Selfies Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⡠⠪⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠁⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠰⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠙⠛⠛⠛⠛⠛⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠀⠘⡙⢏⣨⠀⠀⠀⠀⠀⠀⠀⠦⣤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⡀⠀⠀⠀⠀⣀⡀⠘⣿⣿⣧⠀⠀⢆⡤⠔⠀⠀⠒⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢡⣤⠀⠀⠀⠀⣤⡀⠀⠘⣿⣟⠀⠀⠘⠦⡀⠀⠀⠀⡠⠤⠄⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⣨⠛⢳⠆⠀⠣⡀⠀⠀⠙⠄⠠⠔⠁⢀⠜⡄⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢰⣭⣥⣬⣭⡇⠀⠀⠀⢀⣃⢀⡿⠀⠀⠀⠈⠂⠠⣀⠀⢤⠄⠒⢁⠀⠐⠄⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠙⠛⠛⠋⠀⠀⠀⡠⠊⠉⢛⠣⣜⠀⠀⡠⠒⠈⠙⢄⠘⡄⠆⠉⡢⢀⠀⠀⢀⠀⣾⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⡤⠀⢤⠐⠈⢀⠀⠀⣸⠀⠀⠀⢈⠦⣄⠄⠀⠀⠈⠁⠘⠐⠁⠒⠀⠀⠒⢈⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣇⣀⣾⣿⣿⣿⣏⠡⠐⠊⠀⠀⡄⡔⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠑⡕⢬⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠊⡉⣑⠀⠤⢠⢃⠌⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠦⠨⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⢤⠤⠠⠄⢠⠤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡔⠣⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠌⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠌⠀⠀⠐⢄⠀⠘⡄⠀⠀⠀⠀⠀⣴⢀⡌⠀⠀⠀⡆⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⠢⡀⠈⠢⡀⠀⠀⠀⠈⠛⠷⠀⠀⠀⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠉⠀⠀⠘⠓⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠘⠛⠃⢠⠤⠄⣴⣯⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢀⡈⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢄⠀⠀⠀⢸⠈⠁⣗⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⠀⠈⠢⠀⠀⢰⠤⠒⠌⠐⣠⠀⠀⠀⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⢁⠀⠠⣍⠺⠀⠁⠹⡄⠀⢀⣿⠋⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠡⠒⠀⠄⠀⠀⠀⠘⣆⢸⣇⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⢄⠀⠀⠀⠈⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡴⠆⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠑⢢⡀⣀⢼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡟⠚⠁⠀⠀⠀⠙⠃⢶⡛⠻⠦⠄⠀⢡⠀⠀⢾⡋⠀⠈⡿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡦⣤⣄⠀⠀⠀⠊⠀⣄⠀⠀⠀⠀⢃⠀⠀⡅⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡳⠄⠀⠠⣐⣄⣒⣀⠀⣀⣨⣶⣿⡇⠀⠀⠀⠀⣾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⠇⢠⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠋⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠃⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣣⠀⢘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠟⠛⠉⠀⠀⠘⠲⣯⣍⡻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⣛⠱⢶⣶⣶⣶⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣼⡴⢞⣡⠴⠚⠛⠻⢿⠢⡊⠁⠄
⠀⠀⠀⠀⠀⠀⢀⣠⣰⣶⣟⡗⡸⣷⣽⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⣰⡵⢿⣯⣴⣉⠀⠀⠀⠀⠀⠀⢻⣿⡄⢸⡀
⠀⠀⠀⠀⠀⢤⣰⣿⡿⣿⣧⢹⡀⢰⣿⣇⠀⠀⠀⠀⠀⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧⢠⣷⠀⠠⣮⢛⣱⣿⣿⠀⠈⠑⠀⠀⠀⡀⠀⠈⣿⡆⣾⡇
⠀⠠⠀⢀⣾⣿⣿⣉⣿⢼⣿⠽⠿⠋⠚⠻⣷⣦⡀⠀⠀⣾⢠⡴⠲⠦⠄⠀⠀⢀⣤⣤⣽⡎⣿⣇⣸⣿⣷⡿⠋⠙⠒⠲⠀⠀⠀⠀⠉⠓⢶⣿⣷⣿⣇
⠀⢺⣴⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⣸⡏⢳⣧⣴⣠⣄⠀⠀⠀⡀⠄⣀⣿⣸⣿⣼⣟⣼⠁⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣼⣿⣿⣿⣿
⣤⣿⣿⣿⣿⣿⣿⡃⠀⡠⠤⢤⣄⠀⠀⠀⠤⠔⢿⣷⣿⢠⣾⠀⠀⠉⠀⠀⠀⠀⠉⠉⠉⢿⡟⡿⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⡀⠀⠀⠀⣀⣰⣾⣿⣿⡔⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⣿⡇⣿⣿⡀⠀⠈⣑⠂⣠⠀⠀⠀⢀⣿⣟⣳⣎⢀⢹
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠛⠉⠀⠀⠀⠉⠁⠸⣿⠁⡇⢹⠀⠀⠐⠚⠁⠀⠰⠆⠀⠀⣿⡷⣿⣧⣿⣿⣿⡄⠀⠀⠀⠀⠀⣠⣴⣿⣿⣾⠾⡉⢳⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣿⣿⣦⣄⠀⠀⠀⠀⢀⣴⣾⣿⡟⢻⣿⣽⣿⣿⠀⠀⠀⠀⠚⢩⢿⣿⣿⣏⣿⣆⠑⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⣀⠀⡀⢨⡇⡇⢠⡿⢿⢿⡇⠁⠀⠀⠀⢡⣿⣿⣿⣧⣿⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠻⠟⠛⠻⢃⡞⡄⠁⠸⠃⠰⠋⠀⠀⠀⠀⠀⠈⠟⣿⡟⢼⣸⢿⣞⠁⠀⠀⠁⠀⠀⠀⠀⣹⡾⡏⣿⣿⡷⣇⣻⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠁⠀⠀⡜⢁⣀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠈⡇⠘⣷⣸⣾⢣⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣷⣿⣿⣿
⠎⣿⣿⣯⣿⣿⣿⣿⣿⡿⡇⠉⠙⠛⠒⢚⠁⠀⣾⢠⠈⠉⠉⠉⠉⠛⠉⢁⠂⠀⡀⠀⠀⣻⣦⠈⣽⣾⡎⢧⣄⠀⠀⠀⠀⠀⣼⢻⣟⣿⡿⣿⡿⣿⣿
⣧⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⢦⠀⣿⠈⠀⠀⠀⠛⠲⢤⢄⡀⠁⠀⠑⡄⠔⣫⠝⢷⣌⠻⡟⠀⣯⠙⠦⡀⠀⢀⡇⠘⣿⣿⣧⢿⣆⣿⣿
⣿⣿⣿⡏⣼⢒⣾⣿⣿⡿⠅⠀⠀⠀⠀⠀⠓⠾⣿⠀⠀⠀⠰⠶⣄⣒⠸⠦⠀⠀⠀⠘⠄⠁⠀⠀⠉⠀⢷⡘⣿⡆⠀⠈⠃⣸⠀⠀⠈⢿⣿⣧⣿⣿⣿
⣿⢃⣿⣿⣿⣼⢯⡗⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⣖⠸⠉⠒⠢⣤⡀⠀⠈⢆⢀⡀⠀⠀⠀⢨⣿⡇⠀⠀⢠⡇⠀⠀⠀⠀⠹⣹⣿⣿⣿
⠁⣼⣽⢿⣿⣧⣼⠡⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠉⡒⢤⠀⡠⣿⡆⠀⣼⣸⡇⠀⠀⠀⢸⣿⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿
⠞⣻⡿⢛⠂⠈⠧⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠳⡌⢸⣶⣿⠀⠀⣿⣿⠇⠀⡀⠀⢸⠛⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⢔⡑⠁⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠹⠿⣤⡤⠟⢹⡁⠀⠀⠀⡿⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣘⠝⡽⣿
⠚⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⣠⠞⠁⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠰⠇⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⢰⢛⠂⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⡐⠂⠄
⠀⠀⠀⠀⠀⠀⠒⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⡀⠀⠀⠄⠂⠈⡆
⠀⠀⠀⠀⠀⠈⠗⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⣊⠂⠀⢂⢈⡆⠀⠀⠔⠀⠲⢤⠀⠀⠀⢀⣁⣀⡀⠀⠘⠆⠃⠀⠀⠀⣴⡠
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠀⢀⠀⠀⠀⠀⠀⡇⡠⢤⡀⡟⠀⠀⢀⡤⠄⠂⢨⡇⠀⠀⠀⠀⠈⠁⢆⡶⠈⠀⠀⠐⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠠⢀⢠⡀⠈⢠⠁⠀⠀⣨⡀⣀⢈⡾⠀⠀⢀⡀⠆⠈⢠⠈⢰⠗⠂⠢⣀⠔⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠀⠋⠈⠀⠈⢀⠦⠐⠸⢄⠀⠈⣀⠔⠒⠠⠄⠀⠚⠄⠀⠀⠀⠀⠀⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠠⢀⠌⠉⢀⣱⠁⠞⠀⠁⠈⠀⠀⠀⠀⢀⡄⠀⠐⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⢃⡀⠀⠀⠀⡂⢠⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⢴⡃⠤⢤⠀⠀⢀⠀⠀⣅⠀⠐⠚⠁⠀⠀⢀⠀⡠⠀⠀⠈⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢬⢹⠈⡃⠁⠀⡁⢠⠬⠀⠈⠀⠀⠀⢀⠀⠠⠂⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠓⢀⡶⠀⠀⠠⠠⢰⠆⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⠒⠀⠂⠀⠀⢀⠀⠀⣀⠀⠀⠀⢤⠘⠁⠀⠀⠀⢰⠉⢴⡀⠀⠀⢀⠀⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠠⠀⠀⠀⠤⡊⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠆⠀⠀⠁⠀⠁⢀⠀⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡄⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⢠⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡌⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠤⠤⠀⠐⢠⡄⠀⢲⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⡿⠀⠀⣾⣿⣌⣬⠁⠀⠀⠀⢀⣤⣧⣸⠇⠀⠀⢠⣤⣾⣷⣶⡀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠛⠛⠀⠀⠀⠀⠈⠉⠛⠽⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠈


⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢂⠀⠀⠐⠀⢄⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠰⠀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡐⠂⠀⠀⠀⣄⠀⠀⣀⠀⠄⠀⠀⠀⠀⠉⠒⠄⢠⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣀⡂⠚⠀⠀⠑⠰⢀⡿⡀⠀⠍⡖⠀⠀⠀⠀⠀⠠⠄⢘⡁⠀⠀⠀⠀⠀⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⢧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠐⢇⠀⢀⡀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⢀⠀⢠⡤⣠⠄⠀⡐⠁⠀⠀⠀⠀⠢⡀⠑⠀⠐⢀⠔⠀⠀⠀⠀⢀⡀⠂⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⣉⣁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠠⢒⠐⢘⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⡐⠁⠀⡠⡀⠀⢀⠆⠠⠄⠀⡀⡀⠠⠀⠒⠣⠀⠀⠠⠘⠋⢱⠤⠊⠁⠢⡔⡁
⠀⠀⠀⠀⠀⠀⠰⠃⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠂⠄⠀⢱⠸⠀⠀⢠⣤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠈⢢⠊
⠀⠀⠀⠀⠀⠈⠀⢠⠀⠈⢄⠀⠀⣀⠈⠂⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⡀⢡⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠎⠀⣔⡢⠀⠀⠀⠀⠠⠀⠀⠀⡀⠃⠀⣜⠆
⠀⠀⠀⠀⢀⠓⠀⣀⠥⠐⠈⢀⠄⠐⠈⠀⠀⠈⠐⢠⡀⠆⠂⠁⡀⠀⠐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠐⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⣀⣀⠀⣀⡀⡀⠀⣀⠀⢐⡀⣀⢀⣀⣀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡠⠂⠀⠒⢄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢠⠃⠀⠀⠀⠈⢣⡀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠚⠋⠐⠀⠛⠠⠴⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠛⠛⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⡇⢀⡀⠀⣨⣷⠠⠤⣀⡀⠀⠀⠀⢿⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⡇⠀⠈⠉⢀⡇⠉⠲⢤⡈⠑⠒⠤⠄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠪⢍⡒⠢⠬⢑⣦⡀⠀⠀⠀⢳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡏⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠠⣀⣈⢉⣒⣤⡀⠀⠀⠀⠀⢸⡀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⢄⡀⠀⠀⠀⠀⠈⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⠀⠀⢠⠏⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠻⣄⠀⠀⠀⠀⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠃⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⣧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡟⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⢦⡀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢻
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢸⡇⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡇⠀⡇
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣸⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⠀⠹⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡄⠀⠱⣄⠀⠀⣀
⠀⣠⠟⠀⠀⠀⢀⡠⠚⠁⢠⡇⠀⠀⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉
⠞⠁⠀⠀⢀⠴⠋⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡀⠁⠀⠀⠀⣀⣤⢤⡀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠙⠳⠤⠶⠛⠉⠀⠀⠙⠒⠒⠒⠲⢦⡀⠀⢀⣠⡴⠶⠶⢤⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠖⠚⠋⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠛⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣬⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⣀⣀⣠⣤
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡟⠁⠈⡇
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠶⠄⠀⠙⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣧
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠈⣿⠉⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿
⠀⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿
⠀⠸⣿⣿⣿⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣿⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿
⠀⠀⢻⣿⣿⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⡿
⠀⠀⠈⣿⣿⣷⣤⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠦⣄⣀⣠⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⢀⣠⠤⠞⠋⠉⠀⡏⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋
⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢸⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋
⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉
⢰⡏⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠈⠳⢦⣤⣄⣀⣤⣤⠶⠋⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣴⠟⠁
⡜⠁⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡟⠁
⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⡞
⣇⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣼⠃
⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢦⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⢸⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⢸⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⢸⠃⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⢸⡇⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠸⡇⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢛⠀⠀⢀⡿⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠇
⣷⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣾⣷⣶
⣿⣿⣿⡇⠀⠉⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⡄⠠⠄⣨⠀⠀⠀⠀⠀⠀⡀⠐⠁⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠠⡀⠠⣀⡤⠀⠁⠀⠉⠀⠀⠀⠀⠀⡠⠺⡀⠄⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⣀⣀⣠⠀⠀⠡⡀⠂⢄⠄⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄⠌⠉⠀⠀⠇⠉⠉⠆⠐⠋⡞⢀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢢⠘⠀⠒⡠⠀⠀⠀⠀⠀⡇⢸⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠀⠐⢄⠘⠺⠀⠄⠀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠰⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⢄⠀⠀⠀⠂⠅⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠂⡀⠀⠀⠁⠀⠀⠐⠂⠀⠀⢠⠠⠤⠂⠀⠑⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡀⠁⠀⠠⣤⡄⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠑⠊⠀⠀⠀⠀⡠⠀⠀⡠⠊⠀⠀⠀⠀⣀⠀⠀⠀⢁⠠⠊⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⢀⣠⣊⣉⠀⠀⠀⠈⡀⠀⢘⠀⠀⠰⠦⣤⡤⠄⠀⣀⠀⠀⣰⣽
⠀⠀⠀⠀⠀⠀⡀⠠⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠃⠈⠀⠀⠈⠡⢤⠂⣰⣿⡀⠀⠀⠀⠀⠒⡟⣱
⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⣦⣄⠀⠀⠀⠤⣄⣀⣮⡾⠂⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣁⡵⢈⣹⣿⣿⡏⢲⠄
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢲⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣟⡁⠂⠉⠀⠀⠉⢣⣶⡀⢁
⠀⠀⠀⠀⢀⣠⣿⠿⣿⠸⡄⢹⣿⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠹⣆⢐⡄⠀⣠⠾⢫⣿⡟⠉⠒⠀⠀⠀⠀⠀⣿⡅⣾
⠀⠀⠀⣰⣾⣿⣹⡏⣿⡿⠿⠛⠾⢷⣦⡀⠀⠀⡿⣤⠦⠤⠄⠀⠀⣠⣤⣽⡞⣿⡄⣿⣿⡾⠛⠳⠦⠀⠀⠀⠈⠑⠢⣼⣷⣿⡇
⠀⣦⣾⠿⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⣼⠋⣿⣴⣀⡄⠀⠀⢀⡠⣄⣿⣿⡧⣿⣽⠃⠀⠀⠀⠀⠀⠈⠳⠦⢤⣿⣿⣿⣷
⣶⣿⣿⣿⣿⣿⠃⠠⠒⠒⠂⠀⠀⠀⠒⢹⣿⡏⢰⡇⠀⠀⠀⠀⠀⠀⠁⠀⣻⢸⣿⢺⣿⠀⠀⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠘⣿
⣿⣿⣿⣿⣿⣿⠛⠒⠿⣦⠤⠀⠀⠠⠴⢻⣿⠇⠃⡇⠀⢀⣀⠀⠀⣀⠀⠀⣿⣿⣿⣸⣿⣆⠀⠀⠀⠐⠀⠀⣠⣾⣟⣹⠧⣀⣿
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠐⢀⣷⣄⡀⠀⠀⠀⠁⢀⣰⣿⠿⣿⣿⣿⣿⠀⠀⠀⠠⠠⣾⣿⣿⢿⡄⠆⠹⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⢸⣿⡿⡏⠀⠀⠀⠀⣿⣿⣿⣦⣿⣿⣿⠟⠀⠀⠀⠀⠈⣾⣇⣿⣿⣿⣶⣍⣿
⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠻⠟⠛⠏⣼⡁⠃⠞⠀⠖⠁⠀⠀⠀⠀⠻⢿⡇⢍⣿⡶⠁⠀⠀⠀⠀⠂⠀⡻⣻⢻⣿⡿⣇⣿⣿
⣭⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⡰⢁⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠈⣇⢸⣧⣯⣣⡀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠅⠀⢺⠰⠀⠀⢀⡀⠉⠉⢀⠀⠀⠀⠀⡽⣇⠐⣿⣯⠳⣦⣀⠀⠀⠀⡎⢻⣟⣿⢻⡿⣿⣿
⣿⣿⣿⢿⡏⢿⣿⣿⡿⠀⠀⠀⠀⠸⣃⣾⠀⠀⠀⣀⡈⣙⢐⡀⠈⠀⠁⡈⠔⠈⠳⠆⢋⢠⣷⠈⠳⠄⢠⠃⠈⢿⡿⡞⣷⣿⣿
⣷⢻⣿⣼⣧⣿⣯⣟⠁⠀⠀⠀⠀⠀⠈⠙⠦⠤⠤⣬⣉⣒⠠⢥⣀⠀⠀⠁⡀⠀⠀⠀⠈⢹⣿⠁⠀⠀⡜⠀⠀⠈⢹⡿⣿⣿⣿
⠋⡾⣿⣿⣏⣹⠊⢡⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠈⠒⠤⡄⢈⣽⡦⠀⣀⢸⠀⠀⠀⢸⡟⠀⠀⢠⠁⠀⠀⠀⠀⠸⣻⣿⣿
⠞⣿⡟⡓⠈⠶⡄⠀⠃⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠠⡀⣴⣾⠃⠀⣿⣿⠀⠀⠀⢸⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢠⠁⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡍⠛⠦⠴⠋⣿⠀⠀⠀⡞⠀⠀⣰⠀⠀⠀⠀⠀⠀⣸⡙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣀⡔⠁⣀⡔⣀⢀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢻⢀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⡀⢠⣋⡁⠁⣀
⣿⣿⣿⣻⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣤⣐⠀⠐⠲⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄⠈⠙⠻⣦⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠄⠀⠙⢻⣶⡀⠈⠻⣦⡀⡀⠀⢨⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠉⠉⠁⠰⠤⣻⣷⣟⣦⡹⣿⣧⣾⡿⠃⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠛⠛⡿⠛⢿⠟⠉⠙⣿⠛⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠏⠀⠙⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⣠⣤⣴⣶⣿⣿⣿⣶⣿⣿⣶⣦⣤⣄⡀⢀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡁⡀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠐⠲⠶⢦⣤⠀⠀⠀⣤⡴⠶⠶⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⢿⣿⣿⡟⠀⠀⣸⡿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠛⢻⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⣿⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠨⠇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢈⣿⣿⣿⡿⠟⠛⠿⢿⡇⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠁⠀⣀⣴⣶⣿⣃⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠛⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠻⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⣰⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢉⡿⢻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⠃⡾⢁⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠁⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⣿⠀⠀⠀⣸⠇⣼⠃⠈⠁⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣀⣀⣀⣀⠀⠀⢠⡾⠋⢹⡿⠀⢸⣿⠀⠀⢠⡿⣼⠃⢀⣿⣇⠀⠀⣠⡾⠋⣹⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⢉⣩⣿⡿⢺⣿⡷⠶⠟⠁⣠⣼⣿⠀⢀⣾⡿⢃⡤⢾⣿⣿⠀⢰⣿⠶⠾⠋⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣹⠋⠀⠸⣿⡀⢀⣤⠞⠁⣸⡧⢀⣼⡿⠟⠉⠀⠸⣿⣇⢀⣾⣿⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⠾⠋⠀⠀⠀⠙⠿⠟⠁⠀⠀⢹⣇⣸⣿⣧⠀⠀⠀⠀⠙⠛⠋⠈⠻⠿⠛⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⡏⡄⠀⠀⠀⠀⠀⢠⠀⠤⠠⠀⢀⣠⠀⠠⠀⡄⢨⠀⠄⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⢀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠃⠺⠂⠀⠀⠀⠘⠀⠂⠲⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣭⣁⠒⠢⣤⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠹⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠟⢛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⡿⢛⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠋⣹⡿⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡞⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠙⢇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣄⣰⣿⣷⣧⣾⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣋⣭⡷⣾⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⢟⣫⣥⣤⡜⠛⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣴⠶⠶⢶⡶⡦⢀⣠⣤⣾⣿⣷⣿⣿⣏⡼⠋⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣥⣶⠶⢿⣿⣿⡿⢿⣏⠀⠀⣥⠀⠈⠉⠉⠀⠀⠀⣠⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣷⣿⣿⣟⣉⠿⠋⣿⠀⠀⠈⠡⣤⣀⣀⣤⡴⠟⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⠾⠟⠋⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⣉⡙⠟⣿⣷⠀⣿⣷⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⠉⠢⠈⠁⠀⣿⡇⠙⠳⠶⠶⠾⠛⠉⠀⠀⢀⠀⣴⣤⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢀⡤⠤⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⡾⣻⡿⠛⡏⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠉⢁⡠⠜⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⡀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⣾⣭⣭⣭⣽⣶⢶⣶⣶⣶⣶⡗⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⡌⠓⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣶⣿⣿⣿⠋⢠⡾⠁⠀⡘⢿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠉⠛⠲⠶⠶⠶⠶⠒⡖⠚⠉⠙⢂
⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⡾⠁⡀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⢠⡿⠁⠀⠁⠀⠀⠀⠙⠿⣿⣿⣿⡟⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⣰⡿⠁⠀⠀⢴⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠛⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠛⠓⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠗⠢⢀⣀⣀⣌⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣬⡀⠀⠀⠴⣟⠻⣿⡟⠿⠷⠀⠀⠀⢠⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣿⣿⣿⣷⣶⠖⢋⠉⠀⠀⠉⠀⠀⢀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⢿⣿⣿⣿⣿⣿⣷⣤⣴⣾⠈⡆⣧⠀⠀⣤⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢏⣠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠛⣿⢏⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⣿⣿⣿⣿⡉⠉⡟⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⡼⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠈⠈



⣶⣶⣶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠉⠀⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠄
⠀⠀⠀⢹⢃⠖⠸⡁⠀⠀⠀⠀⠀⠀⠀⢞⣠⠐⠂⢂⠂⡆⠀⣠⠴⡲⠒⢆⢀⠀⠀⠀⣰⠉⠈⠀⠈⢦⡀⠀⠀⠀⠀⠆⠀⠀⠀⠤⠓
⠀⠀⠀⠈⠣⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢘⡀⠀⠀⠠⢶⠇⢰⡣⢁⠀⠀⠀⠋⠂⠀⠀⠎⠁⠔⠢⠀⠀⠐⡀⠀⠀⠀⠉⠉⠀⠁⠰⡴
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠂⠀⢄⠀⠀⠀⠀⢀⠇⠀⢈⠁⠀⠉⠑⠤⠂⡆⠀⢠⣄⠀⡀⠀⡦⠃⢀⠂⠀⠀⠀⠸⠫⠭⠓⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⡠⠉⠉⠳⠤⠛⠘⠁⠺⡴⠀⠂⣠⠉⡄⠀⠀⠀⡃⡅⠀⢺⠀⠀⠀⠐⠒⠀⢀⠖⠓⢆⣠⠗⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⠁⢸⢶⠦⡀⠀⠀⠍⠑⠀⠊⡏⠉⠀⡀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡔⢁⠀⠐⡠⠁⠘⡀⠈⢄⡐⠀⠀⠠⠜⢁⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⢁⠀⠈⡇⠀⠀⠀⠀⠀⠄⠀⠀⠱⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣣⡀⢀⣀⡀⠀⠈⠀⠀⢹⠀⠐⠒⢒⠀⠀⠀⠀⠀⢃⠀⠄⠀⡄⢀⠀⢀⣡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⢄⠨⠄⣸⠄⠀⠐⠂⠁⠁⢀⡸⠃⠀⠐⢬⠀⠈⠢⠀⠀⠀⡄⠀⠈⢹⠁⠀⠀⠀⢀⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠦⣊⣁⣈⣁⣀⡁⠀⠘⢀⠄⠠⠀⢸⠀⢀⠃⠠⡏⡒⠀⠑⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠐⠄⠀⡌⠉⠉⠋⠹⣠⠆⡔⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠄⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠣⠔⠀⠀⢠⢠⠤⠀⢀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢰⠀⠁⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣶⣶⣾⣿⣷⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠋⠉⠉⠉⠻⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠀⣠⡀⠀⠀⠀⢀⣉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠙⠇⢀⣠⢀⠀⠀⠀⠀⣠⣸⠇⠀⠀⠀⠀⠀⢡⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣀⠀⠀⠁⠈⠀⠀⠀⠀⠉⢸⠀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢶⡀⠀⠀⠀⢀⣀⠀⠀⣾⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⣷⠀⠀⠀⠀⠀⢀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠟⠀⠀⠀⢤⠶⣻⡿⠹⠇⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⡤⠖⠋⢁⣤⣶⣿⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣴⣿⣿⣿⠿⠛⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⡿⠟⠋⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠔⠄⠀⠀⠀⢀⠃⠀⠀⠀⣠⣴⣾⡿⠛⠉⠀⠈⢣⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣰⢁⡜⠀⠀⠀⢠⠛⢀⣠⣶⣿⠟⠋⠁⡄⠀⠀⠀⠀⠀⠑⠂⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣷⠎⡇⠀⠀⣤⣉⣷⡿⠛⠉⠀⠀⡐⠐
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣷⠄⠙⢲⣶⠞⢋⡀⠀⠀⠀⠀⡐⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠠⢻⣦⠞⠋⠉⠀⠀⠀⠀⠀⠀⢰⠁⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣴⠞⠛⣷⡀⢰⠖⠀⣄⡇⠀⠀⢠⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠄⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⡴⠛⠁⠀⠀⣿⡇⠈⠂⠀⠺⠀⠀⠀⡾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠁⠀⠈⠉⠀⠀⠀⣠⠾⣹⠏⠙⠀⡤⠃⠀⠀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣷⣶⣶⣶⣶⣤⣄⣀⣀⣤⣴⣤⡀⠀⢸⡇⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠺⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⠀⠀⠠⠀⠀⠀⡰⢀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⠀⠀⡰⠄⠀⠀⠀⢠⡅⢺⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⡼⠓⠀⢀⠀⠠⠀⠀⣾⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⢨⣿⡇
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⡂⠂⢀⣼⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⠈⢈⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑
⠀⠀⠀⠠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⢀⠀⢠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠡⠀⡄
⠀⠀⠀⠠⠦⠀⡸⠀⠀⠀⠀⠀⠀⣈⠈⢀⠀⠀⡄⠀⠀⠁⠀⠈⠠⢼⠁⠀⠀⠀⢠⠐⠀⠀⠀⠠⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣇⠀⡀⠀⠀⡄⠀⠀⠀⠁⡁⠔⠋⠀⠰⠈⠀⠀⢠⠂⠀⣀⠠⣀⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣅⣡⠀⢚⡀⡳⢐⠂⠐⠣⠀⠞⡆⠒⠌⠊⡈⠀⠆⠀⠐⠀⠀⠈⠁⠁⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⣜⠀⠈⠀⡍⠀⠢⠀⠀⠁⠀⠁⠀⢀⠔⠋⠀⠀⠁⡁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠳⡀⠀⢠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠈⠃⠂⠀⠁⠀⠀⢀⡂⢀⢆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡀⠀⡠⠀⠀⠀⢀⢈⡍⣡⠈⠁⠀⠘⠉⠀⠰⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⣄⠁⠀⠀⠀⠀⠀⠀⠈⠠⠈⠁⠈⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⡰⢂⡈⠀⠀⠀⠀⠀⠀⢈⡐⢀⣀⣀⡀⠘⡃⠀⠀⠀⠀⠀⠀⢠⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⠀⠀⢀⣞⠀⠀⢀⠀⠀⠀⠈⡀⠀⠐⠀⠀⠀⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠆⠀⠐⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠀⠀⠀⠀⢠⣰⣶⣿⡇⠀⢀⣿⣿⣡⡅⠀⠀⠀⠀⢀⣭⣬⣷⠀⠀⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠈⠙⠛⠙⠃⠀⠀⠋⠙⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠤⢤⣤⠴⣶⡤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌⠠⢂⡈⠇⣛⢷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠼⠵⣦⣤⣭⣿⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⠊⠀⡠⠐⠋⠁⠈⠉⠢⡀⠀⠔⠈⡉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⠀⠠⢀⠀⠈⡞⠀⠀⢡⠠⢂⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠞⠀⠀⠀⠃⠀⢐⠊⠀⠀⠐⠀⢠⡇⠀⢀⢕⡨⢐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⢪⠎⠀⠀⠀⠀⠀⠀⣠⠤⠔⠡⠔⠃⣼⡄⠀⠀⢕⠨⡢⠅
⠀⠀⠀⠀⠀⡔⢒⢱⡷⡄⠀⠀⠀⠠⡀⡠⣐⠁⠂⣡⠖⡄⠘⠂⠀⠠⡱⢑⠨⠒⠀⡆
⠀⠀⠀⠀⠀⢄⠆⠈⣠⠃⠀⠀⠀⠠⠜⠀⠤⠬⣀⠟⠉⠀⠀⡆⠀⠜⡪⡐⠌⡂⠅⠰
⠀⠀⠀⠀⠀⠀⢁⠀⠸⢀⠄⠀⠐⠃⠒⠒⠳⠶⣤⠑⣄⡀⠀⡁⠀⠐⡨⣐⡕⢰⣤⡀⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠈⠠⠀⡶⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡴⠇⢀⣾⢆⣤⣾⠷⣽⣿⣶⠉⠉⢶⢤
⠀⠀⠀⠀⢠⠠⡤⢒⣡⡀⢑⠈⡀⢐⠨⡤⢀⠄⠀⡀⠀⡚⠀⠀⠀⢀⣒⣒⣊⣤⣀⣈⡉⢛⠤⠴⠂⠘⡆
⠀⠀⠀⠀⠘⡌⢇⠀⠁⠑⠓⠮⢆⣔⡡⡊⢔⠅⣂⡦⠠⣐⠊⢮⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⡔⠃
⠀⠀⠀⠀⠀⠐⡈⠓⡠⢄⡀⠀⡀⢀⠈⢉⢉⢀⢀⠀⢀⠬⠗⠶⠤⢉⣉⣈⣀⢈⣈⣈⡤⠤⠠⢖⢥⠁
⠀⠀⠀⠀⠀⠀⠡⡀⠂⠁⡊⠝⡒⠢⠄⡥⣁⠁⠁⡍⡡⣶⠛⠲⢄⠠⡂⢐⠁⠨⡪⠊⢔⠕⡑⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⢔⠈⡀⠔⠡⢂⠀⡠⡊⢠⠁⢸⠠⡀⠑⠨⡀⢐⠅⡨⢊⠔⠁⠀⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠊⠐⠁⠐⠁⠠⠢⠀⠆⠀⠘⠈⠐⠁⠈⠐⠡⠊⠀⠠⠢⢊⠈⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠄⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠂⠐⠃⢄⠉⠀⠈⠑⡌⠁⠈⠁⠀⠀⠈⣤⣄⣀⡀⠠⠁⠀⠀⠀⠀⠀⠀⡀⠐⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢠⡀⣀⡈⡕⠂⠀⠈⣽⣤⠄⣃⢀⠰⠖⣥⣤⠊⠀⠀⡀⠀⠀⠀⠀⡠⠊⠀⡀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠄⠀⠀⠀⠗⠀⡀⢀⡄⠀⢄⢹⠁⠀⡠⠼⡇⠀⠒⢒⠁⡀⠀⠀⠚⢄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠐⠂⢰⢧⡀⠀⠘⠇⠀⣀⠨⡁⢠⠈⡀⠉⠓⠒⠊⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⢠⡅⠁⢲⡎⠹⡄⠩⠋⠀⠠⠆⢄⠈⠉⠃⠈⢂⠀⠀⢂⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠸⠆⠁⠁⠈⡀⠀⠀⢀⠀⠃⠀⠀⠡⠀⠀⣀⠂⠀⠀⠀⠢⠈⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠁⡆⠀⠀⠀⢃⠀⠀⠈⡀⠰⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⣠⣞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠆⠀⡇⠀⠀⠀⣸⠀⠀⠀⠁⠀⡄⠀⠀⠘⠀⠄⠀⠀⠀⠔⠁⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⢀⠌⠀⠐⠀⠓⠒⠂⠀⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠇⠒⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢂⠀⠀⠀⠀⠒⠀⠀⡀⢠⠀⠀⠀⠀⠸⣇⠀⣈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠰⣤⠀⠀⠀⠠⡇⣼⠀⠀⠀⠀⠰⠁⠄⣀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣃⣸⠁⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⠉⠡⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣉⣀⡇⠀⠀⠈⠀⠀⢰⠐⠂⠀⠠⠠⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡇⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠸⡆⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⣆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠈⠀⠂⠀⠄⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⢘⠲⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠘⠀⠀⠀⢀⠀⠀⠀⠣⠀⠀⠀⢨⠀⠀⡀⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠀⠀⠀⣀⢀⠀⠇⢠⠀⠰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠰⠂⠀⠀⠀⠀⠹⢶⠐⠒⠈⢳⡠⣴⣧⢸⣰⣗⢽⣄⢇⡀⠀⢴⢔⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡆⠀⠀⠀⠀⠀⢰⣿⡦⣧⣄⣸⣧⣿⣿⣹⠿⠯⠟⠷⠽⠿⠥⠟⠓⠚⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠀⠀⠀⠀⠀⠈⠘⠛⠛⠛⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⡁⠀⢶⡄⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⣄⠄⠀⠀⠠⣀⣀⠀⡀⠀⠀⠀⠀⢰⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠀⠀⠀⡀⢈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠀⠀⠀⠀⠀⠄⠀⠐⣄⠰⠤⠤⠣⢼⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠐⠀⢀⠀⠀⠈⠉⠉⠀⠀⠀⢀⡅⢑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⢡⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⡴⡩⠁⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠠
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠁⠀⠀⢀⠀⠀⡠⠄⠰⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⣀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠱⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣫⠆⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠡⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⢰
⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠈⠀⠠⡀⡀⠀⣤⠀⢬⡄⠀⠀⠀⡁⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠁⢀⡀⢀⣀⡇⠐⠃⠂⠀⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠈⠀⠀⠀⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠔⠀⠄⢠⠰⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠂⠀⠀⠠⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⡁⠤⠕⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠀⠀⠀⡄⠂⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡅
⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠷⣄⠀⠀⠀⣤⣦⠀⠀⠀⠜⠉
⠀⣴⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠰⠺⠶⠆⠈⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⢰⢋⠉
⠰⠇⣠⣴⣿⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠀⠀⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠷⠀⠀⠆⢀⠞⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡰⠛⠙⠻⡄⠀⠀⠀⠈⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡿⠿
⠀⠀⠀⣠⣤⣤⣧⠀⠀⢀⡇⠀⣀⣀⠀⠃⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠈
⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠘⠉⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠖⢦⠀⠀⠂⠀⠀⢀⡘⠉⠀⠙⢷⣄⣰⠀⠀⣸⣤⠞⠛⠻
⠒⠆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠹⣧⡀⠀⢀⣿⠋⠁⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠖⢶⣦⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠁⠀⠼⠿⠶⠀⠀⠀⠀⠸⠷⠶⠄
⠀⠀⣠⣤⣄⢸⡄⠀⣰⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⣀⡤⠤⠶⠒⠒⠤⣄⠀⠀⠀⠀⠘⢠⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣼⠁⠀⠀⠀⠀⠀⢀⣀⢳⡄⢀⠔⠁⢸⣠⠷⣶⡀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠙⢦
⠀⢸⠀⠒⠒⠋⠉⠉⠁⠀⠀⡷⠃⠀⠳⣿⠇⡠⡼⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠰⣄⠘⣄⠀⠀⠀⣠⠞⠉⠒⠤⢀⠔⢠⡏
⠀⠈⣇⠀⡠⠤⠤⠔⠒⢀⡼⠁⠘⣄⢀⣟⣠⡟⠀⢀⣀⡀⠀⠀⠀⠀⠈⢹⠇⠀⡟⠶⠾⡆⢀⡴⠓⠤⣀⣀⡴⠋⣰⡟
⠀⠀⢹⣆⠀⠀⠀⠀⢠⣊⠀⠀⠀⣘⣎⠀⣸⣁⡠⢸⣀⠷⠒⠒⠂⢤⠀⡜⠁⣟⠀⠀⠀⠸⡋⠀⠀⠀⣠⠞⢁⡞⡹⠁
⠀⠀⠀⢯⡑⠦⣐⠠⣏⠀⠈⠀⠀⠀⠀⣀⣀⠀⢹⢻⠑⠒⢒⠶⠖⠋⠊⣀⣾⠼⠷⠤⠤⢤⣱⣤⡤⠞⣉⡴⠋⣰⠃
⠀⠀⠀⠘⣧⠀⠈⠑⠪⡳⣄⠀⣀⠴⠊⠁⠀⢣⢸⢸⠇⠀⢤⡞⠁⠀⠀⠀⠀⠀⠤⢖⣊⣭⠥⠶⠚⠋⠁⡀⣰⠃
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⢮⣻⠓⠲⢶⡆⠀⢸⣼⡏⠀⠀⠀⠘⡀⠀⣶⠖⠴⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏
⠀⠀⠀⠀⡰⠉⠙⠓⠲⠶⠶⡬⠿⠶⠾⡇⠀⡸⢛⠇⠀⠀⠀⠀⢡⠀⢹⣝⣋⣁⣀⣀⣠⣤⣄⣀⣀⣤⢼⠃
⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢧⢤⡃⠘⣐⠤⣀⣀⣤⡼⡶⢺⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠑⠀⢳⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢈⣸⡝⠻⠼⠗⠀⣸⡿⠶⠷⣤⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢆⣻⡆⠀⠀⠀⠈⠙⠛⠛⠛⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡐⠀⠄⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⠄⠀⠆
⠀⠠⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠄⠈⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠐⠠⠀⠀⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠁⡄⠀⠀⡀⠠
⠀⠈⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠂⠐⠢⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⡀⠁
⠀⠈⠀⠀⠀⠀⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠂⠀⢀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠐⠁⡠⢄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠅
⠠⠄⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠁⠠⠀⠄⠠⠂⠀⠀⠀⢀⠐⠂⠀⠀⡀⠀⠀⠉⠀⠂⠐⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠈⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠠⠰⠀⠁
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⢀⠲⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠄⠂⠀⠀⠀⠨⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠂⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠄⠀⠀⠠⠀⠀⠀⠏⠀⠀⠉⢩⠗⡆⠀⢀⣴⣒⣒⣦⡀⠀⠀⢶⠊
⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠄⠠⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⠤⠈⠀⡁⠀⣍⠿⠿⠿⠿⣿⠀⠀⠈⢧
⠀⠘⠀⠠⠀⠨⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠂⠂⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⡀⠀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠰⠃⡰⠀⠀⢆⠘⠆
⠀⠀⠀⠀⠀⠐⠁⢠⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠁⠀⠀⠊⢀⠰⠀⠀⡀⠰⠂⠄⢀⠀⠐⠀⠀⠠⠀⠀⠀⠐⠄
⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⠌⠀⠀⠀⢀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠤⠀⠀⢤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠀⢀⠄⠀⠀⠀⡠⠀⠀⠠
⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡡⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢀⠀⠀⠠⠄⡀⠀⠀⠀⠠
⠀⠈⠂⠀⠄⠀⠁⠈⠁⠈⠄⠀⠀⠂⠔⠂⠐⠢⠐⠀⠠⠁⠀⠀⠀⠀⠀⠀⠄⠀⠁⢀⡀⠉⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠘⠀⠐⠢⣄
⠀⠀⠀⠀⠀⠰⠀⠀⢀⠜⢢⠀⠰⢄⠀⡦⡀⠀⠘⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⡇⢠⠖⠁⠀⠀⠑⠼⣄⠉⠁⠈⢰⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡆
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⣀⠠⠄⠊⢹⠀⢰
⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠎⠀⠀⠀⠀⠀⡇⠐⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠠⠣⡀⠀⠀⠀⠀⠀⠀⠀⡐⢸⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠚⠲⠑⢄⡀⠀⠀⠀⣠⠞⢱⠚⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡀⠿⣤⣭⣭⠈⠁⢉⣭⣥⡼⢧⡀⠀⠀⠀⠀⠀⡇⠀⠀⠣⡀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⣼⠰⠎⠉⠈⢄⢑⣴⠁⡔⢉⠏⡆⢹⡄⠀⠀⠀⠀⡇⠀⠀⡀⢈⡓⠒⠒⢺⡁
⠀⠀⠀⢀⠜⠈⠀⢡⢸⠀⠈⠉⡟⠉⠀⢀⢔⠀⠘⠘⣄⠀⠀⠀⡇⡞⠉⠀⢉⢡⡀⢀⡼⢹⠈⠉⢣⡀
⠀⠀⠀⠎⠀⠀⡃⠇⢸⠀⠀⢠⣷⠀⠀⢨⢠⠃⡇⠀⠘⡆⠀⠀⡟⢁⠰⠀⠸⡀⠀⠀⠀⠆⠀⡀⡌⠱
⠀⢀⡄⠀⠀⡐⢣⠘⡀⡀⠀⣸⣿⡀⠀⢈⠚⢠⠓⡄⠀⠘⢄⡜⠀⠀⡇⠀⠀⠑⢄⡠⠎⠀⠀⢹⠀⠀⢣
⢀⠎⠀⠀⡔⠀⠐⠀⠸⡇⠀⢿⣿⡇⠀⡿⠀⠘⠀⠘⡄⠀⡜⠀⢀⡞⠰⡀⠀⠀⠀⠀⠀⠀⢠⠁⠡⠀⠀⢣
⡎⠀⠀⡜⠀⠀⠀⠁⠀⠇⠀⢸⣿⠀⠀⡇⠀⡇⠀⠀⠙⠌⠀⠀⡜⠒⠒⡇⠀⠀⠀⠀⠀⠀⠐⠒⠒⠣⠀⠀⢂
⡇⠀⢰⠀⠀⠀⠀⠆⠀⢰⠀⠈⡿⠀⢠⠀⢠⠀⠀⠀⢰⡀⠀⡜⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢡⠀⢀
⡇⠀⢨⠀⠀⠀⠀⢸⠀⢸⠀⠀⠃⠀⢸⠀⡈⠀⠀⠀⠈⡅⠀⢠⢸⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡌⠀⡜
⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⢰⠀⠘⡈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠁⡰
⡇⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠇⠀⢸⠁⠀⠀⠈⠁⠀⠀⠀⡋⠀⡎⢠⠇
⡧⠤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠀⢺
⡇⠐⣾⡀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠿⡇⠘⡄⠀⠀⡤⢤⠀⠀⠀⠁⠙⡇⢸
⠡⠴⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⠃⠀⡇⠀⠀⡂⠐⠀⠀⢰⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⣀⢸⣀⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⡅⢠⣀⣘⡀
⣀⣀⣀⣀⣀⣀⣬⣤⣤⣤⣤⣄⣘⣤⣤⣤⣤⣭⣆⣀⣀⣀⣀⣀⣀⣼⣥⣤⣤⣤⣇⣡⣤⣤⣤⣬⣥⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⠀⠀⢿⣿⣷⣤⣀⣤⣶⣾⣾⣿⣆⠉⢠⣖⣺⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠿⣿⣷⠒⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣶⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣴⣿⠟⠀⠀⠀⢰⣿⠻⣿⣿⣿⣿⣿⣷⠀⠸⣡⣤⡈⢉⡉⢻⡿⣾⣿⣿⡟⡉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⠿⠿⠿⣦⠀⠈⠁⠀⠻⣿⣿⣿⣿⣿⡆⢠⣙⢛⣁⠻⡿⢚⠃⢿⡿⢹⣏⣁⣌⠁
⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⣿⣶⣋⣤⡀⢰⣶⣾⣷⣿⣿⡿⠒⠈⠀⠀⠉⠉⠙⠈⢿⣯⣽⣶⣶⣿⣿⣿⣷⣾⣿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⡿⠉⣐⣤⣽⣿⠙⠉⣡⣤⣀⡠⠟⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⠿⠈⠙⠻⢿⣧⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣟⡙⠹⢀⣻⣿⣾⡟⠁⠀⠀⠀⠀⠀⠒⠀⠀⠦⣀⣤⣿⣶⣶⣶⣶⣦⠈⠁⠀⢳⣾⣿⠋⠙⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢜⣛⣥⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡿⢿⡿⠿⢿⢿⡿⠿⠀⠀⡄⣾⡿⠟⢤⠀⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣷⣿⠛⠁⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣐⠰⡶⢲⣶⣾⣿⣦⣿⡿⠀⠀⠉⡀⠎
⠀⠀⠀⠀⠀⠀⣿⡿⠟⢿⣿⣿⡿⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣴⣦⣄⠀⠀⠐⠂⠈⠉⠈⠟⡟⠙⠻⠟⢻⣿⡌⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⣿⠁⢀⣴⣶⣿⣿⡿⢇⡀⢸⡿⠋⠉⠙⢶⣦⣀⣠⣤⣤⣤⣸⡑⠂⠀⠲⢸⠋⠻⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠈⢀⣸⣿⣿⣿⡇⡀⠨⣍⣹⢀⡀⠀⣄⠸⣿⡟⠛⠿⣿⣿⣿⣷⣾⣽⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⣿⣿⣷⠀⠀⠠⣶⡶⣤⡴⣦⣤⣴⣿⡇⠀⠰⢿⣿⣿⡿⠉⠙⢹⡀⠀⠀⠀⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠶⠶⠶⠾⠿⠿⠟⣽⣿⣷⣤⣀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣷⠒⠒⠋⠠⣤⠄⠉⠉⢛⣿⣧⣄⣠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⠀⠀⢀⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⣆⢶⢰⣦⣤⣠⣤⣤⢠⡴⠄⣆⣤⣤⠄⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⣿⢸⣾⢹⣗⡀⣿⣏⢠⣙⡦⣿⠀⡇⢀⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⣀⣀⣀
⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠁⠀⠀⠺⣿⣿⣿⡗
⠀⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⢾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⠟⠁⠀⠀⠀⠈⠮⠁⠀⠀⣠⣿⣆
⠀⠀⢀⠄⠂⠀⠁⢠⣶⣿⣶⡄⠀⠀⠉⠀⠀⠀⢠⣶⠶⣶⡀⠀⠀⠀⠀⣿⡟⠛⠂⠀⠀⠀⢠⡶⠳⣦⠀⠀⠀⠀⣾⡏⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣻⠇⠀⣠⣴⣦⡀⠀⠘⠓⠐⠚⠃⠀⣠⣴⣤⡘⢦⣠⡄⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⢀⠉⠁⠀⠈⠉
⠀⠀⢠⣶⣶⣦⠀⠀⠈⠋⠀⠀⠀⠟⠋⠻⠇⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠇⠀⢉⣀⣀⠀⠀⠀⠑⠒⠁⠀⠀⠀⣸⡿⠛⠓⠀⢀⣀⣤⣤⡀
⠀⠀⠹⣱⣤⡟⠁⠀⣠⣶⣶⣦⠀⠘⠿⠛⢀⣴⣷⣿⣶⡀⠀⢸⣿⡄⠀⠀⣾⡿⠛⠻⣿⡄⠉⢠⡾⠿⢦⠀⢰⣿⡇⠀⠀⠀⠉⠙⣿⡟⠁
⠀⠀⣾⠃⠉⠀⠀⠀⠙⠖⠰⠎⠀⠀⢀⠀⠘⠿⠉⠉⠿⠃⠀⠘⠿⠃⠀⠀⠻⣇⠀⢀⡿⠃⠀⠈⣛⣜⣋⠀⠸⢿⠇⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠁⠀⠀⠠⢄⠀⠀⠀⢀⣀⠀⠀⠒⠚⠉⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢴⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡀⠀⠸⡄⠀⠀⠀⡄⠈⢆⠀⡊⠁⠀⠀⠀⡅⠀⠀⠀⠀⡈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠜⠀⠀⠀⠙⢦⡀⠀⢸⠀⢸⠀⠁⠀⠀⠀⠀⠑⠒⢄⠀⠀⠐⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⢀⡎⠀⠀⠀⠀⠀⠀⠙⣄⠸⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡰⠀⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⣰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡜⢸⠂⠀⠀⠀⠀⠀⠀⡴⠸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⢡⠇⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠁⡼⠰⣄⠀⠀⠀⢀⠞⠀⠀⠀⠀⢸⠀⠡⠀⢀⠀⠀⠀⡠⠏⠀⠀⠨⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⢀⡇⢸⠈⠓⠖⠊⠁⡆⠀⠀⠀⠀⡜⢠⠀⠛⡂⠉⠀⡉⣀⠀⠄⠀⠀⠀⢄⡠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⢸⠁⠆⠀⠀⠀⠉⠒⢻⢐⠀⠀⠀⠀⡨⠒⠀⢅⠒⠤⠤⠖⡲⠂⣄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⡜⠀⡌
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠸⣾⢀⠀⠀⠀⡠⠰⠏⣸⡚⠈⢀⠀⡸⠁⠀⠀⠀⠑⠒⠒⠊⠀⠘⢇⠠⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⡰⠁⢠⠃
⠀⠀⠀⠀⠀⠀⡎⠀⢀⠀⠀⠀⢻⠀⠈⠀⠀⠀⢰⣰⡟⠁⠀⠀⢲⠁⠀⠀⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⡰⠁⠀⠸
⠀⠀⠀⠀⠀⢰⠇⢀⡞⠐⠒⠠⠬⠅⠀⠀⣀⠀⢸⠏⠀⡄⠀⢀⡏⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠈⠃⠐⠁⠀⠀⡇
⠀⠀⠀⠀⠀⡸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢰⠑⡼⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠁⠀⠀⠈⠑⢄⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠃⠀⠀⡜⢦⠈⡉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠐
⠀⠀⠀⠀⡜⠀⠀⠈⠧⡀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⣠⢊⠇⠀⠀⠐⠀⠈⢧⠸⡀
⠀⠀⠀⠘⠀⠀⠀⡀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⡀⠀⠀⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠢⢠⠁⠀⢠⠎⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡄⠀⠀⡰⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠏⠀⡠⠣⣀⠀⠉⠚⠭⢑⡒⠒⠒⠒⠒⠈⢧
⠀⢠⠀⠀⡰⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢀⠎⢀⡜⠁⠀⠀⠑⠀⢀⠀⠀⠨⢆⢀⡀⠀⠀⠸⡆
⠀⡘⠀⡸⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⢀⠎⠀⡜⠀⠀⠀⠀⠀⠑⠠⠤⠤⠄⠁⠀⠀⠀⡇
⢀⡇⢀⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠃⠀⠀⠀⠀⠀⠳⣤⠖⠉⠀⠀⠀⠀⢠⡇
⡸⠀⠸⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡇⠀⠀⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄⠀⢠⠇⠀⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠃⠀⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣁⣠⠔⠁⠀⠀⠀⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢀⠃⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠣⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢣⠀⠀⠀⠀⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⣀⠠⢤⡀
⠀⠀⣀⠴⣾⣿⣤⣜⣿⣷⡀
⢀⡞⣵⣾⡿⢿⣿⣿⣿⣿⡇
⣼⣿⣿⣿⣿⣷⣽⣿⣿⣽⣧⣶⣶⣶⣿⣷⣶⣶⣤⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄
⠈⠻⢿⣿⣿⣿⣿⣿⣿⡙⣷⣿⣿⣿⣿⣿⣿⡿⡟⠿⠙⠋⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣟⡋⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣿⣀
⠀⠀⠀⢠⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣶⡅⠀⠀⢀⡤⠖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⣿⠈⢣
⠀⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠇⠀⢳
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠴⠒⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣯⣏⠞⢥⠈⠉⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠊⠉⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣈⠳⠄⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡷⠖⠻⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠈⣉⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⠃⠀⠀⠀⠀⠀⢹⡟⠓⠒⢒⣒⡫⠥⠴⠖⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⣠⣤⣶⡶⠦⠔⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣿⡟⠉⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣤⣤⠀⠀⠀⠀⢰⣿⡟⠉⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣤
⣿⡇⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⣿⣷⣶⡶⣤⣿⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⣿⣷⣶⣶⣤
⣿⣷⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠹⠀⠀⠀⠸⣿⣿⣷⠀⠀⢼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠋⠀⠀⠀⠙
⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧
⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⠠⢤⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠁⠀⠀⣿⡆⠀⠀⠀⠠
⡿⡋⠛⡻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢠⣿⠇⠀⠀⠀⠀⣾⡿⡋⠛⡻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⢠⣿⠃
⡇⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡟⡉⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣤⣤⡀⠀⠀⠀⢸⣿⡟⠉⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣤
⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣾⣿⣿⣷⣶⡶⣤⣿⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣾⣿⣿⣷⣶⡶⣤
⣿⣷⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠉⠀⠀⠠⠸⢿⣿⣷⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠘⡏⠉⠄⠀⠠⠹
⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠙⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⣿⣧
⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⠠⢤⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠁⣿⡆⠀⠀⠀⠠
⡟⡋⠛⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠄⠀⢠⣿⠃⠀⠀⠀⠠⣾⡟⠋⠙⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠄⠀⢠⣿⠃⠀⠀⠀⠠
⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠍


⣀⣤⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⢿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠛⠿⠷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠻⠿⠷⣶⣤⡀
⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⡀
⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⣼⡏⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⢹⣧
⠀⠀⠀⣿⡇⣀⣄⣄⣼⡟⣿⣄⣀⣀⣀⣀⣀⣠⣄⠀⣿⠀⠉⠀⣀⣀⣀⣀⣀⣠⣤⡾⠟⠋⠻⣧⣤⣄⢸⣿
⠀⠀⠀⣿⣇⣬⡉⠉⢉⡀⠈⠉⠉⠉⠉⣉⠉⠉⣿⣀⣿⠀⠀⣀⣿⡟⠛⣛⡛⠉⠁⠀⠀⢀⣀⠈⢹⣿⣸⣿
⠀⠀⠀⣿⡟⠉⠀⠀⠙⠃⠀⠀⠀⠀⠈⠛⠀⠀⠉⠻⣿⠀⣾⠏⠉⠀⠀⠛⠁⠀⠀⠀⠀⠈⠛⠀⠀⠉⢻⣿
⠀⠀⠀⣿⣷⣤⡄⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⣤⣼⣿⠀⣿⣦⣤⡀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣤⣾⣿
⠀⠀⠀⣿⡇⢹⣧⠀⠀⠹⢷⣤⣤⣾⠟⠀⠀⢰⣿⠀⣿⠀⣿⠀⢻⣇⠀⠀⠻⣷⣤⣤⡾⠋⠀⠀⣸⡿⢸⣿
⠀⠀⠀⣿⣷⣶⣿⣧⣀⠀⠀⠉⠉⠀⠀⢀⣴⣿⣷⣶⣿⠀⣿⣶⣾⣿⣦⣀⠀⠀⠉⠉⠀⠀⢀⣴⣿⣷⣾⣿
⠀⠀⠀⣀⣀⣀⡀⠈⠛⣿⡶⣶⣶⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡶⣶⣶⣶⣿⠛⠉
⠀⠀⣾⡟⠉⠙⢻⡿⠿⣿⡇⠀⠀⢸⣿⠿⠿⠷⣶⣄⠻⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⠀⢸⣿⠿⠿⢷⣦⣄
⠀⠀⣿⡇⠀⠀⢸⡇⠀⠹⣷⣤⣤⣾⠏⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣾⠏⠀⠀⠀⠈⢻⣧
⠀⠀⢻⣧⣤⣤⣾⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠿⠿⠿⣿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢰⡆⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢸⣿
⠀⠀⠀⢸⡇⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⢸⣷⣴⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣦⣴⣿⠀⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠺⣦⡀⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡉⠉⠓⣦⣀⠹⣦⣀⠀⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⣀⣒⣾⣿⣷⣼⣿⣶⡛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⠿⢿⠿⣿⠟⠻⣿⢿⣷⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠏⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⢀⣀⣤⣄⣠⣤⣀⡀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣷⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣶⣖⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣀⣀⡀⠀⠀⢀⣀⣀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣈⣉⣀⣀⣉⣁⡀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣸⣿⣿⣿⣿⣿⣿⠃⠀⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠍⢸⣿⣿⣿⣿⣿⣿⠀⢠⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⣿⡿⠟⠿⣿⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⣠⣴⣾⢿⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⢁⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣼⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣦⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⢿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢩⡟⡿⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡾⣰⠃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣴⠋⣀⣀⣀⠀⢀⡴⠛⣷⠀⣿⠀⠀⣸⣵⠃⣰⣆⠀⢠⡾⢛⡷
⠀⠀⠀⠀⠀⠀⠙⠛⢉⣤⣿⠟⣿⡗⠛⢁⠄⣿⠀⢰⣿⡡⠖⣿⡟⠀⣿⠓⠛⢁⠄
⠀⠀⠀⠀⠀⠀⠀⣴⣋⡼⠁⠀⠹⣧⡶⠋⠀⣿⢠⣿⡋⠀⠀⠹⢷⠞⠻⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⢇⠀⠀⠀⠀⠀⠤⢠⠀⢤⠀⠄⠀⠀⠠⢤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡘⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠈⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠀⢠⣼⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣴⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣈⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣦⣠⣶⣾⣿⣿⣿⣿⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣶⡀
⠀⠀⠀⢀⣴⡗⠀⠀⢀⡔⠀⣨⣿⣿⣿⡿⠟⠋⠉⠁⣀⠀⠶⣦⣄⠀⠀⠀⠉⠙⢿⣷⡄⠀⣠⠖⠢⣄
⣠⣤⠿⠛⠁⠘⢧⣤⠋⠀⣸⣯⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣦⣠⣄⠀⠀⠀⠉⢿⣶⣄⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢀⣀⣤⣴⠟⠂⠀⣤⡄⠛⢛⣦⣄⠉⣻⡇⠉⠟⠀⠀⠀⠀⣿⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠿⠿⣯⣤⣤⡤⠋⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⢀⡀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠘⠛⢻⡇⠈⠁⠀⣸⣿⣿⠟⠳⣶⣄⣀⠛⠛⠉⠀⠀⠀⢀⣴⠞⠀⠀⠀⠀⠀⣿⠀⠀⠀⠷⠀⠋⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢱⣦⠴⠶⠖⠛⠉⠀⠀⠀⠈⠛⠛⠲⠶⠦⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣿⠀⠉⠀⠤⠤⠄⠀⠀⠉⠉⠉⠉⠉⢻⠇
⠀⠀⠀⣀⡀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡄⠀⠀⠀⠀⣼⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢶⡆⠀⠸⡇
⠀⣠⡾⠉⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣟⠁⢹⡇⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠸⣿⡀⠀⣠⡀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⢻⣿⣿⣿⡀⢿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠉⠻⢿⣏⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠺⢿⣅⣀⣤⣀⣠⣼⠿⠿⠋⠀⣼⡇⠀⠀⣾⡏⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⢿⡆
⠀⠀⠀⠈⢿⡄⠀⢦⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣧⣤⣀⣠⣶⡟⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡴⠻⣦⣄⠀⠘⡇⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⢁⡀⣤⡿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇⠀⠀⠙⢧⡄⣸⠀⠀⣿
⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣦⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡞⠛⣿⣆⠀⠀⠈⠻⣿⣄⠀⠛
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⡀⠀⠘⢷⣆⠀⠀⠈⠛⣦⣀
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡋⠈⢷⣤⠀⠀⠙⢷⣄⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣀⠀⠈⢳⣄⠀⠀⠉⠳⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠶⠶⠶⣶⠶⠾⠿⢿⡋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠿⢧⡀⠀⠙⢷⣄⡀⠀⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⠀⠈⢿⣤⡄⢠⡶⠒⠒⠲⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣀⣸⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡸⠟⠀⠀⠀⠙⢃⡈⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠃⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠛⠈⠛⣄⠀⠀⠀⠠⡆⠈⠁⠀⠀⠀⢀⠀⠀⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⡀⠐⠆⠀⠀⠀⠀⢻⣧⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⣄⠀⠀⠘⢷⡄⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁⡸⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠙⢦⡀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠎⢀⡼⠃⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠹⢦⡀⠀⠙⢦⣼⣧⠀⠘⡇
⠀⠀⠀⠀⠀⢀⣼⠃⢠⡞⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣀⠈⠙⠊⠀⢰⡇
⠀⠀⠀⠀⠀⡞⠁⢠⡞⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⣺⡇
⠀⠀⠀⣰⠟⠀⢰⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠋
⠀⠀⣴⠋⠀⣴⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣼⠁⠀⠀⠈⠛⠃⣤⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠛⠃⠀⢤⣤⠀⠀⠀⢸⣧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠋⢿⡇⠀⠱⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⢰⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢰⣏⠉⠻⠇⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠙⢷⣤⡼⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⠴⠖⠚⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠸⠿⠁⠀⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⡀⢀⠀⣸⣧⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣶⠞⠛⠛⠛⠋⠉⡁⢹⠇⠀⠀⠘⠿⢉⠉⠁⠀⠉⠛⠛⠷⣶⣶⣤⠄⣀
⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⡶⠞⠛⠛⠛⢉⣉⣀⣀⣠⣴⣶⡶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⢶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠰⠦⣀
⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠲⠶⠶⠟⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣄⣀⣀⣀⣀⣀⣀⣈⣷⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⢑⡭⠘⣻⣿⣿⡇⢲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣶⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣚⣿⠟⡫⠖⠋⠁⠈⠉⢫⣥⡄⠐
⠀⠀⠀⠀⠀⠐⣺⣿⣿⡟⡧⠙⣻⣷⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⠀⠙⣦⠀⢢⠀⠀⣠⡾⣯⣿⡟⠓⠦⠀⠀⠀⠀⠀⢻⡇⢸⡇
⠀⠀⠀⢀⣼⣿⠟⣷⢻⣿⣻⣶⢿⢿⣦⣄⠀⠀⠀⣾⣀⣤⣀⡀⠀⠀⠀⣀⣘⣧⢿⣦⢨⣿⣮⡿⠿⢧⢤⠀⠀⠀⠀⠲⢤⣸⣿⣼⣧
⠀⣄⣴⣿⣽⣿⡿⠋⠉⠉⠀⠀⠀⠀⠘⢻⣷⡀⣸⡗⣽⣠⠄⣀⠀⠀⠈⠉⡉⢹⣾⣿⣼⡟⣽⠁⠀⠀⠀⠀⠀⠐⢦⣄⣀⣽⣿⣿⣿
⣤⣿⣿⣿⣿⣿⡏⠀⣠⠤⣄⡀⠀⠀⠠⠤⢿⣧⡟⢠⡏⠉⠉⠉⠀⠀⠈⠙⠚⢻⣟⣿⡇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡟⣿
⣿⣿⣿⣿⣿⣿⡷⣤⣤⣄⣀⡀⠀⠀⢀⣠⣾⣿⣇⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣷⡀⠀⠡⡒⠠⠀⠀⠀⣰⡿⣟⣿⡓⢸
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⠁⠀⠀⠀⠁⠸⣿⢠⠀⣇⠀⠀⠛⠀⠀⠘⠀⠀⣸⣿⣿⣯⣿⣿⡷⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⢃⠹⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡈⢸⣿⣿⡦⠄⠀⠀⠀⠴⣾⣿⣟⣹⣿⣿⣿⡇⠀⠀⠀⠉⠠⣻⡿⣿⣽⣿⣤⣰⢿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣤⣤⣤⡄⣸⠸⡇⣼⠋⣫⠇⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣻⠏⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⢻⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠩⠀⠀⢠⠗⠃⠁⠁⠀⠁⠀⠀⠀⠀⠀⠈⠙⢿⢨⣿⢻⣷⡀⠀⠀⠀⠀⠀⠀⣾⣽⣾⣿⣿⣹⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠶⠤⠤⠔⠋⣼⢛⠛⠒⠒⠒⠶⠶⠆⠀⠀⠀⠀⠸⣏⠉⣉⣙⣙⣆⠀⠈⠈⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⣼⠀⣿⠘⠀⠀⠐⠦⣄⣀⠈⠂⠈⢀⢀⠼⡯⢦⣤⢼⡧⠬⡦⠦⡄⠀⠀⡿⠹⣿⣿⣿⣿⢿⣿
⣿⣿⣿⢋⡇⣺⣿⣿⣿⠅⠀⠀⠀⠀⠓⠶⣿⠀⠀⠀⠤⢄⡠⠤⠦⠀⠀⠀⢢⠈⠀⠀⠈⠠⢧⢸⣷⠀⠈⠃⢠⠁⠀⠹⣯⣿⣽⣿⣿
⣿⢩⣿⣿⣷⠟⡗⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢶⡈⠉⠒⠢⣄⡀⠀⠲⠀⡀⠀⠀⠀⢸⣿⠀⠀⢀⡞⠀⠀⠀⠀⢏⣿⣿⣿
⢁⣾⡿⡿⠿⡴⠏⠐⢆⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⢉⢲⠀⢔⣿⠀⢰⣧⣷⠀⠀⠀⢺⡏⠀⠀⢸⠁⠀⠀⠀⠀⠈⢹⣿⣿
⢋⡽⠟⠭⠀⠚⢦⡀⠈⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠘⣦⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⣿⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠺⠂⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠉⠛⠒⠋⢸⡇⠀⠀⢀⡇⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⡏⢻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠐⠂⠀⠃⢤⠉⠀⠈⠁⡌⠁⠈⠁⠀⠀⠈⣤⠄⣀⡀⠠⠅⠀⠀⠀⠀⠀⠀⡀⠐⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢠⣀⣀⡈⡕⠂⠀⠈⣽⣤⠄⣃⢀⠰⠆⣥⣤⠈⠀⠀⡀⠀⠀⠀⠀⡠⠊⠀⡀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠄⠀⠀⠀⠗⠀⡀⣀⡄⠀⢀⢸⠁⠀⡠⠼⡇⠀⠒⢲⠁⡀⠀⠀⠚⢄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠐⠂⢰⢧⡀⠁⠘⠇⠀⣀⠨⡑⢠⠈⡡⠉⠛⠒⠋⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣠⡅⠁⢲⡎⠹⡄⠩⠋⠄⠠⠎⢄⠈⠉⠃⠈⠂⠀⠀⢂⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠸⡆⠁⠁⠈⡀⠀⠀⢀⠀⠃⠀⠀⠡⠀⠀⣀⠂⠀⠀⠀⠢⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠁⡆⠀⠀⠀⢃⠀⠀⠈⡀⠰⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣠⣖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡠⠆⠀⡇⠀⠀⠀⣸⠀⠀⠀⢁⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⠴⠁⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡀⢀⠌⠀⠐⠀⠓⠒⠂⠀⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠇⠒⠀⠁⠄⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢂⠀⠀⠀⠀⠒⠀⠀⡀⢀⠀⠀⠀⠀⠸⣇⠀⣈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠴⣤⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠸⠁⠀⣀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢂⣸⠁⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠉⠉⠡⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣉⠀⡇⠀⠀⠈⠀⠀⢰⠐⠂⠀⠠⠠⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⡇⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡆⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⣆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⢈⠰⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠁⠘⠀⠀⠀⢀⠀⠀⠀⠣⠀⠀⠀⢨⠀⠀⡀⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠀⠀⠀⣀⠀⠀⠇⢰⠀⠰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠰⠂⠀⠀⠀⠀⠹⣶⠐⠒⠈⢣⡠⣴⣧⢸⣰⣗⢽⣄⢇⡀⠀⢴⢔⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡆⠀⠀⠀⠀⠀⢰⣿⡦⣣⣄⣸⣧⣿⣿⣹⠿⠯⠟⠷⠽⠿⠥⠟⠓⠚⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠀⠀⠀⠀⠀⠈⠈⠛⠛⠛⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢻⣿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⡿⠻⢻⠏⢻⣿⠁⠀⢉⡀⠁⠈⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⢿⠀⠀⠀⠀⠐⠀⠿⡟⠀⠀⠁⠀⣠⠟⠛⢻⣿⣿⣏⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠉⠁⠀⠀⠀⠀⠹⠆⡀⢀⠔⠁⠀⠀⠀⠿⢻⣿⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣙⡁⠃⠀⠄⠀⠦⠀⡸⠋⡹⠋⠀⠀⠀⠀⠀⣠⠀⠙⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢠⡛⢤⠈⠙⢦⢄⣀⠁⢀⡠⣡⠊⠀⠀⢐⠀⢀⡤⠊⠑⠢⢄⡀⠀⠀⠈⢡⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢸⠂⠀⡸⠂⠀⠚⠦⠠⠖⠠⠞⠁⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠈⠳⣄⠁⠀⠇⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⣠⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⡇⠈⠉⠲⠀⠠⠤⠄⠠⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠉⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢡⠀⡠⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⡀⠀⠀⠀⢀⠆⠀⠀⠌⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠠⣼⠚⠀⠈⣷⣿⡄⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⢸⠁⠁⠒⠰⠇⣀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠴⠊⠀⣀⡤⠒⢶⣽⠁⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⢸⠖⢄⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⠿⠀⠀⠀⢫⡀⠀⠀⠀⠀⠘⠀⠀⢠⠈⠀⠀⠀⣸⠷⣄⠀⠀⠀⠀⢀⠃⠀⠄⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡠⠊⠀⢺⡄⢦⡘⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⠘⡄⠀⠀⠀⡌⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠿⠾⠁⡠⠶⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⡇⠀⠀⢰⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢡⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠸⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠈⠆⠀⢀⠊⠀⠀⠀⠀⠀⠀⡠⠔⠈⢇⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠀⠀⠈⣄⠆⠀⢰⠀⠀⣴⠖⠉⠀⠀⠀⠀⠑⠔⢫⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠋⠀⠀⠈⠀⡜⢀⣀⣠⣤⣶⣶⣶⣶⣶⡇⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢠⠂⠀⠀⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠃⠀⠀⠀⡠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⡿⣿⣶⠷⠤⡶⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠀⠑⠁⢀⣀⣠⣤⡆⠀⡀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣤⣤⣤⣶⣿⣿⡿⢿⣧⡊⣤⡼⠛⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⡿⢻⣿⣟⠯⠙⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⢰⡟⠁⠀⠀⢀⠖⢾⣿⣿⣿⣿⡿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⡖⠁⠀⠈

⣄⣀⣠⠀⢀⡀⠠⠀⠀⠀⠀⠀⠊⢀⣀⣀⠀⢀⠘⠋⠋⠙⠀⠀⡀⠀⠀⠁⠀⠄⢢⠈⠀⣤⡀⠈⠀⢁⡄⠠⠑⠈⠁⠀⠀⠀⡈⠀⠀⢹⠂
⠀⠀⠀⢠⠯⣀⣀⠈⡆⠀⠀⣴⠋⠉⠾⠿⣿⣧⢳⡄⠀⠀⢀⠟⠛⠓⠢⡀⠀⠀⠀⠀⡜⠒⠑⢳⡀⠀⠈⠀⠀⡀⠀⠀⠳⠂⠀⠀⠀⢁⠈⠀⣀⠵⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠇⠀⢀⠃⢠⠀⠃⠀⠉⠐⢈⡄⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢰⠇⠀⠰⠀⠀⣷⠚⠂⠒⢺⣌⣉⣉⣙⡎⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢰⠀⠀⢠⠀⠃⡀⠀⠐⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠰⠰⠂⠀⠙⢄⠰⠂⠈⠦⠤⠤⠤⠥⡀⠒
⠀⠄⠀⠀⢐⣦⣤⡆⠀⠀⠰⡀⠀⡰⠀⠀⢹⡀⠀⢨⠄⠀⠀⢈⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⡌⠂⠀⠀⠀⠀⠀⢠⡀⣼⡋⠂⠀⠀⠀⠒⠓⠡⠐⠀⠀⠈⠉⠈⠁⠀⣠⣄⢀⡉⠀⠀⡀⠀⠁⣴⠶⠦⡀⠀⢟⠢⡶⠓⡦⣤⠔⠠
⠀⠀⢃⠀⣀⠀⠀⠀⢀⠂⠁⠈⠊⡇⠀⠀⠀⣀⠑⠐⠂⠀⠀⠀⠀⠀⠀⠠⠀⠁⠐⠋⠄⠀⠀⠀⢸⡅⠘⠀⢻⡈⠀⠀⠀⢠⠉⠉⠓⠚⡇⠀⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠘⡉⢉⡉⢉⠃⠀⠀⠀⣹⡆⠀⠀⢰⠆⠂⠀⠀⠀⠇⠀⣀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠠⠉⠀⠀⠀⠀⠀⠀⠁⠨⠉⠉⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢁⠀⠀⠀⠀⠀⢸⢢⠀⠠⣞⠀⠀⠀⠀⠀⠰⠀⠀⠆
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠥⣁⡨⠅⠀⠀⠀⠀⠸⠃⠀⢀⠳⠄⠀⠀⠀⠀⠁⣀⣀⠘⠀⡀
⠓⡶⠛⠻⠝⠓⠈⠉⡄⠀⠀⠀⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⡲⣒⠳⣤⠀⠀⠀⠀⢠⣏⣀⠀⠙⡄⠀⠀⠀⠀⢀⠂⡖⠂⠀⠀⠀⠀⠀⠰⠆⡀
⠀⠃⠀⠰⠖⠒⠐⢂⠇⠀⠀⠀⠀⠀⠈⠀⠀⠈⠰⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⢰⠀⠈⠀⠀⠏⠂⡑⠍⠁⠀⠀⠁⢀⢂⠆⡀⠀⢨⡁⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠐⠂⡀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠐⠂⠰⡄⠀⠄⠀⡟⠁⠄⠀⠀⠠⠴⡦⠠⠃
⠀⠀⠀⠀⡈⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⢀⠂⠀⠰
⡤⡤⠀⠀⠠⠐⠂⠀⠀⠂⠤⣀⠀⠀⠀⠀⠀⢀⡤⠀⠠⡀⠈⠐⠀⠂⠁⢀⠄⣀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠚⠘⠽⠄⠀⠀⠀⣀⠸⢅⠀⠀⠀⠀⠀⠀⠘⢀⠁⠀⠀⠀⠂⠀⠀⠀⢠⣀⠀⠸⡓⠀⠀⠀⠀⢀⣾⠋⠙⣶⡄⠀⠀⠀⠀⠜⠁⠉⡸⠆⠀⠊⠀⢰⡿
⠀⠀⢸⠁⠀⠀⠀⢾⠀⠀⠀⢘⡂⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⣹⠿⠤⠴⢿⡄⠀⠀⠀⢘⣗⣇⣀⡟⡗⠀⠂⠒⠂⢸⠁⠀⠀⢸⡀⠀⠀⠈⡇
⠁⠀⠁⠀⠀⠀⠀⠈⣄⠰⢀⡤⠀⠀⠀⠀⠀⠣⠄⠐⠠⠏⠀⠀⠀⠀⡎⢄⠐⢀⡼⠀⠀⠀⠀⢸⡀⢀⣀⠀⣡⠀⠀⠀⠀⠘⠀⠨⠆⠘⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠖⠀⠀⠀⠀⢨⢏⠀⠀⢂⣉⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠁⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠁⠀⠀⠉⠀⠀⣴⠰⢄⡅⠀⠀⠐⠀⠀⢀⡀⠀⠀⠈⠉⠉⠀⢀⡴⠶⠖⠂
⠇⠀⠀⠀⠌⠁⠀⠈⠁⠀⠀⢀⡰⠅⠁⠁⠜⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⡀⠀⢀⢰⠃⠀⠀⢱⠐⡖⠀⠀⢐⣀⠀⢸⠓⣒⣒⣒⣶⡩⠒⠸⠦⠤
⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠈⠓⡆⠀⡀⠀⠰⠀⠀⠀⠀⠀⢇⢀⣀⢠⠇⠀⠀⠀⠀⠘⡄⢀⠀⡘⠀⠁⠀⠀⣼⠿⠄⠴⢷⠀⠀⠀⠙⢾⡄⠠⠀⢠
⠀⠀⠀⠀⠈⣦⠒⣠⣿⠀⠀⠀⠀⠀⠈⠋⠁⠁⠀⠀⠀⠀⠀⢀⡀⠁⣀⠀⠀⠀⠀⠀⠀⠳⠈⠐⠁⠀⠀⠀⠀⡏⡀⠐⠀⣼⠀⠀⠀⠀⠀⠑⠀⠀⠈
⠀⠀⠀⡀⠃⠀⡀⠙⠙⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠨⠜⠀⠀⠀⠀⠀⠀⠃⢀⡀⠁⠀⠀⠀⠀⠓⠆⠀⠘⡗⠒⠀⠐⠀⠶⠆
⠀⠀⡐⢄⠀⠢⢌⠀⠜⠀⠀⠂⠀⡀⠀⠀⠀⠀⠔⠁⢤⣄⡀⠀⠀⠀⠀⠀⠏⠀⠀⠉⠀⠐⠉⠑⠀⠔⢈⢹⢶⠀⠐⢀⠂⠀⢀⡤
⠀⠀⠂⡀⣁⠘⠛⠫⢢⠃⠀⠀⢉⠁⠀⠀⠀⠃⠀⠀⠉⠙⣷⠀⠀⠀⠀⡧⠀⠀⠀⢀⡄⠀⠀⠀⡬⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀⠓⢀⣀⡨⠍⠈⠄⠐
⠀⡀⠀⠴⠉⠀⠀⠀⠘⠧⠴⠦⠞⠈⠀⠀⠀⢁⡄⢀⡀⢀⠏⠀⠀⠀⠀⢠⡀⠤⠀⣸⠀⠀⠀⠀⠈⠀⠀⠄⠀⠁⠀⠀⠀⠰⠇⠠⠀⠀⠏⠀⠈⠀⠙
⠀⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⡍⠀⠂⠀⠀⠀⢡⠌⠁⣶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠖⠶⢶⡾⢷⡶⠦⢤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⠀⡢⠄⠟⢉⣻⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠚⠛⣳⡶⡶⠿⠶⠾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠞⠀⠀⣠⠤⠀⢄⡀⠀⠀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠃⠀⠀⠁⠀⠀⠀⠀⠈⢢⡀⠁⢠⠄⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⢀⡠⠄⠈⢂⠀⢸⡇⠀⠀⢖⠍⡂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⢌⠋⠀⠀⠀⠀⠀⠐⢀⡀⠄⢂⠄⣸⠁⠀⡨⡀⠁⠊
⠀⠀⠀⠀⠀⡠⠤⢣⡏⠀⠀⠀⢠⠀⠀⠚⢍⠈⠄⣀⠀⢻⠀⠀⢨⣂⠁⢀⠀⢀
⠀⠀⠀⠀⠸⠀⡐⠛⢸⠀⠀⠀⠀⣑⡊⣙⡃⠈⡽⠒⠁⠘⡀⠀⡨⢐⠨⡰⢄⠈⡄
⠀⠀⠀⠀⠀⠁⠀⠈⡇⢀⠀⠀⠾⠠⠤⠤⣤⣉⠢⡀⠀⠀⠁⠀⠨⠂⠅⠊⣥⡀⠁⢀
⠀⠀⠀⠀⠀⠌⡉⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠃⢀⣥⠀⠈⣵⢉⣀⡿⣟⣶⠶⠟⠓⢢⢄
⠀⠀⠀⠀⠈⢀⡥⠔⡀⠘⢁⠀⠀⢐⢀⠀⠀⠀⢀⠀⠖⠀⠙⢀⡈⠢⡾⢛⣀⡈⠋⠉⢀⡀⠄⠀⠆
⠀⠀⠀⠀⢠⡸⡀⠈⠉⠂⠴⢥⣢⣀⠔⠀⡪⣀⣡⠀⡀⠢⠄⢀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⢁⠙⠂⡤⣀⠀⢀⠀⡉⠉⠉⠁⠀⠀⢀⠼⠷⠦⣬⢉⣁⣀⡀⣀⣀⣀⢤⠤⠤⡢⡆
⠀⠀⠀⠀⠀⠀⢁⠀⡀⠀⠉⢒⠂⠤⡥⢨⠀⠈⡈⡡⣶⠛⠦⢀⠀⠢⠀⠁⢕⠐⠁⡀⡪⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠁⢸⠀⠀⠀⠄⠀⠂⢀⠔⠀⠀⠀⠈⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐⠀⠀⠂⠂⠂⠀⠈⠁⠂⠀⠁⠊⠐⠁⠀⠀⠀⡔⠐

⠀⠰⠲⠂⠀⡴⡄⠀⠀⠒⠂⠀⠀⡤⢤⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡒⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠐⠂⠀⡔⠆
⠀⢰⡆⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠁⠈⠁⠀⠈⠀⠀⠀⣴⠀⠠⣤⡆⠀⢋⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠱⡆⠀⠈⠀⠀⠀⠛⠓⠀⢶⡶⠀⢠⡆
⠀⠘⠇⠀⠀⠀⠀⠀⣈⣃⣃⠀⠀⠄⠠⠀⠀⠀⣰⣆⠀⠈⠁⠀⠉⠀⢀⣈⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠾⠷
⠀⠀⠀⠀⠀⠻⠗⠀⠻⠋⠿⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⢹⠀⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⢀⣬⠀⠃⠀⢠⣄⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠁⠈⢀⣤⠈⠁⢡⣤⡀⠀⠀⣀⣅⠈⠁⣠⡀⠀⢀⡈⠉⠁⣀⡀⠀⠀⠀⠀⠀⢀⡐⠀⢀⣀⣐
⠈⠁⠀⠀⣠⣄⣤⡀⠀⠀⠙⠀⠀⣠⡀⠃⠀⢀⡀⠀⠀⠀⠀⠀⠈⠦⠃⠀⠰⠃⠀⠆⠀⠀⠹⠀⣘⣀⡀⠀⣥⠀⠀⣀⡀⠀⠀⠀⠀⠀⠛⠉⠉
⠀⠤⡄⠀⣿⣿⣿⣧⠄⢀⣀⣀⠀⠙⠁⠀⠀⣤⣤⠀⢘⡆⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠛⠓⠀⠙⠿⠁⠀⠿⠂⠸⠿⠿⠀⠀⢤⡄⠀⠀⠐
⠀⠰⠃⠀⢙⡅⠉⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠿⠀⢸⡟⡇⠀⢸⣾⣶⡆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩
⠀⠠⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠠⠄⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠿⣆⠀⠀⠀⠀⡼⠿⡆⠿⠛⠛⠛⠀⠀⠀⢰⠛⠋⡷⠀⠀⠀⠀⣼⠛⠛⣿⠄⠀⠀⠀⠀⣼⡟⢻⣦⠀⠀⠀⠀⣸⠿⢿⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠠⠀⢰⣿⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⢠⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠂⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⢤⠄
⠀⠀⠀⠀⠚⠙⠛⢰⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠋⠋⠉⠁⢰⡏⠀⠙⣧⠀⠀⠀⠀⢠⣾⠋⢻⡆⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⣿⠀⠀⠀⠀⢸⣿⡆⢼⣷⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡧⠄⠀⠀⠀⠀⠀⢶⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠉⠀⠀⠀⠀⠀⠹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢳⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢾⠀⠀⢸⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣄⠘⡇⠀⢸⠀⠀⠸⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿
⠀⠀⠀⠀⠀⡔⠒⣄⣀⠀⠀⢸⡄⠀⢹⡇⣠⠞⠛⠓⠶⠞⠛⠓⢦⠀⣿⠀⠀⠀⠀⠀⢠⠚⢲⣀⣀
⠀⠀⢀⡞⢻⡇⠀⡏⠉⡇⠀⠀⣧⠀⠈⠁⢿⠀⠀⠀⠀⠀⠀⠀⣸⠂⣿⠀⠀⠀⢰⠋⢻⠀⢸⡇⢸⡆
⠀⠀⢸⡇⢸⡇⠀⡇⠀⡟⠛⡆⢸⡄⠀⠀⠈⠳⣄⠀⠀⠀⣀⡴⠃⠀⡿⠀⠀⠀⢸⠀⢸⠀⢸⡇⢸⡏⢻
⠀⠀⢸⡇⢸⡇⠀⡇⠀⡇⠀⣧⠀⢳⡀⠀⠀⠀⠈⠳⣤⠞⠉⠀⠀⢠⡇⠀⠀⠀⢸⠀⢸⠀⢸⡇⢸⡇⢸
⣞⠳⣄⡇⠘⠃⠀⠃⠀⠇⠀⣿⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⡟⢳⣼⠀⠘⠀⠘⠁⠸⠃⠸
⢹⠀⢹⡇⢀⡤⢤⣠⠤⣄⠀⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣧⠀⣿⠀⣠⠤⣤⡤⢤⡄
⠈⡇⠈⠁⢿⡀⠀⠀⠀⣸⠂⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠈⠘⣇⠀⠀⠀⢀⡿⢀
⠀⢻⡀⠀⠈⠛⢦⣠⠞⠁⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠈⠳⣄⡴⠋⠀⢸
⠀⠀⠳⣄⠀⠀⠀⠁⠀⠀⢰⠇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⣶⣶⠶⠶⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⡀⠀⠀⢀⠤⠴⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢋⢩⠀⣰⡀⠈⢦⠔⠀⠀⣼⠁⠀⠀⠷⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢸⠀⠈⠃⠀⡞⠀⠀⠀⡏⠀⠀⠠⢠⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡀⠈⢧⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⡜⠄⠇⢰⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⡀⠀⠀⠈⠢⠀⢣⠀⠀⡇⠀⠀⢸⡂⡴⢠⠇⢀⡆⡨⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠑⠦⣀⠀⠀⠀⠀⢇⠀⡷⠀⠀⣸⠁⣵⠏⣠⠞⠁⢠⢻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠉⠒⠦⡀⠘⢆⠹⡄⡴⠁⡴⣡⠞⠁⣀⠔⣡⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡤⣑⠦⢤⣤⣀⣉⢦⡈⢧⡟⣰⣻⠟⣡⣤⠞⣡⣾⡟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠐⠀⠀⠀⠉⠢⣀⢀⣾⣻⣛⣾⣇⣿⣷⢿⣿⠶⠿⠍⠁⠬⠖⠒⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠊⣝⠿⣾⣀⡀⠒⠀⠀⠀⠀⠈⠻⣖⢧⡈⣹⠟⠉⡟⠋⠉⠉⠀⠒⠒⠂⠉⠃⠀⢐⠂⡈⣢
⠀⠀⠀⠀⠀⠀⠀⡸⣦⣶⣬⣄⡈⠙⠛⠻⠿⠶⠶⠶⠶⠞⢛⡏⠛⢧⣠⠞⡷⢀⠀⠰⠀⢀⠉⠀⠁⠀⠒⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣏⡛⠿⢶⣦⣤⣭⣭⣭⣥⣴⡎⡙⣶⢾⢵⣰⠃⠤⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠑⡇
⠀⠀⠀⠀⠀⠀⠀⡯⢑⣦⣴⡇⠈⠉⠐⠂⠤⠍⠉⠉⠁⢼⣄⣡⣼⣿⣿⣥⡲⠀⠈⠁⠂⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣛⣿⣟⣿⣐⣂⣐⡀⠤⠤⣀⣀⠤⣿⢈⣿⣏⣾⣿⣿⢿⠃⠀⠀⠀⠀⠁⠀⠛⠀⠀⢀⠐⠠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣧⣈⣉⣉⣽⣝⣛⠻⠿⠿⠷⠶⠶⠾⣿⢨⠏⢸⡹⣿⣝⡂⠂⣐⠀⡈⠀⠈⠀⠀⠀⠀⠀⢀⠢⠀⡛
⠀⠀⠀⠀⠀⠀⠀⡭⠭⠛⠉⡽⡛⠿⢷⣿⣶⣶⣶⣶⣿⠿⣏⡗⢋⡑⡝⣾⠍⠀⡀⠀⠁⢀⡀⠉⠀⠀⠃⠀⢀⠄⠐⡇
⠀⠀⠀⠀⠀⠀⠀⣧⣤⣶⠶⣦⠙⠛⠶⠶⠶⠶⠶⠶⡾⠀⠋⠀⠉⡮⢷⠃⠂⢁⠀⠀⠄⠀⣀⠀⠂⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢨⠀⡀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⡿⠿⠋⠀⠙⣿⣿⣿⣷⣦⡀
⣿⣿⣿⠇⣀⡀⠀⠀⣀⣈⢻⣿⣿⣿⣿⠀⠀⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⡏⠈⠁⠁⠀⠀⠀⠈⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣦⣤⡀⣀⣀⣻⣿⣿⣿⣿⣿⣄⣀⣤⣀⣀⣀⠀⠀⢸⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿
⣿⣿⣿⣄⠀⠐⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⣿⣿⠟⠛⠉⠛⠿⣿⣿⣯⢸⣿⠯⠞⠿⠋⠕⠛⠁⢹⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠹⣿⡇⠸⠧⠴⠶⠂⠀⠀⠶⠶⠄⢹⣿⣿
⢻⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⢿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠻⢿⡿⠿⣿⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡏⠰⠒⠒⠂⠀⠒⠋⠓⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⢀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣠⡤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⣉⣉⠉⠉⢉⣛⡻⣿⣿⡄
⠀⣤⣤⣴⣿⣏⣵⣶⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠄⠀⠀⠀⠤⠀⢺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⡿⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⡏⣁⣄⠀⠈⣤⣄⢙⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⣿
⡟⠁⠁⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠄




⠀⠀⠀⠀⣠⣤⣤⣠⣄⣀⡀
⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⠄

⣶⠈⠀⣀⠀⠀⠈⢻⣿⣿⡏⠁⠂⢤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⡇⠀⠀⠙⠃⢠⣴⣾⣿⡿⠇⢀⠀⠀⠀⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠉⣹⠟⠉⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⢹⣶
⠁⠀⠀⠀⢠⣾⣿⣿⣟⣁⡀⣀⠀⠀⠀⠀⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠛⣴⣿⣶⡄⢀⣤⣀⠀⣿⠏⣿⣿⣿⣿⣿⠰⠆⠀⠒⠆
⠀⠀⠀⠀⣺⣿⣿⡿⠿⠿⢿⣿⡄⠀⠀⠀⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣆⠀⣄⠙⠛⠋⡁⠹⣿⣿⠃⠏⣀⣿⣿⣧⣤⣿⣤⣤⡶⡤
⣾⣿⣧⢸⡟⠉⠀⠀⠀⣀⣤⣼⣷⣀⣠⣤⣶⣶⣶⡶⠄⠉⠉⠉⠛⠛⠛⢿⠀⠸⣿⣿⣛⢳⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣁⣤⣤
⠛⢿⣿⣿⣴⣾⣿⡆⠀⠻⠿⠛⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡿⠟⠛⢻⣿⣿⡇⠈⠉⠛⠻⠿⢻⣿⣿⡿⠟
⣤⣷⣟⣿⠌⠉⠁⣰⣶⣦⣀⣠⠜⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠰⠆⠀⠰⠦⠀⠈⣿⢟⠈⠑
⣟⢛⠫⢸⠀⢶⣾⣿⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡀⠀⣀⣸⣷⣦⣤⣤⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿
⣶⡆⢄⣸⣴⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢁⣴⣤⣤⡀⠀⢫⠏⡱
⣉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⢰⣿⠿⠿⠿⠟⠛⢻⣿⣿⣿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡓⢤
⣵⣿⡿⠟⠉⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⣤⣶⣶⣶⣦⣼⡟⠉⠉⠛⠋⠉⣿⣿⣷⣶
⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⠀⠀⠓⣀⡀⠀⠰⠆⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⡄⠀⠠⣤⣶⣿⣿⣿⣿
⣿⣿⣿⡏⠀⢀⡀⠀⠀⢸⣿⡟⠃⠄⠀⠀⢸⣿⡿⠛⠛⠛⠻⢦⣶⣄⠉⠀⠀⠀⠀⠀⠘⠣⡏⠀⠀⠉⠉⠉⠀⣿⠁⠀⠀⠀⢿⡿⠛⠉⠙
⢹⣿⡏⠀⠀⢈⣀⣤⣴⣾⣿⣿⣶⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠚⡇⠒⠂⠀⠠⠦⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠙⠇⠀⢠⣿⣿⣿⣿⣿⠟⠛⠉⠛⠷⠶⠾⠡⠦⠄⠀⠠⠦⠀⢿⣿⣴⣶⣶⣦⣤⣤⣴⣿⣧⣠⡶⠶⣄⣠⣾⠀⠀⠀⠀⠀⠀⡶⠂⠀⠁
⠀⠀⠀⢤⣼⣿⣿⣿⣿⣏⢀⡀⠠⠶⠶⠶⠶⢦⣠⣴⣦⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠸⠀⠠⠄
⢀⣴⣾⣶⣾⣿⣿⣿⣿⡉⠈⠁⠀⢰⣶⣶⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠉⠃
⠈⣿⡿⠛⠛⠛⠛⢿⣿⣇⡀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⣹⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡆⠀⠀⡀
⠀⠉⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣿⡟⠛⡉⢉⠻⣿⡷⣶⡶⠀⠉⠉⠉⠙⠀⠀⠀⢨⣿⣿⣿⣿⠇⠂⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠉⠈⠀⠐⠆⠀⣾⣧⣤⣤⣿⣾⣿⣾⣿⣿⣿⣷⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠈⢡⣿⣿⡿⠀⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡂
⣶⣜⣶⣶⡳⣄⣀⣀⣴⣿⣿⣿⣿⣯⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠻⠿⠀⠀⣿⡿⠟⠛⠛⠛⠻⣿⡇⠀⣠⣶⣿⣿⣿
⠻⣿⡘⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⢀⣠⣴⣶⣦⣄⠀⠀⢀⣀⠀⠚⢀⡀⠀⠀⢀⣀⠈⣁⣰⣿⣿⠛⠛⠛
⢀⠙⠃⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⢤⠀⠀⣀⠀⣵⣿⣿⡿⠿⠛⠛⢻⣾⣿⣿⣿⣦⡌⠁⣀⣀⡀⢁⣤⣹⣿⣿⣇
⠋⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠰⠆⢻⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯⣼⣿⡿⠏⠲⠆
⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⢸⡿⢿⣿⣿⣿⣿⣤⣀⣄⣴⣶⣿⣿⣿⣿⡄⠶⠀⠀⣀⣀⣬⣿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠀⠘⣿⣷⡄
⠀⢀⠄⠀⠘⢿⣿⣿⣿⣧⣉⡃⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣴⣏⣽⣿⣿⣿⣟⣛⠛⠉⠠⣤⢄⣠⣴⣶⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠙⠆⠐⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢠⢲⠏⠀⣀⣀⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡰⢋⡆⠀⠀⠉⠉⠀⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠶⠛⠛⠃⠀⠀⠀⠁⠃⠉⠀⠋⢠⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢤⣀⣀⡤⠀⠀⢀⣿⣿⡇⠀⠀⠠⣄⣀⡀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣳⡀⠀⠀⠀⠀⣸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⡡⠤⠢⠤⠦⣤⡀⠰⣽⡆⠙⢿⣶⣦⣄⣠⠀⠀⣰⠇⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠙⠀⠈⢷⠀⠀⠀⠀⠀⢸⠇⣰⠏⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠏⡆⠀⢣⣄⣤⡀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⢸⡇⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠆⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠘⠻⢿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡎⢸⣧⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠉⠻⣿⡇⠀⠀⠀⠀⠀⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⣷⠘⣆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡿⠥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢷⠀⢸⣧⣿⣧⠀⠀⠠⡀⠀⠀⢻⣦⣤⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡸⣇⢸⣿⣿⣿⣷⠀⠀⢿⡆⠀⠈⢿⣿⣧⠀⠀⢄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠏⠿⡀⢿⣿⠉⠈⠀⠀⢸⣿⠀⢠⠈⢿⣿⣧⠀⠈⣆⣹⡄⢸⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⢸⣿⡄⠸⣧⠈⢻⣿⣧⠀⠘⣿⡇⢸⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠿⠇⠀⠹⠧⠀⠛⠛⢧⣤⣿⣧⣿⠿⠿⠿⠧⡏

⠀⠂⠀⠀⠀⠀⠀⠀⣧⠀⠀⠔⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠐⠂⠀⡩⠀⠀⠀⣀⣀⡀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠅⠀⠀⠀⢸⡇⠀⠀⢀⣤⣶⣤⡲⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡶⣫⣿⢻⣿⣷⣦⡀⠀⠀⠀⠀⠀⡀
⠉⠠⠀⠀⠀⠀⡀⠀⠛⠃⠀⠀⠀⠈⠉⠀⢰⣿⣿⣿⣿⣿⡜⣿⣿⡄⠀⠠⠄⠀⠀⠀⢠⣿⡟⠛⠁⠈⠁⠙⢻⣿⡄⠀⠈
⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠣⠉⠹⠍⠻⣿⠼⢻⣷⠀⠈⠀⠁⠀⠀⠀⠘⠀⢠⡀⠀⢀⣤⠀⠏⠀⠀⠠⡀
⠁⠐⠉⠀⠠⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠈⠘⠃⠈⠉⠀⠈⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠀⠀⠀⠀⣰⣾⣿⡿⠻⡿⣿⣷⣄⠀⠀⠠⠄⠀⠀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⡈⠀⠀⠀⠀⠀⠐⢿⠏⠉⠀⠀⠀⠈⠙⣿⡆⠀⠁⠀⠄⠀⠛⠛⠉⠀⠀⣠⣤⢴⣦⣀⠀⠀⠀⠀⣈⡀⣀⡀
⠀⠂⡀⠀⠀⠀⠀⠘⠀⠰⠦⠀⠀⠴⠂⠉⠀⠀⠀⠓⠀⠄⠠⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡶⣤⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡟⠂⠙⠋⠛
⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠹⣿⠋⣧⠁⠐⢉⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢤⣄⣴⡄⠀⠀⠀⠀⣀⡀⠂⠀⠀⠫⣔⡆⠀⠀⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢣
⣀⡋⠈⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠤⠀⠠⠄⠘⡏⠀⠀⠀⠉⠓⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⣾
⠉⠀⠀⠁⠀⠀⢔⢂⡴⠔⠦⠆⠠⣄⡀⠂⠀⠀⣀⠀⠁⠀⠀⠉⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀
⠀⠠⠖⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠋⠁⠀⠀⢸⣆⠀⠐⠂⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⠐⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⢀⠀⠳⠀⠀⠀⠠⡷⠀⠀⠀⠀⣿⡀⠀⠀⠤⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠈⠛⠀⠀⠀⠀⠉⠀⠀⡠⠀⣐⡄⠤⠸⠀⢠⡀
⠀⠀⢀⣤⠤⣤⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣤⣦⣤⣀⠀⠀⠀⢀⠔⠈⠀⡰⠋⠀⠀⠀⠀⠈⠁
⠶⣾⣿⣿⣿⣾⣿⣦⠀⠀⢁⡨⠀⠀⣰⣟⣵⡿⠹⡟⣿⣷⣄⠀⠠⡀⠀⢺⣇⠠⠄⠀⠠⠄⠘⠁
⠋⠱⢞⣿⣿⣿⢻⠇⠀⠀⠀⠀⠀⠐⢿⡏⠉⠀⠀⠀⠀⠙⣿⠆⠀⠀⠐⠀⠈⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⣐⡂⠈⣼⡹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠦⠀⠀⠶⠂⠁⠀⠀⠀⢀⣀⠀⠠⠀⠉⠁⠀⠀⠀⢀⣴⣾⣿⣷⣝⢿⣶⡄⠀⠀⣓⡀
⠀⠀⠀⢀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠀⠀⠀⠀⣾⠿⣿⣿⢿⣿⡎⣿⣿⡄
⠂⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠟⣂⠀⢸⣤⠙⠿⠉⢹⣇
⠀⠀⠀⢀⠀⠀⠀⢰⣀⠄⠀⠀⠰⢅⣢⠀⠀⢴⡄⣤⠄⠀⠀⠀⠄⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇
⠀⠀⠀⠂⠀⠀⠀⣾⠃⣀⡀⠀⣀⠀⢽⠂⠀⠀⠀⠀⠀⠀⠀⠈⠒⠞⠉⠐⠁⠀⠙⢶⠄⠀⠀⠀⠀⠀⠘⠂⠀⢰⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡶⠶⢆⡒⠢⡀⡠⠂⢉⡿⠹⢹⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠸⢌⠈⣷⠀⡝⠀⠀⣾⠀⠀⢀⣁⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡀⠹⡄⡀⠀⡇⡀⠀⡇⠀⠀⣎⠸⢀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢆⠀⠀⠙⢦⠘⡄⠀⡗⠀⠀⣇⣴⣱⠇⣹⠢⢸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠈⠓⠤⣀⣀⠐⢱⡀⣇⠀⢠⠟⣵⢃⡼⠃⣠⡻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠸⡄⢠⡀⠀⠈⠻⣀⠱⡜⡶⣣⣾⠟⢉⣤⢞⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠪⣉⠙⣳⡾⢦⣽⢣⣿⣥⣾⣋⣴⠟⠓⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠤⢚⢿⣷⣄⠀⠀⠀⠀⠈⠻⢮⢯⠙⢻⠟⢻⠖⠛⠂⠀⠀⠀⠒⠂⠉⠉⠀⢂
⠀⠀⠀⠀⠀⠀⡾⣴⣮⣥⣉⠛⠛⠻⠶⠶⠶⠶⢚⣿⢛⣧⡰⣳⠂⠀⠰⠀⡈⠀⠀⠀⠂⠀⠈⠀⠆
⠀⠀⠀⠀⠀⠰⣀⡀⠀⠭⠝⣛⠷⠶⣦⣤⣴⠶⡾⠉⢻⣿⣧⠏⠠⢀⡐⠀⠀⠀⠀⠠⠀⠠⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣧⣻⣿⣧⢀⠀⠉⠀⠀⠀⠀⠀⡗⢶⡾⣿⣿⣾⣁⠀⠀⠀⠠⠀⢠⠀⠀⠐⡀⠀⡇
⠀⠀⠀⠀⠀⠀⡛⠛⠛⢻⡷⣶⣶⣬⣽⣿⣶⣽⡗⣿⣷⢿⣿⡟⠁⠀⠀⠀⠀⠄⠀⠀⠀⠒⢀⠀⢥
⠀⠀⠀⠀⠀⠀⣛⣻⡛⣻⠿⢶⣶⣤⣤⣥⣤⣶⣷⣿⢞⠋⠿⣟⠂⠈⠀⠂⣀⠐⠀⠀⠂⠀⡡⠠⡄
⠀⠀⠀⠀⠀⠀⣦⣴⣶⣦⠙⠒⠦⠬⠭⠽⢷⡇⠘⠁⠈⡿⡖⠑⢀⡁⠀⠄⠈⡀⠒⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⢨⠠⠀⠀⠀⠰⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⢟⡻⢿⣿⣿⣿⣷⡄
⠀⠀⠀⣸⠛⠛⠋⠉⠉⠈⢳⡀⠀⠀⠀⢐⣁⠀⠉⠉⠁⠀⠉⠉⠀⣈⣆⠀⣻⣿⣿⣿⣿⠿⠋⠙⠳⢿⣿⣿⣿⣿⡆
⠀⠀⠀⢭⠀⣤⠀⠀⢠⡄⢈⡇⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⡄⣽⣿⣿⡿⣧⠀⠀⠀⠀⢐⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⡇⠐⠐⠀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠛⠿⠿⠛⠈⠉⠘⠻⠟⠛⠁

⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⢠⣿⡿⠋⠁⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⢰⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⠋⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⠙⠛⠋⠉⠈⠻⣿⡇
⠀⢸⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠁⠀⠀⠀⠻⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁
⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂
⠀⢸⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠉⠉⠉⣀⣤⡀⠀⠈⠉⠉
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⡚⠛⠛⠓⠲⠦⣄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⢸⠃⠀⠨⠍⠁⠀⠉⠭⠀⠈⠦
⠀⠀⠀⢻⣿⠟⠉⠁⠈⠛⢿⣿⣇⠀⠀⠀⠀⣿⣷⣦⣄⣀⣠⣴⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠂⡀⠂
⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⢿⣿⣿⣿⣬⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⡆⠀⠐⠂⠀⠠⡧⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣄⣀⣀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣠⣤⣤⡄⠀⠀⢠⡤⢤⡀⠀⠀⣀⡤⣤⠀⠠⣄⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⡇⠉⠙⢆⠀⠀⢸⠀⠀⠀⠀⣇⠀⢀⡞⠀⠀⡇⠀⠀⠀⠀⠀⣟⣀⡠⠇⠀⠸⣁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠳⣤⠞⠁
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⠀⠀⢸⠀⠀⠀⠀⢹⢀⡞⠀⠀⢸⠋⠓⠒⠀⠀⢀⡟⢆⠀⠀⠀⠀⠈⠙⣦⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢀⡰⠃⠀⠀⢸⠀⠀⠀⠀⠘⡟⠀⠀⠀⣾⣀⣀⣀⠀⠀⠸⠃⠀⠱⣄⠀⠠⠤⠖⠁⠀⠤⠼⠤⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠚⠉⠀⠀⠀⠉⠉⠉⠉



⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣷
⠀⠀⠀⣿⣿⣶⡀⠀⠀⠀⠀⢀⠀⠀⠀⣷⣿⣿⡿⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣼⠻⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⡿
⠀⠀⢾⣿⣿⣿⠃⠀⢠⣶⣿⢿⣇⡀⠀⠘⣿⣿⣿⡟⠀⠀⠰⣾⣿⣷⣆⡀⠀⠘⣯⣀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⢙⡿⠀⠀⢀⣀⣶⣴⣴⡆
⠀⠀⢘⡿⢛⠟⣆⠀⠀⠙⢢⣤⠽⢥⠀⢀⣿⡿⠿⣤⠀⠀⠀⣿⣿⣿⠋⠀⠀⢸⡭⠤⠤⠼⡄⠰⣾⣿⣷⡖⠀⠀⠀⠀⢠⣟⣶⣛⣳⣀⠀⠀⢻⣿⣿⣿⣡⡆
⠀⠀⡞⡰⠋⢀⡿⠀⠀⠀⠗⠒⠉⢹⠀⢸⠐⠀⠂⢸⡀⠀⠀⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠹⣿⣿⣿⠟⠀⠀⢠⠋⠁⠉⠉⠉⠉⡆⠀⠈⣿⣿⣿⣿⠁
⠀⠀⡟⢁⡴⠋⡟⠀⠀⠀⠱⠀⠀⢸⠀⢸⡀⠀⠀⠀⢧⠀⠀⣿⣽⡏⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢿⣿⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⡠⠃⠀⠀⣸⡿⢿⢻⢻
⠀⠀⣧⠊⠀⢠⡇⠀⠀⠀⡆⠀⠀⣼⠀⠈⡇⠀⠠⠀⣺⠀⠀⣿⣿⣿⠀⠀⠀⠈⡆⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⢀⡜⠒⠒⠒⠙⣄⠀⠀⠀⡇⡇⠸⢸⢸
⠀⠀⡇⢀⠔⠉⡇⠀⠀⠀⡇⠀⠀⡇⠀⢀⠇⠀⠀⠀⢸⠀⠀⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⣾⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⠀⡇⡇⡆⣼⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠀⢠⠠⠒⣇⡄
⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⢀⡀
⠀⠀⠀⠀⠀⢀⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠉⠒⠤⣀⡀⢀⣀⣐⠁⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠤⢄⠀⠀⠐
⠀⠀⠀⠀⠀⡊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡁⠀⠀⠀⠀⢸⠀⠤⠤⠐⠊⠁⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠊
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡜⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡖⠂⠒⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⣀⡤⠪⢀⣀⣀⠠⠋
⠀⠀⠀⠀⠀⡠⠋⠀⠀⢋⠑⣄⡔⢉⠇⠀⠈⠣⠀⠀⠀⠀⠀⠀⡠⠒⠂⡶⢄⠀⡠⠷⡐⠂⠤
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠒⢹⠑⠊⠀⠀⠀⠀⠱⡀⠀⠀⠀⡐⠇⠀⠀⠑⠄⣿⠠⠌⠀⠀⢀⢇
⠀⠀⠀⡰⠁⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠰⠁⠘⡀⠀⠀⠀⣿⠀⠀⠀⠀⡌⠀⢣
⠀⠀⡔⠀⠀⡔⢡⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠓⡀⠀⠑⡤⠁⠀⡜⢡⠀⠀⠀⣿⠀⠀⠀⡐⠑⡀⠀⢣
⠀⡜⠀⠀⡘⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⠀⠐⠀⠐⠁⠀⡌⠀⠀⠂⠀⠀⣿⠀⠀⠀⠁⠀⠱⡀⠀⢣
⣏⣁⣁⣈⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⢘⠀⠀⣘⡇⠀⢠⡆⠀⠀⣿⠀⠀⠀⡄⠀⠀⠱⠒⠒
⢸⠀⠀⠇⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠈⡅⠀⢹⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⠀⠀⠘⠁⣘
⠘⠀⢠⠀⠀⠀⠀⢠⡄⠀⠀⡸⡀⠀⠀⡸⠀⠀⠀⠀⠰⠀⢸⡆⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⠀⢀⠃⢀⠃
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠋⠀⠈⠋⠁⢘⠀⠀⠀⠀⠀⠆⠘⡇⠀⢸⠀⠀⠀⠉⠀⠀⠀⢸⠀⠈⠀⡌
⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⡀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⣃⠀⠈⠀⠀⠀⡀⠀⠀⠀⠸⢀⡃⠘
⢸⠀⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⢀⣶⠈⠻⠀⠀⡀⠀⠀⡇⡅⠀⠀⠀⠘⢃⢠
⠈⣤⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠈⠁⢃⠄⠀⠘⠃⠀⠀⡇⡇⠀⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⡀
⠀⠀⠀⠀⠀⠀⣠⠀⠘⡒⢚⠆⢗⠒⡓⡀⢠⠀⠀⠀⠀⠀⠀⠀⣠⢀⠒⢓⢘⠃⢓⠒⢓⠀⢠
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠀⠰⠂⠀⠀⠀⣴⣿⣿⣿⡿⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠉⠀⢀⠘⣿⣇⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣄⡀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢫⣴⡤⡼⣿⠂⠀⢀⣤⣤⣤⣤⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⡀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠖⠀⠉⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣿⣶⣿⣦⣶⠘⠛⠀⠹⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠣⠀⠀⠀⠉⠉⠙⣿⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⠟⠉⠉⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣿⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣧⡐⠂⠀⠀⠀⠀⠀⠴⠀⠘⠃⣿⣿⣟⣉⡉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠁⠀⠘⠋
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠟⠃⠸⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠄
⠀⠀⠀⠀⠀⢸⣿⡏⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⡤⣤⣴⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠙⣿⣦⣄⠀⠀⠀⠿⠋⠁⠀⠈⠀⠀⠀⢠⣾⣿⣿⡿⠛⠛⢿⣿⡏⠛⠃⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⠿⡿⠛⠉⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⣿⣿⡏⠛⢁⠀⠀⢀⠁⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⠻⡄⠀⢀⡄⢻⠃⠀⠀⠀⠀⠀⠸⣿⠃⠀⠈⠁⠀⣽⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠰⠆⠀⠉⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠋⢀⡀⠀⢀⡀⠀⠀⠁⠀⠀⢀⣤⣾⣿⠀⠀⢀⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⢀⣀⣈⠉⠉⠉⣙⣛⡛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢩⣤⣬⠀⠀⠀⣥⣬⡍⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠈⠁⠀⡇⠀⠈⠉⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⡀⠀⠙⠛⠋⠀⢀⣴⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠦⠤⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠋⠁⠀⠀⢰⣶⡶⣶⣦⠀⠀⠈⠙⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣶⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣾⢧⡉⠻⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠀⣿⠢⠈⠀⠈⠣⠀⠀⠀⠀⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⠤⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⣄⠀⠀⢀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠀⠀⡜⠀⠀⠚⣇⠀⢠⠀⠀⠂⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇⠀⣾⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠘⠉⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠃⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠸⠋⠛⠇⠀⠈⠀⢀⠀⠀⢀⡈⡈⢉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠈⠻⠋⠉⠹⠋
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠠⠟⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠀⠘⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⡴⠶⣆⠀⠀⠄⠀⠀⠀⠀⠠⠒⠦⠀⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠐⣢
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂
⠀⠀⣰⡾⠿⣦⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣄
⠀⠀⠻⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⡂⠀⠄⠄⠀⠠⠀⠀⠆⠀⠰⠈⠁⠁⢠⠀⢀⠀⠈⠀⠀⠿⠛⠻⠀⠀⣰⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠃⠽
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠈⠀⠀⠀⠈⠀⠂⠀⠀⠞⠙⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⢠⡿⠉⠻⣦⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡆⠀⠸⠧⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠉
⠀⠀⠰⠂⠀⠄⠀⠀⡄⠦⠀⠀⠀⠈⠀⠀⠀⠀⢰⢥⢈⣆⠀⠀⠈⠉⠉⠂⠀⠀⠀⠀⢀⠀⠀⢰⡄
⠀⠀⣸⠁⠀⣆⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠜⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠃
⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠐⠂⠐⠃

⠀⠀⢀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢀⠀⠀⠀⠀⣾⣿⠄⠀⠀⡀⡀⠀⠀⢰⣿⡧⠀⠀⢀⢀⠀⠀⠠⣿⣿⠄
⢀⣤⣤⣤⡀⣠⣼⣿⣤⡀⣠⣤⣤⣄⢀⣤⣿⣧⡄⢀⣤⣤⣄⡀⣠⣼⣧⣤⠀⣠⣤⣤⡀⢀⣤⣿⣦⡀⣀⣤⣤⣄⠀⣤⣾⣷⣄⢀⣤⣤⣤
⠉⣹⣿⡏⠙⠛⠛⠛⠛⠋⢉⣿⣿⠉⠉⠙⠛⠛⠛⠉⣽⣿⡏⠉⠛⠛⠛⠙⠋⢩⣿⣯⠉⠉⠙⠛⠛⠋⠉⣽⣿⡍⠙⠛⠛⠛⠛⠋⢹⣿⣿
⠀⣙⣿⣃⠀⠀⣀⣀⠀⠀⢈⣻⣟⡀⠀⢀⣐⣀⠀⠀⣙⣿⣁⠀⠀⣀⣀⠀⠀⣈⣻⣋⡀⠀⢀⣀⡀⠀⢀⣙⣟⣁⠀⢀⣀⣀⠀⠀⣈⣿⣏
⠾⠿⠿⠿⠷⠾⣿⣿⠿⠶⠿⠿⠿⠿⠾⢿⣿⡿⠷⠾⠿⠿⠿⠷⠿⣿⣿⠿⠾⠿⠿⠿⠿⠾⢿⣿⡿⠷⠿⠿⠿⠿⠷⠿⣿⣿⠿⠾⠿⠿⠿
⠀⠀⠤⠀⠀⠀⢿⡿⠃⠀⠀⠠⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⡿
⣴⣾⣿⣶⣤⣶⣿⣿⣷⣤⣶⣿⣷⣦⣴⣾⣿⣿⣦⣴⣶⣿⣶⣤⣾⣿⣿⣷⣤⣶⣶⣷⣦⣴⣿⣿⣿⣦⣴⣾⣿⣶⣤⣾⣿⣿⣷⣤⣶⣾⣷
⠀⢾⣿⡇⠀⠀⢀⠀⠀⠀⠰⣿⣿⠀⠀⠀⣀⠀⠀⠀⢾⣿⡆⠀⠀⠀⡀⠀⠀⢰⣿⣷⠀⠀⠀⣀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣷
⣠⣴⣿⣦⡀⣠⣤⣦⣄⢀⣤⣾⣧⣄⢀⣤⣤⣤⡀⣠⣴⣿⣦⡀⣠⣤⣤⣄⢀⣤⣾⣧⣄⢀⣤⣤⣤⡀⣠⣶⣿⣤⡀⣠⣤⣦⣄⢀⣴⣿⣧
⠉⠙⠛⠉⠉⠉⣿⣿⡉⠉⠉⠙⠋⠉⠉⢹⣿⣏⠉⠉⠉⠛⠉⠉⠉⣿⣿⡉⠉⠉⠛⠋⠉⠉⢹⣿⣏⠉⠉⠙⠛⠉⠉⠉⣿⣿⠉⠉⠉⠛⠋
⠀⣀⣀⡀⠀⢀⣹⣟⣁⠀⢀⣁⣀⠀⠀⣈⣿⣋⠀⠀⣀⣈⡀⠀⢀⣹⣟⡀⠀⢀⣀⣀⠀⠀⣈⣿⣃⠀⠀⣀⣀⡀⠀⢀⣻⣟⡀⠀⢀⣀⣀
⠺⢻⣿⡟⠳⠿⠿⠿⠿⠗⠛⣿⣿⠓⠾⠿⠿⠿⠷⠚⢻⣿⡛⠲⠿⠿⠿⠿⠖⢛⣿⣟⠓⠾⠿⠿⠿⠷⠚⣿⣿⠟⠲⠿⠿⠿⠿⠖⢻⣿⡟
⠀⠻⣿⠇⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠠⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⠟
⣴⣿⣿⣿⣦⣴⣾⣿⣶⣤⣾⣿⣿⣷⣤⣾⣿⣷⣦⣴⣿⣿⣷⣦⣴⣿⣿⣶⣴⣾⣿⣿⣶⣴⣾⣿⣷⣦⣶⣿⣿⣷⣤⣶⣿⣿⣶⣴⣿⣿⣿
⠀⠀⢀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⢀⠀⠀⠀⣿⣿⠄⠀⠀⢀⠀⠀⠀⢸⣿⡧⠀⠀⠀⡀⠀⠀⠀⣿⣿⠀⠀⠀⢀
⣠⣤⣶⣤⣀⣤⣾⣷⣦⡀⣤⣴⣤⣄⣠⣴⣿⣶⣄⢠⣤⣦⣤⣀⣤⣾⣷⣤⣀⣤⣴⣤⣄⣠⣴⣿⣦⣄⣠⣤⣦⣤⣀⣤⣾⣷⣤⣀⣤⣴⣦
⠉⣽⣿⡏⠉⠉⠉⠉⠉⠉⢩⣿⣿⠉⠉⠉⠉⠉⠉⠉⣽⣿⡍⠉⠉⠉⠉⠉⠉⢩⣿⣯⠉⠉⠉⠉⠉⠉⠉⣽⣿⡍⠉⠉⠉⠉⠉⠉⢹⣿⣯
⢀⣹⣿⣅⠀⢀⣈⣈⡀⠀⣈⣿⣏⡀⠀⣀⣁⣀⠀⢀⣹⣿⣁⠀⢀⣀⣀⡀⠀⣈⣿⣏⡀⠀⣀⣁⣀⠀⢀⣹⣿⣁⠀⢀⣀⣈⡀⠀⣈⣿⣏
⣿⠿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿
⣯⣀⣼⣧⣽⣭⣭⣭⣿⣼⣭⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣽⣽⣿⣭⣭