⠀⠀⢀⡤⠒⠚⠛⠓⠶⠀⠀⠀⠀⠀⠀⠀⠴⠚⠛⠛⠛⠓⠒⠦⢄⡀⠀⠀⠀⠀
⠀⢠⠋⢠⣰⣒⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠄⠀⠠⠤⣀⠀⠁⠀⠀⠀
⣀⠑⢼⣿⠛⣿⣿⣶⡑⡀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣿⡿⣿⣷⣦⣕⡦⡀⠀⠀
⠈⠙⢿⠃⢰⡏⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠠⠛⢁⣿⠃⠀⢸⣿⣿⡿⣿⣏⡁⠀
⠀⠀⠈⠆⢸⣧⣤⣾⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣴⣿⣿⠿⡇⠸⣏⠉⠉
⠀⠀⠀⠀⠀⢃⡿⣽⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢹⡿⣹⣷⣱⠃⠘⠙⠀⠀
⠀⠀⠀⠀⠠⠤⢍⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢟⡋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣒⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠉⠉⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠠⠍⠉⠄⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡑⠢⠤⠤⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠼⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢄⠀⠀⠲⠴⢝⡛⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠇⠀⠀⠱⡄⠀⠀⠀⠙⢄⠈⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀
⠀⢀⠔⠁⢀⣠⡤⠂⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠇⢸⡸⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠳⡀⠀⠣⡀⠀⠀⠙⡄⠀⠀⠀⠀⠘⣆⠀⠀
⢀⠎⡠⢖⡽⠉⠀⠀⢀⣾⠋⠀⡴⠁⠀⠀⠀⡸⠀⢸⡇⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠑⡄⠀⠱⡀⠀⠀⠈⢆⠀⠀⠀⠀⠈⡆⠀
⣼⠋⣠⠋⠀⠀⠀⡰⢣⠃⠀⡸⠀⠀⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⠀
⠃⢰⢃⠆⠀⠀⡰⢁⠏⠀⢠⠃⠀⠀⠀⠀⠀⡇⠀⢸⡄⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⢰⠀⢱⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠃
⠀⣾⣿⠀⠀⢀⡇⡜⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠀⠀⠇⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⡞⡇⠈⣇⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀
⠀⠟⡇⠀⠀⢸⠀⠇⠀⠀⠘⡆⠀⠀⢸⠀⠘⡏⣆⠀⠀⠀⢸⡇⠀⠀⡏⢀⡇⠀⠀⡰⠁⡇⢰⠻⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀
⠀⠀⡇⠀⠀⢸⡆⠀⠀⠀⠀⡟⢤⡀⠈⣧⡀⢳⣹⡄⠀⠀⢸⡇⠄⢰⣧⣼⣀⣀⣜⡁⣸⣠⠃⠀⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀
⠀⠀⢹⡀⠀⢺⢳⡀⠀⠀⠀⡇⠀⠉⠒⠺⣮⣶⡿⠿⢦⠀⠈⣇⢀⣮⣼⠭⠟⠉⠉⠙⠛⠓⠄⠀⢲⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀
⠀⠀⠀⠱⣄⠘⡆⠱⣄⠀⠀⠹⡀⢀⣴⠞⠋⠁⠀⠀⠀⠑⢤⣘⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀
⠀⠀⠀⠀⠈⠑⠺⠦⢈⠗⠢⠤⣽⠿⠂⡀⠀⠀⠀⠀⠀⠀⠚⠁⠉⠙⠒⢰⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠘⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣶⣶⣶⠾⠛⠁⠀⢸⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡎⣠⠀⠀⡀⠀⢸⣶⣿⣷⣶⣶⣾⠷⠛⠀⠀⠀⠀⠀⠈⠍⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⢿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⢰⡇⠀⢠⠃⠀⢀⣿⡉⠉⢉⡡⠤⠖⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣇⣿⠁⠀⡜⠀⠀⢸⡇⢣⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⢹⠀⢠⠇⠀⠀⠈⡇⠀⢧⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠀⢰⢣⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡀⠀⠀⠀⢣⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⣠⠎⣰⣷⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⡸⡄⠸⣇⠀⠀⠀⠘⡆⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⡞⠀⣠⡶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠓⢳⡀⢻⣆⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠈⠑⣦⣄⣀⡠⠔⠊⠁⠀⣠⣎⢴⠏⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠑⠄⣻⣷⣄⣠⠀⠈⣦⣤⣔⣀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠉⠉⠐⠒⠉⠉⠉⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠐⠒⠊⠉⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀
⠀⠀⠀⢀⡞⠀⠔⢁⠃⠀⢠⠊⡐⡝⢡⡾⠁⢴⠃⣼⠀⢨⠁⢠⠀⠀⢂⠀
⠀⠀⢀⣮⡁⠍⢀⣏⠃⢀⠆⡰⡜⢠⣇⢀⣬⠇⡰⡇⠀⡘⠇⢈⠀⠀⠀⠆
⠀⠀⣼⢨⠀⢀⡺⠉⠀⢾⢠⣙⠳⣤⣴⣿⠟⠐⢀⠇⣰⡛⠂⣿⠀⠀⠀⣻
⠀⠀⢻⠈⠀⢸⠁⣆⢸⢸⣾⠙⡆⠁⠨⠙⠟⠀⣸⣐⠝⣽⣷⣾⡆⣆⢀⢹
⠀⢰⠂⠀⠀⡞⠠⣾⢸⡈⠈⠀⠁⠀⠀⠀⠀⠀⠉⢀⠄⠙⢬⢽⣶⣽⠎⠘
⢀⠇⡤⠀⡘⢀⠞⡟⠹⣧⠲⢰⠀⢀⡄⠀⠀⠀⠀⠀⠀⠰⠁⢾⣿⡟⠀⠀
⡜⢰⠁⣾⠃⠸⠀⢷⠆⡘⢠⠈⢸⣶⣾⣿⣿⣿⣷⢂⡇⠆⠀⡏⠇⠃⠀⠀
⠁⣷⠀⢀⠀⠀⠀⡆⠀⡁⢀⠀⢸⠉⣀⠉⠉⠻⣿⡿⠀⢀⡔⠀⠀⡇⠀⠀
⢸⢸⡄⠈⡀⠀⠀⢡⠀⠇⠈⢄⢀⡈⠁⠀⠈⠀⠐⡁⣔⠣⠋⠁⢀⠁⠀⠀
⡈⡌⡿⡄⠐⡀⠆⠀⡄⠀⠀⠀⠀⠰⠤⢀⢀⠄⠞⠁⠀⠀⢀⠔⠀⠀⠀⠀
⢰⡰⡘⢚⣆⡑⠌⢦⡀⠀⠀⠀⠀⠀⠃⢤⡁⠀⠀⣀⣀⣴⡁⠀⠀⠀⠀⠀
⠁⠱⠕⡼⣛⠻⠤⣚⡎⢄⡀⠀⠀⣀⠴⡄⢔⠂⠾⢁⡈⠡⠘⠂⠄⠀⠀⠀
⠀⠀⠀⢀⡍⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⢯⠉⠉⢏⠉⠙⠯⡉⠉⠉⠉⠉⠩⡉⠻⡉⠉⠉⠉⠉⠉⠉⠙⢿⣍⠉⠉⠉⠉⠉⠛⠥⡀⠀⠀
⠀⠀⢀⡎⠀⠀⢠⡏⣀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠈⢆⠀⠀⠈⠢⣀⠀⠀⠀⢡⠀⠹⡀⠀⠀⠀⠈⠣⡀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠈
⠀⢠⡞⠀⠀⠀⣸⠃⡇⠀⠀⠀⠀⠀⠀⡟⢸⡄⠀⠘⣦⡀⠀⠀⠈⠑⢄⡀⠀⢃⠀⢣⠀⠀⠀⠀⠀⠑⡄⠀⠀⠙⡏⠑⣞⠓⠶⠤⣤⣤
⣴⡿⠁⠀⠀⠀⡏⢰⠁⡄⠀⠀⢠⠀⠀⡇⢸⣿⡄⠀⢹⡿⢦⡀⠀⠀⠀⠈⠢⢼⡀⠀⣷⡄⠀⠀⠀⠀⠘⡄⠀⠘⣿⡀⠀⢳⣄⠀⠀⠙
⣿⠃⠀⠀⠀⡸⠁⣼⠀⢣⠀⠀⠰⠀⠀⡄⢸⡿⣿⣆⠀⢳⡀⠈⠑⠤⣀⠀⠀⠀⠈⠓⠾⣿⣦⡀⠀⠀⠀⠰⡀⠀⠘⡇⠀⠈⡟⠳⢄⠀
⠃⠀⠀⠀⢠⠃⣰⡇⠀⢸⡄⠀⠀⢇⠀⢠⣼⠃⠈⢿⣦⡀⢹⣄⠀⠀⠀⠉⠒⠢⢤⡤⣤⠠⠀⠉⣰⠆⡤⠄⣧⠀⠀⠸⡀⠀⢻⢆⠀⠉
⠀⠀⠀⢠⠃⣴⠟⢇⠀⢸⣷⡀⠀⠘⡀⢈⡿⠀⠀⠀⠉⠛⠢⣿⣦⠀⠀⠢⡀⠀⠀⠉⠛⠀⣤⡶⠟⢦⣇⠀⢹⣧⠀⠀⢣⠀⢸⡀⢳⣄
⠀⠀⠐⢃⣼⣿⠀⢸⠀⢸⡿⣿⡄⠀⠁⠸⣇⠀⠀⠀⠀⣀⣀⣈⣙⣷⣄⠀⠑⢄⠀⠀⠀⣴⣟⡤⠦⠾⢿⠀⣼⣿⣇⠀⠘⡄⠀⣷⡀⠻
⠀⠀⣠⣾⠏⢹⠀⢸⠀⢸⣧⣼⠿⣦⡀⢀⢿⠙⠛⠓⢒⣒⣒⡒⠛⠉⠉⠳⣄⠀⠳⣀⣶⣿⣥⣶⡍⠉⢻⣧⣿⢿⣿⡄⠀⣧⢠⣯⠻⡄
⣠⣾⣿⡇⠀⠘⡄⠀⡇⢸⡇⠀⠀⠈⣑⣮⣿⣤⣴⣟⣛⡒⢂⡴⠖⠀⠀⠀⠙⣷⠢⣌⣛⣿⣿⢛⠃⢀⣾⢿⣿⣿⣿⣧⠀⢹⡜⠘⡀⠘
⡿⢿⠀⢳⠀⠀⢳⡄⢡⢀⡧⢖⣺⣭⣷⣶⣿⣿⣷⡀⠀⠉⠙⠂⠀⠀⠀⠀⠀⢸⣀⡿⢋⣿⠿⠟⠒⠛⠁⣸⣿⡇⣿⣿⠀⣸⠁⠀⣇⠀
⠁⠘⡀⠀⢧⠀⠀⢻⣾⣧⠙⠿⣐⣿⡟⠿⢻⢻⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠳⣾⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⢠⣿⡇⠀⢻⡀
⠀⠀⢧⠀⠘⣷⣄⠀⠻⡏⠳⢄⠀⠈⠙⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠲⣄⡀⠀⠀⠀⣿⣿⢧⣿⣿⠃⠟⣿⡀⠸⣷
⠀⠀⠘⡆⠀⠸⡌⢧⢄⡈⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡿⣸⣿⣿⢠⠀⠈⢧⡀⢻
⠢⣦⠀⠘⡄⠀⠱⡘⠀⢿⠦⢭⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣿⣧⣿⣿⡏⠘⠀⠀⢸⠁⠈
⡦⢌⡑⠀⢸⡄⠀⠱⣦⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣿⢿⣿⣿⢁⡇⠀⠀⡾⠀⠀
⢣⠀⠘⣷⢮⠭⣒⣤⡌⣣⣹⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣱⢃⣾⠁⠀⠈⠀⠀⠀
⠀⡄⠀⢻⡈⣷⢤⡻⣄⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠊⠀⢀⡏⢰⡴⠓⠁⠈⠢⡀⠀⠀⠀⠀
⠀⢣⠀⠈⢇⢸⡀⢻⡍⠑⢤⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⠶⠒⠉⠉⠁⢹⣿⠁⠀⠀⡼⠳⡈⢿⠦⣦⠤⠴⠾⢶⣲⠆⡀
⠀⠘⡆⠀⠈⢦⡇⠐⣿⣆⠈⣻⣶⣾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⡙⠛⠀⠀⠀⠀⠀⠻⠟⠀⠀⣸⡇⠀⠈⠺⠦⠄⠉⠉⠉⠉⠉⠉⠀
⠆⠀⠹⡄⠀⠈⢹⠀⠸⡙⢧⠘⣮⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⡰⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣳⣄⡙⣄⠀⠀⢇⠀⢡⠀⠀⢹⣧⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠙⣿⢢⠀⠈⢆⠀⢣⠀⢸⣬⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⠈⠂⣷⣄⠈⢆⠈⢿⣿⣿⣿⣧⣿⣿⣶⣶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⣀⣴⡟⣦⣀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⣰⣷⡈⡷⠄⢳⣎⡹⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠉⠉⠋⡏⠉⠀⠱⣼⣄⠉⠒⠢⠬⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀
⟡ pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
completely free, NO signup required (ever), and unlimited!
⠀⠀⠀⠀⠀⢀⣠⡴⠶⠾⠿⠷⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠿⠛⠛⠻⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢄⡀⠀⠀⠀⠀⠀
⠀⠀⢀⠞⠀⢀⡴⣺⣉⡉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠤⠒⠒⠒⠲⠦⢄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⢮⣀⢐⣿⣿⣿⣿⣿⣿⣶⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣨⣿⣷⣶⣾⣿⣿⣿⣶⣶⣤⣈⠙⠢⣀⠀⠀⠀⠀⠀⠀
⠢⣄⣀⣙⣿⣿⠏⠀⣼⣿⡿⠿⣿⣷⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣶⡾⠳⣄⢀⡀⠀⠀
⠀⠉⠛⢻⣿⡇⠀⠀⣿⠋⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠁⢰⣿⡟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀
⠀⠀⠀⠀⢻⡇⠀⢸⣿⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⡅⠀⠀⢠⣿⣿⣿⣿⣿⣷⠙⣿⣿⣿⣶⣦⢤
⠀⠀⠀⠀⠀⢣⠀⠘⣿⣦⣤⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣾⣿⣿⣿⣿⡿⢿⡟⠀⢸⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠻⠉⣿⣟⢻⣿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⢿⣿⡿⢿⡿⣯⠙⣶⠃⠀⡸⠙⠧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣬⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣸⣟⣻⣦⣿⣿⡷⠋⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⢶⣤⣄⣉⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⣷⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣉⣉⡉⠉⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠛⠉⠉⠉⠉⠙⠛⢿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⠤⠴⠂⠀⠠⠄⠀⠀⠒⠢⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⣅⡒⠒⠂⠁⠀⠀⠀⡀⠀⣀⡀⣀⣀⠀⠀⠀⠈⠑⢄⠀⠀⠀
⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⢀⠺⠏⠈⠢⠀⠈⠢⡈⠣⡀⠀⢀⠀⠀⠑⡀⠀
⠀⡐⠡⡔⠊⢀⡤⠂⠄⠀⠀⡆⣶⠀⠀⠀⠅⠀⠀⠈⠄⠑⡀⠀⠢⠀⠀⠈⡄
⠰⢂⠊⠀⢀⠢⠁⡌⠀⠀⢀⠀⢏⠀⠀⠀⢸⡀⠀⠀⡈⡄⠀⠀⠀⢡⠀⠀⠐
⠀⣬⠇⠀⡆⠃⠀⡀⠀⡀⢸⡆⠸⠀⡀⠀⠈⠁⠀⠀⠃⢰⠀⠀⠀⠀⢃⠀⠀
⠀⠀⠀⠀⡇⠀⠀⡧⡀⢱⡘⡴⡀⠀⡇⠀⣆⣆⢀⠎⣄⠂⡇⠀⠀⠀⢸⡀⠀
⠀⠀⢃⠈⡗⡀⠀⢃⠈⣀⠿⠚⠓⢄⠰⡜⠚⠊⠁⠉⠁⠂⢴⠀⠀⠀⠈⡇⠀
⠀⠀⠀⠑⠒⢌⠂⠬⡞⢃⠀⠀⠀⠀⠋⠙⠂⡆⠀⠀⣀⡄⢸⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⢀⢂⠀⠀⢰⣼⣤⣤⣤⠄⠀⠀⠘⠛⠛⠋⠁⠀⢸⠀⠀⠀⢠⠇⠀
⠀⠀⠀⠀⡜⡆⠀⠃⠀⢣⠀⠔⠒⠁⠄⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣼⡄⠀
⠀⠀⠀⠀⣿⡇⠸⠀⠈⡄⢂⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⠃⠀⡀⡐⡼⠀⠀
⠀⠀⠀⠀⢳⠇⢰⠀⠀⢡⠀⠁⠢⣀⠀⠀⠀⠀⠀⣀⠔⠎⢀⣴⠗⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠸⢌⢧⡀⠀⠢⣀⡀⠀⠁⡖⠀⠒⠉⠠⠎⠚⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠁⠀⠉⠙⠓⠒⠋⠉⠁⢀⡅⠀⠀⠀⠀⠀⢰⠠⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠠⠄⠐⠈⢰⠁⠀⠀⠀⠀⠀⠀⠍⠈⠐⠄⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⣏⣀⣀⠀⠀⠀⠙⠻⣿⣿⣿⣛⡛⠛⠿⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⠿⢛⣿⠿⠛⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⠈⠻⣮⡉⠻⢷⣤⡀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠉⠉⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⢤⡀⠀⠈⠻⣦⡀⠙⢿⣦⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⣠⣾⣫⠴⠶⠶⠲⠶⢤⣀⠀⠀⠀⠀⠀⠐⠦⣤⣿⣶⠶⠶⠟⠻⢷⣦⡹⣷⡀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠰⠾⠿⠷⣶⣤⣤⣤⣀⣀⣀⣉⠙⠶⣄⣀⢀⣴⠟⠉⠉⠉⠁⠀⠀⠀⠀⠙⢷⣽⣧⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠉⣀⣈⣉⣭⣭⡿⠿⠶⠶⢯⣿⡁⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠙⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣭⡶⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠿⣦⣄⡀⠀⠀⠀⢀⣠⣿⣾⣛⠉⠙⠿⣦⣰⣧⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣾⡋⠉⠙⢧⡉⠙⠦⡀⠈⠙⢷⣄⠀⠀⠀⠉⠙⢷⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⡄⢠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⡄⠀⠀⠙⠄⠀⠈⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⣼⠀⣼⠀⠀⠀⠀⣸⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⡀⣿⣇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⡀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢳⠇⠀⢠⣿⠀⣿⡆⠀⠀⠀⣿⡆⠀⠀⠀⠰⣧⠀⠀⠀⠀⠀⠻⣽⣿⠀⢻⡀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠘⢷⡝⠻⣦⡀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣾⠃⣿⠀⠀⣸⢹⠀⡇⣷⠀⠀⠀⣿⣷⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⠀⢹⣿⡄⠀⣷⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⢿⡄⠘⢷⡌
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⡟⠀⢹⡆⠀⣿⠘⡆⡇⢻⣄⠀⠀⣿⢻⡄⠀⠀⠀⣇⢻⣄⠀⠀⠀⠀⢸⣿⣧⠀⣹⠀⠀⠀⠀⠀⠀⣸⣧⣤⣴⣶⡶⣼⣷⠀⠈⢿
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠃⠀⠈⣷⠀⢿⣄⣷⣷⡶⢿⡄⠀⣿⠈⣿⡀⠀⠀⣿⠀⢻⣆⠀⠀⠀⢸⡇⣿⠀⡿⠀⠀⠀⠀⢀⣼⠟⡇⠀⠸⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⢿⡀⠀⣿⠶⠒⠚⠻⣇⢸⣏⠹⣿⠀⠈⢿⡀⢸⡀⠈⣷⡀⢠⡿⣤⣀⡻⣆⠀⠀⣿⢀⣿⣰⠃⠀⠀⠀⣠⡾⠃⠀⡇⠀⠀⣿⡇⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⢸⡜⣷⡀⢻⣇⣒⣋⣩⣽⣷⣿⣭⡻⣆⠀⠈⠿⣜⣇⠀⠈⢷⣼⠃⠀⠉⠉⠛⣷⡀⣿⠾⣿⢷⡶⠶⠾⢿⡟⠁⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⡀⠀⠸⣇⣿⣷⣌⣿⠛⠉⠉⠉⠉⠻⢿⡿⣿⣆⠀⠀⠙⢿⡀⠀⠀⠙⠚⠓⠶⢤⣀⠈⢿⡁⠀⠀⠈⣷⠀⠀⢸⡇⠀⢠⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢿⣆⡀⢻⣿⡻⠟⢿⣆⠀⠀⠀⠀⠀⢸⠀⠈⠈⠁⠀⠀⠀⠀⠀⣨⣿⠿⠿⣶⣶⣭⣙⠶⠻⣦⡀⠀⢿⠀⠀⢸⡇⢀⣾⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡎⠻⣾⣿⡇⠀⠀⢹⣧⡀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⠀⠀⠀⠉⠛⢿⣿⣶⣬⣿⣆⢸⡇⠀⣸⣠⡾⢹⣾⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⡿⡄⠸⣿⡿⢄⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⡌⠻⢧⢠⣿⣿⡖⠈⣽⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣧⠹⡄⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣀⣀⣀⣠⠞⠀⡿⠛⡇⠀⠀⣸⡇⠈⢁⣼⠏⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣸⠀⠘⣄⢻⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠄⠀⠀⢠⡇⠀⢠⡟⢀⣴⠟⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⡟⠀⠀⠸⣆⠳⡌⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣾⢿⣿⡏⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣸⠇⠀⠀⠀⢸⣧⠀⠀⢳⡙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⣼⠏⡸⢸⡇⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⡏⠀⠀⠀⢰⡏⠀⠀⠀⢀⡾⠘⡆⠀⠀⢳⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⣿⢃⣾⠃⢠⡇⢸⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡟⠀⠀⠀⢰⡏⠀⠀⠀⢀⡾⠃⢰⠇⠀⠀⠈⡇⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠋⠁⣰⣿⣿⠁⠀⠈⠁⣿⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⠃⠀⠀⢰⡟⠀⠀⢀⣴⠟⠀⢀⡿⠀⠀⠀⠀⡿⠀⣿⡇⠹⣷⣄⠀⣀⣀⣠⣴⠶⣾⠿⠉⢉⡟⣸⠇⠀⣼⡟⠁⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡇⠀⠀⢠⡟⠀⢀⣴⠟⠁⠀⢠⡾⠁⠀⠀⢀⣴⠃⢀⣿⠀⠀⠈⠿⣯⠉⠉⠉⠀⣴⠋⠀⠀⡾⠀⣿⠀⠈⢠⠃⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡿⠁⠀⢀⡞⠀⣠⡟⠁⠀⢀⣴⠏⠀⠀⠀⣠⣫⠋⢀⣿⠋⠀⠀⠀⠀⠙⣷⣄⠀⢰⡏⠀⣰⣰⠁⣸⣿⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⣼⡇⠀⠀⣸⠁⡴⠋⠀⠀⣰⠟⠁⠀⢀⡤⢞⡷⢃⣴⡿⠃⠀⠀⠀⠀⠀⠀⠈⠿⣦⢸⠀⢀⠇⡿⠀⣿⡇⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀
⢠⣿⠁⠀⢰⡇⡼⠃⠀⣠⡾⠉⠀⣀⡴⣋⣀⣵⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⢸⠀⡇⠀⡇⡇⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⢸⢿⠃⣠⡾⠃⢀⣠⣾⡷⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠚⠒⠳⣶⠀⣧⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⣼⣏⡾⠋⢀⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⢀⣀⡴⠀⠀⠀⠈⠳⣿⡀⠀⢸⡀⠀⣿⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠃⠀⠀⣧⡿⢁⣴⠟⠁⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣀⣶⡿⠋⠀⣀⣠⠴⠖⠀⠈⠙⣆⠀⣇⠀⢿⣄⠀⠀⠀⠀⢸⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⣿⢡⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⣴⠿⠉⣀⢴⡾⠟⠁⠀⣀⡀⠀⠀⠙⢷⣽⡄⠘⣿⣧⠀⠀⠀⠸⡇⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⣯⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠸⣧⡤⣾⠏⢀⣴⠿⠋⢀⣠⢖⡯⠿⠛⠉⠁⠀⠀⠙⠿⣤⣻⡜⣦⠀⠀⠀⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⠀⠀⠀⠀⣯⠴⣿⠉⣀⢴⣫⠶⠉⠀⣀⣀⣠⣤⣀⡀⠀⠀⠈⠎⠙⢾⣧⡀⠀⢸⡆⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀
⠘⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⡀⠀⠀⠀⠀⠀⠉⠉⠹⢯⣀⠤⠶⠋⠉⠁⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠉⠻⢶⡌⣷⡀⢀⠘⣿⡆⠀⠀⠀⠀⠀⠀
⠀⢹⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⢠⣶⠶⠖⡒⠺⠛⢿⣧⠸⡆⣛⣷⠀⠀⠀⠀⠠⠄
⠀⠈⢃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣄⣉⡉⠉⠉⠁⠒⠚⢻⣟⣿⣻⣿⣗⠒⠒⠒⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣭⣗⡲⠦⠤⠤⢤⣼⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢙⣛⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⡟⢿⣿⣿⢻⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⡇⠈⢻⣿⡎⣿⣿⣟⣛⡻⠿⣿⣿⣿⣛⣛⠛⠙⢷⡀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢟⡞⢹⣿⠈⣿⣿⣿⢻⣷⠀⢀⡘⣿⣿⣿⡇⠀⠈⢻⣿⢹⣿⣿⡽⣿⣿⣷⣦⣌⡉⠛⠿⢷⣄⣽⣦⡀
⠀⠀⣠⢶⣿⠟⣻⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠔⢻⣏⡇⣿⣿⣿⣿⡟⠀⠀⠙⢿⣿⣿⡏⠀⠐⠀⢿⣿⣿⣿⣧⣿⣿⣿⡟⣿⣿⣷⣦⣄⡈⣧⠙⠻
⠴⠞⠛⠉⣠⢞⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⢫⡞⠀⠀⣸⡿⠁⣿⣿⣟⣿⡇⠀⠀⠀⢘⣿⣟⠇⠈⠓⠢⠼⣿⡾⣿⣿⢸⣿⣿⣿⢻⣿⣿⣿⡿⣿⣿⡄⠀
⠀⠀⢀⠞⢁⣼⣿⣿⣿⣿⡏⣾⣹⣿⣿⣿⣿⣿⣿⢸⠇⣿⣿⣟⣵⣟⡀⣀⢀⣿⠇⢠⣿⣿⢻⡿⠀⠀⠀⠀⠀⣿⡿⣀⣀⣀⣀⣀⣹⡇⢹⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣜⣿⣽⡄
⣠⣞⣭⣿⣿⠟⣿⣿⣿⣿⢻⡟⣿⣿⣿⡟⣻⣿⣿⣟⣼⡿⣵⣿⡏⠉⠙⠛⣾⡏⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⣤⠟⢋⡅⠀⠀⠀⠀⠉⠿⢿⣿⡇⣿⠿⣿⡇⣿⣿⣿⡟⠁⠸⡿⠻
⣷⣿⠿⠋⠁⢀⣿⣿⣿⡏⣾⡇⣿⣿⣿⣷⣿⣿⡟⣿⡇⣴⡿⡟⠁⢀⡄⢀⡟⠀⠀⡿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⠘⡄⠀⠀⠀⢀⣅⠀⣠⣿⣷⣿⠀⠈⢷⣿⣿⣿⡇⠀⠀⣿⣦
⠉⠀⠀⡠⡄⣸⣿⣿⣿⣷⣿⡇⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⡿⠓⠒⠚⢲⡾⠁⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡽⠲⠿⠖⠒⠒⠻⢔⣚⡍⣿⣿⣿⡄⠀⠀⠻⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠸⡄⠀⠻⣿⣿⣿⢿⣿⡇⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⠐⣾⢟⠀⠀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢋⠀⠀⣹⣿⣿⣿⡆⠀⠀⢻⣿⡇⠀⠀⢸⣿
⣇⠀⠀⢹⡄⠀⠈⢿⣿⢸⣿⡇⣿⣿⣿⣏⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠩⠄⢊⣡⠖⠊⣿⣿⣿⣿⣷⡀⠀⠘⣿⡇⠀⠀⢸⣿
⠉⠳⣄⣾⣷⡀⠀⠈⢻⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢻⡇⠀⠀⠘⢿
⠀⠀⠘⢿⣿⣿⡄⠀⠈⢻⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠐⣶⣖⣒⡿⠭⠄⠒⠒⠒⠢⠭⠷⣒⣀⣶⠇⠀⠀⠀⠀⣇⡄⠀⢠⣿⣿⣿⣿⡿⣇⠀⠀⠸⡇⠀⠀⢸⣷
⠁⡀⠀⠀⠙⢿⣿⡄⠀⠀⢻⣿⣆⣿⣇⢿⣿⣿⣿⣟⡇⠀⠀⢠⡀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠉⠀⢀⣼⣿⣿⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠘⠿
⢈⣿⣄⠀⠀⠈⠻⠿⠂⠀⣠⡽⠿⣼⣿⡾⣿⣿⣿⣿⣅⠀⠀⢸⣷⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⠟⠧⣤⣀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣤⣔⣀⣀⣰⠟⠁⠀⢀⠀⠙⠷⣿⣿⣿⣿⣿⣦⣀⠈⠉⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⣀⣴⣿⣆⣼⣿⣿⡿⠁⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀
⣿⣷⠛⠁⠈⠉⠉⢹⣅⣀⣠⠔⣧⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⢀⡤⠖⠋⠈⠀⠀⣀⣴⣾⣿⡏⣽⢻⣷⣿⣿⠁⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀
⣼⡧⠤⠤⠤⢤⣀⠀⠀⠹⣄⡆⠀⢿⠛⠂⠀⠸⣟⢳⣿⣿⣿⣿⣿⣿⣿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠁⠀⠀⡀⠀⠈⢷⣄⠀⠈⢳⠀⠀⠀⠀⠀⠀⣿⣯⡉⣿⣿⣿⣿⠛⢮⡀⠉⠻⣷⣦⣄⣀⣀⣀⣠⣴⣾⣿⠟⠁⠈⠈⢿⠿⠿⣿⣿⣷⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣷⠈⠈⡽⡆⠀⣰⠊⠓⢦⡞⠀⠀⠀⠀⠀⢀⣿⡿⠿⠾⣿⢿⣯⡀⠀⠛⢦⡀⠀⠙⠛⠿⢿⣿⣿⠿⠋⠁⠀⣠⠞⠁⠈⠳⣾⡁⢸⣿⡟⠀⠈⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣷⡀⠀⠙⠚⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⢹⣾⣿⣇⠀⠀⠀⠈⠛⠒⠦⢤⡀⠀⠀⣠⡔⠚⠉⠀⠀⠀⠀⠀⠀⡇⢸⣿⠇⠀⠀⣰⠃⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣭⡿⠞⠉⠀⠸⣼⡇⠀⢰⠈⣿⡸⣿⡄⠀⠀⠀⠀⠀⠀⢸⣉⣀⣐⣀⣽⡀⠀⠀⠀⠀⠀⠀⣰⠁⢸⡝⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⡿⣿⣿⡿⠙⠳⣄⠀⠐⠚⠃⠀⠀⠀⠀⠀⢿⣿⡀⠀⠣⡇⢳⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢠⠏⠀⢸⡇⠀⠀⢰⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠀⣿⣿⠇⠀⠀⢄⣣⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⣇⠀⠀⡇⠀⢹⣇⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⠋⢧⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣼⡇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠃⠀⣿⡏⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡹⣆⠀⣇⣄⠈⠉⢷⡀⠀⠀⣸⠀⢿⣿⣿⣿⣿⡟⠀⠸⡆⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⣿⣇⠐⠛⠒⠒⠢⢾⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠀⠀⠀⠀⠀⠀⠱⢄⠀⡿⠀⠘⣿⣻⣿⣿⠁⠀⠀⢳⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠗⠀⠀⢹⣿⣿⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⢀⣤⠔⢒⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠁⠐⢋⣉⠀⡚⠉⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠚⠛⠉⣉⣭⠭⠛⠛⠛⠓⠶⣤⣀⡉⠛⠳⢶⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⣁⠀⠀⠀⠈⠀⠀⢀⣠⠴⠖⢋⡽⢿⡄⠉⠳⢄⡀⠀⠀⠉⠻⣙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠁⢠⡟⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⢢⡈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⢤⡤⠤⠴⡺⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣇⠀⠀⠀⠀⠀⠀⠁⠀⠙⢤⠀⠀⠀⠸⣷⠤⠤⠦⢤⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⣴⠞⠁⠀⠀⠀⠘⣹⣷⠊⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠸⣷⠶⠶⠦⣝⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⣠⠞⠁⠈⡇⠀⠀⠀⡀⠀⠀⣠⡾⠖⠛⠛⠉⠙⠻⣟⡢⢄⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢹⣄⣀⠀⠀⠈⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣴⠟⠁⠀⠀⠀⣠⢖⣠⠞⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠹⡏⠲⢽⣶⣄⡀⠀⠀⠀⠀⢳⡀⠀⢿⠈⠉⠲⣄⠘⢇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣀⠔⠁⢀⡞⠁⠀⢀⣤⣶⡿⠷⣻⣏⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠉⠛⢽⡶⣄⠀⠀⠈⢷⡀⠈⣇⠀⠀⠈⠳⡜⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡾⠃⠀⣠⠏⣠⣤⣾⣿⣿⣥⣀⡾⠛⠁⠀⠀⣀⣐⣒⡒⠤⢤⡀⠀⠀⠀⠀⠈⣧⠀⣆⠀⠀⠙⢮⡛⢦⡀⠸⡇⠀⢿⣆⠀⠀⠀⠘⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡿⠁⠀⣴⣯⠞⠙⡏⢿⡇⣦⣽⠁⠀⠀⠀⠀⠰⠞⠛⠉⣹⠛⠛⠶⢦⣄⣀⠀⠀⢹⡀⢸⠀⠀⠀⠀⠙⣦⢳⡄⡇⠀⢸⠸⡄⠀⠀⠀⠈⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣸⠁⠀⣴⡋⠀⠀⢰⠃⠨⣧⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣅⠀⠈⣹⣻⣶⠆⡇⢸⠀⠀⠀⠀⠀⠘⣇⢹⡇⠀⣼⠀⢱⠀⠀⠀⠀⢹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣸⡟⠀⠀⢠⠏⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠬⢷⣅⣀⣠⠴⠋⠁⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⢸⡆⡇⢀⡇⠀⠈⣧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⡿⠀⠀⢀⡏⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣸⠁⣿⠀⠀⢸⠀⠀⠀⣼⣧⡇⣾⠁⠀⠀⢹⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠋⡇⠀⠀⢸⡁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣼⡟⠀⠀⢸⠀⠀⣴⣿⡟⣻⠃⠀⠀⠀⠈⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⡼⢸⠀⢀⡄⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⡇⠀⢀⣿⢀⡼⠵⠋⣰⠏⠀⡏⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⢸⠀⢸⡇⠀⢻⡄⠀⠀⠲⠖⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⢁⡞⣽⠁⢀⣞⣿⠎⠀⠀⣰⡏⠀⣼⠁⠀⠀⠀⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠇⠸⡇⢸⣷⠀⡏⢿⡀⠀⠀⠀⠀⠀⠘⠛⠃⠀⣀⣀⡤⢤⣖⡶⠿⠛⠋⠁⠀⣠⠞⢺⡏⣠⣿⠟⠁⠀⠀⣴⡟⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⡾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠀⠀⢳⡘⣟⣶⡇⠈⠳⡀⠀⠀⠀⠀⠀⢀⡴⠚⣩⠴⠚⠉⠁⠀⠀⠀⠀⣀⠞⠁⢀⣿⠞⡽⠁⠀⢠⢄⡼⣹⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⢰⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⠇⠀⠀⠈⢳⡽⣿⡇⠀⡀⠹⡄⠀⠀⠀⢠⣏⣴⠋⠀⠀⠀⠀⠀⣀⣤⠴⠋⠁⠀⢀⣼⠋⣰⠃⠀⢀⣿⣿⣦⡏⠀⢰⣿⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠻⣿⡇⠀⣧⠀⢷⣄⡀⠀⢸⣿⣁⣀⣀⣠⣤⠖⠛⠉⠀⠀⠀⠀⢀⣾⠃⣰⠃⠀⣠⣿⠋⠀⢻⠀⠀⣸⡏⠀⠀⠀⠀⠄⢠⡞⠀⠀⠀
⢰⠀⠀⠀⠀⠀⣠⣟⠟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⠿⡄⠀⠉⢙⡏⠉⠻⣍⠉⠀⠀⠉⠻⣄⠀⠀⠀⠀⢀⡾⣇⡴⠃⣠⠾⠃⠁⠀⠀⡞⠀⢀⡿⠁⠀⠀⠀⣸⣠⠏⠀⠀⠀⠀
⠈⢷⣦⣤⠤⣚⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣿⣧⣷⠀⠀⣸⠃⠀⠀⠈⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⣾⣰⡟⣡⠞⠁⠀⠀⠀⠀⠨⡇⠀⢸⡇⠀⠀⠀⣸⣷⠋⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⣧⢿⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⢸⡈⣇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⣿⡏⠀⣇⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⢸⡇⠀⣠⠿⠦⢤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⢀⡟⡇⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡏⠀⣧⠀⠸⣆⠀⠀⠀⢀⣠⠞⠁⡇⠀⢸⣣⣾⠃⠀⠀⠀⠀⠙⠳⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⠗⠁⠀⠀⠀⣠⢏⣴⢧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢱⡀⠘⣆⠀⠘⢧⣴⠶⠋⠁⠀⣸⡇⠀⣼⢯⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡵⠋⠁⠀⠀⠀⠀⣴⣷⠋⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡞⠀⠀⢀⣳⣤⠼⣧⣄⠀⠈⠛⠒⢒⣾⢿⡇⠀⡏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢀⣾⢟⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⡧⠖⠛⠋⣀⡤⠞⠋⠈⠙⢓⣒⡺⢏⡼⣿⠁⣸⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⡇⢸⣀⡤⣶⠿⣋⣀⡤⠴⠖⠚⠉⢁⡴⠋⢠⡇⢠⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢋⣤⠔⣾⣇⢸⣤⠾⠛⠋⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⡾⣠⠏⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠞⠉⢠⠾⢃⣽⣾⣇⠀⢀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⡾⣱⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣆⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⡴⠁⣠⠞⠁⠈⢻⣷⣁⠀⢀⡴⣾⠟⠁⠀⠀⢀⣼⣿⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣈⠳⣤⡤⠀⢀⡴⠯⡟⠀⣰⠋⠀⡴⠃⠀⢀⣴⡟⠁⢈⠝⢋⡼⠃⠀⠀⢀⣴⣿⢿⠏⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣰⠞⠀⠀⣇⣾⠁⠀⡼⠁⢠⠞⣽⢻⢃⡴⠉⢀⡾⢀⣀⣠⣴⠿⠋⠁⡼⠀⠀⢠⡇⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⠟⠈⠛⢾⠃⣴⣃⣰⠃⣿⠊⣀⣤⣾⠯⠛⠛⠉⢀⣀⣠⡴⠧⢤⣄⣸⡇⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⣼⠇⠀⠀⠀⣸⡾⠀⠀⢹⠀⡇⠈⠁⠀⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⠙⠶⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠶⣶⡶⠟⠛⠉⠉⠀⠀⠀⠈⠻⣿⡳⢶⣄⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠉⢁⡴⠛⠁⠀⠀⠀⠀⠀⠉⠓⠢⢄⠀⠈⢳⣄⠙⢷⣄⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⢀⡴⠯⠒⠒⠛⠒⠢⢄⡀⠀⠀⠀⣒⣾⠷⡞⠛⠋⠛⢦⡹⣧⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠉⢉⣹⠟⠛⠳⠶⠶⣦⣌⣓⣦⡞⠁⠀⠀⠀⠀⠀⣀⠀⠹⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⣴⣫⡥⠶⠖⠛⠋⠉⠉⠉⠉⠉⠳⣤⣀⠀⠀⠀⢀⣼⣶⠖⠚⠷⣄⣸⣁⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⡾⡉⠉⠣⡉⠳⢄⠈⠻⣦⡀⠀⠈⠙⢶⣄⠀
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡸⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡀⠀⠙⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠹⣆
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢠⡇⢸⡀⠀⠀⣾⠀⠀⠀⢸⡀⠀⠀⠀⢠⣻⡆⢣⠀⠀⠀⠀⠀⢀⠀⠀⠙⢿⡳⣤⡀⢻
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠀⠀⣸⠃⡇⠀⣸⡇⡏⣇⠀⠀⣿⡆⠀⠀⢸⢧⠀⠀⠀⠀⢻⣧⠈⣇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⠈⢻⡜
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡇⠀⢀⡏⠀⣷⠀⣿⢱⡇⢻⡀⠀⣧⢷⠀⠀⢸⡜⣦⠀⠀⠀⢸⢿⠀⣸⠀⠀⠀⠀⢀⣧⠤⢶⡶⠼⠇⠀⢻
⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⡇⠀⢸⣇⣀⣼⡄⢻⠾⣿⠋⢷⡀⢻⠘⣧⠀⢸⡇⠘⣧⠀⠀⣼⢸⣀⡇⠀⠀⠀⣰⠟⢸⠀⢸⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢿⡆⠀⠀⢸⢻⡄⠸⡇⠴⢒⣻⣼⣖⢿⡄⠈⢷⣸⠀⠘⢧⣸⠈⠓⠺⢷⡀⣯⣾⣿⣤⣤⣴⡾⠃⠀⡞⠀⢸⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡿⣆⠀⠸⣾⣿⣄⢿⠛⠛⠛⠛⠿⡷⡷⡀⠀⠙⣇⠀⢈⠛⠒⠢⢄⡈⢳⡋⠈⠈⣇⠀⠀⡇⠀⢰⠃⠀⢸⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠘⡷⣄⣻⡏⠋⠻⣦⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⠀⡸⡟⠛⠻⢶⣮⣗⡙⣦⡀⢻⠀⠀⡇⢠⡿⡄⠀⢸⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢻⡈⢿⣷⡄⠀⠸⠦⠤⠤⠾⠆⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠈⢻⣿⣿⡟⢼⡀⢰⣷⡋⢼⡿⠀⢸⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠁⠀⢸⢳⡈⣿⣌⠁⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠢⠷⣤⣀⠀⣀⡸⢘⡿⡇⠀⠁⣼⠙⢂⡼⠃⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡟⠀⠀⢸⠀⠱⡘⣟⢧⣄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂⠀⠀⡇⠀⢰⣇⣴⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠃⠀⠀⣼⠀⠀⢱⣌⠆⢻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢠⡿⡿⡿⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀
⠀⠀⠀⣸⠏⠀⠀⢰⠇⠀⠀⢸⠏⡆⠀⢳⠙⢷⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⡿⢠⠟⢀⠇⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⢠⡟⠀⠀⢠⠏⠀⠀⢠⡞⠀⡇⠀⠀⡇⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡟⠋⣰⣷⠏⠀⠘⢰⠇⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀
⠀⠀⣾⠁⠀⢠⠏⠀⢀⡴⠋⢀⡾⠁⠀⠀⡼⠀⡿⠙⢧⣀⣀⣠⡤⠶⣾⠋⠉⡝⣼⠀⡴⡏⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⢰⡏⠀⢀⡏⠀⡴⠋⠀⢠⡞⠀⠀⢀⢦⠃⣼⠇⠀⠀⠻⣄⠀⠀⣰⠃⢀⡸⢠⡟⠀⢰⠁⡸⠀⠀⠀⠘⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀
⠀⣾⠀⠀⡼⢠⡞⠀⢀⡴⠋⠀⢀⢴⡿⢁⡼⠋⠀⠀⠀⠀⠘⢧⡀⡏⢀⠇⡇⢸⡇⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀
⢰⡏⠀⢠⢧⠎⠀⣤⠞⠀⣠⢔⣁⣭⠾⠋⠁⠀⠀⠀⠀⠀⠀⠈⢻⣷⢸⢸⠀⡏⡇⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀
⢸⠃⠀⢸⡞⣠⠞⢀⣤⡾⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠉⠉⠳⣇⡇⠀⢸⠀⢸⠀⠀⠀⠀⢢⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀
⣸⠀⠀⡟⡿⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣀⣴⠞⠁⠀⣀⠈⠻⣄⠘⡆⢸⡄⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀
⣿⠀⠀⣿⢡⠟⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣰⠃⢀⡾⠋⢁⣴⠾⠋⠀⠀⠀⠘⢦⣣⠀⣷⡆⠀⠀⠀⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀
⢸⠀⠀⣯⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠧⠴⡿⢀⣼⠟⢁⡤⣲⠝⠛⠉⠀⠀⠙⠣⣼⡜⣄⠀⠀⢧⠀⠀⢿⡆⠀⠀⠀⠀⠀
⢸⡀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⠖⢻⣡⢴⠽⠋⣀⣠⠤⠶⣦⡄⠀⠀⠙⠈⠻⢦⡀⢸⡄⠀⢸⣇⠀⠀⠀⠀⠀
⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠀⠀⠈⠻⣆⠀⣀⣀⣀⡠⢽⢦⣷⡸⡌⢿⡀⠀⠀⠀⡀
⠀⠸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣅⣉⠒⠒⠒⠒⠚⣷⣷⣻⣷⠒⠒⠒⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢈⣉⣉⡁⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠔⢋⠄⣊⠥⠤⠄⠤⠤⠍⣒⠠⡙⠢⡀⠀⠀⠀⠀
⠀⠀⠀⡰⢃⣔⠕⠉⠀⠀⠀⠀⠀⢄⠀⠀⠉⠪⢦⡘⢆⠀⠀⠀
⠀⠀⡰⢁⡾⢁⠀⡘⢆⠀⠀⣄⠀⠀⠹⣆⠀⠀⠈⢳⡈⢆⠀⠀
⠀⠀⡇⡼⠀⡌⢀⠃⠈⢆⠀⠸⡕⢤⡀⠰⡑⡀⢆⠀⠇⢸⠀⠀
⠀⢰⠀⡇⢠⠁⡮⠔⠀⠀⠳⡀⢱⠀⠙⢖⣷⢼⣸⡄⢰⠀⠄⠀
⠀⠀⡄⡇⢸⡜⣀⣤⣀⣀⠀⠈⠙⠂⢀⣤⣽⣄⠉⢃⡈⢠⠀⠀
⠀⠀⡇⢸⣼⠀⣾⠟⠙⢻⠃⠀⠀⠀⢻⠛⠙⣷⡅⢸⠇⢸⠀⠀
⠀⠀⢱⠈⢎⡆⠛⢆⠀⢈⡄⠀⠀⠀⢃⠀⢀⠟⠁⣦⠃⡎⠀⠀
⠀⠀⢸⠀⠈⠳⡀⠀⠉⠀⠀⠀⠄⠀⠀⠉⠁⠀⡸⠁⠀⡇⠀⠀
⠀⠀⢸⠀⠀⠀⠳⣀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡰⠁⠀⠀⡇⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠙⠢⠤⣀⠀⣀⠤⠒⠃⠀⠀⠀⠀⡇⠀⠀
⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢳⠀⠀
⠀⠀⡇⠰⠀⠀⢀⡇⢰⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠂⢸⠀⠀
⠀⢠⠀⢰⠀⠀⢸⢇⠎⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡆⠈⣄⠀
⡰⠋⡆⢸⡆⠀⡇⠸⡀⠉⠉⠉⠓⠒⠈⠁⢰⢹⠀⢰⡇⢰⠈⢢
⡇⠀⢧⢸⠘⡼⠀⠀⠱⣄⠀⠀⠀⠀⢀⡴⠃⠀⢧⠃⡇⡼⠀⢸
⡇⠀⠘⡌⡆⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⢰⢡⠃⠀⢸
⢰⠀⠀⠘⣼⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠃⠀⠀⡎
⠀⢧⠀⠀⠈⠛⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠞⠁⠀⠀⡰⠁
⠀⠀⠌⠉⡽⠉⠉⠉⠉⣏⠉⠍⠙⠉⡉⠉⠙⡙⠍⠉⠉⢩⠉⠫⣉⠉⠉⠙⠀⠀
⢀⡜⠀⢀⢇⠁⠀⠀⠀⡏⡆⠈⣆⠀⠈⠂⢀⢡⠘⡀⠀⠀⠑⡀⠈⣇⠲⡒⠠⢤
⡿⠀⠀⡘⠈⢠⠀⢠⠀⡇⣿⣄⠸⡙⠢⢀⠀⠉⠢⢼⣆⠀⠀⠐⠀⠹⠀⢹⠦⡀
⠁⠀⠠⣠⡇⢨⡄⠀⠄⢷⠃⠙⠦⡹⣄⠀⠈⠐⠲⢦⠂⣩⡖⠂⣇⠀⢃⠈⡢⡈
⠀⠐⣱⡇⢀⢸⡿⣄⠀⢸⣀⡀⠀⠀⢙⣦⡈⠂⠀⢠⡎⢵⣼⡇⣿⣆⠀⡀⣧⡹
⣠⣾⠃⢃⠘⠸⠋⠉⡢⣨⣄⡤⠦⠔⡤⠀⠈⢦⢕⡻⣿⢷⢀⣷⣯⣿⡀⣇⢡⠑
⠛⡀⢆⠈⢦⡆⢶⢼⣷⣾⣿⣆⠀⠉⠀⠀⠀⠈⠼⣹⠛⠁⠉⢸⣿⢿⡇⣏⠀⡄
⠀⢁⠈⡦⡈⢏⠢⡉⠙⠒⠚⠁⠀⠀⠀⠀⠀⠈⠀⠛⢠⡀⠀⢸⡟⣿⡗⠿⡄⢷
⢤⠀⠆⠘⡸⢢⢕⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢸⢷⣿⢣⠀⢰⠈
⡖⢱⣨⢄⠐⢎⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⡏⡌⠀⠎⠀
⢠⠀⡏⡮⣉⣈⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠂⢠⠹⡜⠈⠣⡀⠀⠀
⠈⡆⠘⣰⠸⣆⢳⣴⡤⠀⠀⠀⠀⠀⢶⠺⠉⠀⠀⢸⠇⢀⡎⠑⠭⣙⠉⠙⠛⠂
⢢⡘⡀⠈⠆⢋⠂⢫⡳⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠎⡇⠀⠀⠀⠀⠀⠀⠀
⣿⠏⢺⢄⠘⡀⢆⣸⣵⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢡⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠀⣸⡱⠌⣬⣻⡿⣿⣿⣿⣿⣷⣶⠒⠒⠀⡖⠚⢼⡒⠠⠑⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣾⠃⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⣠⣾⣿⠏⠀⠀⣀⣠⣴⡶⠖⠒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣀⣤⣴⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣜⣡⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣯⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠜⣉⣿⠻⡌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣽⣿⣿⣿⠶⠆
⠀⠀⠰⣎⠡⡄⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡉⠀⠀⠀⠀⠀
⠀⠀⢀⣽⠑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣻⢦⣀⠀⠀⠀
⠀⠀⠸⣾⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡿⡷⠀⠀⠀⠀⣿⣿⣿⠉⠉⠛⠛⠓⠂⠀
⠀⠀⣀⠿⢿⠛⠀⠀⠀⠀⠀⠀⠀⠞⠀⠚⠫⠟⣥⠃⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀
⢀⣜⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⣰⣤⠖⠋⠁⠀⠀⠀⣠⣿⣿⠙⠛⠿⣷⣄⠀⠀⠀⠀
⠺⠛⡟⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣿⡏⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠣⢄⣀⣀⣤⡴⠚⠉⠀⠀⠀⠀⣿⠇⠀⣠⣶⣿⣿⡟⠀⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣿⠀⠠⡟⣿⠃⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡇⠀⠀⣧⣼⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⢸⠁⠀⣠⠞⣁⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⢀⡿⠔⢋⣀⠐⡯⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⡙⠛⠿⠿⠛⠒⢉⣁⠀⠀⣫⣹⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠚⠓⠳⢴⣹⣆⣀⣀⠿⣼⠒⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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