⣿⠁⠀⠀⠀⠀⠀⢴⠀⠀⠀⣀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⣧⣤⣴⣾⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢲⣿⠀⢹⣿⠿⠛⣿⣿⣿⣿⣿⣿⠿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠧⣄⠀⠏⠀⠀⠈⠧⣸⣿⣿⣿⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣺⢥⣵⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢑⡦⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⢪⠏⠀⠀⠀⠙⢿⣷⣄⡤⢄⡀⡠⠋⠀⡠⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣜⠢⢸⣏⠀⣠⠤⣀⡀⠱⠤⠤⠚⠀⠀⠀⠀⠀⢈⣿⣽⣽⣿⠗⠀⠀⠈⠂⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣮⣿⡅⡐⠟⣀⠈⠿⣦⡀⠀⠀⠀⠀⣴⣶⣭⠛⣿⣿⠁⠀⢀⣠⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣆⢶⣶⢹⣿⣦⡙⣷⣤⠀⠀⠀⠻⢿⣭⣿⣿⣿⡀⣴⣏⡊
⠀⠀⠀⠀⠀⠀⠀⣏⡈⣿⣿⣷⣧⣤⣿⣿⣷⡙⣿⣧⣤⣤⣤⣴⣿⣿⣿⣿⢿⡞⠻⠿⠟⠛⢶⡘⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣎⢿⡏⠉⠉⣹⣿⡟⠰⢶⣿⣽⣭⡕⣧⣽⣷⣿⣧⣼⣃⣀⣀⣤⣾⣿⡵⣩⢿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⠸⣟⣿⣿⣅⠀⣠⡄⢼⣿⣿⠿⡿⣿⣿⣿⡿⣿⣽⣋⢉⣙⡻⠟⣋⡾⠚⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣇⠙⠛⠋⣁⣼⣿⣽⣻⢿⣿⡛⠓⠛⠉⠁⠀⣠⣤⣭⡉⠁⠀⠀⠈⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣤⣼⣿⠏⠀⠙⠻⠷⣦⣍⣂⢤⣤⡴⠎⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠿⠴⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣧⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢰⡆⠐⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⡠⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠦⢇⣠⣾⣷⠀⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣰⡀⠀⠀⢀⠀⠀⠛⠀⠉⠀⠀⣿⣴⣾⣿⣿⣿⣄⣰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⢠⢻⡟⣽⣧⠀⠀⠀⠀⠀⠀⢠⣤⣶⣴⣿⣿⣿⣿⣟⠁⢆⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣏⠁⠉⢽⣆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⣀⠀⠠⠍⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠑⣿⣾⣏⡉⣿⣿⣿⣶⣦⣝⢦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⣶⣆⣠
⠀⠈⠖⠛⠒⣶⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣐⣸⠟⠓⠛⠋⠉
⠀⠀⢀⣄⣔⣸⠿⣽⣿⢿⡿⠷⠍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣏⣩⣿⣶⣶⣦⣦⡶⠶
⢀⣀⣀⣿⣿⣿⣷⣽⣿⢸⣇⣠⣴⣾⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣬⣶⣿⣿⣿⣿⣯⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣭⣿⣿⣿⡿⡿⠿⣞⣛⠟⠻⠿⢏⢛⣋⣿⣟⣿⠿⠿⣫⣭⣿
⠈⠙⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣛⣛⣃⣼⡭⢝⡛⣩⣭⠇⠯⣭⠛⠛⠓
⠀⠀⠀⠂⠚⠛⠈⠙⠛⠛⠛⠿⢿⣿⣿⣻⣋⣻⣿⣿⣿⣿⣿⣿⣯⢤⣿⣽⣿⡟⠿⠯⠭⠭⠀⡁⠤⠤⠤⠀⠀⣀⣀⣀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⢠⢀⠀⠀⡤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣤⡀⠀⢸⣦⣁⡴⠈⠁⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⣸⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡁⢸⣿⡟⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣫⡤⠀⠐⡆
⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣿⣯⡁⠙⠶⠞⠀⡾⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣔⠣⢠⡷⠀⢠⡇
⠀⠀⠄⠀⠀⠀⠐⠁⠀⠀⠀⠃⢸⣿⡆⠀⣄⠀⠀⠈⢈⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡇⡈⠙⢻⠃⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠻⢩⢥⣤⢿⠀⠀⣀⠾⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⠀⠅⡀⢾⠲⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣾⣿⣠⣁⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡟⠀⠋⣔⣾⠀⠄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣩⣼⣿⠻⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢰⠀⠠⡍⠄⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣯⣠⣤⢶⣿⣿⣿⣦⣠⣆⣼⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⡇⠸⢀⣈⢱⣌⣾⡆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡡⠟⢋⣼⣿⢪⣟⣽⡿⠀⠽⠃⣿⣿⠻⠋⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⠁⠘⠈⣁⣀⠛⢿⡏⣉⣷⠂
⠀⠀⠀⠀⠀⠀⢰⠜⠁⣸⠟⠘⢡⣏⢀⣿⠃⠈⡇⠀⡇⠻⣃⢷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣃⡘⠀⠁⠀⠈⠉⠳⣾⡀⢸⠘⣇⠂
⠀⠀⠀⠀⠀⣼⠟⠀⢰⠃⡂⢠⠏⠃⣼⣸⡀⡐⠂⢰⣅⠀⢿⠂⠆⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣸⣿⣠⣀⠀⠀⠈⠁⠸⠇⠀⠀⢘⣂⠄
⠀⠀⠀⠀⣬⠟⢀⡾⠇⠀⠐⡾⡎⢸⠃⠁⠓⠁⠀⣾⠉⠠⠸⣿⣡⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⡏⠀⠀⢹⣿⣿⣿⡄
⠀⠀⠀⣰⣯⠄⠞⠀⣸⠗⡐⠛⣼⡯⠂⠐⠁⠀⢸⠁⠀⠠⡀⠻⣿⠻⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⠀⠀⠀⠘⣿⣿⣿⠇
⠀⠀⡰⠿⠀⠀⠂⢘⠋⠐⠃⠀⣿⠃⠀⢀⡤⠀⠈⠀⠀⠀⣡⠡⠜⣷⡜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠀⠀⠀⠀⢿⣽⣿⡇
⠀⢀⢣⠀⠀⢈⠏⠊⠀⠀⢀⡼⠁⢀⣴⡟⠀⠀⠀⠀⠀⠀⠸⡇⠝⡘⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⡇
⢀⡞⠉⢀⠼⠔⠀⢠⢦⡤⠞⠀⠀⣸⢻⡧⠤⢀⡀⠀⠀⢀⡀⣐⡄⢱⢘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⡇
⠈⠠⢵⢚⣶⢖⠤⠋⠀⠀⠄⢀⣼⣝⣈⣩⡃⢐⡀⡆⣒⣠⠂⢲⣻⡆⠃⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡇⠀⠀⠀⠀⢼⣿⡟
⠠⣀⠠⡄⢀⠂⠀⠀⣀⡀⢠⣯⠏⢉⠙⠉⠋⠘⢻⠉⠋⠈⠟⠻⠟⣿⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣿⣿⣇⣤⠀⠀⠀⣩⣿⡇
⠀⠀⠈⠀⠛⠲⠶⡟⠋⠺⢮⣿⠖⣮⡶⢿⠿⠃⢫⢷⣆⣠⢆⣾⠓⢺⡷⠦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠛⡿⠃⠀⠀⠀⠻⠾⠿⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⣿⣿⣿⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣦⣿⣿⣿⣿⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠻⣿⣿⣿⣿⠿⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⣿⣿⢿⣿⣿⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣶⣬⢿⣀⡀
⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢛⣇⣉⠘⠃
⠀⠻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠉⢻⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠻⠇⠘⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠛⠉⠉⠈⠉⠉⠙⠓⠲⠤⣄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⢷⣾⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⣸⣷⡆⠀⠀⠀⠀⠀⢠⣿⠃⣌⡀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⣿⠿⠃⠀⠀⠀⠀⠀⣾⡍⣽⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⢸⡏⠙⠀⠀⠀⠀⠀⢠⣿⠋⠩⠅⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡔⣋⠄⠒⠀⠷⠲⠀⢀⠀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⣿⣁⡄⠀⠀⠀⠀⠀⠀⣿⢳⡇⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠟⡜⠁⡠⠜⠋⠃⠀⢀⣤⠶⠛⠛⠛⠛⠲⠿⣅⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣸⡟⣉⡅⠀⠀⠀⠀⠀⠀⣾⣿⢤⠂⠁⣴⠁⠀⠀⠀⠀⣠⣜⡡⣿⢉⠀⠁⠔⠀⣣⠞⢻⣷⡆⠀⠀⠀⠀⠀⠀⠈⠑⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⣿⣷⣬⣧⠀⠀⠀⠀⣠⣼⣇⠰⡆⠀⣸⣻⠀⠀⠀⣠⣾⣯⡊⠤⣼⠃⠀⣴⣣⡾⠃⠀⢘⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣆⠩⠀⠲⣀⣘⣧⣞⡁⠸⡆⠀⣸⣿⣟⣻⣯⣽⣻⣯⣀⡿⠁⠀⡀⣽⠏⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢿⣿⣿⣤⣀⣉⠈⡉⠉⢅⡀⢀⣘⡦⣤⠙⠿⢿⠟⢿⡛⠋⡽⣴⣫⡿⠃⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢉⣿⣿⠿⣷⣞⣣⣶⣾⡇⢸⣿⣿⣾⡓⡌⢳⡴⠬⣿⣿⣷⠟⠋⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢰⠁
⣠⣾⢿⣋⡁⠴⠉⢻⣿⣿⣿⡏⠻⣿⣿⣿⡿⠻⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⡞
⡿⠓⠀⠀⠀⠀⢀⣾⣿⣿⡏⠓⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⣿⣷⡀⠀⣠⢾⣿⣿⣿⡯⢀⣤⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⡾⠛⠋⢳⡄⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⠙⢳⡶⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⡟⠈⢷⡾⢿⣿⣯⣿⠟⠀⢨⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣿⡄⠀⢸⡄⠀⠀⠀⠀⢀⣀⣴⠋⠐⠈⠳⣤⡀⠀⠀⠀⣠⠟
⡇⠀⣿⣿⠷⢿⣿⣦⡤⠞⠋⢸⣿⣿⠀⠙⢿⣿⣆⠀⠀⠀⠰⡇⠀⠀⠀⢠⡿⠀⠀⠀⢻⡄⠀⠀⠀⣸⠏⢄⣠⠔⠀⠀⠀⠙⢲⣤⠞
⡃⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠉⠻⠷⢄⣀⠈⣳⠀⣀⠠⠋⠁⠀⠀⠀⠀⠙⢦⣤⣠⠟⠓⠊⠉⠀⣀⣀⣤⠶⠊⠉⠳⣤
⣇⠀⢿⡇⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⢷⡀⠀⠀⠀⠀⠀⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠛⣀⣀⠶⣦
⠹⣆⢸⡗⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡉⢓
⠀⠘⣾⠇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠱⢦⣀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡃
⢀⡼⠋⠐⠀⠀⠀⠀⠀⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂⠀⠀⠀⠄⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⠰⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣆⣏⣿⣶⡤⠀⠀⣀⣶⡀⠀⢸⢂⣸⣿⣄
⠀⠀⠀⠀⠀⣿⢠⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⡹⡏⠀⠀⠀⢨⠀⠁⣄⠸⣈⣼⣻⠉
⠀⠀⠀⢀⡤⠔⠛⠻⢲⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣄⣛⣡⠞⠂⠀⠀⢸⡏⢀⠁⠇⠆⠯⠞⠂
⠀⠀⠀⠨⠀⠀⢐⠀⠁⣛⣻⣀⡀⠀⠀⠀⠀⣠⣤⠀⠁⣰⣆⠀⣸⠀⢸⠇⢸⠀⠀⡆
⠀⠀⢠⡶⠦⢀⣨⣀⠒⠛⢥⡤⠁⠀⠀⠀⠄⣿⣟⢰⣴⠧⢶⣻⣿⠀⢸⠀⣼⢱⠀⠃⡂⠃⣼
⠀⠀⣾⣾⣟⠛⠻⢿⢻⣶⣾⣿⡅⠀⠀⠀⡀⣨⠋⢘⠉⠊⣿⣿⡇⠀⢸⠀⢡⣿⡀⠘⣷⡷⠉⠠⠄
⠀⠀⢿⣿⠃⠀⠈⡉⢲⣿⣿⣿⣿⠀⠀⢰⢹⠇⢠⣏⣐⡻⣶⣿⠇⠀⢸⡇⣾⠃⠀⠀⠤⡙⠀⠰⡃⠐
⠀⠀⠀⣿⡄⠀⢈⠁⢄⣽⣿⣿⡿⠀⠀⢸⡾⢀⡿⠻⡟⣿⢿⣿⡆⠀⢸⡗⠁⢀⠀⠀⢰⣧⠀⠀⢀
⠀⠀⠀⣧⣀⠈⠉⣐⠀⣹⣿⡿⠀⠀⠀⢸⡇⣾⠙⠶⢮⢵⢿⡿⡇⠀⠸⠁⢀⣀⠀⠘⣾⠉⠀⠀⠸⠇
⠀⠀⠀⢸⣇⠀⠉⠀⠈⣻⣿⡇⠀⠀⢠⠘⡳⠇⠁⠀⠀⡜⣾⠁⣧⠀⠀⠀⣧⣿⠉⠒⠈⡿⢣⠀⠸⡇
⠀⠀⠀⠘⠈⠄⠀⠀⠀⠿⣿⠀⢀⠀⠀⣸⠋⠀⠀⠀⠰⣴⠛⢰⣿⡀⠀⠀⡏⢹⡆⠀⠀⣷⠀⠄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⡈⠀⠈⠀⠀⠘⠀⠀⠀⠀⣠⠿⢁⡾⣿⣇⠀⠀⠠⠊⠀⠀⠀⡹⡆⠈⢧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠠⠾⠄⠘⠻⡄⠀⠀⠀⠀⠀⠀⠃⢁⠀⠘⠇⣰⡅
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢁⣠⡀⠀⠀⠀⠀⠀⣀⠆⢀⠀⠀⠀⠀⠀⠜⠀⠀⣀⠀⠀⠀⠌⢀⠀⠀⡉⢻⣿⡆
⠀⠀⠀⠀⠀⠘⠐⠓⠀⢹⠟⠋⠀⠀⠀⠀⡐⢊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢾⠛⠀⠀⠐⠀⠬⠲⠶⠕⠢⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⢂
⠀⠀⠀⠀⠀⠀⠀⢰⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠠⣄⠀⠀⠀⠀⠀⠀⢲⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠜⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢧⠀⠀⠀⢀⠐⠋⠉⠁⠐⠀⠐⢢⡀⠔⠒⡪⠄
⠀⠀⠀⢠⠒⠲⣄⠀⠀⠀⠀⣸⠁⠜⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣰⣿⡀
⠀⠀⠀⠘⠂⠀⠈⡆⠀⠀⣰⠃⣴⠂⠀⡀⣷⣀⡴⣶⢟⠟⣴⣿⣿⣿⡿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⢻⠄⠚⢀⣴⢻⠏⢿⣭⡽⣥⣦⣿⣿⣿⣿⣀⠃⠀⡃⠆⠉⠛⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⢧⡞⢉⡿⠦⣀⣾⡇⢹⣿⣿⠿⣿⣿⠟⠀⠀⢧⡌⠢⠀⡷
⠀⠀⠀⠀⠀⠀⢆⢹⠀⠀⠀⠠⠋⢰⣿⠁⢠⣿⣿⣥⠈⠻⣿⣤⣌⠙⠤⡀⠀⠘⣿⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠸⣄⢆⣀⠐⢣⣶⡟⣧⠀⣺⡇⠘⢻⡃⠆⠈⢯⠙⠷⣄⠙⠦⠄⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⣶⣿⡟⠀⠹⣄⠘⠣⠀⠈⠘⡎⠀⠸⣷⡄⠈⣣⡆⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠧⠀⠳⡀⠀⡆⠀⢰⠿⣿⡆⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠀⡆⠀⣇⠴⠃⣠⠟⠀⢸⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠢⣄⣠⣄⣠⡤⠞⣋⠤⠖⠋⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢂⣨⡿⠋⠀⢠⢪⠔⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠁⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠆⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⠀⠀⠠⠠⠀⠄⠠⠀⠠⠠⠠
⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠙⡶⠒⢦⡀⠀⠀⠀⠀⡴⠋⠲⣄⢀⢰⢖⢢⢀⣠⣤⢀⡼⠛⣳
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢧⢿⡃⠻⣄⠀⢀⣀⣁⠀⠾⣿⣼⣿⠉⡵⣻⢟⣽⡿⠃⠚⡁⠂⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣏⢻⠷⡹⣾⡏⠉⣝⡿⢿⣿⣿⣶⣾⣿⣧⣤⣷⡶⠿⠿⠶⣤⡐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢐⣾⣾⣸⡿⠿⠪⣛⠚⢿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠖⠂⠀⠀⠀⠈⠻⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⣉⣩⣀⠀⣠⡼⠿⠛⣛⣿⣿⣿⡻⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⡴⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡧⢉⣪⡿⣡⣤⣀⣿⡿⣿⣿⠿⠛⢛⠿⣿⡿⣤⣤⣀⣠⠤⠞⠁⠀⢴⣤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⡟⣠⡉⠙⠚⠂⣈⣽⡏⣎⡀⡠⡌⢌⠳⡀⠀⣂⡂⠀⠀⠀⠀⢀⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⡼⠃⠙⣷⠀⠀⣼⣛⣹⢃⢹⣷⠀⢠⠈⣣⡱⣤⣿⡇⠀⠀⠘⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⠀⢠⡿⠀⠀⠘⠺⠒⠀⠈⡿⣶⠀⠁⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣶⠶⢠⠀⠀⠾⢿⣿⠃⣰⡏⠰⡀⢀⠀⡄⠀⣀⠀⠀⣤⡿⠿⡄⠀⠀⠀⢮⠍⣷
⠀⠀⠀⢠⡿⢀⡾⠀⠀⠀⡀⣋⠐⠛⣧⣼⣂⠑⡄⢁⡀⠄⠀⠀⠈⠛⠇⠀⠀⠀⠀⢸⡒⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢶⣿⣦⡀⡠⣫⠋⣍⠹⢰⠀⠀⠀⠀⠁⠀⠀⠀⠲⠒⠀⣄⠀⠉⠀⠀⠀⠑
⠀⢈⣠⣦⢠⣥⣔⠐⠹⣷⣞⣿⡏⠀⠀⣿⠆⠰⠂⠀⠀⠀⠀⠛⠲⠶⠶⣈⠙⠛⡇⠀⠀⢰⡄
⠀⣦⣫⣶⡏⣉⣙⠂⢀⣿⣿⣿⣿⡄⠰⠧⡈⠀⠀⠀⠀⠐⠦⣮⣄⣀⡠⠈⢽⣷⡦⠀⠀⠀⣀⣠⠆
⠀⠀⠈⠁⠈⠈⠉⡾⢿⣟⠻⣿⣿⠁⠀⣿⠇⡀⠀⠀⠀⠁⠀⠏⠀⠀⠀⠀⠘⣿⣸⣄⠀⠈⠛
⠀⠀⠀⠠⠀⠀⠰⡇⠘⣿⣷⣿⠇⡀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡟⠃⠀⠀⠀⠀⢠⡄
⠀⠀⠁⠘⠀⠀⠰⠀⠀⣿⠁⠀⣼⠀⠀⣿⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢸⡇⠀⣄⠀⠀⠁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣿⠀⢰⣿⡇⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢸⣇⢀⢿⣄⢠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡉⢰⠤⣻⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠹⠀⠄⠻⡄⢸⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣅⠁⢘⠲⠟⠿⠅⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⡶⠄⢉⡀⠀⠤⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠠⣠⡿⠧⠒⠀⠀⠶⢀⡀
⠀⠀⠂⠀⠀⠠⠌⠀⠠⠒⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠋⠉