Airplane Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠉⠁⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⢀⢀⠀⢀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡎⠉⠉⠉⠉⠉⠑⣲⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠁⠠⠔⠋⠑⠄⠠⠌⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿
⣿⠿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠛⠿⣿⡷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿
⡅⠀⠀⢻⣿⣿⣿⣿⣿⡦⠀⠂⠀⠀⠀⠀⠀⠈⢘⠀⠂⠀⠀⠀⠀⠀⠀⠀⢁⠀⢱⠍⠙⠻⢿⣿⠟⠀⠀⠈⠀⠀⠀⠈⠻
⣷⠀⠀⢸⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡄⠀⠀⠀⠈⠉⠁⠂⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣧⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣧⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⡇⠀⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⣿⣿⣿⣇⠀⠈⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣘⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣄⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠰⠁⠀⠀⠀⠀⢠⠊⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠠⠁⠀⠀⠀⢀⠔⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠀⠈⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠖⠉⠐⠈⠃⠀⠀⠀⠽⠀⠪⠂⠪⠂⠸⠇⠐⠕⠀⠀⠀⠀⠀⢀⣀⠀⢎⡁
⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠒⠂⠉⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⣩⠴⣶⡿⢿⣿⣶⣶⣶⣶⣭⣭⣭⣭⣖⣒⣒⣠⣤⡤⠤⠄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⠧⢄⣉⣀⡈⢠⡎⠁⠊⠡⡆⠩⠚⠝⠛⠝⠻⠛⠿⢟⢿⠿⢿⢿⣿⣿⣶⣶⣶⣶⠬⠇
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⣧⡏⠉⠉⣷⢒⠒⠒⠒⣚⢧⣶⠒⣺⢇⠦⢌⠝⠉⠁⠀⠁⣾⣷⡀⡠⡄
⠀⠀⠀⢀⠔⣿⣿⡷⡀⠀⠀⠀⠀⢻⢰⠀⣀⣽⡜⣒⠿⠟⣾⣿⡿⡟⠁⠀⠁⡘⠀⠀⠀⣸⠀⣇⣜⡛⣞⠁
⠀⠀⠀⠀⡆⠸⣿⣿⣎⢦⠀⣀⡠⠼⡏⡟⠛⠀⣇⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣷⣴⣾⣿⡿⢂⣥⣺⢿⠁
⠀⠀⠀⠀⡇⠀⠻⠿⠿⠓⠉⠁⠀⠀⢻⢠⣀⣀⣹⣰⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡀⠛⡜
⠀⢠⡒⠩⠥⠶⠶⠶⠂⢀⣀⣠⠴⢚⠭⣭⢶⣶⣾⣭⣭⣭⣿⣟⣛⣛⠿⣻⡏⣋⣉⣙⣤⠤⠒⠊⠉
⠀⠀⠀⠉⠉⠓⠚⣿⢿⠿⠿⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠐⠓⠒⠛⠛⣛⠿⢱⠁⠘⣿⣸⣤⣄
⠀⠀⠀⠀⠀⠀⣟⣵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢦⣧⣀⣼⣷⡋⢻⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠂⣸⡿⠉⠉⠷⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠰⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣠⡤⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠁⢢
⠀⠀⠀⠀⠀⠀⡸⠵⠖⠒⠀⠐⠀⠠⠦⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠐⠁
⠀⠀⢀⠔⠁⠀⠂⡀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠠⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠄⠈⠀⠀⠀⡠⠊
⠀⠀⢠⠀⠀⠀⠀⠀⠁⠂⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⣀⠀⣀⠀⠠⠄⠂⠁⠀⠀⠀⢀⠔
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⡀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⢠⣀⡀⠀⡀⠀⠀⠁⠐⠠⢠⡊
⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⡠⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⢌⠐⠠⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⡀⠢⡀⠀⠀⠀⠁⠐⠤⡀⠀⢀⠀⠠⠤⠔⠒⠂⠑⠀⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡑⢤⡀⠀⠈⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠌⡀⠀⠑⠠⡀⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡂⠁⠀⠀⡀⠊⠑⠠⢀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠁⠂⠬⠶⠀⣠⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⣧⣀⠠⠄⠰⣖⢆⢀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠦⢄⣸⣿⣷⢤⣀⣀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠈⠳⣄⠀⠈⠉⠁⠀⠨⣝⣓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠒⠛⠉⠉⠉⠈⠉⠉⢙
⠀⠀⠀⠀⠀⣀⠤⠒⠻⣝⡻⣶⣦⣄⣤⣴⣾⠇⠀⠀⡀⠀⠀⠀⠉⠻⢶⣮⣍⣒⠢⠤⣀⡀⢀⣀⣠⡤⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⣠⠚⠭⠈⠛⣦⣠⣾⠟
⠀⠀⠀⠀⠀⠧⠤⠴⠶⠞⠛⠛⠉⠉⠁⠘⣧⡀⠀⠸⣙⠷⣤⣀⠀⠀⠀⠈⠙⠻⣿⣷⣦⣍⣙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣥⡎⢀⣠⣿⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠳⣎⠙⠷⢦⣀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣮⣍⡓⠦⣄⠀⠀⠀⠀⠀⣇⣽⣶⣿⡿⠉⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠷⣦⣌⠙⢧⣸⠉⢳⢦⣀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠓⠈⠙⢦⣄⣠⣶⣿⡿⢏⠀⠀⢸⣫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠉⠻⢦⣌⠳⢾⡀⢹⠓⢦⣀⠀⠀⠀⢀⣠⡤⣤⣀⡀⢰⠋⠹⡿⠋⠉⢦⣑⠀⢩⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⢀⡤⠤⣄⡀⠀⠀⠀⠀⠉⠻⢦⣍⠺⣄⠀⠘⣧⠀⠀⡟⠀⠀⠀⠀⠹⡜⣆⣄⣹⡄⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⢀⢞⢕⢰⠂⢐⢝⢦⠀⠀⠀⠀⠀⠀⠈⣻⣾⣷⢦⣽⠀⠀⢻⣠⡄⣀⠀⠀⢹⣜⣟⣣⣧⣤⣄⡀
⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⢯⣿⡏⠀⠀⠀⢳⣈⣧⣠⣤⣶⣶⣿⣿⣿⣿⣿⣧⣀⣠⣄⡈⢿⠻⠿⣀⡴⠛⣩⢞⢕⠸⣦⡀⢙⢦⡀
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣰⣿⣥⣴⣟⣾⣿⣿⣿⠿⠿⠟⠛⠛⠉⠻⣧⡉⠙⠛⠁⠉⢻⣬⣷⡼⠋⠀⣰⢣⣳⠓⣈⣬⣏⢢⡍⢷
⠸⣿⣦⣄⣀⣀⣠⣤⣤⣶⣶⣾⣿⢿⢿⢿⡟⠛⠛⠉⣽⣯⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠳⣤⣀⠀⣀⣴⠀⠀⠀⢠⡇⣿⣿⡽⢿⣿⣿⣾⣾⢸
⠀⠈⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⢧⠳⣍⠂⢰⠐⣩⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣦⡄⠉⠛⠷⢾⣷⣄⣀⢸⡇⣿⣿⣧⣤⣼⣿⢿⡿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠈⣿⡀⠀⠀⠀⠀⠉⢿⣿⣟⢻⠟⢏⠉⠉⠀⠿⢅⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢦⠁⢸⡈⣢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠈⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠈⢑⠤⣀
⠀⠀⠀⡀⠤⠐⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⠃⠀⠀⠉⠑⠢⢄
⠠⠂⠁⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⡴⠒⠲⡄⠀⡏⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁
⠘⡄⡠⠀⠀⠀⡰⠀⠀⠀⠑⢄⢀⡠⠊⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⣧⠀⠸⣇⠀⢀⡇⠀⠳⢤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠜⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣤⠏⠀⣀⡈⠩⠭⠄⠀⠖⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀⡤⠊
⠂⠀⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠁
⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣧⠀⠀⠀⠀⠀⢀⣀⠠⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⢴⡁⠀⢸⡤⠄⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡠⠒⠁⣀⡹⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠑⠄⢀⣀⡀⠠⠐⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠶⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠁⠀⣠⠴⢊⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣾⣿⣭⣤⣤⣤⣤⣴⣋⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⠶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⣡⠔⠋⠀⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣶⣦⣤⣾⠟⠁⣠⠎⠀⠀⠀⣼⡟
⠀⠀⠀⢠⣾⣟⠁⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣶⣧⣦⣤⣤⣴⣿⡁
⠀⠀⢀⣿⠋⠙⣿⠲⢦⣤⣤⣍⣻⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣿⡇
⠀⠀⠀⢿⣆⠀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣈⣿⣿⣀⣘⣿⣏⣀⡻⠿⠁⠀⠻⠿⠁⠹⣿⣏⣉⣿⣏⣉⣉⣿⡿⢿⡿⠿⠿⠾⣷⣿⡇
⠀⠀⠀⠈⠻⣿⣇⡀⠉⠉⠉⠉⠉⠉⠉⠓⠒⣾⡿⠛⠛⠛⠛⠋⠉⠉⠛⠛⢿⡛⠿⠿⣿⣭⡉⣉⣉⣉⣩⣭⣭⣭⣭⣿⣿⣿⣶⣬⣓⠦⣀⣀⣙⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣤⣤⣀⣀⣀⣀⣙⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠙⠿⣿⣟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠋⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣬⣽⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠙⠻⠿⣶⣦⣤⣀⣀⡀⠀⠀⠀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⠁
⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠉⠉⢙⠉⠙⡛⠛⠻⠿⠿⠿⢿⣿⣿⠛⠻⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠠⠿⣦⣴⣉⡻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠰⠿⠷⠌⣽⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⡀⠤⠴⠒⠚⠙⡆⠘⠛⠶⠶⢤⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡴⠞⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⢦⠀⠄⢠⣤⣤⣤⢤⡤⠾⠟⢱⣟⡷⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠐⠦⢈⡀⠕⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣦⣴⠇⠀⠀⠀⠀⠀⢂⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⣴⣧⡤⠖⣛⢑⡀⠀⠈⠉⠉⠛⠛⠛⠚⠒⠛⠋
⠀⠠⠄⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠨⠉⠀⢿⣛⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡂⠄⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⠤⢀⣀⣠⣤⢤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣍⡛⠛⠻⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣠⡤⠈⠙⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⠄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠘⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⢻⣆⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠈⠉⠁⠀⣀⣤⣬⣉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠁⠀⢀⠀⢀⡀⠀⢠⠄⢈⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⢀⡀⢐⡖⣀⣴⣳⡅⢋⣱⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢤⣤⣄⣲⣤⣤⠛⠉⠀⡠⣀⣄⣽⣿⣿⣿⣾⡯⣾⣶⣿⣿⣷⠁⠹⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⣿⣿⣿⡿⣿⣿⣿⣭⣿⣿⣿⣄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣽⣿⣿⣷⣟⡿⣟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣯⣿⣻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣾⣻⣿⣿⣞⣛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⣿⣿⣿⣿⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣿⣿⣿⣿⣿⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣶⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣽⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢞⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢈⠃⠀⠀⠀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⡆⠀⠀⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⡄⠀⠀⢨⠀⠀⠀⠑⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠘⢆⠀⠈⠂⠀⠄⠘⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠣⠘⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃⠀⠀⠀⠀⢄⠀⠱⡄⠰⡄⠈⠀⢃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠘⠃⢀⠰⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡄⠑⢄⠀⠈⠳⡀⠈⠢⣑⡀⠀⢪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢃⠀⠀⢂⠃⠀⠠⠀⠀⠀⠀⣀⡞⢰
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠈⠀⠀⠁⠀⠀⠙⠦⡀⠈⠳⠀⠀⠙⠀⠀⠠⠀⠀⠀⠀⠀⠀⠳⠰⡀⠀⢃⠀⢢⠀⠈⠡⡀⠀⣰⣿⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠑⢤⡀⠄⡀⠀⠐⠢⠀⢀⡀⠀⠐⠄⠀⠀⠀⠱⡀⢳⠀⠀⠀⠀⠀⣣⠀⠀⣂⠀⢾⢣⠀⢡⠀⢿⡿⣾⠃
⠀⠀⠀⠀⠀⠀⠰⣦⢀⣈⠠⠀⠈⠃⠀⠠⣀⠀⠀⠀⠉⠓⠢⠄⢀⠀⢠⣀⠈⢦⠀⠀⠀⠀⢢⠘⢗⣄⠈⠆⣸⠀⠀⠀⡆⠘⠁⠹⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⠙⠓⠆⠠⠄⠈⣁⡁⠀⠀⠀⠀⠀⠀⠁⣀⣯⠀⠈⠣⡀⠀⠀⠈⡗⠀⠪⡀⠐⠈⠃⠀⠀⣡⠀⠂⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠓⢀⡁⡘⠂⠡⠀⠹⣄⠀⠐⡟⠂⠀⠀⠊⠀⠀⠀⠀⢀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⡐⠲⠙⠁⠀⣤⠀⠀⡹⠄⠀⠁⢀⠻⠿⡀⠁⢀⣴⠁⠀⠀⠀⠀⠀⣸⣷⡀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠛⠉⠉⠀⠀⠈⠁⠀⢀⡀⠠⠀⠂⠀⠐⢋⣶⣀⠀⢁⠂⠀⠀⠀⠁⠀⢧⡀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠉⣠⠤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠒⠒⠂⠈⠁⠀⠀⠀⠄⠊⠀⠀⠠⢹⠃⢄⡈⡁⣄⠀⠒⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⠦⣀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣀⣠⣤⡠⠆⠀⠀⠀⢀⡠⠊⠀⡀⢸⠂⠆⠈⢠⠤⠀⢉⠄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠔⠉⡠⠀⠀⢀⠃⣠⠀⠀⠀⣁⠀⠁⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠀⠈⠀⠐⠀⠀⠀⠁⠀⡆⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠓⢂⠀⠠⠄⠀⠀⢠⠃⡈⢣⡎⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⢀⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⠀⠀⠛⠈⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣂⠠⢔⡄⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⣄⠤⠒⠀⠁⠀⠀⠀⢿⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡤⠟⠋⠴⠋⠀⠈⠀⠀⠀⠉⠉⠙⠀⠬⠛⠒⠲⣶⠒⣢⠄⠈⠁⠄⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⣀⣤⠴⠞⣋⣥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠴⠚⠚⢉⡡⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⢤⠞⣹⠇
⠀⠀⠀⠀⡝⠃⠤⠀⠴⢚⣀⠤⠒⣈⣡⠄⠀⢀⡴⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⢀⠀⠀⠈⠂⠐⠀⠡⠌⠱⠂⠀⠌⢀⣤⠆⠁⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠒⠊⠡⠁⠒
⠀⢨

⠀⠠⣄⡀
⠀⠀⠈⢯⣕⡢⢄⣀
⠀⠀⠀⠀⠉⢶⡩⠘⣙⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣔⣐⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⠤⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡄⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢴⠢⠄⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠅⠀⠀⠀⠀⠻⣦⡀⠀⢀⡴⠊⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠬⠄⠀⠀⠀⠘⠷⣤⠋⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣤⣼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠦⡤⠴⠶⠶⠾⠮⠾⠮⣮⣴⣴⣵⣵⡵⠟⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠙⢷⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⡟⠻⣧⡀⠀⠀⠀⢰⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣯⠑⢾⣄⠈⠻⣦⡀⠀⢿⠻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣄⠙⠳⣄⠈⠙⢦⣸⡄⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣈⠓⡤⠀⠙⠿⣄⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡻⠦⣄⡈⠙⢷⠀⠀⠀⠈⢳⡈⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠀⠈⠉⠚⢷⠂⠀⠀⠀⣿⢌⡢⠙⢷⡀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠛⠒⠒⠚⠳⡆⠀⠀⠹⣮⣕⡀⠀⠹⡄⠀⠀⣀⡼⠋⠀⣠⣦⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⠋⠉⠉⢉⡹⣅⡀⠀⠙⢿⣄⠀⠀⠙⠏⠉⠁⠀⠀⠀⠙⠛⠀⢀⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣍⣉⣀⠤⠚⢢⠤⢀⠀⠉⠳⠶⠄⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⣤⠔⠊⢁⡤⢚⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣞⣁⡠⠯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣭⠎⠀⡴⢩⡟⣠⣶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠛⢉⣠⣴⠟⠁⡰⠃⡻⢛⠟⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡿⡻⠟⠁⣠⠎⢀⠜⢠⠎⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠟⣫⠊⠀⢀⡜⠁⣠⠊⢠⠏⣰⠋
⠀⠀⠀⠀⠀⠀⠠⣞⣋⣠⣴⣇⣠⡴⢿⣀⡴⠁⣠⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⣿⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⢠⣶⣆
⠀⠀⠀⠀⠀⠀⣾⠀⢿⡀⠀⠀⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠈⢷⡀⠀⣇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿
⠀⠀⠀⠀⠀⣠⡈⢷⠀⠈⢻⣄⢻⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⠃⢠⡟⣀
⠀⠀⠀⠀⠀⣿⠙⣾⣧⡀⠀⠙⢿⣷⡀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⡾⠁⢀⣾⡾⢻
⠀⠀⠀⠀⠀⢻⡆⠀⠙⢿⣄⠀⠀⠙⢷⡄⠀⣸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣼⠏⠀⢀⡾⠋⢀⡿
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠈⠻⢦⣀⠀⠉⠳⣿⣆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⡴⢿⠁⢀⡴⠋⠀⢀⡾⠃
⠀⠀⠀⠀⠀⢸⡷⠾⣿⣦⣀⠀⠀⠉⠓⠦⣄⣿⡈⠳⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠔⠉⣰⣯⠔⠁⠀⢀⣴⡿⣶
⠀⠀⠀⠀⠀⠈⢻⣄⠀⠉⠙⠓⠶⢤⣄⣀⡀⣾⠻⢆⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⡀⠐⠈⣼⣃⣠⠴⠚⠋⠁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠈⠉⠙⢧⡀⠙⠲⠄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡧⠶⠶⠶⣤⣤⡞⠉⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠛⠛⠓⠒⠒⠒⠒⠒⠛⠳⢦⣤⣀⡀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⣤⣀⣀⠈⠻⣶⠚⠛⠛⣻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣠⣤⡤⠤⢠⣼⢧⣤⠀⠀⠀⣿⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠀⠈⠑⡄⠘⣧⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⡤⠤⠤⠤⠤⠤⠺⣧⣀⣀⣀⠀⠀⠘⢷⣄⣀⣠⡟⠀⠀⠀⠀⠒⠾⣿⣿⠀⠀⢸⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⠤⠄⢾⡉⠀⠀⠀⠀⠀⠙⢿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠉⠁⠀⠀⢀⣨⠷⣄⣀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢶⡖⠋⠁⠀⣀⠌⠋⢙⠛⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣖⠋⢁⣠⠖⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⡋⠀⠀⠀⠀⠀⢻⡖⠀⠀⣀⣤⣞⣀⣤⣤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣏⡡⠀⠀⢀⡔⠀⠀⠀⠀⣾⢷⠾⡏⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⡿⠛⡁⠄⢀⡴⠃⢀⠌⠀⡌⢰⣿⢸⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⠟⠉⠄⠀⢀⡴⠋⠀⡰⠃⢀⠞⢠⡏⣿⠘⡇⢿⡀⣧
⠀⠀⠀⠀⠀⠀⢀⣴⣞⡁⢀⣀⣠⡶⠋⠀⣠⠞⠀⣠⠏⢀⡿⠀⠹⢦⡿⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⣼⠁⣀⣴⠃⢀⣴⡏⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⢿⠶⠟⠛⠷⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⡗⢦
⠀⠱⣄⣦⠀⢄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡀⡀⠈⡓⣄
⠀⠀⠘⢿⡷⠾⢷⡢⣳⣦⣀⣦⣤⣀⣀⣀⣀⣀⠬⠿⠍⢛⣉⣉⣉⣙⣓⠲⣄⣀⣀⣤⣤⢔⣊⣥⠎⠸⢱⡀⠀⠘⢆
⠀⠀⠀⠀⢳⡑⢄⠈⠢⢬⣉⣉⡁⢨⣍⣋⠀⣀⠠⠶⢚⣉⡤⠴⠒⢦⡤⠐⠈⠉⠀⢶⣝⡉⠉⠅⠀⢨⠘⢿⣄⠈⡈⡆
⠀⠀⠀⠀⠀⠻⣦⡀⠐⠠⠉⠻⣦⣄⣈⣱⣤⣬⣴⣤⣠⣤⣴⠾⠿⠏⠀⠀⠀⠀⠀⢠⡿⠿⠛⢁⡠⠁⠀⠄⢻⢆⣻⢷
⠀⠀⠀⠀⠀⠀⠈⠒⢅⣘⣶⢀⣒⡂⠙⠉⠁⢀⠤⠊⠵⠟⠁⣴⠿⠀⡠⢤⣤⣀⠒⠦⠄⠀⠀⠋⣰⠃⠀⠃⢀⠀⢳⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠤⢬⡭⣤⡀⢀⣠⣔⠀⣐⣝⠁⠀⠐⠀⠠⠃⠈⠹⠮⡑⠒⠋⣊⡵⢂⣠⠀⡀⢀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⠿⠭⠥⢤⢠⣄⣀⣀⣀⠀⠀⠈⡄⣸⣯⣰⡿⠿⠞⡁⣺⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢲⡂⠭⣉⣉⣷⡿⠿⢖⡂⠈⠀⡴⣛⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣭⠯⣉⡷⢘⣧⣤⣿⣿⣿⣿⠄⡜⣟⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢚⡆⡼⢷⣿⡿⠿⠋⡡⠋⠋⢺⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣏⡵⢂⠌⠠⠂⢀⠆⢸⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⡞⢰⠁⢠⠎⠀⡄⠰⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢛⢠⢿⢀⢾⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠇⠘⠇⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠈⠛⠛⠛⠷⡶⠲⢶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣀⣄⣀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢧⣄⣴⠂⠀⠀⠈⠉⠉⠉⠙⠛⣿⡀⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⠞⣰⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⣿⣟⠉⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠰⣿⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢠⣿⠏⠀⢠⣿⠃
⠀⠀⠀⠀⣤⡀⠀⠀⣿⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⣼⠇⠀⣴⣿⡇⠀⣠⣿⣧
⠀⠀⠀⠀⢻⣧⠀⠀⣿⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢹⣿⠟⣠⡾⣫⠟⢀⣼⠟⢸⡿
⠀⠀⠀⢠⣦⣽⣷⡄⠸⣇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣸⣯⡼⢋⠴⢃⡴⠟⠁⢠⡿⠁
⠀⠀⠀⠸⣯⠈⠛⠿⣷⣽⣆⠀⢷⡀⢠⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⣁⠀⢠⡿⣫⠖⣡⠶⠋⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠉⠛⠷⣦⣿⣼⣧⡀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⣿⣰⢟⡫⠴⠋⠁⢀⣤⣶⡛⠁
⠀⠀⠀⠀⠀⣨⣿⣦⣄⣀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣼⠟⢋⣁⡤⠴⠖⠛⣉⢩⣽⡟
⠀⠀⠀⠀⠀⠻⣧⡀⠉⠙⠛⠓⠶⠶⠤⢽⣷⣤⣄⡀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⣿⠭⠥⠤⠤⠤⠤⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⣀⡀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣿⣒⠒⠒⠶⣶⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⣛⡉⠉⠉⠉⠉⠩⠽⢷⣤⣤⠀⠀⠀⠻⣦⣀⣤⡾⠃⠀⠀⠀⠀⢀⣴⠿⠟⠛⠛⠿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣤⡤⠤⠶⠒⠻⣧⡀⠀⠀⠀⠀⠈⠻⣧⣤⣤⣤⣤⣤⣴⠟⠁⠀⠀⣀⡀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⠴⠖⢚⣉⠿⢦⣤⣀⣀⡀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⢒⣊⣡⠤⠒⣉⡤⠛⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠶⠚⢉⣡⠴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣯⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠋⣠⠖⢁⡤⠀⡀⠠⣿⡆⠀⣴⣟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠋⢀⡴⠊⠀⡠⠊⢀⡞⠁⣰⠏⠹⣦⠹⣟⣷⣶⠶⠄
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⠞⠉⠀⡠⠊⠀⣠⠋⠀⣴⠏⠀⠀⢸⡷⢿⣏⠛⠃
⠀⠀⠀⠀⠀⣩⣽⣿⣿⣿⣿⣁⣀⡴⠋⠀⢀⡜⠁⢀⣼⠏⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠙⢋⣽⣿⣿⡿⣿⣏⢀⣠⣴⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⢴⣿⡿⠟⣿⣿⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⢦
⠀⠀⠀⠀⢀⣴⢲⡴⠲⡀
⠀⠀⠀⠠⢧⡴⠋⢀⢆⠡
⡀⢿⠀⢸⢄⠉⢻⣙⠂⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠂
⢇⠈⢆⠈⠶⠑⠚⠤⡾⠁⡸⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣯⣭⣭⣶⣷⣶
⠈⢦⡀⠑⠆⠀⠀⠀⠙⠶⠳⢄⠑⢄⠀⠀⠀⠀⠀⣠⣼⣏⠉⡹⢮⡉⠉⠻⣅⡀
⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠑⢌⠳⢄⠀⣶⠎⠀⠥⠾⠀⠔⠛⢠⡄⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⡏⠀⠀⠐⠮⠤⠀⢀⠞⣷⡀⠀⡷⠈⠀⢱⠂⠀⡀⠀⠀⢀⠀⠀⠀⢀⠰⠋⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠤⢶⢋⣸⠏⡇⢠⣧⡂⠀⠘⠶⠒⠉⠑⠲⢤⣀⠈⠁⠀⠀⢀⡰⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⢯⣡⡴⣡⠟⠱⡎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠉⠀⣠⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡴⠚⠁⠑⠀⡇⠈⠻⣅⣂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢘⠃⠑⠢⣌⠀⢷⠀⠀⠙⢆⠉⠚⢕⡢⡶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣄⡙⠹⡀⠀⠀⠈⢳⡀⠀⠈⣇⣘⢉⡉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⣹⢄⠀⠀⠉⢧⣱⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡞⠃⠀⣕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠉⠩⠴⠈⠀⠉⠀⠀⠪⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⠬⣽⡀⢴⠈⠓⢅⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢱⠀⠈⠳⣌⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠂⠀⠢⡈⠛⢄⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠢⠀⠙⢦⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⣖⣒⣭⣭⣵⣶⣍⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⣒⣚⣯⣭⣷⣶⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠠⢄⡀⠀⠀⠀⣀⣀⡤⠤⣖⣒⣫⣭⣷⣶⣾⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⣀⣀⡤⢤⣓⣶⣯⣽⣶⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢠⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⣒⣂⣿⣽⣷⣾⡿⠿⡻⠻⡿⢿⡿⠟⠛⠋⠉⣁⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣷⡀
⠀⠀⠀⠀⣠⢤⣶⣶⣯⣿⣼⣶⣾⣿⣿⣿⡿⠿⢿⣿⠶⣦⡈⠄⣶⣶⡤⠤⣈⣉⣉⠛⠛⠻⠿⢷⣀⠀⠀⠀⠤⣀⠀⣠⠏⢀⣿⣿⣷⡀⠠⠤⢤⣤⢄
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠇⠀⠂⠀⣿⣥⣤⣸⣧⡄⣿⣿⣧⣭⣿⣶⣶⣯⣭⣭⣗⣒⣒⣠⠤⠤⣀⣀⣈⢭⣟⣺⣭⣽⣶⣾⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⣟⣻⣯⣿⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⠉⢉⡽⢫⣿⡿⠿⣿⣿⣜⢿⣋⣭⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠥⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣐⢒⣚⣫⣴⣿⣷⣾⣿⣿⣿⣿⣮⢿⡉⡛⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠸⠿⠿⠿⢿⣿⣿⢿⡿⢿⢏⡟⠛⠉⠉⠉⠀⠀⠀⣁⣤⣤⣉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠉⠐⠂⠠⠆⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠐⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⡝⡆⠀⠀⡬⡻⡄⠀⠒⣦⡤⠧⠀⣒⡂⠠⠧⣠⠖⠂⠀⡼⡣⡄⠀⠀⡞⣭⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠚⠁⠀⠀⠎⣛⠜⠀⠈⣿⠁⠀⠠⢾⠂⠀⠀⢹⡏⠀⠘⢜⡫⠆⠀⠀⠙⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠴⠂⢺⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠈⢧⠘⣿⣿⣿⣿⣦⡀⠀⠈⠀⠀⣸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠻⢽⣿⣿⠆⠀⠀⢰⣿⣿⡿⠛⠀⠀⠀⢺⣆
⠀⠀⢀⠀⢰⡇⠀⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠸⣿⠏⠀⠀⢀⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⡀
⠀⠀⣸⠀⢸⡇⠀⠀⠀⠉⠉⠉⠙⠻⢣⣶⣤⡀⠐⠛⠁⠀⠀⢀⢞⣻⣿⠁⠀⠀⠀⠀⢠⡄⢸⡇
⠀⠀⢹⡀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⠀⠀⠀⢄⡛⠿⣿⡇⠀⠀⠀⠀⠀⠀⣷⠸⠇
⠀⠀⠸⣇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠙⠶⡼⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠻⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⣀⣀⠀⣀⣤⣤⣤⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢻⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣻⡟⡉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠤⣙⠂⠱⠄
⠀⠀⠀⠀⠀⠀⠈⠹⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣢⡀⠒⢤⡀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠮⣽⡳⠮⣽⣦⣌⠳⡄⠀⢀⣠⣴⠦⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡇⠀⠀⠀⠀⡇⠀⠀⣀⠴⠋⣹⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⡇⠀⠀⠀⠀⢸⡤⠚⠁⢀⠜⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠙⠲⢤⣀⠀⠀⣇⢀⡴⢃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⠙⠲⠿⠉⠲⠮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠋⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⢄⡀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣠⠴⠊⢉⣢⠄⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⠓⠦⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⢀⡠⠞⠁⢀⡤⠖⣋⡠⡴⠚⢫⡀⠀⢀⠔⢦⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠰⣉⣀⢴⣚⠥⠒⠋⠁⠀⠘⢆⠀⠙⣄⠳⣤⠎⢀⡤⢦⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠙⠲⣄⡴⣫⠊
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠈⠳⣄⠀⠻⣤⠎⢀⡠⢤⠀⠈⠓⢤⡀⠀⢀⠴⠺⣉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⢄⢀⡨⠖⠲⢤⡀⠪⣀⡼⠀⢀⡠⡀⠉⠒⠃⠀⠀⠈⠑⢄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⠟⠊⠁⠀⠀⠀⠀⠈⠑⠦⣀⠰⣁⢀⡞⠀⠀⣀⠀⠀⠀⠀⠀⠳⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡇⠈⠉⠀⢴⠋⢀⡇⠀⠀⠀⠀⠀⠱⡄⠘⢦
⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣚⡭⠖⠧⣄⡀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⣘⠶⠋⢣⡀
⠀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⣒⠭⠕⠒⠉⠓⢤⡀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢴⠒⠉⠁⠀⠀⠀⠳⡀
⠀⠳⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠉⠳⣄⠀⠀⠘⢆⠀⠀⠀⢀⣠⡖⠳⡄
⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠈⢧⠀⠀⠀⠉⠉⠉⠉⠀⠘⢢⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⢣⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣉⠻⡷⢄⡀⠀⠀⡸⠁⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠋⢠⠇⠀⠈⠙⠒⠧⠤⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⢸⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣔⣂⣰⣶⠖⠀⠀⠀⠀⡀⣴⡟⣻⣿⣿⣦⠀⣾⣭⣧⠀⠀⠀⠈⠀⠁
⠀⠀⠀⢤⣴⣾⠟⡛⠩⠁⠀⠀⠀⠀⠀⠀⠀⠼⠻⣿⣿⣿⣿⡇⠀⡹⢻⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢠⠀⠀⠀⠀⡠⢬⣿⣿⢟⠗⡁⢀⡼⠋⠀⢠⣤⣶⣤⡀⠀⠀⠀⠀⡎⣾⠀⣀⢀⡆⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠋⢀⣀⣆⠀⡔⠋⢱⡀⠀⠸⣬⣷⠶⡋⠀⠀⠠⣿⣿⣿⣿⡷⠄⠀⠀⠀⡟⣿⣆⣀⣾⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠾⣵⣧⣴⡟⢳⣦⣴⣿⡿⠛⢿⣿⠀⠀⠙⢿⣿⠿⠃⠀⠀⠀⠀⡇⣿⣯⢨⣿⡇⡇
⠀⠀⠀⠀⢠⣀⣄⡀⠀⠀⠄⠰⠀⠀⠀⠀⠀⢸⣵⣸⣿⣿⡿⠖⠒⠚⢋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇⣿⣇⠀⣿⣇⡇
⠀⠀⣤⠀⠀⠉⠛⠷⣶⣄⡀⠀⠀⠀⠀⢰⠀⠀⠹⣯⣀⣿⡇⠀⢠⣴⣄⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡿⣇⢀⡿⡧⡇
⠀⠀⢀⡀⠀⣴⠂⠀⠀⠈⠙⠻⠦⣤⣤⣾⡀⣄⡀⠀⠁⠹⣿⡊⠉⣻⡟⢴⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⡧⠀⡇⢳⡇
⠀⣠⢾⡽⠛⠿⣇⠀⠀⠑⢤⣤⣤⣶⠟⠉⠙⠛⠣⠄⠀⠀⠹⣷⣂⢩⡝⢾⣾⡟⠀⠀⠀⠀⠀⠀⢀⡴⣣⣶⢣⣤⠷⣶⡝⣦
⠀⠈⣻⣇⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠗⠈⡟⠇⠀⠀⠀⠀⠀⠀⠺⢛⡟⣧⣼⣺⣆⡟⣿⠻⠃
⠀⠴⠿⠛⠳⢤⡀⢀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢰⣸⠠⣀⠀⠀⠀⠀⠀⠈⣶⡟⠹⠿⠉⢷⡎
⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣄⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠛⠶⣄⡶
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠳⠦⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠊⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠈⠙⠲⢬⣢⡀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠀⠀⠀⣰⠋⠀⠀⠋⠈⠉⠰⠂⣀⠈⠀⢰⡄
⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠠⠄⡄⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⢀⢌⠈⠀⠀⢠⠘⠁⠰⠆⠀⠀⠀⠂⣼⡟
⠀⠀⠀⠀⠀⠢⢀⣀⠀⢀⢀⣠⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣠⣴⣯⠞⢐⡂⠀⠈⢳⣄⡠⢠⢤⣏⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠷⠇⠀⠾⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠾⠛⠉⠀⣨⣴⣟⠁⠀⠀⠈⠻⠿⢿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⢀⠈⠀⠀⡀⠀⠀⠀⠀⠁⣀⣤⡴⠚⠉⠀⢀⣤⣶⠿⠛⠿⠿⠟⠺⠤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡰⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⢘⠄⠀⠀⢀⣜⠅⠄⢀⣠⣴⣿⣟⡭⠔⠒⠋⠉⠉⠉⠙⠉⠉⠀⣀⣀⣤⡤
⠀⠀⠀⠸⠀⢄⠀⡂⠀⠀⠀⡐⠀⠠⡘⠀⠀⣴⡟⢇⣠⣼⡿⠿⠛⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⣛⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠊⠀⡂⠀⠰⠈⠂⠊⠀⠀⠘⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⢖⣒⡶⠶⠖⠲⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⡁⠀⠀⠀⠯⠤⠒⠂⠁⠈⠀⠀⠀⠙⡆
⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣲⡦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⢉⡤⠀⠀⠹⠤⠄⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⣠⠴⠊⠉⢇⡀⡀⠀⢈⡭⠓⠲⠤⢀⡀⠀⠀⣴⠂⠀⠈⠳⠐⠀⣀⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⢸⠁⠀⢀⡀⢀⡬⠚⠉⠈⢧⣀⡠⠀⠀⠀⠀⠀⠈⠉⢀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢍⡉⠁⠀⡏⠀⠀⢀⡀⠀⠈⢀⡠⠄⠂⢁⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠤⢀⠀⠀⠀⠀⠉⢓⣦⣌⠉⠉⢀⣠⠔⠊⣁⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠁⠂⢀⡠⠞⠉⡔⠈⠙⠋⣉⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠐⠁⢴⡀⠀⣉⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠖⢲⡋⠀⠰⣄
⠀⠀⠀⠀⠠⣀⠀⠈⠉⠉⠉⢁⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⢈⠁⢰⠋⠀⠀⣀⣵⢮⡖⢈⢢⡀
⠀⠀⠀⠀⠀⠈⠉⠒⠲⠖⠋⠁⠈⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠙⠢⣍⡉⢸⠉⢀⡀⠁⠊⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢍⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⣛⣷
⠀⠀⠀⠀⠀⠀⢀⠀⠘⢻⣶⠞⠃⠀⠀⠢⣔⠁⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⢀⠤⢿⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠉⠙⢿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢻⠦⣀⠀⠀⠂⡆⠁⡀⠠⡁⠠⠀⠀⠀⠀⠀⠠⣾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣞⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⢠⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡃⠁⠀⠁⠁⠀⠀⠀⠀⠀⢤⠊⠀⠀⠀⠀⠀⠀⠐⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣴⣠⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠤⠀⠀⠀⠀⣀⣾⣾⣟⣹⣥⣮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠖⠀⠰⣶⣿⣿⠛⠟⣛⣟⣟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣝⣦⢷⣦⣴⣤⣶⣶⣿⡀⠀⠀⠀⠀⡉⠟⡟⣔⢕⡒⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣢⣀⠭⢉⡍⣿⢹⢻⠑⢄⡀⢀⡀⠑⠼⠮⠎⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢧⢔⣝⡜⡜⡜⡌⣀⠬⠛⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡃⡀⡔⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠱⠓⠋⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢔⣀⡀⠀⠀⠀⡀⠈⡀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠈⠀⠠⠂⠀⠀⠀⠐⡀⠄⠐⠪⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⡀⠀⠀⠀⠐⠀⠀⠀⠢⡀⠀⠀⡀⠀⢀⠀⠤⠀⢀⠀⡠⠂⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⢀⠀⠤⣀⢀⡀⠀⢀⡒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠈⠁⠐⠜⡋⠈⠀⠌⠐⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠔⠉⠀⠈⠰⡀⠀⠈⢲⠚⠒⠂⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⡀⠀⠀⠀⢀⠃⠀⠀⠀⠳⡀⠀⠀⠡⡈⠀⠐⠀⠂⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠣⡀⠁⠢⠠⠔⠁⢐⠂⢄⠀⠀⠈⢂⠀⠀⢈⡶⡀⠀⠀⠐⠀⠀⠁⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⡑⠢⡀⠀⣱⠐⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠒⠂⠤⣀⠀⠀⠈⠂⢌⠚⢄⠀⡴⠚⠅⠦⠀⠀⢀⢠⠀⠚⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠘⠀⠀⠐⠒⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠉⠐⠤⠤⠋⠑⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠠⢀⠀⠀⠀⠀⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⠁⠀⠀⠠⠠⠄⠀⠀⠁



⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣟⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⣰⡄⡌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠷⣔⡒⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢵⡍⢢⢠⠙⣆⠀⢀⠹⡄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣇⠑⠴⢚⠜⠀⠸⠈⣠⠇⢧⠀⠈⠃⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⣁⣈⢑⠂⠀⠀⠀⠀⢀⢐⣰⢸⠀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡟⢺⠖⣸⠆⡆⠀⠀⠀⠀⠈⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⢸⣹⡇⢀⡉⠁⠊⠀⠀⠀⠀⠀⢄⣈⣄⣦⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⣁⣽⣄⠀⢸⡼⡇⠗⣨⢆⠀⠀⢀⣀⣤⣶⡿⠿⠟⠋⠉⠀⢀⡴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⣿⠿⡿⡙⣆⠀⠳⣷⡌⣀⣠⠤⠒⠉⣾⠟⠋⠀⠀⠀⠀⠀⣰⡿⢇⡠⠾⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡷⢛⣉⣺⣷⣵⡟⣿⣆⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡼⢻⡤⠔⢻⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣟⣧⠻⣿⠿⣷⠈⣇⣸⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣶⣷⢋⣷⡆⢉⠾⣳⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠏⠲⣾⣇⡘⠣⣹⣿⣧⣧⠈⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣸⣹⡺⢿⡣⠖⢻⡄⠚⡽⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣴⣿⣿⠛⠀⠀⢻⣿⢹⣾⠀⠀⠀⠀⠈⠀⠀⠀⢴⠀⠀⠀⠟⠟⣒⢼⣸⡵⠂⣉⣷⠊⡀⢻
⠀⠀⢀⣤⣶⣶⠶⢶⡮⣽⣧⣀⢁⡀⠀⠙⠂⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡏⠸⢪⣿⡞⣋⣀⣼⠏⠠⠊⠉⣷⡀
⠀⢠⣯⡽⠁⠛⠗⣸⣿⠴⠿⣽⣻⣾⡳⣄⠻⣾⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⢣⠀⠊⠿⢿⣉⣀⠴⢚⠷⡆⠀⢀⣽⡂
⠀⢸⣒⣧⠙⣹⠒⠳⢶⣄⣀⣪⣽⣿⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠈⠀⠀⠀⢿⣹⣤⡤⠀⠚⢻⣋⡉⢀⣹⡆
⠀⠈⠳⣞⣶⣁⣾⣳⣾⠤⠟⠛⠛⠉⣩⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣦⣀⣀⠛⣿⢻⡆⠀⠐⢿⠆⢀⣤⣤⠟⠲⠶⠦
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣯⠉⠉⠛⠛⠿⣍⣉⡻⢓⡤⠷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠉⠙⠒⠛⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠒⠒⠲⢦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣀⣠⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⠐⠈⠁⠀⠀⠀⢄⢀⠀⡐⠀⠀⠀⢀⣿⢀⣤⠶⠛⠉⠸⡏⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢠⠞⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠘⠓⠶⡾⢛⡿⠋⠉⠉⠉⠙⠓⠠⣄⡀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣠⠞⠳⡇
⠀⠀⠀⠀⠀⠀⢻⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⢷⡀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⡄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠄⣣⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⣇⠀⠘⢧⡀
⠀⠠⠄⠱⡄⠀⠀⠀⠈⠢⡀⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⠀⠦⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢷⡀
⠀⢰⠖⠇⠀⠀⠀⠀⠀⠀⠀⠙⢳⡷⢦⡄⠐⠀⠈⣷⠒⠂⠐⠀⠲⠒⠒⢦⡀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠸⡇⠘⠁⠀⠀⠀⢻⣄⣀⣠⢀⡄⠀⠀⠰⠉⠂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣟⠀⢻⣾⡆⠀⠘⠀⣼⠻⡄⠀⠀⠉⠙⠲⠶⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢣⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠈⣷⠀⠃⢠⡏⠀⢹⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡀⠘⢷⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡀⢶⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷⡀⠀⣿⠀⠀⠙⣆⠀⠀⠀⠀⢠⠄⠀⠀⣀⠀⠀⠀⢀⡾⠆⠉⠀⠖⠉⢿⣄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢑⠠⡿⠂⠀⠀⠀⣸⠁⠀⠀⠘⡏⠰⡿⠀⠀⠀⠈⢷⡀⢀⠴⠐⠒⠢⠄⠀⠉⢂⢀⡞⠠⠐⠈⠀⠀⠀⠀⠻⢇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠾⠙⣧⠀⠀⠀⠀⣽⠄⠀⠀⠀⠹⣄⣧⠀⠀⠀⡠⠤⢋⠌⠁⠀⠀⠀⠀⢁⠀⣸⡋⠠⠄⠀⠀⠠⠤⢀⡀⠀⠃⠉⢰⡶⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⠇⠒⠈⠀⠀⠀⠀⠙⣆⠀⠀⠂⡴⠁⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢴⠖⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⣠⠁⡂⠀⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⠜⣿⡀⠁⠀⠃⠘⠀⣴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⠀⡀⠀⠀⠀⠀⢀⡜⠃⠀⡠⣡⠊⠀⡿⣀⢀⡁⣀⣰⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢰⠆
⠀⠀⠀⢀⣠⠶⠛⠀⠐⠤⠀⡀⠢⡀⢀⡴⠋⠀⠀⢠⡜⠁⠀⢠⠃⠈⠉⠙⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⢈⠓
⠀⢰⣉⠉⢀⡀⠀⠀⠀⠀⠀⠈⣴⠟⠉⠀⠀⠀⢀⡿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡴⠊⠉⠁
⠀⠀⢉⡟⠁⠀⠀⠚⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢺
⠀⢀⡟⠀⡔⠁⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢿⡀⠀⠀⠀⠀⠀⠛⠁
⠀⢸⡅⠀⢀⠄⠀⠂⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀
⠀⠘⢧⣤⡥⢶⠱⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡀⠀⠀⠀⠀⣶⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⡀⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠰⡄⠂⠀⠁⠀⡀⠀⠘⣷⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠿⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠁⠈⠀⠀⠈⢷⡄⠀⠀⠈⠳⣄⠀⠀⢀⡀⠄⣀⡔⠉⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠘⢯⣀⠀⠀⠚⠁⠀⠐⠉⠀⠴⠈⠲⡆⠀⠀⠀⠀⠀⠀⠠⠂⡀⠀⠀⠀⡿⣧
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⠀⠀⠀⠘⢷⡀⠀⠀⠀⠙⠢⣄⠀⠈⠀⠠⠀⠀⠀⡀⠀⠉⢲⡀⠁⠀⠄⠀⠁⠈⠃⠀⠀⡜⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠳⢆⠀⠀⡀⠄⠀⠀⣀⠄⢫⡝⡟⠁⠀⠀⠀⠀⠀⣤⠜⣡⡟
⠀⠀⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠙⠦⣤⣴⠶⠾⠉⠀⠈⢰⡟⠁⠀⠀⠐⢓⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠴⠊⣠⠞⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡂⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⣏⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠊⢤⡀⢰⡇⠀⠐⠊⣁⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣄⡁⠐⠀⢀⣠⠤⠂⠁⠀⠀⠜⠒⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡀⠄⠋⢉⡿⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣄⠀⣉⣠⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡗
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⡟⣷⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣷⠄⠀⠀⢸⣿⣿⣽⣿⣷⠀⣾⣿⣿⣽⣿
⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠘⢸⡿⢻⡇⠙⠀⠀⠀⢿⣿⡿⢿⣇⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠁⣷⣿⣿⣷⣿⠈⠁
⠈⠛⠻⣿⡿⠟⠛⠀⠀⠀⠀⠀⢺⠃⠘⡟⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⣤⠀⠀⠀⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢑⣶⣾⣶⣄⠀⠀⠀⠀⠀⢾⣿⣷⠄⣀⣠⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⣿⣦⣤⣶⣶⠤
⠀⠀⠀⠻⣿⣋⣿⡿⠃⠀⠀⠀⠀⠀⠙⢡⣾⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⣿⣷⣊⣽⣷⠃
⠀⠀⠂⣸⣿⣿⣿⣿⡄⠂⠀⠀⠀⠀⠰⣝⠿⢋⣴⣿⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣻⣧⣞⣹⠿⣿⠖⠁
⠐⠃⠀⠀⠀⠛⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠈⠒⠛⠛⠐⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢐⠉⡆⠀⠀⠀⠀⠀⠀⢀⢶⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣿⣿⠀⠀⠲⢦⡄⢀⣤⣶⣤⡀
⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⣾⡆⣻⣿⠿⣃⣠⢼⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿
⠀⣾⠿⣿⠿⣷⠀⠀⠀⠀⣾⣿⣿⡞⠛⠒⠛⢽⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠼⢦
⠀⡏⠀⣿⠀⢹⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⣤⣀
⢠⣿⣿⣿⣽⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡿⢷⣦⣀
⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⣴⣶⣯⣽⣹⣽⣷⣶⣤⡀⠀⠀⠀⠀⠀⢀⠋⠂
⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⣸⣟⠛⠟⠛⠁⠀⠀⠀⠈⢹⠟⠛⠻⡟⠛⠛⢿⠉⠀⠀⠀⠀⠀⢀⠂⠘⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠹⡇⠀⠀⠰⠿⡟⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣀⢝⣀⠀⢐⠠⠀⠀⠀⠹⣛⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡞⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡰⣧⡔⠛⠁⠀⢹⡆⠀⢣⣇⠀⠀⠘⠁⠀⠘⣷⠀⠀⠀⢀⠀⠀⠀⠹⣦⣀⡠⠀⠀⠀⠀⢀⣠⡤⠴
⠀⠀⠀⠀⣠⡞⠁⢀⡇⠙⠃⠀⠤⠞⠁⠀⠀⠹⠦⣤⠀⠀⠀⠀⢸⠆⠀⠀⣾⡷⣤⣾⣆⠀⠀⠀⠹⣤⣀⡴⠁
⠀⠀⠀⣸⣟⣀⣀⣸⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠀⢰⡿⣴⠿⡁⠛⢦⣀
⠀⠀⠀⠈⠁⠈⠉⠀⠓⠒⠛⠀⠀⠀⠀⠀⠀⡀⠀⣤⠶⢦⣄⠀⠀⠀⠀⠘⡇⡏⠀⠀⣠⠞⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠹⣇⡤⠚⠃⠀⠀⢸⡇⠀⢠⡶⠴⡶⠢
⠀⠀⣀⣀⠀⠀⠀⠀⠀⡠⠂⠙⣿⠃⠀⢸⠁⠀⠀⠸⡄⠀⠀⠀⠀⠙⡷⠀⠀⠉⠙⠀⠉⠀⠤⠟⠀⢠⡟
⠀⠀⢻⣇⠀⠀⠑⢤⡜⠀⠀⠀⡿⠀⠀⡞⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢰⡤⣀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⢀
⠀⠀⠀⠻⣦⠤⠀⠈⣧⠀⠈⠉⢳⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠵⢓⡄⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⣸
⠀⠀⠀⠐⡇⠀⠀⢀⠀⢠⡀⠀⡼⠁⠀⠀⠀⣀⠀⢀⣤⠀⠀⠀⠀⢀⣾⠃⠠⣿⣿⣀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠞⠉
⠀⠀⠀⠀⠘⢳⠤⠞⠀⠀⠙⠋⠡⠄⠀⠀⣸⠃⠀⠞⠁⠀⠀⠀⠀⢸⣧⢠⠄⣸⣿⣿⣶⡦⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠⣞⡻⠃⠀⠀⠲⠀⠤⠀⠀⠀⠀⠙⠁⠀⠡⠆⠈⠋⠱⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠀⠰⠶⠶⢶⠞⠻⠿⠿⠇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣄⣀⡀⠀⠹⣆⠀⠄⠀⠀⢀⣠⡄⠀⠀⠀⠈⠁⠘⣆⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⣾⣳⣿⣳
⠀⠀⠀⠀⠀⣰⠿⡾⣭⣹⣧⠀⠀⠈⠉⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⣴⠃⠙⠃⠛
⠀⠀⠀⠀⠀⣟⣛⠛⠖⠈⣿⣦⡄⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠙⢦⡀⠀⠀⣽⠦⡠⠀⠀⣠⣶⣺⠃
⠀⠀⠀⠀⠀⢻⣿⣿⡦⠀⠘⢻⣿⡂⠀⠀⠀⠀⠈⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢴⣿⠏⠁⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⢨⣿⣿⡇⠠⣤⠠⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⡆⠀⠀⠀⠀⠀⣀⡼⣯⣄⠀⠀⠀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⢂⣩⣭⣭⣭⣭⣭⣭⣥⣐⣒⣒⣀⠤⠤⠤⠄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣞⠁⠐⠚⠉⠒⢋⠕⠋⠝⢛⡉⢛⡭⢟⠿⣻⢿⣿⢿⡿⢷⣶⣶⣶⣶⣬⣭⣥⣤⣒⣒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⢺⣰⠤⠤⢼⡇⣤⠤⠤⠄⠠⣄⣈⢁⣈⣆⠉⠀⢽⡿⠛⠛⠙⢛⡟⡍⠉⠀⡀
⠀⠀⠀⠀⢀⣤⣶⣦⠀⠀⠀⠀⠀⠘⡏⡄⠀⠀⣿⢰⣀⠤⣴⣲⣾⣾⢦⠞⠁⠪⢁⠃⠀⠀⠀⡄⢸⠛⣛⡖⡩⠃
⠀⠀⠀⠀⡇⠸⣿⣷⣕⣄⠀⠀⠀⠀⣿⠱⢔⡒⢹⡆⠊⠉⠀⠙⠛⠋⠁⠀⠀⠀⣸⡀⣀⣤⣴⣧⠸⢒⣶⡮⠃
⠀⠀⠀⠀⠇⠀⢹⣿⣿⣮⣢⠤⠒⠉⠸⡇⠀⠀⠀⣧⢃⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⠟⣡⡖⠳⡜⡆
⠀⠀⣀⡀⠼⠀⢈⣛⡋⠉⠀⠀⠀⢀⣀⠷⠷⠒⠒⠿⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠛⢓⣠⠴⠃
⠀⠸⠥⠤⠭⣉⢉⣉⣥⣤⣤⣶⠚⠉⠒⠚⠛⠟⠻⠟⠿⠛⠷⠶⠶⢿⣦⣍⣱⡖⡠⠤⣶⡞⡏⠉
⠀⠀⠀⠀⠀⠀⢉⣽⢟⠖⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⠉⠀⠀⣠⣛⡃⢇⠀⠹⣷⢻⢔⣆
⠀⠀⠀⠀⠀⠀⠻⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠛⣾⣖⣶⣿⠏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣈⣠⣿⠃⠀⠈⠳⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠄⡠⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠉⢀⣄⡴⠀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⠀⠌⠀⠀⠀⢠⡄⠀⠀⠓⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠂⠔⠀⢄⡂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠈⠓⠀⢀⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠉⠢⢄⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠐⠆⠀⠀⠀⠀⠑⢄⠀⠰⡄⠒⠀⠏⢂⢸⡤⢢⡀⠀⠀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠑⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠑⠦⠀⣴⢊⠔⢁⡼⡤⠊⢀⠤⢀⠈⠁⠒⢠⣤⡄⠀⠰⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣈⡁⢡⢁⡎⢠⢋⠜⠀⠀⡇⠀⢈⠀⠀⡰⢿⠞⠉⠐⠤⡇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠰⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠠⢧⠂⢀⢀⡀⠈⠀⠈⢀⡞⡷⠃⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠐⠂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⢣⠎⡜⡱⠀⢠⠛⠟⠀⠀⢀⣀⣀⣀⣀⡀⠀⠉⠢⡀⠀⠃⠀⠀⠄⠘⠤⠀⠀⠁⢀⠤⠠⠠⠄
⠀⠀⠀⠇⠆⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠂⢀⢡⠇⡞⡐⠀⢠⠿⠏⠀⣠⣾⠟⠓⠋⠙⠚⠿⣳⣄⠀⠈⠢⡄⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁⠁⠐⠄
⠀⠀⠀⠀⠀⡀⠤⠤⠴⠀⠤⡁⠴⢲⠤⣀⡘⠀⢈⡜⢸⢡⠁⢀⢿⡟⠀⣮⠟⠠⠂⠁⠀⠀⠀⠀⠈⢻⣥⠀⠀⠈⢆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠂
⠀⠀⢖⠈⠁⠀⠀⡄⠒⠒⠓⠈⠇⡏⢰⠃⠁⠀⠀⠀⠉⠂⠀⣼⣶⠀⢨⡟⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⣟⡆⠀⠀⠀⠱⡀
⠀⠀⠀⠁⠢⢄⣀⡀⠁⣐⣂⠴⠀⡇⢸⠰⠀⠀⢀⠀⠀⠀⢀⣧⡄⠀⠘⣣⠀⢄⠀⠰⠆⠀⠒⠀⠀⠀⠿⠇⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠠⠔⠇⠧⠘⠺⠀⠰⠁⠈⠂⠀⢸⣭⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⠐⠀⢈⢼⠟⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⠐⠁⠀⢸⣹⠀⠀⠀⠀⠙⠛⣶⣤⡤⣤⣤⡰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⠄⡀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠦⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠐⠂⠁
⠠⠀⡌⠀⠀⢀⢀⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰⠄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠰⠀⠀⠀⡀⠉⠀⠀⠀⠈⠐⠂⠀⠠⠤⠄⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠒⠒⣶⣿⣿⣿⣿⡶⠒⠒⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠒⠒⠲⠶⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣠⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠶⠖⠒⠒⠒⠚⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠉⠉⠉⠉⠻⢿⣿⣿⡿⠋⠉⠉⠉⠉⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⡀⠀⠀⣠⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠐⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠿⠟⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⠿⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣄⣀⣠⣈⣿⣿⣿⣿⣇⣠⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛


⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⠶⡦
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣟⣿⣿⣟⣿⣿⣟⣿⣿⣏⣽⣿⣿⣭⣿⣿⣯⣽⣿⣿⣶⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠚⠋⠐⠂
⠀⠀⠀⠀⣦⣤⠶⢶⣤⣤⣄⣀
⠀⠀⠀⠀⢻⣿⣷⣦⣤⣈⣉⡛⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⣿⣿⣷⣦⣍⡛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢻⡺⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣙⣳⣤⣠⣤⣤⣤⣤⣤⣥⡄⢠⣴⣶⣶⣶⣶⣶⣶⡶⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⣤⣦⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⡿⠿⠟⠛⠿⠁
⠀⠀⠀⠀⢶⣶⣶⡝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡛⠻⣿⣿⣁⣀⣉⣀⣤⣤⡤⠤⠤
⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⠉⠻⠍⠉⠻⠏⣿⠝⠛⠛⠿⣿⣿⣿⣷⣯⣝⣾⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⠆⠀⠀⠀⠘⠛⠛⠛⠋⠁

⠀⠀⠀⢀⡀
⠀⠀⠀⣸⠷⠀⣠⡄⠀⠀⢠⣤⣤⣼⡏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⣾⣶⢀
⠀⠀⠸⣿⣆⣠⠟⠁⠀⠀⠀⠉⠙⢿⣿⡾⡇⠀⠀⠀⣠⣶⡤⠀⣐⠶⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠙⠛⠺
⠀⠀⠀⠉⠚⠙⠓⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣿⣿⡜⠋⠀⠀⠀⠀⠀⠀⠀⢸⡼⠟⡖⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⠄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⢴⣟⣻⡇⠀⠀⠄⠀⠀⡀⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⠦⠀⠀⠀⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠿⠿⠁⢨⠷⠿⠛⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠞⠀⠀⠀⠀⠀⢐⡄⢠⡅
⠀⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⠀⢀⣀⠄⣻⣿⠛⣁⠀⣀⡙⣉⡁⠀⠘⣃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⢀⠸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢻⣧⠀⠈⠀⢹⣧⠀⠀⠈⠀⠰⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡀⠀⠀⠈⠛⠀⠀⠀⠀⡀⠉⢁⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⡁
⠀⠀⠐⢦⢠⡀⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣈⠀⠀⠀⡀⢰⡇⠺⡖⡆⠀⠀⢀⡀
⠀⠀⠘⠋⠉⠃⠉⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⢸⠁⠈⠡⠛⠀⠀⠈⡁
⠀⠀⢮⡄⠀⠀⠀⠀⠀⠀⠐⢨⠀⠀⠀⠈⠉⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⠀⠀⠀⢠⣦
⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⣀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠘⢷⡂⠀⠀⠀⢸⣤⠀⠀⠀⠀⣴⠟⠀⠀⠀⡄⡠⢿⣿⡇⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣏⢠⡀⠀⢀⣴⠇⠀⠀⠀⠀⢼⠀⠠⠁⠀⠀⠀⠀⠀⠀⣠⡀⠘⣿⡀⡀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣴⡿⠸⢿⣦⡾⡅⠀⠀⠀⠀⠀⢸⡆⠐⠒⢲⢀⠀⠀⢠⣤⣼⣿⡟⠋⠰⢱⣤⣤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣁⠀⣠⣿⣿⠄⠀⠀⠀⠀⠀⢘⣇⣊⠀⢸⠹⠀⠀⠈⠉⠉⣹⣷⣻⣿⣏⠉⠉⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣙⠻⠿⠛⠋⠙⠀⠀⠀⠀⠀⠀⠈⠛⣀⡄⠁⠀⠀⠀⠀⠀⢾⠟⠁⢸⣿⠻⠃⠀⠀⠀⢰⡄⣿
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠈⠁⠉⠁
⣶⣶⠶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣽⣯⠉⣹⣿⣟⡀⠀⠀⠀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⢋⣽⣿⣿⣧⡈⢣⣶⣤⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣴⣾⣿⣿⣿⣿⣧⡾⠛⠿⢿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣷⣆⠀⠈⠻⣇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡃⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡇⢧⣾⢗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡿⡟⣻⠱⠀⠀⠀⠙⢚⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢾⣿⡿⠙⢿⣿⣿⣏⣉⢛⣀⣉⣍⣿⣙⣟⢲⣾⣶⣶⣤⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠽⠶⠺⣿⣿⣯⣹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⢭⣯⣿⣿⣿⣿⣟⣿⣿⣿⣏⣽⣿⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣾⣯⣿⣿⣿⣿⣿⡿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⢿⣿⣿⢿⣷⣿⣿⣿⣿⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣻⣿⣿⣿⣿⢻⣯⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣻⣿⣿⣿⣿⠇⠀⠙⢿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣿⢿⣿⣿⣀⠀⠀⠀⠙⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣶⣿⣿⣿⣯⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣼⠿⣿⢟⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠗⠋⢿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⣽⣿⣷⣷⡠
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠛⠛⢿⣿⣿⣶⣆⢀
⠀⠀⠀⠀⠀⢹⣿⣶⣤⣀⢀⡀⢀⣀⢠⣴⣶⣶⣦⣤⡶⣆⣀⠂⠀⠠⢾⣿⣿⣿⣷⣵⣄⡀
⠀⠀⠀⠀⠀⠐⠤⣽⣛⠛⠛⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣍⠉⠣⠠⠒⠁⠀⠀⠉⠉⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠟⠒⠶⠤⣤⣄⣤⣈⣉⣿⣿⣿⣿⣿⣦⡁⠀⠀⠀⠀⠀⢰⣿⠁⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⢿⣿⣿⣿⣷⣔⠶⢷⣾⡿⠓⠀⠨⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡟⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣹⠿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⢧⣼⠇

⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠄⢸⠀⠆
⠀⠀⠀⢀⠀⢳⡂⠰⡀
⠀⠀⠀⡸⡱⡀⢫⠂⢁
⠀⠀⠀⣍⢷⡑⠂⠀⠀⢢
⠀⠀⠀⡜⣷⡉⠀⠀⠀⠀⠳⣄⡀
⠀⠀⠀⠱⣌⠙⠦⠀⠀⠆⠀⠀⠱⡀
⠀⠀⠀⣤⠌⢳⣄⠀⠀⠀⠀⠀⠐⠘⢄
⠀⠀⠀⠈⠳⣶⣆⠀⠀⠀⠐⠀⠀⠀⠀⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠠
⠀⠀⠀⠀⠲⢦⣦⣀⠀⠀⠀⠀⠀⠠⠐⠀⠢⣍⠲⢤⣀⠀⠀⠀⠀⠀⠀⡞⠀⠈⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠐⠮⣭⣭⣀⠀⠀⠀⠀⠁⠠⢃⢌⠙⠲⠬⣝⣒⡶⠤⢴⠊⠠⠀⠀⣀⠴⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠴⠔⠀⠀⠀⠀⠠⠂⠀⠚⠸⠕⣴⡰⠂⠃⢱⠆⠐⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠓⡚⣋⡡⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⢋⠀⠀⠀⠀⡄⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠜⣢⡀⠀⡀⢀⡀⢀⣴⠀⠄⠀⠀⠀⠀⠀⠄⣼⠶⢦⡑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⢻⣴⠟⠘⠉⠀⠀⠀⠀⠀⠀⢀⢀⡜⠉⠁⠀⡀⠁⠈⠙⠲⠤⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣊⠵⠋⠁⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⡙⠈⠙⠙⠛⢋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠉⢀⡤⠂⢀⠀⠀⢀⡤⠖⢋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠁
⠀⠀⠀⠀⡤⠐⣀⣈⣉⣤⣴⠶⠒⠈⡀⠈⠀⡴⢩⠖⠉⠁⠀⠀⠈⢫⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣄⠒⠉
⠀⠀⠀⠀⠈⢩⣋⣡⠴⣚⡥⡘⠁⠀⠈⠀⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⣠⡔⡀⠠⣄⠠⡀⡠⠀⠴⠤⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠶⠞⣡⠎⡰⠃⠀⠀⡼⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⠈⠋⠙⠢⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⣵⣯⣰⢀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠹⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠑⡀⣉⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⠊⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⡀⠀⠉⠁⠀⠀⠀⠈⠁⢀⡎⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣄⣀⠀⡼⠁⠈⢇⠀⢀⣠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⣶⣶⠤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠃⠀⠊⠎⢁⡈⡀⠰⠀⠐⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡤⠄⠠⠀⠀⢤⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⣴⡇⠀⠀⠀⠀⢸⣤⠠⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠒⠒⠒⠂⢺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡟⠀⡇⠀⠀⠀⠀⢸⠀⢻⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡽⠀⠚⡏⠀⠈⠉⠀⢹⠛⠁⢯⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⡫⠃⠄⢀⡇⠀⠀⠀⠀⢸⡀⠀⠘⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊⡠⠐⠀⠈⡏⠈⠉⠀⠁⢸⠁⠈⠂⢄⠑⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠊⡠⠊⠀⠀⠀⢀⣇⠀⡀⢀⠀⣸⡀⠀⠀⠀⠑⢄⠑⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⢠⢏⡔⣁⢀⣀⡀⣀⣀⣀⣀⡰⠃⠀⢰⡆⠀⠘⢆⣀⣀⣀⣀⣀⣀⣀⣈⢢⡹⡄
⠀⠀⠀⠀⠀⠀⠸⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⢸⡇⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠴⠀⢀⠀⢀⠀⡀⠀⠀⢸⡇⠀⠀⢈⠀⡀⠀⡀⠀⠦⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⠒⠂⠏⠹⣒⣒⣿⣟⣖⣒⡋⠸⠒⠒⠖⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠻⠿⠟⠛⠿⠿⠃⡀⠀⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠚⠓⠒⠺⠂⠀⠀⠀⠀⠀⠀⠀⡗⠒⠚⠓⠒⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠁