Pasture Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡋⠉⠙⠛⠋⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⣠⣄⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿⡀⠀⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⢿⣿⣿⣿⡄⢹⣿⣿⡇⠀⢾⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠙⠿⠿⠁⠀⠙⠋⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣆⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢸⢿⣿⡿⠋⠀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⠟⣠
⠀⠀⠀⠀⠀⣿⣾⡟⠀⠀⠈⠉⠉⠉⠉⠙⢳⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⢀⣀⣀⣀⣀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⣸⢻⣿⠀⣰⣿⣶⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡇⠀⢀⣿⡿⠋⢹⣿⣿⣷⣦⡈⠻⡿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⡟⣿⠀⣿⣿⣿⣿⡟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⡇⠀⠈⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⣿⠋
⠀⠀⠀⢸⡿⢁⡏⠀⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠸⠃⠀⢿⢻⣿⢿⢿⠀⠀⢿⢿⠿⡟⠛⠛⠸⠏⠇⠿⢻⢹⠹⡇⠀⠿⠇⠻⠀⠀⠛⠙⠘⠃⠏⠏⠏⠄⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠂⢘⣛⠛⠻⠿⠛⠛⠃⠀⠉⠻⠟⠃⢀⡀⢀⣲⠶⠷⠤
⠀⠀⠾⣿⣾⣾⡶⣾⣿⡇⠀⠀⠀⠀⠀⠄⣵⣐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣻⣿⠀⣀⣤⣿⣿⠇
⠀⠀⠀⠻⠾⠛⠺⠶⠤⠼⢿⣿⣶⡄⠐⠶⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⡟⠛⠛⠂⠙⢿⢻⣧⣴⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⣛⠲⠂⠀⠀⠀⠀⠀⠀⠀⠿⡻⠋⠈⣻⣿⠆⠀⢺⡆⠀⠀⠀⠀⠀⠀⠐⠂⠷⠖⠒⠀⠀⠈⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢰⡌⣏⠀⠀⢰⠇⠀⠀⢀⣤⣤⣄⡙⣦⡀⠋⠛⠄⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡦⠈⠁⠙⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡈⠁⠓⠀⠀⠀⠀⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⡀⠀⠛⠉⢱⣦⡀
⠀⠀⠐⠈⠀⠀⢀⣤⣀⢀⠀⠉⠉⠀⢀⣁⣈⣀⠒⠀⠀⠀⠀⠀⠘⣾⡏⢻⣿⡏⣀⠉⣵⡂⠠⠐⠊⠛⠀⠘⠻⣛⠟⠚⠂⠀⠉⠉⣄⣄⠀⢀⣔⠠⠆
⠀⠀⠀⠀⠀⠈⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈⠁⢁⣘⡟⠈⠓⠐⠛⠉⠀⠀⠀⠀⠀⠁⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠚⠉⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢄⡀⠀⣠⡀⠀⠀⠀⠀⠀⡠⠤⣄⡸⢠⣤⣶⣦⠀⠀⠀⠘⠲⣄⣀⣀⣀⠀⠀⠀⢀⠔⣒⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠉⠁⠀⢀⣤⣍⠐⢿⠾⠀⠀⠀⢀⡜⣠⣤⣀⣴⣾⣿⣿⣿⣿⣦⡀⠀⣰⣬⣴⣦⣭⣵⣴⠂⣩⣾⣿⠃⠀⠈⢉⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠔⢀⣀⠀⠀⣴⣦⣉⣭⣰⣾⠷⠀⠈⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡿⢿⣿⣧⣼⡤⡄
⠀⡀⢀⠤⡄⢠⢼⠲⠆⢰⣿⣶⣿⡿⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠉⣛⣿⣿
⢀⡇⣤⣀⠈⣁⠈⠳⠿⠟⠫⣿⠀⡷⢯⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧
⢺⠀⠈⣩⣾⣿⣷⣶⣶⣶⣶⣾⣾⣷⣾⠟⢿⣿⣿⣿⠛⠻⠽⠟⠛⠛⠯⠿⠉⠉⠉⠛⠀⠀⠀⠘⠋⠀⠀⠀⠀⢹⠋⢻⡏⠙⡏⠈⠉⣿⣿⡿⠃⣿⣭
⠳⢄⣶⣿⣿⣿⣇⣿⣶⣶⣶⣿⣿⣿⣿⡀⠀⡁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠘⠀⠈⡇⠀⡄⠀⢀⣿⣯⣶⣿⣿⣿
⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣭⣍⠉⠉⠉⢉⣉⠉⠉⠉⣉⠉⢉⣀⣸⠇⣈⠁⢀⣀⣤⣶⡟⠀⠙⢷⣶⣶⣶⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣤
⠀⠀⢀⠀⡄⠀⣀⣠⣴⣿⣿⣿⣿⣿⣭⣭⣭⠤⢄⣠⣠⠠⠌⠉⢉⡙⢻⣿⣿⠁⢠⠈⠿⢹⣿⣿⣿⡇⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⠈⠛⠙⠋⠘⢛⠋⠻⠛⠛⠭⠍⠉⠉⠭⠭⠭⢍⣉⣭⣏⣁⣮⣉⣉⣉⣩⣭⡅⠀⢀⡰⠀⠀⡄⠁⠀⠀⠀⠉⠀⠈⠁⠀⠀⠉⠓⠀⠘⠄⠙⣿⣿⣷⣿
⢈⣭⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣷⣿⡟⠿⢿⠟⡿⠟⢉⡉⢻⣿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣸⠀⣿⣿⣿⣿
⢸⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠺⡿⢷⣤⠄⡤⠀⠉⠑⢯⣿⡷⣻⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠟⢠⣿⡆⢸⣿⣵⣿
⢸⣶⡟⣻⣿⡇⠀⠀⠂⢀⣤⣤⣤⣤⡌⢀⡂⣠⡀⠀⠀⠐⠻⣽⣿⠆⣐⣤⣾⣾⣯⣾⣿⣿⡶⠀⣰⣶⣶⢶⣶⢶⣧⣀⣀⣦⢰⠀⠸⣸⣜⡎⢿⡿⣿
⢸⣿⣯⣿⣿⣿⢠⢷⡒⣿⣛⢿⣷⡿⡇⣸⣿⣿⡿⢷⣀⠈⠀⣿⣿⠏⠙⣿⣿⡿⠛⠋⠉⠛⠓⠒⠛⠛⠛⠋⡉⢻⡞⢁⣿⣿⢸⠇⣰⣿⣿⡇⠸⣻⣿
⠀⣩⡽⠛⣻⣿⣼⣿⣷⣿⣿⣿⣿⣿⣇⣘⣿⣿⣷⣦⣾⣷⣤⣾⣿⣶⡄⠾⣻⣧⠀⠀⣐⠀⠀⠀⠀⠀⢀⣤⡉⢨⣵⣾⣿⣧⣾⣾⣿⣿⣿⣷⣾⣿⡿
⢠⠿⣏⣱⣿⣿⣿⣿⣿⡾⣫⣟⡩⢻⣿⣟⣿⡿⣿⣿⢯⣻⣏⠛⠛⠛⡇⣿⣿⣿⠀⣴⠉⡶⣶⡶⠀⢰⣿⣿⣿⣿⡟⢻⢟⣿⢿⢿⣿⢃⣭⣿⣿⡷⠚
⠀⠀⣿⡏⣽⣿⠏⢋⣿⣷⣿⣟⣠⣎⡍⠉⠛⢷⣶⣽⣿⡿⣿⣤⣶⣄⠁⠙⣨⣿⡈⣿⣆⢱⣿⣇⢶⡤⣿⣽⡿⢿⣷⠿⣸⣧⣿⣿⣿⣷⡿⠟⠋
⠀⠀⠟⠳⡏⠉⠀⠈⢡⠿⢛⣽⣛⣁⠀⠐⠂⠀⠹⣟⢻⡿⣶⣿⣯⣛⣷⡶⢽⣿⡧⢸⣿⣤⣿⣿⣼⣧⣸⣿⡶⢿⣶⣿⡯⣷⠾⠻⠟⠁⠾⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠧⢬⣿⣿⢿⠋⠀⠈⠀⠈⠹⠿⠟⣿⣿⣽⣿⣿⡿⠃⠼⣿⣿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⣶⢿⣟⡩⢩⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⣿⠅⠀⠀⠀⠉⡾⢆⠁⡴⢤⠇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⢹⡆⢀⣀⠀⣀⣃⣰⣠⠦⠾⠤⠶⠖⠒⠉⠉⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣊⣱⣦⣼⣤⡤⠴⠿⠓⠚⠻⠉⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣀⠒
⠀⡀⣀⣤⠤⠤⠤⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⠉⠀⠀⢀⣤⠀⠀⠀⠈⠁
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠃⠀⠀⠈⠉⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⢰⡆⠀⠀⠀⣶⠀⠀⠀⠈⣏⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⣶⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⢿⣿⢹⡿⢻⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⠿⢟⣛⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣿⢸⡟⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⣿⡿⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢠⣉⠶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⢆⣿⣌⠻⡇⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣝⠛⣴⣶⣶⣶⣶⣶⣶⣶⡜⢛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢶⣶⣮⢰⡿⢛⠻⣿⣿⣿⢟⡻⣿⢨⣶⣶⡮⣹⣿⣿⣿⣿⡟⢿⣿⢹⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣶⡄⣷⣬⣥⢻⣿⢃⣭⣵⡟⣰⣦⣵⣾⣿⣿⣿⣿⣿⣿⣦⣽⣼⣯⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠹⣿⣿⠸⡿⢸⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢉⣄⣶⣶⡖⣬⢡⣿⣯⡻⣿⢸⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠸⠿⠿⠿⠿⠿⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠷⠌⠛⠛⠋⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠝⠇⠿⠱⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⢡⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿
⠀⠀⠀⣠⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⠀⠉⠿⣿⣿⣟⣋⣿⣿⣟⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠛⢻⣿⣿⣷⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢢⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢿
⠀⠀⠀⣿⡏⠀⣉⠁⣹⣿⠛⢛⠻⢿⣿⡀⠀⢀⠸⣿⡿⠉⢹⡇⠀⠉⢹⣿⡇⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠁⢤⣄⠁⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⢡⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠜⠁⠉⠈⠱⠂
⠀⠀⠀⠀⠀⡆⠀⢠⣦⣀⣤⢤⣖⡗⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡇⠀⠁⠘⣿⣾⣾⣾⡏⠀⢀⡀⠀⠀⠀⢸⡟⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠂
⠀⠀⠀⠀⠀⢸⡄⠇⠀⠈⠻⣿⣿⣤⣼⣾⣠⡖⠀⠀⠈⠃⠃⠀⠙⠒⠒⠆⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠈⠁⢰⠀⠀⠀⠀⠈⣷⠀⠸⠟⠿⢾⣀⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⡀⢁⣤⣖⡊⠀⠈⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠠⠀⠀⠀⠀⠀⡇⠈⠉⠉⡇⠁⠀⠀⢸⠉⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠈⢁⠐⠀⠀⠀⡀⠀⠠⠆⠀⠀⢿⣿⠀⢠⠏⠀⡒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠁⠁⠀⢹⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠁⠀⠁


⣿⣯⢽⡟⢿⣿⡻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⢀⠔⠒⣀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠀⢀⣄⣠⣶
⠀⠀⠀⢀⠀⡐⡿⢷⣼⠃⢀⡄⠀⢀⡏⢠⣊⡁⠀⠀⠃⠀⢠⠠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠋⢥⠀⠀⠀⠀⣀⣀⡄⢰⣷⣶⣿⣿⣿⣿
⠀⡀⠀⠈⡀⢡⣷⡞⣿⣦⡘⣧⣂⣾⣿⢻⣟⣾⡗⣶⣠⣄⣸⣁⣿⣧⣦⣴⡀⣡⠆⡴⡅⢠⣸⣆⣠⣰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣦⣾⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢏⣿⣸⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠤⠂⠄⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠐
⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⠄⠀⠀⠁⠀⠽⠀⠠⢤
⠀⠀⠀⠀⠀⡌⠘⢶⠑⡆⠐⠂⠈⠃⠀⠀⠀⠀⠀⢰⠀⢀⡆⠀⠀⢀⢀⡀⠄⠀⣲⡟⣔⣿⣤⣾⡦⡀⠄⠀⠦⠼⠟
⠀⠀⠀⠀⠀⡁⠠⠦⡀⢠⡶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠐⠠⢝⠦⠄⠠⠏⠀⠁⠀⠀⠀⢘⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⢀⣈⣉⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢸⡗⣠⡴⢰⠦⢶⠀⡆⠰⡫⠀⠀⠀⠀⢽
⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⡄⣃⢀⡲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠤⠠⠄⠀⠂⣀⣢⣘⣜⣃⡠⡠⣷⣤⢴⣷⢶⣤⣴⠤⠠⠀⠄⢒⡀⢀⡀⡤
⠀⠰⢵⣄⡺⢿⣬⠛⠞⠳⠫⠿⠑⠒⠉⠓⠛⠑⠉⡁⡉⠀⠈⠀⠀⠈⠁
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢄⠰⠾⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⡈⢠⡀⠀⠀⠐⠐⠊⠁⠉⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠠⠀⠀⠤⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠓⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠙⠂⠊⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣀⠠⣤⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠘⠃⠀⠀⠈
⣿⡿⠿⠿⠻⠿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣶⣾⠟⠉⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⡶⢶⣶⣤⣄⡀
⠀⠁⠀⠀⠠⠀⠀⠀⡀⠀⢛⣈⠀⡀⣈⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠫⢦⡀⠀⠉⠻⢿⣿⣶⣤⡀
⠠⠀⠀⠂⠀⡀⠀⠠⠀⠐⠀⠈⠁⠀⠀⠀⠀⡨⢭⡉⠉⠉⠛⠻⠿⢿⣿⢿⠋⣁⢀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠻⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠂⠙⡆⠉⠃⠀⠀⠀⠀⠀⠈⠓⠶⢧⠀⠀⠠⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⣠⠤⠀⠖⠚⠉⠉⠂⠀⠀⣐⢤⢀⣤⣤⡄⠀⠀⠀⢀⣠⣀⣀⣠⣿⣿⣿⡶⠶⣾⣦⣅⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠉⠉⢉⣤⣤⣦⡄⣑⣱⣶⣶⠈⠒⠃⠠⣾⣷⣀⣘⠛⣿⠀⠰⠶⠄⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠛⠋⠉⠁⠁⠀⠁⠁⠁⠀⠈⠈⠀⠀⠈⠘
⠀⠀⠀⠳⡌⢸⣼⣷⣿⣿⠿⠿⠿⠓⠀⠋⠈⠉
⠀⠀⠐⠰⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀⠀⡀⠀⠀⠀⢀⡀⢀⠀⢀⡀⠀⣀
⠀⠰⣦⣄⣶⣤⡦⠄⠀⠀⠠⠷⠿⠚⠛⠺⠳⠓⠖⠁⠷⠿⠄⠀⠀⠐⠄⠁⣸⠬⠥⠤⠛⠉⠉⠉⡉⠈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁

⣷⣶⣰⣶⣧⣤⣀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠈⡱⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⢄
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⠘⢳⠊⠀⢠⣖⡀⠀⠋⠧⠞⠃⠀⠀⠀⠀⠀⠎⠀⠀⠄⠀⠀⠀⢁⠀⠐⡦⠀⠀⠰⠷⣠⠄⠀⡐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⢈⡄⠀⠀⠠⡚⠳⡄⠉⠺⣾⣿⣷⢾⣷⢆⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢀⡀⠀⠄⢷⣿⣷⣤⣔⠉⠀⣀⢠⡖⠓⠑⠈⠄⠀⠀⠉⠛⠻⠿⠽⢷
⣿⣿⢿⣿⣿⣶⣾⣿⣿⣿⣿⣯⠉⠩⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣽⣿⣿⣟⣶⣿⣧⣴⡧
⢿⢿⣷⣬⣭⣭⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠀⣤⣤⡄⢤
⣶⣶⣵⠯⣿⣭⣿⣿⣿⣿⣿⣇⡀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣾⣿⣿⣥⣄⣈⣷⣤⣤⣤⣀
⣿⠏⢻⣿⣿⣿⡿⡉⠉⡻⣟⠛⠛⠃⠤⠀⠀⠀⠀⠒⠤⣄⣠⣀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠉⠉⠛⠿⠿⢤⢈⠀⠻⠟⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⢿⣿⣿⣷⣤⣤⣦⣤⣄⡀⠀⢀⡀⡛⠃⠀⠀⠀⣀⣈⡉⠉⢁⡂⠀⣤⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⣄
⣿⣿⣿⣿⣿⣿⣿⠿⠟⣻⣿⠿⠿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⠿⢯⣭⣿⣿⣿⣿⣿⣿⣾⡿⢿⢷⡿⣷⣴⣼⢿⣦⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣴⣶⣾⣿⣿⣿⣻⣿⣿⣷⣆⣉⣭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣶⣿⣿⣿⣿⣟⠿⣿⡿⣿
⣥⣽⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣿⣿⣿⣿⣴⣿⣅⣿
⠹⠟⠛⠟⠿⢿⣭⣿⣽⣤⣤⣤⣠⣤⣬⡽⠋⠉⠁⢸⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠟⠻⠿⣿⣿⣛⠛⢛⣳⣖⣖⠶⠶⠶⠶⠶⠶⠴⠯⠭⠙⠻⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣇⡁⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢷⡾⢶⣶⠶⠤⣀⡢⠤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠃⢀⠀⠈⠛⢻⣈⣁⣀⡈⠙⠛⠛⠛⠛⠿⠿⠷⣶⣶⣿
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠀⠒⠦⢄⣠⣦⠈⠀⠀⠀⠀⣶⡦⢄⣀⠀⣀⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠄⡀⢈⡉⠓⠀⠀⠀⠀⠀⠐⠻⢷⣇⡱⣀⡀⠐⠀⠁⣾⣾⡛⠛⠻⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡼⠛⢿⢿⡇⢀
⠀⠀⠀⠀⠀⠀⢠⣤⠀⢠⡘⠿⠷⠀⠀⣾⣿⣿
⠀⠀⠀⢀⣤⣌⠲⠟⠒⠚⠧⣶⠷⠾⣿⣿⣿⣅
⠀⠀⠀⢼⡿⢋⡉⠧⠀⠀⠀⠈⠳⣾⣿⡿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣶⣦⡤⣄
⠀⠀⠀⠘⠃⠈⢁⠀⢰⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⣀⠀⣤⠔⠶⣻⠀⠀⢀⠔⠉⣹⣀⠐⠀⠠⠊⠁⠰⠤⠤⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠠⠩⢘⠏⠁⢀⠏⠃⠀⢹⣦⣴⣿⠃⠀⠐⢠⣴⠃⠀⠀⠀⠀⠀⠉⢫⠙⡀⠀⠈⠻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⢰⡿⠿⠃⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⡇⢃⢀⡀⠢⠹⣿⣿⣿⣿⣝⡂
⠀⠀⠀⠀⠂⠄⡀⠋⠀⠀⠀⢸⣧⡀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⢡⡀⡇⠙⠌⠻⢿⣿⣿⡧
⠀⠀⠀⠔⢢⠀⠉⠂⠀⠀⠀⠀⠙⣿⠿⠿⠛⠋⠁⠀⢢⠀⠀⠀⠀⠀⠀⠀⡠⠒⢢⠀⠐⡀⠀⠰⣿⣦
⠀⠀⠀⡀⣰⣧⡀⠀⠀⠀⠀⡆⠀⣿⡆⠀⠀⠀⠀⠀⠀⣁⣀⠀⠀⢀⡠⠞⠁⠀⠀⢆⠀⠬⠛⣿⣿⠛⠁
⠀⠐⣀⣿⠿⠁⠙⢦⣀⣀⢴⣁⡀⠘⣿⣄⢀⣀⡠⠔⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠐⠒⠀⠈⠁
⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣶⣶⣶⣶⠶⠶⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀⡹⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⣾⣿⣿⣿⣿⣿⠃⢠⡄⢤⣀⣦⡀⠀⠙⣿⣶⢄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣂⣿⣷⣀⣙⣿⣿⣦⣤⣿⣿⡆⢻⣄⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣸⣿⣿⣿⡿⠿⠿⠿⠚⠛⠉⣉⣩⣿⣿⣿⣿⡟⠋⠉⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠘⣿⣌⠛⠛⠛⠛⠓⢀⣠⣤⣶⣿⣿⣿⣿⡿⠋⣿⣧⠀⢀⣴⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢸⣿⣿⣷⣶⣿⣿⣿⠿⣻⣿⣿⣿⣿⠟⠁⠀⣿⢸⡀⡛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣾⣿⣿⣿⣿⣿⠟⢡⣾⣿⣿⣿⣿⠋⠀⠀⠀⣿⠀⣯⣻⡿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⣛⣛⣽⠟⠁⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⠀⢸⣿⡇⢸⡟⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠰⣦⣤⣬⣿⠟⠋⢀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡆⠀⣿⠀⠀⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣴⣶⣿⣿⣿⣿⡟⠉⠀⠸⣿⡇⠀⠀⠀⠀⢸⣿⣦⣸⣇⣀⣠⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣄⠀⠀⠀⠈⣿⣿⡟⢻⡁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠻⣦⡀⠀⠸⣿⣿⣦⡀⠀⠀⣿⣿⡇⠀⠃⠀⡀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠈⠻⣦⣀⠻⣿⣿⣿⣷⣦⣸⣿⣷⡇⣀⣸⣷⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⢸⡀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⠋⠉⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢻⣿⡇⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠈⣿⣷⣄⠀⠀⠀⣿⣆⠀⠀⠘⣿⣿⣿⡃⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠸⣿⣿⣷⣤⣤⣿⣿⣷⡀⠀⢿⣿⣿⣿⡀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⠻⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⣉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⣿⣿⣿⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⣤⡄⢠⣀⣴⣿⠟⢉⣴⣿⣿⣿⣻⣷⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣁⣉⠉⣉⣠⣾⡿⠿⣄⣠⣿⣿⣿⠋⠙⢻⣿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡶⠻⣿⣿⣿⣿⣶⣶⣶⢿⣿⣏⣀⠈⠻⣿⠏⢿⣿⠋⣠⡄⢀⣿⣿⡿⠿⠞⠛⠉⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⣼⣿⡇⢶⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣷⣦⡑⢼⣿⣿⣿⣀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢠⣿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⠘⠉⠉⠁⢳⣈⣿⣆⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⢘⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣸⣿⣿⣿⡿⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⣸⣿⣿⣿⠿⣿⣾⣿⣿⠏⠉⠛⠿⢿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣅⠻⠁
⠀⠀⠀⠀⠀⣠⣾⣿⠟⢁⣼⣿⣿⠟⠁⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢻⣯⣿⠏⠙⣿⣧⡄
⠀⠀⠀⠀⠀⠉⠉⠀⣸⣿⡟⠋⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⣠⣤⣤⣤⣠⣬⣻⣲⣶⣤⣤⣤⣤⣄⡀⣀⢠⣤⣤⣤⣹⣷⣤⣤⣤⣶⣌⣿⡄⡀⣀⣀⡀⣄⡀⣴⣿⣧⣠⣶⣶⣶⣦⣦⣦⣦⣠⣤⡀⡀
⠀⠀⠈⠉⠀⠉⠉⠁⠀⠀⠈⠈⠁⠀⠁⠁⠈⠉⠉⠉⠛⠙⠋⠙⠛⠛⠋⠉⠉⠋⠀⠙⠛⠛⠛⠛⠋⠀⠈⠉⠁⠉⠉⠉⠁⠈⠉⠁⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠛⢻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢹⡿⠃⣿⡟⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⢰⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣭⣥⣤⣤⣤⣄⣀⣄⣠⣼⣇⣤⣿⣣⣄⣀⣠⣀⣀⣀⣀⣠⣾⣿⣠⣴⣿⣤⣀⣠⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣅⠀⠀⠀⠀⠀⠀⠐⠫⠟⠉⠙⣟⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠈⠁⢠⡃⠀⠀⠳⣍⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠘⢸⡆⠀⢶⣿⠀⠉⠓⠺⢷⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢶⣤⣶⣺⣷⣤⠘⣆⣄⠀⠄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⣤⣾⡉⠙⢋⡙⠻⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣿⣦⣀⠉⠻⢿⣿⡆⣀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣶⣾⣿⣿⡏⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣧⠠⠒⠂⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣤⡶⠂⠀⠙⣀⠀⢘⣁⠂⠈⠛⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣿⣿⣿⣆⠀⠸⠁⠀⢀⠀⠂⢹⡇
⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠈⠛⠃⠈⢋⣤⡀⢸⣶⣶⣀⣤⡼⣿⣿⡿⣿⠿⠟⠙⠿⠋⠀⠀⠐⠚⠛⠛⠳⢾⡇
⠀⠀⠀⢘⣿⡗⠀⠀⠀⠀⠀⠐⠂⢠⠄⠈⠀⠘⣿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠞⢷⡀
⠀⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠛⣤⡀⠀⢀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣍⡙⠳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠙⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠟⢿⣿⣷⣦⣤⡴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣀⠀⠈⠓⠀⣉⠻⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⣤⢀⣤⣶⣶⣶⣿⣣⣾⣿⡧⠀⠀⢸⠃⠀⢹⣆
⠀⠀⠀⠀⠀⠀⣴⣘⠷⢎⠸⠋⠀⠀⠺⢯⣿⡿⣿⣿⣿⣿⠀⡄⠘⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠉⣼⣿⡇⠀⠀⠀⠀⠀⠈⠙⢮⡝⢿⣿⣾⡇⠀⠀⡐⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠢⠙⠿⢁⣤⡴⠃⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣀⣀⠜⢸⡇⠀⠀⠀⠀⠀⠀⢰⡷⠛⠉⠀⠀⢀⣴⡇⢘⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠁⣩⠟⠁⣀⣨⣧⠤⠔⠒⠉⢀⡔⠁⠀⠀⣠⠤⠞⠀⠠⣴⠺⠿⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠈⠉⠁⠀⣿⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⢰⠟⠂⠀⠻⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠘⣧⣹⣿⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠉⢻⠀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠶⠿⠶⠆⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢀⣾⣿⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡠⠚⠛⠛⠒⠒⠒⠂⠀⢻⡀⠀⠀⠀⢀⣠⣴⠞⠋⠀⢠⠂⠀⢸⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣴⠾⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢰⠋⠉⡄⠀⠀⢰⠏⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⢰⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⡀⠀⠹⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⣧⠀⠀⠹⣆⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠿⠟⠀⠀⠀⢹⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣦⡀⣀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣷⡀⢀⣾⣟⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⣤⣾⡟⠁⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⢤⣄⣠⣀⣀⡀⠀⢀⣠⣤⣶⣦⢀⣤⣶⡿⠟⢱⠟⣉⣅⠀⠀⢀⣼⡿⠛⠋⠀⣐⠕⠖⠚⠗⠾⢿⣿⣿⣿⡿⠿⠿⠿⠻⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠂⠰⠞⠛⠛⠛⠛⠛⠋⠈⠙⠚⠋⠐⠓⠲⠶⡾⠋⠈⠃⠴⠿⠛⠁⠀⠀⠐⠹⠑⠾⠀⣠⣆⡄⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢂⡄⠀⢀⠀⢀⡀⠒⠀⠛⠒⠀⠀⠀⢒⣀⣀⡀⠀⠀⠀⠀⠖⠂⠉⠁⣠⣩⠰⡆⣶⠶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠉⠀⡒⢀⠐⠀⠀⠸⢛⠛⠋⠋⠁⠁⠀⠀⠴⠒⠋⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡃⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠍⠹⠧⠥⠬⠄⣀⡀⢀⣀⢀⣶⣀⣤⢤⡶⣿⢸⣗⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠋⠁⢨⡇⣿⡨⡛⣼⡦⢿⡆⠀⠀⠀⠀⠀⠀⢀⣄⣂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢹⣿⣿⣿⠽⠉⢿⣷⣿⣇⠖⣿⣇⠸⠷⠀⢀⡀⣀⣤⣤⣴⣿⡧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠤⠄⢀⣀⡀⢀⠀⣀⣴⣴⣻⣯⣭⣶⣶⣿⣿⣿⣿⣟⣹⢟⢰⣴⣾⣿⣿⣿⣿⠿⢿⢺⠓⠚⠿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠙⣿⠉⣹⠉⠀⣽⠀⣀⡠⠔⠊⣁⡀⠀⠀⡀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⣿⡄⠀⣿⣙⠀⣠⣾⣷⣄⢉⠳⠦⣄⣁⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⡇⠀⣿⠟⠈⠈⠙⠋⠛⠻⢷⡶⠀⠉⠛⣶⡀⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣟⠀⣿⡟⠀⠀⠀⠀⠀⠀⡦⢹⡆⠖⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⣤⠤⢤⠤⠿⠤⠌⠁⢀⣿⣿⠄⠠⠤⠄⠀⠴⠁⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠂⠀⠐⠀⣈⠁⠀⣿⣿⡗⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣤⣤⣤⠬⢻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣽⣤⠎⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣵⣿⠀⠀⠀⢀⣰⣞⠉⠉⣀⣿⡑⠀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠴⠞⢩⣤⠽⠛⠋⠁⠈⣳⡞⠁⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⠻⡟⠉⣿⣿⡧⠞⣠⠶⠊⠁⠀⠀⠀⠀⢸⠛⣷⡐⠶⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⣉⠢⣜⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⢳⡱⡄⢀⣀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠼⣿⣿⣿⣿⣿⣿⡋⠙⠻⠾⠿⠦⠤⠤⠤⠤⠤⢤⣤⣞⣉⣧⣀⣝⡿⢭⣁⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠒⣶⡟⠻⠿⢶⣿⣿⣿⢳⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠛⢼⣏⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⣿⣿⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⡽⠉⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣰⠁⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣾⣯⣋⣞⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⢀⡀⠀⠀⢀⣠⡾⠁⠀⣿⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⠿⠛⠷⠟⠀⠀⠀⠹⣇⠀⠀⣤⠀⠀⠀⠀⠠⣤⣀⢿⡃
⣘⣏⠛⠋⠈⠁⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⣿⡀⠀⠀⠀⠀⠀⠙⢷⣽⣦
⠘⠧⣄⣠⠀⣠⣶⠊⠈⠀⢹⡄⠀⠀⠀⠀⣼⠛⠻⣿⡉⠛⢿⣿⠒⠶⠤⠤⠤⠶⠒⠛⠋⠉⠛⠓⠒⠓⢦⣄⣀⡀⠈⠉⠓⢦
⠀⠀⠙⠛⠛⠁⠁⠀⠀⠀⠀⣷⠀⠀⢀⡾⠁⠀⠀⠀⠻⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠉⣹⢶⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡟⠀⠀⠀⠀⠀⠀⣷⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣩⡏⠀⠙⢁⡼⠻⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠎⠀⠀⢹⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡙⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣉⣙⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⢹⣆
⡶⠒⠲⡶⠶⡶⡶⡶⢶⡶⣶⡶⡶⣿⢿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⣿⣿⣿⡇⠀⠀⠀⢾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠸⡀⠀⠀⢀⣤⣤⣀⡀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⢫⡭⠉⣙⡿⠁⠀⣬⡉⠉⣷⣒⣷⡄⢀⣀⠍⢿⣿⠃⠀⢰⡀⠀⡀⢤⣤⣤⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠸⢳⠀⣀⠀⠙⠁⠀⢠⡏⢀⡀⠤⢄⣼⢇⣮⡔⠘⠒⠛⠋⠈⠙⢧⢀⠳⠊⠳⣝⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠁⢸⢰⠏⠀⠀⠉⠈⡏⠃⠁⠀⠀⠸⠏⠘⡄⠀⠀⠀⠀⠀⠀⠀⠘⡞⠀⠀⠀⠈⠁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢇⠂⠀⣐⡏⢀⣄⡀⡀⢤⢀⡀⡀⣆⡠⢁⣠⢆⡴⠀⠀⢀⠀⣀⠄
⠀⠀⠀⠀⠀⠴⠴⠦⠲⢶⣧⢀⡠⣠⢬⣴⣾⣤⠤⢟⠉⠉⠉⠉⢈⡉⠹⣿⣭⣻⣵⠟⣸⣿⣖⡚⠂⠈⢃⣠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠤⠶⠶⠶⠆⠀⠀⠀⠀⠰⠦⠄

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⣿⣿⣛⡛⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⣻⣧⣶⣍⣽⣿⡟⢿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⢯⣿⣵⣺⣿⣿⣿⣿⣿⣧⡼⢷⣟⡻⡾⣷⡿⣿⣿⡹⢏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣾⢾⣿⣿⢿⣷⣿⣛⣿⣿⣿⣿⣿⣿⣧⣾⣝⣷⡷⣾⣿⣿⣿⣿⣿⠋⣿⣟⢻⣿
⠀⠀⠀⠀⣿⣿⣳⣿⡿⣷⡿⠯⣽⣿⣿⠿⡫⠲⣾⣯⣭⣽⣗⡾⡻⠿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠻⠻⠿⢳⣷⣿⣿⣿⣿⡵⢶⠊⢀⠀⠙⢿⢿⣿⣿⠟⠁⠀⠉⡟⠿⠿⠿⠟⢿⣯⡿⣿
⠀⠀⠀⠀⠅⠀⠀⠄⢹⠇⡀⠀⠈⠁⢺⢸⠭⡀⠀⠈⣎⣙⠄⡜⣭⣥⠀⠁⣿⣿⠀⠀⢸⠤⠽⠿
⠀⠀⠀⠀⠄⠀⡀⣀⣸⣀⣀⣀⣀⣀⣉⣘⣚⠃⠤⠬⠤⠤⠤⠧⠧⠴⠤⠴⠠⠀⠄⠀⠚⠒⠂
⠀⠀⠀⠀⣦⣤⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⣤⣁⣀⣀⣒⣂⣀⡀⡄⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⢀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠑⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈
⠀⠀⠀⠀⠀⠀⡤⠚⡩⠛⠉⠉⠙⢢⠀⠀⠀⠀⢸⠀⠀⠀⢼⡃⠀⠈⠑⢄⠀⠀⠀⠀⠀⠈⢧⠒
⠀⠀⠀⠀⠀⣸⠀⡘⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢸⡄⣋⠂⠛⠀⠄⢢⠠⠀⢧⠀⠀⠀⠀⠀⠈⢯
⠀⠀⠀⠀⠀⡗⠀⡷⠶⠆⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⣄⡸⠀⢘⢀⡓⠀⠁⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣤⣗⣾⡥⠜⢴⡂⣤⠄⠃⠱⡒⠚⠛⠋⠡⣍⡝⡏⢨⠉⠢⠈⠀⢸
⠀⠀⠀⠀⠃⠬⠉⠭⠂⠀⠁⠀⠀⠀⠀⠑⠠⠀⠀⠀⠈⠓⢙⡲⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠈⠉⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠒⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄
⠀⠀⠀⠀⢸⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠸⡇⠀⣼⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣄⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠐⠈⡆
⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣶⡤⢦⣆⣇⣸⣟⠀⠀⠀⠠⣼⣿⡇⠀⠀⠀⠘⡆⣷
⠀⠀⠀⠀⠀⣷⠻⣿⣾⡟⠀⣿⣿⣿⣩⣿⣯⠀⡾⣿⣷⣾⣿⣷⠀⠠⠀⠸⢁⣿
⠀⠀⠀⠀⠀⢹⡆⣸⣿⡇⢀⣾⣿⣿⠟⠀⠙⠃⠀⣾⣿⣿⣿⣿⣇⠘⠃⠀⢠⢹
⠀⠀⠀⠀⠀⠸⣇⣿⣿⢠⣿⣿⡟⠁⠀⠀⠀⠀⡄⣿⡟⠉⠉⢻⣿⡀⠀⠀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⢿⡈⣿⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⢾⡟⢻⣇⣀⡄
⠀⠀⠀⠀⠀⠀⢺⠻⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢈⡹⠀⠀⠀⢸⣿⡇⠂⢸⣧⣬⣿⡏
⠀⠀⠀⠀⠀⠀⠘⢷⢡⠀⢸⣧⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⠀⠴⣼⠇⠀⠀⣸⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠸⢰⡀⠈⣿⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⣿⠀⠀⢰⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣼⡿⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⡟⠂⠄⢸⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣿⣿⣄⣀⣴⢢⣿⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⢰⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠉⠙⠛⠋⢻⣟⣦⣀⣤⣤⣤⣀⣹⣷⣲⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠈⠘⠿⠛⠛⠛⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣄⣧⣀⣼⡿⠈⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣏⡿⣧⠀⠇⢰⢸⡇⠀⠁⠀⡄⠀⠀⠊⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⣿⣿⣿⡿⣿⡳⡄⢀⠸⣾⡿⠢⠆⠰⡗⠀⠀⠀⠤⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠚⠋⢹⣿⣿⣿⠝⣧⣼⣾⣿⣧⡀⠃⠀⡇⣤⠙⠖⣿⣾⢀⣯⢡
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⢻⣬⣿⣿⢿⣦⣭⣿⣿⡿⢿⣿⢀⢀⡷⢻⣎⣖⣉⣀⣀⣇⣠⣀
⠀⠀⠀⠀⠀⠀⢘⠄⠀⠀⠀⣀⠀⠸⠛⠛⢑⣿⣿⣿⣿⣿⣷⠿⢿⣿⡟⠟⢻⡏⠈⣼⡇⠉⣹⣻⠏⠁⢹⡿⠧⠤⠴⠖
⠀⠀⠰⡄⢀⠄⡌⠂⠀⠀⢈⡷⠀⠀⢰⡶⣁⣾⡛⠟⠃⠻⠼⠁⠘⠋⠃⠱⣆⠁⠀⠻⠀⠈⢹⣟⢤⣾⠐⡧⠤⠄⠶⣶
⠀⠀⢀⣷⡎⣴⣇⠀⣄⢠⡟⣠⣤⢔⡿⠃⠛⣛⣧⡴⠃⠄⢦⠀⢦⡄⠀⠀⠉⠀⠐⠘⠀⠂⠐⠀⠀⠃⠀⡷⠴⠃⠐⠂
⣇⠀⢈⣿⠳⣾⣯⣾⡏⣸⡶⠟⠋⣹⡵⠖⠛⣩⠏⠀⣀⠀⢀⠀⠀⠀⠤⠀⠠⠀⢀⣠⠀⡤⢶⠖⢸⠇⠘⡗⠂⠀⠐⢶⣶⠦⢤⡄
⡟⠀⣼⠸⣷⣿⣿⣵⡿⣿⠗⢋⣸⣇⣤⡾⠿⢓⣦⡂⠁⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⣀⠀⠇⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠁
⠺⢀⡷⣠⣿⣾⢣⠟⣤⣾⢒⣿⠿⢋⠝⠀⣀⣾⣏⠉⢀⣈⣠⣶⡿⠤⠍⠒⠒⢀⠀⣿⡿⠀⠼⠀⠀⢀⣰⡇⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢺⣷⣿⣿⣵⣾⠟⣱⣯⣿⣷⠢⣈⣠⣾⣿⣻⣿⡟⢻⣭⣯⣉⣙⣛⣏⡛⠉⣵⣷⡿⠁⠀⠀⠀⠀⠘⠀⠀⠀⢀⠾⡟⢷⣄⢀⣤⣾⣿⣦⣄⡈
⠀⢸⡿⡳⣿⣿⠕⣫⣾⣿⣿⣿⣿⣿⣻⣟⣧⣽⣦⣔⣦⣭⣽⣿⣿⣽⠿⣶⣾⣿⣿⣧⣀⣀⣀⣤⣠⣤⣤⣄⣠⢋⡀⡃⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⢠⣿⢀⣷⡿⣫⣾⢿⣻⡟⢨⠿⠛⢾⣅⣹⣿⣯⣿⠿⢶⣟⡛⠖⠙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣒⡀⡠⠆⣿⢿⡿⡿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢉⣿⣾⠑⣿⣏⠻⠞⣿⣿⠛⠒⠓⢸⡍⡉⣉⣻⣟⣛⢷⣁⢈⣳⣦⣬⣭⣿⣿⣻⣿⣿⣿⣿⣿⣿⣛⣿⣻⣳⣿⣾⡓⣗⣿⣾⣾⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⣿⣿⠿⠿⠾⠶⠾⠶⣶⣶⣾⣷⣾⡦⠤⡿⢷⡤⠼⢶⣶⣦⣤⣯⣿⢷⡿⠧⠧⠿⠿⠿⠿⢿⣿⣿⠽⠿⢿⣭⣿⣿⣻⣙⣛⢹⣟⣓⠻⠺⠺⠗⠿⠫
⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⠀⠁⠂⠀⠜⠃⠒⠖⢙⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠉⠛⠛⠛⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠁⠀⠀⢠⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣀
⠀⠀⠀⡀⠀⠴⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣧⢄⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣳⣛⣝⣱⣫⣬⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣾⣷⣾⣿⣿⣿⣷⣤⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣀⣤⣶⣿⣟⣁⣀⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣽⣿⠟⠀⣀⣾⣿⣿⣟⣉⣈⣉⣉⣁⣀⣀⣐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⣾⣿⣿⣶⡿⠛⢁⣤⣾⣿⣿⣿⣁⣠⢀⣠⣤⣤⣄⣀⣤⣤⡤⠤⢬⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡗⠀⠀⠀⣠⣶⣿⣿⣯⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠈⠉⢹⣿⣿⣿⡿⣻⣿⠉⠉⠉⠉⠉⠉⢹⡏⣿⠋⠙⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣬⣀⠀⠀⢸⢿⣿⣿⣷⣺⣿⠀⠀⠀⠀⠀⠀⠸⠀⠃⣀⣠⢤⣤⣤⣿⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣰⠏⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡄⠾⣼⣿⠻⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠲⣼⠇⠀⠉⢠⣶⣆⡻⣇
⠀⠀⠀⠀⠀⢰⠻⡀⠸⠿⣟⡙⣿⡟⠉⠛⠿⠋⣴⣿⣿⡀⠀⠉⠙⠲⡽⣿⡀⠀⠀⠀⠀⠀⠤⢤⣟⣿⠗⠈⠀⠀⠀⠀⠀⠛⠃⣿
⠀⠀⠀⠀⠀⡟⠀⣇⠀⣿⣿⣿⣥⣿⠀⠀⠀⠀⢈⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⡡⠁⠀⠀⠀⠀⠀⠀⠀⢰⡘
⠀⠀⠀⠀⢸⠃⠀⢻⠀⢻⡿⡟⠻⢿⣦⢀⠀⠀⠈⢆⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡚⣉⣏⡔⠁⠀⡠⠇⡐⠉⠩⡲⠂⠞⠇
⠀⠀⠀⠀⣸⡄⠀⠘⡆⠰⡞⣏⠉⠙⣟⢺⣄⠀⠀⠈⠳⡜⣍⠉⠓⢶⠄⢀⣤⢶⠀⠀⠈⢣⠀⠌⣹⣽⠃⠀⢃⡇⢀⠂⠀⡠
⠀⠀⠀⠀⠟⠃⠀⠀⢻⠰⠉⠀⠀⠀⢸⢸⠀⠉⢲⡰⡶⠋⡉⠉⣨⠆⠀⠀⠰⣶⡶⣦⣤⡹⣃⡌⣼⣧⠀⣴⣮⣥⠆⢻⡆⠺⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢠⣸⣏⢆⣠⠀⠀⢸⣏⣀⠀⠈⣯⣟⠦⡀⠀⢱⠀⠀⢀⣀⠀⠀⠀⠈⠃⠈⠁⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠉⠉⠚⠋⠀⠙⣷⡾⠿⠋⠐⢿⠾⠆⣡⡄⢨⡴⠷⠿⠻⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣙⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡭⠄⣀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠳⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠗⢆⠘⠆⢣⣀⠤⣄⣀⠀⠀⠀⡆⡌⠑⠦⠀⠀⡠⠀⠀⠃⠠⡄
⠀⠀⠀⠀⠀⠀⣰⠋⠉⠑⣰⡌⠆⠀⠈⠉⠓⠦⢅⠁⠀⠠⠒⠪⠴⠒⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡇⢀⡔⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣉⠀⣤⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⢃⡞⠈⠁⢸⠇⢀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⢄⠘⣆⠀⠘⠆⠀⡀⡀⠠⣄⠀⠀⠀⠀⠀⠀⠀⡠⢞⡭⢭⣉⡓⠲⢖⡂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⣸⣧⠔⠋⡁⠀⠀⠀⠀⠀⠀⠘⠦⠘⢦⠀⠀⠐⠁⠸⡔⢬⣀⠑⠒⠒⠶⢴⣋⠐⠁⠐⠒⠦⢭⣉⣩⠴⠂
⠀⠀⠀⠀⠀⡞⠀⠉⢉⠀⠀⠚⠉⠈⢧⠀⠙⠄⠀⢀⣠⠴⠂⠀⠀⠀⠈⠳⣄⠈⢦⡀⢻⡀⠈⣳⠀⠠⡀⠀⠈⠳⣄
⠀⠀⠀⠀⢸⡇⠺⢀⡝⠊⠀⠀⠀⠀⢸⡆⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠱⠀⢏⠉⠁⠀⠀⢹⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠘⠃⠀⠀⠀⠀⠀⠈⠋⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠀⣀⠘⢦⡀⠀⠀⠀⠇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠁⠤⠤⠤⠄⠀⠀⠀⠀⠀⣸⢠⠇⠀⢹⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠀⠐⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡾⠀⠀⠀⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢠⣀⠀⢳⠀⡇⠀⠈⠉⠁⠀⠀⢀⠞⠀⡇⠀⢀⣀⡤⠴⠚⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⡁⠸⠀⠇⠑⠲⠤⠤⢀⡴⠟⠒⠀⠀⠉⠉⢠⣀⣀⣀⣀⣀⡤⠤⠌⠓⠒⠀⠀⢠⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡄⢰⠆⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠈⠀⢈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡄⠀⠀⣧⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣈⠀⠠⢿⣀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣉⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⡀⠀⠘⣿⣀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣛⣫⣥⣤⣶⡾⣡⣤⠤⠀⠁⠈⠀⢀⠀⠀⠀⠀⢀⡿⢹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣤⠀⠘⠡⠭⠭⠵⠶⠶⠦⢤⣴⣟⣿⣶⣤⡀⢀⡴⠋⠀⠀⢀⣀⠉⡰⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠶⠄⣸⠷⠂⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠙⠻⠷⢏⠀⠀⠀⠀⠀⢠⠞⠀⠀⡴⠁⣲⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣿⠟⠛⠉⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⢶⠻⠿⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⣿⣿⠁⠳⡀
⠀⠀⠀⢀⣿⡇⠀⠀⠀⣠⡆⠐⢲⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⠣⣴⣶⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⡟
⠀⠀⠀⡞⢿⣦⣤⣴⡾⠛⣠⡴⠋⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢦⣈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⣻⠀⠀⠈⠙⣧
⠀⠀⣼⣇⣀⣼⢛⡥⠖⠋⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠬⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠘
⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⣠⠄⠀⠀⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠘⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣂⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠛⠋⠁⣀⣤⠶⠛⠉⠀⠉⠀⠀⠀⠀⠀⢀⣀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⣾⣿⣿⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⢀⣀⠤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢹⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣾⡇⠀⢐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⢩⡟⠚⠋⠙⠻⣤⠴⠾⢉⡁⠠⠛⠂⠚⠷⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⡁⠙⠗⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⣠⡌⢳⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢃⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⠛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣇⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢈⡃⠶⠂⣤⡄⠰⠀⠀⠀⠀⠀⠀⣚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢙⡋⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠛⢡⡦⢠⣀⣤⡆⠘⠋⢠⠆⡀⢠⠟⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣲⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠄⣠⠀⠀⠀⠀⠈⢹⡏⡇⠀⡀⢸⢀⠃⢸⠀⠛⡃⠀⡀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠸⠃⢴⠆⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣉⠛⠂⠉⠛⠺⠴⠷⡆⠈⡇⢁⠀⡇⣸⡞⠀⢸⠀⢰⠃⠀⠷⠦⠶⠞⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣁⡁⠀⠀⠀⠸⡆⢀⡀⢱⡀⢷⢸⠀⡇⢻⠁⠀⢸⢀⠇⠀⠀⠀⡖⠀⡼⠁⠀⠀⢠⣤⠢⡶⠈⠉⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⠁⠀⠀⢠⡄⢳⠈⢧⠀⢧⣀⠈⣆⡇⠘⡄⠀⣾⡞⠀⠀⠀⣸⢀⠞⠁⣴⡷⠞⡻⠃⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣆⠹⣌⢧⠀⠳⣌⣿⠀⠸⡇⠀⢳⢠⠏⠀⠀⠀⢰⢧⠋⠀⡼⢹⣤⠎⠁⣼⠃⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡀⠈⠳⣌⠉⡄⠀⠈⠏⠀⠀⢻⡀⠈⡟⠀⠀⠀⠀⡿⠀⢀⣾⠤⣿⡘⠀⢰⠇⣠⠞⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣠⣄⣀⡶⡆⠀⠀⠈⠉⠙⠓⠛⠳⢿⡄⠀⢹⠀⠀⠀⢧⣸⠁⠀⠀⠀⢸⡇⢠⠎⠀⠀⣧⠃⢠⣏⠜⠁⡀⠶⢢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣛⠛⣮⣿⣿⡿⠹⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⡇⠀⠀⠈⠿⠄⠀⠀⠀⠿⡷⠋⠀⠀⠀⢳⠀⡼⢩⣀⣛⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⢻⠋⠆⠀⣙⢾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣾⣷⣆⠈⣻⠃⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣀⣴⠋⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠞⠉⠻⣄⠀⠀⢾⣿⠿⢋⣩⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠁⠀⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣴⣾⣿⣀⣤⣄⡀⠀⠀⢀⣴⣶⣦⣀⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⢻⣿⣿⣿⢷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⣴⣿⣦⣾⡿⠃⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⠇⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡠⣄⣠⡀⢤⣠⠀⡿⣆⣠⣿⣿⣷⣾⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⢿⡀⠀⠘⠛⣿⠀⠀⣿⣇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣠⣿⠸⡟⠓⠈⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠸⠿⠟⠋⠁⠀⠀⠀⠙⣦⡀⠀⢿⢸⠆⣿⣿⣄⢾⣇
⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⠖⣶⣾⠍⠉⣿⣿⣿⣿⠛⣿⡿⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⢿⡁⠈⠻⣄⠸⡟⠀⠘⠻⣿⣧⠉⠛⢦⡀
⠀⠀⠀⡄⣼⢀⣤⠀⠀⠈⠉⠙⠛⣆⡀⠈⢻⣿⣧⡞⠁⠀⠀⠀⠳⣾⠂⢰⢃⡠⠖⠛⠉⠉⠉⠉⠁⠀⠀⠀⡸⢹⠗⠒⠻⡄⢹⡆⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⢹⣿⢻⠷⡆⠀⠀⠀⠀⠀⠈⠹⡆⠀⠸⣿⠀⠀⠀⠀⠀⠀⣼⢠⡟⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡟⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠻⣄⣠⠇⣠⠄⠀⠀⠀⠀⡗⡼⠃⢻⣏⠀⢀⣴⠆⠀⡀⣤⣄⡆⣼⡟⣠⣶⠆⢠⣧⠇⣀⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠛⣠⡄⠀⢲⡀⣤⠾⠏⡆⠄⠀⢦⠰⢿⣇⡤⠘⠹⠠⠏⠟⠻⠀⠃⠉⠀⠀⠉⠀⠉⠛⠀⠋⠙⠴⠟⠀⠶⣞⣁⠀⠠⣎⠁
⠀⠀⠀⠀⠀⠈⠛⠳⣤⣼⡄⢰⢻⡞⣿⢀⠀⠁⠀⠀⠀⠀⠀⠉⠀⣈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠆⡠⢸⢋⣤⠄⣀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠘⠁⠙⠈⠀⠘⠃⠀⠀⠀⠀⠀⠀⠿⠚⠃⠙⠛⠷⠚⠇⠀⠘⠛⠛⠛⠛⠒⠛⠲⠖⠖⠸⠟⠛⠸⠇⠻⠋⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣀⠤⠂⠊
⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡤⠋⠀⢀⠴⠃
⠀⠀⠹⠘⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠰⡀⠀⠀⠀⠀⡀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠒⠒⢦⡄⠷⡀⠀⠀⠀⡸⣿⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁
⠀⠀⠀⠙⢷⣄⠀⠀⢸⣿⡏⠀⠙⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠙⣷⣾⣿⣹⠃⠀⠘⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡅⠀⢀⣴⡆⠀⠛⠛⢧⡀⠱⣄⠀⠀⠀⢀⣴⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣯⡃⠀⢊⡥⠐⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢰⣿⠟⠉⠀⠀⠈⢹⣿⠄⠀⠀⠀⠉⠀⣠⠀⠀⠀⠀⠋⠘⠁
⠀⠀⠀⠀⠀⠀⣼⣿⡟⢡⠖⠉⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠺⡷
⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⣸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠉⠉⡛⠛⠲⠶⢤⣄⣀⡀
⠀⠀⣰⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠠⠄⣀⠉⠛⠛⠳⠾⠷⠶⠒⠒
⠀⣰⣿⣿⣿⣍⢀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣴⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣤⣤⣀⡀
⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿
⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠉⠈⠉⠛⠛⠟⠛⠙⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⡘⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠢⣶⣾⣿⣿⣿⣦⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡖⠶⠀⠀⡀⠈⠋⠀⠀⠀⡤⠀⠀⠀⣠⠀⠀⢋⠁⢂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⡩⠁⠈⠀⡄⠀⠀⠀⡀⠀⢀⡀⠈⠀⠀⠋⣰⣿⣷⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢄⠀⠀⠘⢄⠀⠀⢻⣤⣤⡔⠀⢀⠌⠀⢻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠁⠂⢠⠀⠑⣄⠀⠉⢉⠠⠐⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠬⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⠀⠀⠀⠀⠀⢀⠈⡄⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠿⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠂⣀⣻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⠛⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣨⠀⠀⠀⠀⠀⠀⠀⠄⠻⣿⣯⣟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠠⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠔⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢶⣾⣿⠉⠻⢿⣿⣶⣤⣤⣀⣠⣤⣴⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⠁⣄⡈⠂⠀⠀⠤⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠁⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠄⠄⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠒⠀⠉⠁⠒⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⣿⣧⠀⠀⣀⠠⢆⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⠐⠛⠛⠃⠉⠀⠀⠀⠱⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⡰⠀⠀⠀⠀⠠⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⡄
⠘⢿⣦⣤⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠊⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠑⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⣀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠻⣄⣀⠟⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⣠⠴⠖⠚⠛⠋⠙⠛⠓⠲⠦⣄⠀⠈⠓⠒⠋
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠻⠭⣉⠙⠒⠒⠶⠤⣤⣄⡀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⢀⣠⣤⠤⠴⠒⠒⠋⣉⠭⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⡀⠀⠀⣹⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⣏⠀⠀⢀⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠀⡸⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢇⠀⠀⠈⠙⠲⠦⣄⡀
⠀⠀⠀⠀⢀⣠⣴⣚⣉⠤⠤⠴⠒⠚⠋⠉⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠉⠙⠒⠒⠢⠤⠤⣉⣓⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⡀⠀⠉⠓⠲⠤⢤⡤⢤⡤⠤⠖⠚⠉⠀⢀⡴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⣼⠉⠉⣧⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⡄⠀⠀⡤⠤⠄⢀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠐⠀⠀⠀⠀⠀⠷⠄⠄⠉⢀⠠⠀⢈⣄⠈
⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⡂⠀⢀⢀⠀⡀⠀⠀⠀⠀⢀⡈⠆⠜⠆⡨⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⣰⡛⢻⣳⢛⣡⠀⠀⠀⠘⠒⢲⣀⠁⠠⠞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⣾⣄⣀⣈⣣⠀⠀⠴⠥⠿⠺⠚⠒⠓⠆⠀⢰⡈⠉⠈⠙⢄⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⣆⡀⠀⢄⠄
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡃⠈⠃⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡍⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⠤⠀⠈⠀⠠⠉⠀⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁
⠀⠂⠄⠃⠁⠀⠀⠈⠁⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠈⠀⠁
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡄⢡⠀⡆⠀⠤⠄⠀⠰⠆⠁⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠔⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠈⢊⠺
⠀⠀⢠⠀⠐⠃⠀⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⠀⣤⠦⠀⠐⠀⠀⠀⠀⠀⠀⠠⠤⠖⠂⠀⠀⠈⠀⠐⠐
⠀⢀⠰⠤⠘⠀⠀⠄⠀⠐⠁⠀⠀⠀⢰⠀⢀⣲⡋⠉⠀⠀⠀⣠⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⣀⠉⢀⡀⢀⡔
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣈⣀⣀⣉⣈⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡻⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣬⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠻⣷⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠯⣍⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠛⣯⣿⣿⣯⣱⣎⡛⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⠱⣾⣤⣀⠀⠀⠀⠀⠀⢠⡾⡿⠻⡉⢠⣿⣿⣿⣿⣿⣿⣽⣶⣏⣬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⠉⢉⢩⡁⠈⢰⣤⣿⣿⠁⠀⠁⠾⠁⣿⣿⠉⠦⣈⠉⠛⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⢀⣼⣿⣅⠁⢈⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⡀⠘⠀⠀⢠⡇⠀⠀⠀⠉⣙⠿⠟⠻⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠁⠀⠀⠀⠈⠙⢿⣾⣿⣟⣿⡗⠐⢾⣷⡦⠀⠘⠑⠽⠿⠿⠏⡈⠉⠛⠛⠒⢾⣗⣒⣒⠒⠌
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⠀⣠⡶⠂⠀⠀⠀⠀⢻⣿⣿⣾⣟⠀⠀⢶⣾⣿⠆⠀⠀⠀⠀⠀⢻⣦⠀⠀⢀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠁⠁⡄⠀⠀⠀⣀⠀⠙⠻⠿⣿⣆⠀⠈⠁⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠒⢿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣧⡀⠀⠀⠀⠉⠉⠐⠒⠺⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⠁⠀⢀⣬⣶⣦⣾⣧⣴⡄⣤⡀⢰⢿⡏⠀⣰⠀⣰⠀⠀⠀⠀⠀⢀⣀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⡸⣿⣿⣿⠟⠻⣿⣿⣿⣷⣸⣾⣷⣏⣹⣾⣿⠀⠀⠀⣠⣶⣿⢏⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⡰⢡⡟⠉⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣏⢸⣿⣿⠀⠀⠠⢿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢀⡜⣱⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠛⢻⡄⠀⠇⠸⣿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡇⠸⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣄⠀⡀⠀⢻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⣻⣦⡀⠈⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢤⣀⣀⣀⣻⣎⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⣧⣡⠀⠈⠙⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣯⠇

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠒⠀⠲⣖⡶⠒⢲⠖⠒⠒⠒⠒⠒⠒⢒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠤⡄⠀⠀⠎⠂⠉⢦⠈⠀⢠⠛⣄⠠⠒⠦⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠦⡀⠀⠀⠀⢸
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡀⠐⠀⠀⠘⡄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢰⠀⠀⣠⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠒⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠣⣀⠤⠆⠒⠊⠉⠀⠈⠉⠉⠉⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠢⣄⡀⠀⠀⢀⣀⡇⠀⠀⣇⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⡀⢸
⠀⣂⣀⣀⠀⠌⠀⡄⢨⣶⣀⡉⠦⢀⠀⣀⣀⡀⠀⠀⠉⠒⠉⠀⠀⡇⠀⠀⡏⠉⠁⠀⠈⠉⠁⠐⠒⠁⠀⠈⢣⣀⣀⠔⠒⠢⠖⠊⠁⠀⠀⠈⢾
⠀⠀⠀⠀⢈⠀⡘⢝⢸⣇⡜⢧⡤⠀⢩⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⡇⠀⠀⡏⠉⠉⠁⠉⠉⠀⠀⠐⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠒⢸
⠀⠀⠀⠀⠈⡶⢣⡀⡱⡊⠈⢉⠇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠙⠠⣈⣚⣒⣚⠩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⢀⢆⠀⣾⠅⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣾⣷⣶⠶⠶⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣀⡐⣌⣾⣈⠀⡯⠀⣜⣰⠕⢲⠆⣀⣤⣴⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⡋⢰⡥⣟⡹⢒⡷⢻⣹⣏⣿⣝⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢤⣤⠀⢰⣄⡴⠊⠁⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠘⠷⣆
⠀⠀⠀⠀⠀⠒⠚⠤⠀⠄⠀⠘⠻⣶⣿⣿⢧⡄⠀⠀⠀⠈⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⣀⡜⠠⠀⠀⠀⠾⣷⣄⠉⠀⣀⣶⣶⣦⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠙⠆⠀⠃⠀⢜⣿⣿⣏⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⠀⠀⢠⠀⠀⠀⠀⢀⣆⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡿⠊⠀⣰⠏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⢃⣀⡀⠀⠀⠀⠾⠟⠋⠀⣿⣦⡀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠀⣸⢃⡾⢹⡇
⠀⠀⠀⠀⠀⡀⣤⣼⣂⣽⣽⠏⠙⣿⣿⠈⠙⠷⠀⢀⠀⣤⠒⠀⠀⢻⣎⢿⣶⣶⠂⣐⣿⣿⣿⣿⡟⠀⠀⣣⣾⠃⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠑⠀⠘⠿⠀⡴⠠⡀⠀⢰⣶⡦⠀⠐⣾⣷⠻⠿⠷⠾⠿⠿⠟⠻⠟⡄⠀⢺⣿⣿⡄⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠄⠀⠀⢰⠟⠃⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⠛⣿⢿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⣿⠀⠀⢠⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡌⠀⠀⢀⣧⠻⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣧⠘⠶⣿⡄⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⣸⣠⠟⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣸⣿⠀⠀⣿⡿⠜⠁⠀⢠⣄⡔⠴⠀⠀⠀⣿⡟⠀⠀⠀⠀⠘⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠙⠀⠀⠀⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡀⠀⣠⣠⣶⣻⣽⣿⣷⣀⢺⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢺⣿⣾⣾⣉⣟⣹⣿⣧⠙⢿⠫⠈⣵⡿⣶⡂⠴⠶⠶⠶⠶⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠰⢤⡀⠀⠀⠀⠀⡀⢤⣮⡧⣍⢛⡉⠀⠉⠉⠁⢙⡿⠛⡛⣱⣢⣸⠋⠱⠒⢀⡀⠀⢤⡴⠬⠿⠄
⠀⠀⠀⠆⢀⠰⠀⠛⢻⢷⡀⢨⠗⠚⢻⣿⣿⣷⣄⡒⣢⡠⣽⢃⡛⢿⡇⠐⠀⠐⠂⢿⣴⠀⠀⠉⣻⣿⠀⠷⠀⠀⠀⠆⡀⠐⢂⣠⣄⡀
⠀⠀⠀⠒⢦⡌⠉⠁⠀⠘⠛⠀⠘⠄⠁⠀⠀⠑⠛⠛⠓⠛⠋⠈⠃⠈⠙⠀⠀⠁⠀⠉⢉⠑⠂⠁⠈⠙⣰⣴⡞⠽⠶⡾⣿⣶⣿⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠠⠀⠨⠀⠀⠀⠀⢀⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠀⠠⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠠⠀⠀⢴⠦⠀⠀⠺⠖⠒⠀⠀⠴⠀⢠⡀⠀⠀⣠⡀
⠀⠀⠐⠆⠷⣾⠇⢶⢾⠞⠠⠇⣾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⢀⣄⡀⡐⡀⢠⡄⢦⠴⠂⢮⣄⡄⠶⣀⡄⢤⢰⣸⠈⢀⡅
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠓⠈⠁⠃⠀⠘⠀⠀⠁⠈⠀⠀⠉⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢆⠀⣠⣤⣠⢀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠴⠿⠀⠀⠀⠀⠭⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠆⠀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠉⠥⠜
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢄⡜
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡟⠂⠀⠀⣘⠓⠂⠀⠀⠀⠔⠀⠁⠀⢱⣄⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⠀⠀⠊⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢂⠀⠁
⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡏⠀⣘⠄⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠈⡀⠀⠀⡀
⠀⠀⠀⠀⠠⢶⢖⠑⡀⣿⣿⢡⡅⣴⣦⡷⣁⠁⢁⡆⢮⡄⡴⢺⣾⣿⣷⠀⢁⣠⣦⣎⣠⣉⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠀⠀⠙⠈⠀⠁⠁⠀⠁⠉⠀⠁⠁⠁⠈⠉⠈⠈⠁⠉⠋⠉⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⡄⠀⠀⢀⠤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠈⠀⢁⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠙⢀⠔⠁⠀⠘⢢⠀⠈⣉⣒⡶⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣄⠀⠀⢀⡼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠥⠴⠃⠀⠉⠉⡁⠀⠰⣌⠣⡀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠦⣤⠴⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢸⡆⠀⢧⡆⠀⠈⠉⠉⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⢀⡤⠀⠉⢷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡰⠉⠀⠈⠉⠉⠙⠉⠉⠀⠀⣠⠞
⠀⠀⠀⢀⠔⠋⠙⠲⡴⠋⠉⠉⠙⢦⡤⠶⠶⠶⠤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢦⠀⠀⠀⠀⠀⢰⡇⠀⠀⡀⠀⠀⠀⢀⡟⠛⠉
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠉⠛⠋⠛⠦⢤⠴⠚
⠀⠙⠒⠒⠻⣄⡀⢀⣀⡼⠲⠶⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢧⣀⡀⢀⣤⣀⠀⢀⣠⠏⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢸⢆⢠⢣⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⠒⠦⢈⣃⣀⣁⣈⡋⠸⠔⡹⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣏⠉⡠⠊⠁⠀⠀⠀⠀⠈⠑⠢⡉⢡⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠉⠛⢶⡄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣔⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠓⠒⠉⠉⠉⠑⠒⠢⢄⡀⠀⠀⠀⢸⠠⣔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢀⡌⢠⡐⠓
⠀⠀⠀⠀⢠⠔⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⠊⠰⡒⠳
⡠⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⣓
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⣬⣵⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣯
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣶⣶⣿⣼⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⣀⣶⡿⣫⣴⣿⡿⣿⣿⣤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣅⣀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣄⠠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠀⠀⠀⠀⢲⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣤⡾⡇⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⣈⣿⣿⣼⣿⣿⣿⣿⣿⡿⣯⠉⢙⠿⣿⣿⣹⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⠀⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⡜⡗⣩⠞⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣄⠀⣽⣿⣷⣿⣿⠻⣿⣿⣿⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣾⠿⣿⣿⣿⣿⠞⢛⢿⣯⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⢿⡛⣻⣤⣀⣼⣿⣦⣀⠉⠈⠙⠻⠷⠌⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⡿⠁⠀⠀⠈⠻⣿⣿⡝⢿⣿⣿⣿⣷⣶⣤⣤⣀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠟⠛⢻⣿⣿⣧⣄⡀⠀⠀⠀⠈⠻⣿⡀⠹⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣤⣴⣶⣿⣿⣭⡉⠙⢿⣶⡆⠀⠀⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡟⢿⣷⡀⢸⣿⣿⣤⣼⣿⡇⠀⣼⣿⡿⣿⣿⣿⢻⣿⣶⣶⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⠘⣿⣿⣧⣿⣿⣷⣼⣿⣿⣿⣿⣿⣥⣼⣥⣽⡿⠛⠁⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣷⣼⣿⣇⣹⣤⣿⣿⣿⣿⣿⣿⣿⣿⡟⢏⠁⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢻⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠈⠛⠿⣿⣾⣷⠀⠀⠀⣀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠈⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣈⣿⣿⣿⣿⣿⣿⡟⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⣹⣿⡅⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠟⠛⠛⠛⠿⠿⠛⠓⠈⠀⣴⣾⣿⣤⣤⣴⣶⡿⠿⠛⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⡿⢿⣿⣿⣿⣿⡆⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠟⠋⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⣠⣾⣿⣿⣌⣻⣿⣿⣿⣿⠾⠃
⠀⠀⠀⠠⠶⠟⣻⣿⣿⣿⣿⣿⢸⠏⠀⠀⠀⣹⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠃⠘⠀⠀⣶⣿⣿⣿⣿⠿⢿⣿⣧⡀
⠀⠀⣤⣭⣿⣿⣿⡿⢻⡿⠃⠀⠀⠀⠀⢹⣿⣿⠟⠀⠀⠀⠈⠛⣿⣷⡄
⠀⠀⠀⠈⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⣀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⢾⠞⠁⣄⠙⣾⠁⠀⠀⣹⡀⣆⣠⠂⣤
⠀⠀⠀⠀⠀⢠⣀⠘⡟⢛⡛⣦⠈⣧⠴⠯⡁⢣⣸⠄⠀⣿⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⡷⠋⠀⠈⢳⠇⣀⠀⣄⢀⣟⡤⠖⠋⠉⠀⠀⢀⠔⠛⢯⡉⠛⢋⢛⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣀⡀⣼⠚⠁⣀⠘⣾⠃⠀⣁⣀⡀⠀⣰⢡⠤⢦⠀⢹⢛⣛⣛⠛⠛⡇⡀
⠀⠀⠀⠀⠀⢘⣩⣉⣩⣭⣉⣉⣛⣙⠛⠛⠒⠳⠞⠧⠭⠿⠭⣿⣻⣸⡀⣸⠀⢸⠻⠼⠼⠀⠀⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠲⠦⠤⣀⡟⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠉⠉⠉⠉⠉⠙⠓⠓⠒⠲⠤⠤⢤⣄⣀⠉⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⠤⣤⣀⣀⣀⡀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢄⣴⢻⣯⣇⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣠⣄⣄⣈⣉⢉⠉⠒⠒⠦⠆
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⡾⢌⡟⣚⡇⠀⠀⠀⠀⠀⠀⠙⢿⡛⣁⠐⠀⠀⠀⢸⡿⣯⠓⠦⣄⡂
⠀⠀⠀⠀⠀⠀⢀⡾⣯⠗⣄⡘⣼⡩⠏⠀⣀⣤⡤⣤⣴⡄⠀⠀⠙⢲⣤⡀⠀⠀⠌⣳⡋⠠⠝⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠦⢼⠜⢠⠿⢯⡾⣠⡞⢹⣠⠷⢯⠟⠀⠀⠀⠀⢿⡽⠋⣶⣂⠂⢺⡷⢾⣻⡇⡇
⠀⠀⠀⠀⠀⠀⠸⡓⠤⡗⢁⡆⢸⣱⣇⠷⣯⡭⠟⠁⠀⠀⣀⠀⠀⣮⣄⡀⢸⣿⠉⢽⡇⣈⣇⡲⡇
⠀⠀⠀⠀⠀⢀⠀⠈⠓⢷⣪⣄⠙⡟⠋⠉⠁⠀⢀⠀⡀⣿⡋⢳⢠⡟⡾⠃⢸⣷⠐⢺⡒⠚⡇⠤⡇
⠀⠀⠀⠀⠀⢸⠠⠀⠙⠛⡏⠉⠻⢾⣿⡶⠗⡀⢈⡅⢈⡝⢻⠋⠀⡇⢻⠀⢸⢿⠤⢼⠥⠤⡇⡁⡇
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠁⠀⠀⠈⠉⠀⠈⠉⠈⠁⠉⠉⠉⠁⠀⠁⠉⠀⠈⠉⠀⠈⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡆⠀⣠⡀⠀⠀⠀⠀⣀⢀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⠃⠁⠄⠻⡧⡀⠀⠀⠀⠄⠠⡄⠛⠻⢿⠙⢣⣤⠀⠀⠀⠨⠷⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢮⠟⠒⢒⣤⠛⡂⣴⣦⣤⣤⠀⢠⡀
⠀⠀⠀⢰⣦⢀⡀⠀⠀⣠⣿⣿⠿⢒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠒⢀⢯⣿⣆⠣⠿⠿⣿⡃⠀⢺
⠀⠀⠀⠸⣿⡿⠱⢀⣀⣉⡛⠂⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣿⣿⠙⣴⠄⠈⠉⠀⣦⣼⡇
⠀⠀⠀⢰⡈⢰⣲⠟⠿⠿⠿⢴⡀⢹⣿⣿⣇⣠⠀⠀⠀⠀⠀⠀⠀⣸⣏⠋⠀⡔⠀⢀⣀⣀⣀⡘⢈⡀
⠀⠀⠐⠋⠀⠀⠙⣆⠀⣀⣀⠰⠁⠈⡝⢇⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠐⠐⠛⠉⠉⠉⠉⠙⠊⠘⠓⠚⠲⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠸⡄⢸⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠁⠀⢁⣀⠀⠁⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠴⠋⠁⠀⠉⠲⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡄⠀⠀⠀⠀⠀⡇⢀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠢⡀⢀⠡⣄⡈⠋⣀⡴⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠁⠀⠀⠀⠀⠁⢀⡉⠉⢁⡠⠤⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣀⣀⠀⠀⠐⠋⠀⠀⠁⠐⠀⠀⠙⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠔⠀⠀⣀⣠⣤⣄⣀⠀⢀⡤⠶⠒⠒⠦⢤⡀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠋⢀⡴⠊⠁⠀⠀⠀⠀⡴⠋⢀⠀⠀⠀⠀⠀⠙⠀⠉⠁⠉⠙⠢⠤⠔⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠚⠀⢀⣀⡤⠤⠤⠤⢤⣀⡀⠀⠀⠀⢀⡠⠴⠒⠒⠲⢦⣄
⠀⠀⠀⣰⠛⠁⠀⠀⠀⣠⠞⢩⠂⡀⢐⠆⠀⠀⠀⡭⠗⣦⠰⠋⠀⠀⠀⢀⣀⠀⠈⠳⣄
⠀⠀⢰⠃⠀⠈⠀⠀⡰⠁⠀⠀⠀⢀⢨⠆⠀⠀⠀⠦⣀⠉⢳⠀⠀⠠⣆⢠⠚⣢⠀⠀⠘⣇
⠀⠀⢸⠀⠀⠀⡀⢠⠃⠀⠀⠀⠉⠁⠀⢀⠠⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⠢⠜⠁⠀⠀⠀⣿
⠀⠀⠘⣧⠀⠀⠀⢸⡀⠀⠠⠄⢠⠀⠀⢙⠀⠆⢐⠄⠀⠀⢰⡇⠀⠄⠀⠀⡠⠀⠀⠀⣰⠃
⠀⠀⠀⠈⠓⠦⢤⠀⢷⡀⢸⢀⡠⠃⠀⠈⠑⠁⠀⠀⠀⢀⡞⠀⠰⠦⢤⣤⣥⡥⠾⠛⠁
⠀⠀⠀⠀⠀⠀⢲⡀⢠⠙⢦⣉⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⣄⠸⡄⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⣷⠈⢰⠂⠸⡍⠛⠓⡚⠛⢁⠄⠀⠀⠀⠀⠸⡄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⡟⠀⣾⠀⠀⠙⡄⢠⠇⣰⠋⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇
⠀⠀⠀⠀⣠⠶⠒⠒⠲⠦⡀⠀⠀⡏⠀⣿⢠⣀⣀⠀⢀⡤⠤⣸⠁⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢫⡇⠀⣿⠀⠀⠈⠙⠲⠄⠀⠀⠀⠀⠀⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⡿⠟⢻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣊⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡴⠂⢋⠏⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀⢀⣴⠟⢀⡴⠇⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⡆⠀⠀⠀⢀⣀⣀⠹⠿⠋⢈⣁⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣠⡤⠶⣿⣫⣿⣥⠴⠓⠁⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⡿⠟⠉⠀⣠⠲⠛⠛⠟⠃⠀⠀⢀⣿⠠⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⢠⠞⠁⢠⣰⠆⠄⢠⣶⠞⠋⠁⠀⢀⣠⠖⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⠿⠋
⠀⠀⠀⠀⠀⠀⢀⣄⣴⣿⣿⠟⠁⠀⠀⠀⢠⡇⠔⠀⣼⠏⠀⢠⡿⠛⠿⠳⠟⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠀⠀⢰⣠⣾⡏⠀⣴⣾⡟⠐⢦⡿⠁⠀⠀⠀⠀⠀⢀⢀⣀⣄⣿⠁⠀⠀⢠⡆⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⢀⣀⣾⣿⣿⣿⡗⣾⣏⠛⠃⠀⡿⣧⣶⣶⣶⣶⣿⣏⣿⣿⣿⣟⡍⠀⠀⠀⢀⣿⠛⠿⠛⠋
⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⣶⣿⡿⠋⠉⠈⣷⣼⡏⠑⠲⡄⠘⠛⠻⠿⢿⣿⡿⠿⢿⣿⣯⣿⡇⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠸⣿⠃⠐⠋⡙⢏⠀⠀⠀⢠⣿⣿⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢠⣾⣾⠋
⠀⠀⠀⠀⠹⠿⣿⠖⠋⠉⣿⣺⣆⠀⣠⣾⡿⡩⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⣇⠚⢿⣿
⠀⠀⠀⠀⠀⠀⠙⣷⣶⣞⣽⣿⡶⠖⢻⣿⠃⢷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣧⠀⠀⣿⡄⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠀⣼⠇⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣷⡍⠀⠀⢸⣷⡀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠷⠙⢿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠈⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢼⣿⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠂⠀⠸⢋⠅⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⠄⠀⠁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣶⠶⠦⣤⣤⠆⣤⣤⣤⣤⣶⡷⣿⠿⢗⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⣀⡀⣾⣿⣷⣿⣿⣿⣿⣿⡶⠈⠉⠀⠰⠿⠿⢿⣿⣿⠟⠶⠗⠀⠈⡉⠛⠛
⠀⠀⠀⠀⣛⡃⠀⠀⠈⢹⣿⣿⣿⣿⡄⠀⠀⠀⠀⡸⠟⠋⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠛⢁⡀⢀⣴⡿⠁⠀⠙⢿⣿⣶⣴⣴⣎⠁⠀⢠⣶⣴⣦⡀⠀⠰⣶⣄⣀⣀
⠀⠀⠀⠀⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠹⣿⡿⠁⠀⠀⠈⠙⢿⣿⠁⠀⠀⣀
⠀⠀⠀⠠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⣼⣿⡇
⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠠⠀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠲⡆⠀⠀⠀⠘⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈

⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠀⠀⡤⠤⠀⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢠⠄⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠄⠈⠐

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢀⠀⢀⢡⢀⠀⠀⠀⠀⣠⠀⠀⠠⠶⠒⠒⠒⢦⣄⣀⠀⠀⠀⣦⠀⠀⢠⡄⠀⢷⠀⠀⠀⠀⠀⡀
⢸⡇⢸⢿⣼⣄⣾⠰⡇⢻⢸⣶⣄⣀⡀⡀⠲⠶⠉⠉⠁⠀⠀⢿⢿⠄⢸⡇⡆⢸⠀⠀⠀⠠⠀⠀⠀⠃
⠸⠇⠈⠸⠃⠸⠀⠀⠁⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣠⣀⣀⣀⣄⣀⣀⣀⣤⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣀⣤⢀
⠀⠸⣷⣾⡿⠀⠀⣄⠀⠀⣄⡀⠀⠀⠀⢀⠀⠸⠂⠀⢸⣹⣃⣴⣄⠀⠀⢀⣤⣶⣿⣿⣾⣿⣿⣿
⠀⠀⣾⣿⣧⠀⠘⣏⠠⠿⠿⠗⣰⣿⡅⢸⣷⠶⠃⠠⡺⠀⠉⠙⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟
⠀⠀⠈⠁⠈⠀⡠⠈⠀⣀⠠⠘⡛⠻⣿⣿⣿⣄⡀⢀⠀⠠⢠⠀⡀⠀⠀⠹⣿⣿⣿⡿⠻⠿⠟⠛
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠋⠀⡔⠀⠀⠀⠹⣿⣿⣿⣮⠏⡇⠢⠄⠄⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠔⣈⡀⠙⢦⢐⡥⠚⠁⡄⢀⠀⠀⠈⢿⣿⣗⠓⡿⠊⠱⣶⣤⣀⠒⠚⠻⠿⣁
⠀⠀⠠⣤⣈⣡⠆⠈⣧⣤⡤⢾⠀⠀⠀⠀⠀⠀⠻⣿⣶⣷⡄⠙⣿⣋⠈⠙⢦⠀⠀⠀⠙⢄
⠀⠀⠀⠰⢦⣅⠎⠻⢄⡀⠉⠚⡦⢄⣀⣀⣀⣀⣀⠼⠋⠹⣷⠀⢻⣿⣆⠀⢸⡇⢐⡄⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⢷⣄⣹⣧⢀⡾⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠀⠀⠀⢀⠔⠀⠀⠹⣦⣽⣿⣿⣿⡀⠀⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⡀⢹⡇⣷⣿⠏⠀⣰⠁⠁⠀⡸
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⠦⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⡇⣼⠇⠉⠉⣀⠔⠳⡄⠀⠰⠁
⠀⠀⠀⠀⠀⠀⢈⣿⡟⠻⡟⠀⠠⠀⠀⠀⠀⠀⡔⠂⠀⠀⡄⣰⣟⡠⠔⢺⠁⠀⠀⢸⢀⣠⠀⢀
⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠘⢆⠀⢀⡴⠤⠷⢤⡇⠀⠂⢸⣿⣿⣿⣶⣿⣾⣦⡀⠀⢸⣼⣿⣋⠀⠈
⠀⠀⠀⠀⠀⠈⣿⣿⣀⠀⠀⠀⠉⠉⠀⠀⠀⢀⠇⠀⣠⣿⣧⡀⠉⠉⠙⠛⠛⠁⠀⠈⠻⠛⠁⠱⠀⢄
⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⡎⣠⡜⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢸⣇⠀⣿⠀⢸⡇⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠀⢻⡦⠘⣋⣤⠥⠴⠶⠦⠬⣥⣘⠃⢰⡟⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠷⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠾⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡈⠻⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡰⠟⠃⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣃⣸⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠲⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠚⠉⠉⠉⠙⢦⡙⠦⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠛⠮⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣤⣤⡀
⠀⠀⠀⠀⢀⣤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⠀⠀⠀⠀⠀⠀⠀⣼⢡⣄⡉
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡆⠀⠀⠀⠀⢀⡼⢡⣄⠉⠛⠷⠂
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⠀⠀⠀⣀⡴⠋⣴⣄⠙⠃
⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡕⠧⠴⠖⣋⡁⢲⣆⠈⠻⣷
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢻⡆⠸⣧⠀⠉
⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠏⠀⠈⠀⠀⠹⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⡿⠆⣉⠽⢛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣾⢁⠀⠈⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⢨⡟⠀⠀⠀⠀⢶⣶⠏⠀⠀⢸⡜⠛⡄⠙⠋⠲⡍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣀⣼⣷⡦⠄⠀⢀⣸⡿⠀⠀⠀⡈⠀⡀⠹⣆⣈⠀⣠⡶⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢇⠀⠀⠀⢘⡂⠻⣇⠀⠀⠀⠟⡃⠘⢶⣾⣏⡼⠋⣀⠳⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢀⠀⠀⠸⣿⣶⡉⠦⡀⠀⠀⠡⡀⠉⢢⡙⣷⢲⡏⢋⡁
⠀⠀⠀⠀⠀⠄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠈⠳⣤⡀⠁⢠⣤⠿⣁⡷⠈⠋
⠀⠀⠀⠀⠀⠀⠀⡴⣯⣤⡀⠀⠀⠀⠀⠀⣿⡽⢻⡇⣀⠀⠀⠀⠉⣉⠉⠉⠀⠈⣤⣀
⠀⠀⠀⠀⠀⠀⡄⠀⠹⣦⡀⠀⠀⠀⠘⣻⠞⠁⠙⣇⠐⠡⡀⠙⠋⡁⠉⢳⠀⠈⣠⠀⠁⢦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣷⠅⠀⠠⠊⡁⠀⠀⠀⣿⠀⠀⠈⠃⠀⠉⠈⡌⠀⠀⠁⠀⡀⠀⠣
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡷⢈⣴⠀⠀⢇⣀⡀⢸⣿⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠘⠊⡀⣡⠀⠀⠀⢀⠀⠀⠅
⠀⠀⠀⠀⢠⠄⣶⠀⠠⡟⠉⢘⠁⠀⢸⡏⣿⣿⢿⢁⠀⠀⠙⠀⠀⠀⠴⢞⠂⣀⠉⠂⠀⢀⠀⠁⠤⠀⣠⠜⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣀⢷⠀⣆⠀⠀⣸⣧⣿⣿⠈⣆⠁⢀⡀⠀⠰⠁⠀⠈⠀⠈⠁⢀⢀⡎⠐⠀⠀⡠⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠘⠼⠿⣿⣿⣿⣿⣧⣿⣿⡄⡘⣦⠈⣧⡀⠀⡄⠚⠳⡌⢂⣤⠀⣄⡴⠄⠴⠋⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣵⢞⣿⣿⢣⡾⠁⠈⠑⢬⣁⢀⠘⠢⢀⠘⣮⡧⣽⠃⠀⠀⢀⠴⠓⠊⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣥⠀⠆⠀⣿⣿⢉⣠⣐⡛⠲⢄⠉⠛⠦⡂⠀⠀⠈⠲⡀⠀⠀⠀⢨⡐⢤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠶⠀⠀⠀⢿⠛⠤⠀⠀⠀⠀⢀⣽⣷⣶⢶⣿⡷⠆⡀⠀⠐⠀⠀⠀⠁⠁
⠀⠀⠀⠀⣀⡀⠀⢀⡞⠀⠀⠀⠡⡄⠀⠈⠀⠀⠀⠀⠀⠐⠋⠐⣿⣿⡿⠟⠁⠀⠀⢬⠃⠀⡄
⠀⠀⣠⡞⠛⣻⣿⣿⡇⠀⠀⠀⠈⡛⢶⢶⣤⢤⡶⠀⠀⣠⣀⣮⠔⠉⠀⠀⠀⠀⠀⠀⠙⢦⠠
⠀⠀⢿⣤⣿⣧⣉⡻⣧⠀⠀⠀⠠⠀⣜⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢣
⠀⢠⣾⣿⣿⣏⣉⣿⣿⡇⠀⠀⠂⠀⣸⡿⠻⣿⣿⣿⣿⡟⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢱
⠀⠀⠈⠛⠛⠛⢶⣄⣮⣇⢀⠀⠀⠀⣼⠁⠀⠈⢻⣿⣿⠇⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡆⢀⠀⢀⡟⠀⠀⠀⢸⠗⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⣀⣃
⠀⠀⠀⠀⢐⣿⠛⢙⣧⣾⠇⠀⢠⡎⠀⠀⠀⠀⠈⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⡹
⠀⠀⠀⠀⣺⣿⢿⠿⠛⠏⠀⢠⡆⠀⠀⠀⠀⢠⡘⠀⠸⡀
⠀⠀⠀⠀⠻⡏⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠑⠡⡂⠱⣄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣈⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠂⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠤⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠘⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠿⢿⠟⢻⠿⢿⠿⠻⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣷⣿⣶⣿⣷⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠲⡄⠀⣬⠀⠇⢦⠲⣀⠀⠠⠶⠂⠖⠀⠀⠂⠀⠐⢐⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠃⣤⠀⠀⣠⡇⠀⡀⠸⣧⠀⠀⠂⠀⠐⠚⠀⠐⠀⠱⠺⠷⠦⠤⢬⡉⡟⣀⣀⠈⠉⠈⠉⠩⠀⠮⣅⡐⠂
⠀⠀⠀⠀⠉⠁⠉⠉⠀⠐⠁⠀⠙⠓⠀⠐⠛⠚⠒⠂⠀⠐⠀⠀⠐⠒⠒⠀⠀⠀⠀⠉⠁⠐⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠆⠀⠒⢰⣂⠀⡄⣦⠠⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣤⣦
⠀⠀⠀⠀⡀⣠⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠈⠋⢢⠜⠃⣰⡆⠨⣿⣷⣟⡠⣬⣴⡆⠀⠀⠈⠛⠁⠸⠆
⠀⠀⠀⠀⢿⡇⠀⠰⠿⣽⡃⠀⢀⣀⢰⠀⠀⠀⠀⠀⣄⣴⡿⡿⣛⣟⡛⠃⢀⢘
⠀⠀⠀⠀⠈⠀⢀⡰⠃⣾⠁⣴⢦⣿⡬⡇⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠛⠀⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠒⠟⡈⢿⣷⠃⢀⡀
⠀⠀⠀⠀⠀⢰⢠⣤⡄⠠⠀⢠⠁⠈⢻⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠈⣤⣤⠤⣤⡀
⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠞⠉⠠⠤⢈⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠆⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠁⠐⡟⠐⠠⠀⢼⡳⠽
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠱⠀⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⣀⠈⢀⠀⠁⠻⠗⠂
⠸⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡙⠀⠀⠆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡀⣁⠀⠀⠀⠀⢀
⠘⢋⣍⠁⠀⠀⠄⠀⡀⠀⠀⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠄⠈⠉
⠐⣋⡉⣇⠀⠀⠀⠸⠉⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠯⣀⠠⡄⠠⠀⠊⠀⡀⢦⠤⠤⠄⠀⠀⡀⢀⠀⢀⠀⡀⠀⠄⠀⠀⡀⠀⢀⠀⢆⡀⠀⣄
⠸⠟⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠈⠀⠐⠂⠐⠐⠃⠈⠉⠈⠁⣄⠛⠉⣿⠁⡡⢀⣦⣙⠁⡬⣜⠒⠀⣬⠀⠀⡇⠀⣪⠀⢀⠀⠀⡇
⢀⣀⡠⠀⠀⠀⠀⠀⠄⠌⠀⠀⣀⠀⠀⠉⣄⡤⠘⠋⠀⢠⣶⠀⢀⠀⠀⠀⠀⠀⠰⠗⠚⠀⠀⠀⣤⠖⡗⠻⠂⠐⠀⡧⠀⢸⠀⠐⠂⠀⢈⠀⠰⠂⠀⡀
⠋⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠕⠠⠀⠀⠙⠀⠂⠆⠠⠈⠉⠀⠘⠀⠀⠀⠀⠀⠀⣶⠘⠆⢀⡀⠀⠀⣃⢸⡆⢀⠀⢖⠀⠀⡂⠠⠦⠀⠈⠀⠀⠆⠀⠁
⠀⠀⠐⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⢴⠨⠄⠈⠀⠄⠀⠋⢸⡇⠐⠀⠐⠉⢠⡇⠀⠀⠀⠀⠀⠀⠇⠀⠂
⠀⠀⠀⠀⠀⠄⢠⠀⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢸⣅⡄⠀⠀⠀⠀⢀⢸⡆⠐⠀⡠⡀⠐⠁⢠⠄⠀⠈⠀⠀⠀⠤⠤⠃
⢀⠀⠀⠀⢂⡈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠈⠦⠄⢠⠏⢠⡤⠐⠃⠀⠀⣦⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠄⠀⠀⠀⠐⠉⠁
⠠⠳⠄⠀⠠⠂⣀⠀⠀⠀⠀⢀⠀⠀⡀⡐⣀⢠⠤⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠤⠐⠂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⡟⠀⠀⡰⢤⠠⠞⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢠⣀⡀⠠⠔⠒⠚⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠁⠈⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣿⣻⣞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢄⣀⠀⠀⠀⢀⣿⣄⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⡁⣀⣀⡼⢿⣿⣿⠟⠛⠛⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣾⣿⣿⢿⣇⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⢧⣸⣿⣌⠀⠀⣱⣄⣀⣀⣀⡀⠴⣿⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣾⣿⣿⣿⣿⠃⠀⠝⣿⣿⣷⣾⡉⣉⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣁⣸⣿⣿⣿⣿⠏⠀⠀⠀⠹⢮⢻⣿⣷⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⠛⠋⠙⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣶⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⡏⢸⠿⠀⠀⠀⠀⢐⣃⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣏⣿⣿⣿⡹⣆⠈⠆⠀⠔⠈⢫⣀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⢻⣷⣽⡳⠄⣤⢰⣿⣾⠟⡋⣸⣯⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⠈⠹⠟⠉⠋⣠⣇⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠛⣷⣄⡀⠀⠀⢠⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡆⠀⠀⣾⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣾⣻⡀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⠁⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠟⢀⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣶⣶⡶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⠀⠉⠁⢉⣡⣴⣶⣄⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠉⠉⠉⠉⠉⢡⣾⣿⣿⣿⣯⣿⣿⣦⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣀⠀⡀⠀⠀⠀⣰⣿⣿⣿⡿⢿⢿⣯⡿⣿⣷⡜⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠀⠀⠉⣀⣡⣤⣷⣾⣿⡿⣿⣛⣛⡛⢛⣛⣛⢻⣿⣿⣶⣦⣤⣠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡻⣿⢿⣿⢿⡷⣶⣿⣿⣿⣿⣿⣿⣿⡇⣯⡿⣿⡏⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⡀⣠⢸⣧⣤⡿⣸⣿⣸⠇⣿⣿⠟⡟⢻⣿⣿⡟⠃⠛⣱⡙⠇⠟⣱⡙⠋⣿⣿⡟⣿⢿⢿⣿⢻⣧⠀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠈⠉⠉⠋⠀⠀⠀⠘⠼⢿⣿⡧⠭⠭⣭⣀⣒⣒⣴⣧⣾⣿⡿⠧⠦⠬⠭⠅⠄⠐⠥⢤⣤⣿⣿⣇⣛⡛⠚⣛⣙⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⣉⣉⣉⣀⣀⣀⣈⣭⠤⠤⠤⣤⣤⠤⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⣠⠤⣤⡤⢤⣤⣤⣤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠞⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣀⠀⠀⠐⠂⠤⠤⠄⠀⠀⠀⠀⠀⠀⢠⣞⡓⢦⡿⠄⠀⠁⠀⣶⣶⡈⠿⡆
⠀⠀⠀⠀⠀⠀⣸⢿⠀⣸⣿⣿⠿⣿⣿⡿⠛⢿⢿⡿⢋⣵⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⡿⠀⠁⠀⠀⠀⠀⠈⠹⠟⢠⣧
⠀⠀⠀⠀⠀⢠⡇⢸⡀⠈⣭⣶⣷⡜⢛⡵⠀⠀⠈⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣽⠋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉
⠀⠀⠀⠀⠀⣾⠀⠀⣇⠀⣿⣿⣿⣷⣿⡇⡀⠀⠀⠀⠈⣌⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠺⡿⢁⠎⠀⠀⢀⡄⢠⠤⠤⢤⣠⠀⣵⡇
⠀⠀⠀⠀⢀⡇⠀⠀⢿⠀⡙⠟⣯⣀⣛⣿⣷⢠⠄⠀⠀⠘⢦⠉⢿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠶⠳⢧⡄⣤⠔⠋⠃⡇⠀⠈⠓⠁⡈⠈⠁
⠀⠀⠀⠀⢸⣧⠀⠀⠘⡆⠘⢟⢻⠀⠀⠙⣏⢹⢦⣀⠀⠀⡀⠳⣌⣦⣀⠘⡻⡷⠀⠰⠿⢛⠂⠀⠀⠈⣷⠀⢁⢴⣷⠃⠀⠀⣲⠁⢠⣡⠁⢡⣃⡀⠀⠘⡛⡟
⠀⠀⠀⠀⠸⠛⠀⠀⠀⢷⠘⠈⠀⠀⠀⠀⣿⢸⠂⠈⠑⣎⢲⡟⠋⡉⠉⢀⡽⠀⠀⠀⠚⠾⡟⠿⡶⣤⡋⣀⡃⠼⣾⠄⠰⠿⢧⡷⠃⠙⠿⠘⠛⠷⠃⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⢦⢢⢀⡄⠀⠀⠉⣎⠀⠀⠀⢹⡽⡳⢄⠉⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡞⠛⠛⠼⠿⠃⠐⢶⣧⣽⢾⡶⠂⢤⣧⣷⡀⢃⢀⠸⣃⡴⣴⣿⢿⣠⢶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠛⠀⠈⠻⠋⠀⠟⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁
⠀⢀⣤⣾⣛⣛⣓⣚⣃⣐⣶⣤⣤⣤⣤⣤⣀⣤⣴⣤⣤⣤⣤⣤⣶⣶⠖⢲⣤⣄⣤⣤⣤⣤⣶⣶⡿⢳⣟⡆
⠀⠀⢠⣬⣭⣭⣟⡟⠛⠛⢻⣿⣿⠶⣿⣷⡿⠿⠿⣿⣟⡛⠋⢀⣴⣶⣶⣶⣤⣷⣽⣭⣭⣽⣽⣟⣟⡛⠛⠁
⠀⠀⠛⠛⠟⠿⠿⢿⡯⠻⠛⠛⠛⠒⠛⠋⠿⠷⠾⠿⠿⠿⠿⠟⠾⠮⠼⣿⣶⣯⣯⣿⣿⣦⣤⣬⡉⢷⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⣶⠀⠀⠀⠀⠐⢷⣤⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣿⠆
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣀⣀⢀⣤⠂⢠⡄⠉⠀⠀⠀⠒⢿⣾⣿⠀⠀⠀⠤⣤⡄⣤⡀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠀⣿⡿⠋⣻⣿⣿⡿⣧⣿⣿⠤⠄⠀⠀⠀⠐⠂⠀⠈⠁⠙⠂⣇⣿⣷⣼⣷⢝⡇
⠀⠈⠀⠉⠀⢰⣿⣷⠁⠹⠛⠫⠄⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⢿⡟⠉⠳⢸⠗⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⣇⠀⠂⢀⡀⠀⢀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠂⠚⠁⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠈⠉⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢲⡄⠀⠀⠀⠀⠀⠀⣀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣄⡀⠀⠀⠀⣰⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢉⣿⣿⠿⣿⡷⢤⣼⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣤⣤⠀⠒⠒⠒⠛⢛⡤⠚⠛⠈⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢀⣼⣿⣿⡷⣿⣿⣿⣿⣿⣿⡦
⠀⠀⢸⡄⠘⣇⠐⣆⣀⡀⠀⠀⠚⠻⠋⠙⠋⠉⠛⠉⠀⡉⠙⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⡁⡀⢀⡀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⠁⠀⠁⠀⠁⠀⠀⠉⠈⠒⠂⠤⢀⢀⡀⠀⠈⣀⠢⣿⣿⣿⣟⡀⢀⢀⢀⣀⣠⣤⣴⠏⠉⣿⡎⠈⢹⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⢃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡷⢶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠿⠯⠀⢸⣫⣿⣯⣿⣿⣟⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣒⣤⣤⠿⣿⣿⣿⣀⡀⢸⡇⠰⠇⠀⠀⠀⠀⠀⠀⣰⢠⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⠿⠁
⠀⠀⢀⣀⣀⣤⣤⣤⠤⠐⠒⣀⢀⣉⣠⣠⣤⠶⠶⠚⣁⣈⣰⣟⣙⣻⣛⡿⠿⣿⠷⣶⣶⣶⣶⣴⣤⣼⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠶⠿⠛⠉⠃⠀⣄⣰⡴⠶⠗⠋⢉⡉⢉⣡⣴⣶⠶⠾⠟⠛⠉⣉⣉⣬⣷⣦⡶⠺⠚⢒⠉⡀⠉⢹⡿⠻⠿⢿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠂
⢤⣄⣶⣤⠿⠟⠟⠋⢈⣀⢀⣐⣾⡿⠿⠟⠉⢁⣄⣠⣶⣼⣿⣿⠿⠟⠋⢉⣤⣶⣧⣿⣶⣿⣦⣿⣿⣻⡥⠼⣯⢄⡥⢀⡀
⠛⠛⠋⠀⣀⣀⣦⣠⣦⡿⠋⠛⢩⢤⣴⣴⣽⣷⣿⡟⠋⡉⠋⢀⣰⣶⢶⣼⣿⣿⡿⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣳⡍⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢠⡾⠓⢤⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⠤⠖⣂⠂⠉⠓⠻⠤⠶⠄
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠈⢀⣴⠟⠓⢹⠚⠑⢖⠀⠀⠆⠀⠐⢾⣧⡀⣀⡀⠈⢛⠹⠏⠜⢤⠀⠀⢈⠀⠀⠈⣆⠀⠀⢤⡀⡀
⠀⠠⡤⠀⠨⠤⠤⠤⠰⢠⡞⠁⠀⠀⠉⠀⠀⠈⢣⣤⡄⠀⠀⢿⣧⣀⣀⣀⡀⢁⡎⠁⠀⠈⢧⠀⠄⢰⣄⣴⣿⣀⣀⣼⣇⡜
⠀⠀⣀⠀⢄⣀⣀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⣿⣿⣿⡇⠸⠀⠀⢠⣀⣧⠆⠀⠘⠉⠁⠠⠚⠛⠉⠀⠤⠄
⠀⠀⠀⠀⠀⠁⣖⡋⣉⢀⡀⢴⠀⠂⡖⢸⠀⠶⢸⣿⡇⠀⠀⢹⣿⡿⠟⠋⡡⣆⣁⣹⡞⠛⠁
⠀⠀⠀⣀⡥⠄⡝⠃⣿⠘⣁⣀⣀⠀⠦⢸⣀⠀⢸⣿⣇⠀⣠⠟⠋⠁⢀⡐⠁⠀⠀⠙⢹⠢⢄
⠀⠀⠀⠀⠀⠐⠒⠒⠀⡈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠀⠒⠐⠒⠛⠋⠉⠙⠓⠒⠲⠦⠤⠤⢤⣀⣀⣀⡀
⠀⠀⠀⠒⠀⠐⠂⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠉
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡠
⠀⠀⠀⠀⠀⠈⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠨⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠠⢄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡤⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⣀⠀⠀⠀⠀⣑⣄⠀⠀⠸⣿⣿⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⡄⠀⣠⣄⡀⣀
⠀⣤⣿⣷⡀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣄⠀⠀⣀⣀⡀⠀⠀⢠⣼⣿⣿⣿⣿⠆⠀⠀⠰⠶⢴⣶⣦⣤⣼⣧⣄⣉⡛⡓⢉
⠀⢫⡸⠤⠧⠧⠽⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡄⣶⣜⠛⠃⣰⣷⠈⣧⠍⠁⠀⠀⢈⢶⢠⡶⠀⢠⡉⡉⠉⠉⠉⠉⠉⠁⠃⠒⠀⠄
⠀⠀⠐⠒⠚⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠸⢿⣧⠙⢿⡧⣴⠙⠛⣟⠇⠐⠒⠒⠂⠘⢜⡎⠀⢸⣜⣿⣿⠄⡄
⠀⠀⠀⣀⣀⡀⢀⢀⣀⡀⢀⣀⠀⠀⠀⡀⠀⠀⡿⢹⠃⠀⠀⠀⢹⢱⡆⠀⠀⠀⠀⠀⠀⠞⠸⡏⠈⣜⢢⠀⢿⣧⠃
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣤⣤⣤⣥⣄⣉⡉⠸⠀⠤⡈⣁⠐⠂⣀⣀⣀⣈⡡⣀⡠⣬⣅⣀⠹⠴
⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡦⣄⠀⠀⠀⠀⠀⠀⠀⡠⠄⡖⣿⢐⠺⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⠀⢀⠀⠀⣰⡊⠀⢸⣇⠐⠂⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡈⢿⠿⡇⠀⠀⠀⠀⠁⢀⣴⠉⠀⠀⢠⡎⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠘⠂⠈⡀⠀⡀⢸⡋⠀⠀⠀⢸⠻⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡙⠒⠲⠾⡀⣟⡄⠀⠀⠀⠈⢧⣿⣤⡴⠛⠙
⠀⠀⠀⠀⢀⠄⠠⠳⠀⠸⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸⠀⠀⢸⡇⠀⠀⠀⠠⣄⣘⣿⠤⢀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠒⢈⠀⡆⠄⠘⣧⠀⠀⠀⠀⠀⠀⠁⠁⠌⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠰⠀⠎⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡄⢀⠀⠀⠹⠀⠀⠠⣀⡠⠆⠐⣶⠀⠀⠤⠀⠈⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⠍⠀⢰⣶⡄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣿⡀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢹⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠁⠀⠀⠀⠁⠀⠀⠉⠉⠁⠂⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⡀⠀⠐⠊⠀⠀⠀⠴⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠰⠀⠀⠉⠰⠂⠀⠀⠀⠀⠀⠠⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠚⠀⠀⠁