Schoolwork Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣰⠓⢄⡀⠘⢦⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡤⢄⡴⠃⠀⠀⠉⠒⠺⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⣎⠀⠀⠀⠀⠀⡀⢠⢄⠀⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣠⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⢸⠎⢸⡇⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣲⣶⣆⣀⣠⠋⠑⢄⡀⠸⠵⠂⢀⡼⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⡏⠀⠀⠀⠀⠀⠉⣶⡒⠒⠋⠀⠀⠀⠀⠠⣖⢠⠰⠇⠘⠆⠳⡄⠠⣄⣄⠀⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠻⠉⠙⡖⠦⣄⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣀⠀⠉⠓⠲⠤⠤⠤⠤⠖⠛⠀⠀⠈⢣⡀⢀⠞⠉⣆⠰⣿⠀⠂⠀⠀⢰⡏⠈⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⣴⣁⣀⣀⣀⣤⣤⣤⡤⠤⠤⠤⣄⡀⠀⠀⢈⡏⠀⠀⠈⠳⣄⡁⠚⢀⣠⠎⠀⠘⡆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⠉⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣗⣆⣼⠀⢺⡹⡄⠀⠀⢻⡉⡡⠋⠀⠀⠀⠹⡶⠶⠒⠚⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃⠀⠀⢀⣀⣀⣤⠤⠤⠤⣀⣠⠾⢮⡀⠀⣿⡤⠤⢧⣹⡄⠀⠀⠉⣠⠴⠒⠒⠛⠓⠛⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣙⣶⡤⠤⠼⠶⠒⠿⣿⠛⢒⣒⠛⢢⣀⣼⣃⣀⣀⣙⣦⣿⡀⠀⠀⣰⣽⣆⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⢳⡳⡀⠈⣭⣥⠀⠈⢧⠘⠛⠦⠀⠻⡀⠀⠀⠀⠀⡰⠋⠉⠛⠒⠛⠻⣧⣙⣷⣆⣔⣒⣒⠒⠒⢒⡞⣻⠋
⠀⠀⠀⠀⠀⠀⢀⡎⡀⠀⠀⠹⣝⡤⠤⠤⠤⠤⠤⣷⣒⣒⣲⣦⡇⠀⠀⠀⠘⠧⠤⠤⢤⡤⠤⠤⠤⠭⠭⠭⠭⠭⠭⠤⠤⠋⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠭⠋⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⠴⠶⠖⠒⠒⠒⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⢅⠀⠟⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠲⠂⠀⠀⠘⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⡄⠀⣤⠀⠡⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢢⡀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠄⠰⣒⡶⠙⢄⠀⠀⠁⣀⣀⡠⢞⣷⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠀⠀⠀⠹⣀⠀⠀⢙⠋⠉⠀⢀⣴⣷⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠹⣧⡀⠀⠀⠈⠉⠐⢸⠀⠀⢸⠁⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⠀⠀⠀⡟⢷⡄⠀⠀⠀⠀⢸⠀⠀⠀⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⡃⠈⢻⣆⠀⠀⠀⢸⠀⠀⠀⠘⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠲⠤⣀⠔⢛⠳⢤⡀⢸⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⠀⠸⡀⠀⠀⠀⠀⢀⢐⠢⠍⣾⡇⠘⡄⠀⠀⠀⡸
⠀⠀⠀⡎⣉⠭⠛⠉⠉⠉⠁⠀⠉⠉⠙⠻⣒⠂⠐⠒⠚⠪⠭⠿⠋⠻⠁⠉⠙⠒⢞⡓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀
⠀⠀⢸⠈⠁⠒⠠⠤⠐⠒⠈⠉⠉⠀⠒⠒⠂⠷⠤⠤⠒⠒⠒⠀⠀⠀⠉⠉⠉⠉⠒⠚⠓⠀⠀⠀⣀⡠⢤⡢⠀⠀⠀⠀⠙⠢⣀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣒⠭⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣢⣄
⠀⠫⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠈⠉⠀⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠄⠀⠀⢠⢊⠁⠀⠀⠀⢠⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡜⠀⣐⠲⢁⣨⠤⠀⣀⡠⠂⠑⠤⡤⢄⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠁⠀⡐⣢⣤⣤⡀⠀⠀⠀⠀⣠⢋⣉⡠⡉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠚⠀⠘⠛⠚⠘⠛⠃⠀⠀⠀⠀⠙⠛⠘⠻⠾⠀⠨⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠑⡄⠀⠀⠀⠀⡀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢦⡀⠀⠀⠈⠙⠭⠈⠭⠋⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⡄⢈⢢⡄⣀⠀⠀⠀⠀⠀⠀⣀⠤⢺⠄⢀⣀⡀⢀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣡⠔⠉⠀⠀⠐⡀⠀⠈⠢⢈⠁⠀⠀⠉⣁⠤⠒⠁⠀⠌⠀⠀⠀⠈⠢⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠈⠒⣄⠀⠀⡜⣓⠮⣁⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣥⠾⡑⠊⠀⣉⡁⠈⠣⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢺⣇⠱⡀⠀⣉⡁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐⠂⠤⢜⡀⠀⠀⠀⠀⠙⣆⠱⡀⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣣⣀⣀⣀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠜⠑⠂⠊⠉⠉⠉⡒⢤⡀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⣠⣶⣯⣭⣅⣀⣈⣉⠉⠉⠙⢛⣛⣿⠶⠆
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢈⡲⢹⠉⠉⠉⠉⣉⠉⠭⠭⠭⡈⡈⠯⠧⠄⢀⣀⡉⠀⠈⢹⠟⢹⣟⣩⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠐⢢⣀⠀⠀⠀⠀⠂⠴⠳⢄⠆⢒⠉⠀⠐⡂⠄⠉⠤⠓⠩⡑⢄⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠒⠀⠁⠀⠀⠻⠀⠀⡔⠁⠀⠀⣀⠴⠂⣒⡜⢎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⣀⠐⣢⠐⠀⠀⠚⠍⡉⠀⠀⠸⡛⢛⠛⠒⠒⠊⠀⠈⠦⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣓⣉⡵⠤⣬⣥⣄⣀⡂⠀⠀⢀⣉⡤⠒⠪⠭⠅⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢂⠼⡛⠿⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡰⠋⣤⠘⣆⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠏⢠⢸⣀⠀⠀⢢⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⡇⢷⢢⠙⢄⠑⠌⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇⣀⠀⢠⠀⠸⡟⣆⣇⠈⡆⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢁⣼⢧⠀⣇⣿⣽⣶⡧⡟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠉⢻⡷⡿⠿⢿⣶⢿⠟⠉⠉⠉⠹⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⠀⠠⠀⢠⡏⠐⢄⠀⠈⠉⠀⠀⠠⠀⠀⠰⠆⠀⠀⠀⡎⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠀⡈⠀⢠⢠⠁⢀⣄⠙⣲⣤⣀⡀⠀⠀⡹⠃⠁⢀⠃⠄⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⢫⠀⠸⠒⠋⠀⠢⠈⠒⠀⠁⠔⠀⠀⠀⠀⣼⢀⣀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢣⢸⠘⠀⠀⠀⠀⠀⠀⠀⠁⠿⠀⠀⠀⠀⠀⢰⠛⢯⡈⡄⠀⢀⠔⠁⠚⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢀⡴⡀⠀⢀⣄⡘⣢⣽⠃⢀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠃⠀⠀⠙⢦⣀⡁⠀⢀⠀⢀⣐⣯⡄
⠀⠀⠀⠀⠀⠀⠪⠊⠀⠔⠁⠀⠛⠁⠀⠈⠃⠀⠀⠉⠆⠂⠠⠀⠌⠉⠛⠀⠂⠙⠠⠀⠀⠀⣀⠉⠛⠒⠛⢠⡄⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠁⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⢦⡀⠀⠀⠀⠁⠀⠐⢧⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠄⠖⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠱⣄⠀⠀⠀⠐⢧⡀⢁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢳⡀⠀⠀⠀⠘⠀⣀⠠⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠙⠖⠐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣎⣁⣤⣤⣤⣐⣶⣒⣒⣒⠀⠀⣄⣰⣀⡤⠖⠒⠒⠀⠤⠤⠤⠤⠠⠤⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠊⠉⠉⢢⡀⠀⠀⠀⡠⠒⠛⠒⢦⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠈⠁⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣮⠵⠒⠊⠉⠉⠉⠉⠙⠓⠶⡰⢄⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢀⡴⠚⢢⠤⠴⠄⠖⠤⠵⢦⡀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠐⠇⢤⡀⠀⠀⢇
⠀⠀⠀⠀⠀⢰⠁⣰⠒⠒⠚⠉⣀⠀⠘⡖⠒⠚⠛⠛⠒⢲⠳⡄⠀⠀⠀⠀⢀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠦⣄⣀⠀⢱
⠀⠀⠀⠀⠀⡏⠀⠘⣆⠀⣰⢋⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⠑⠼⣄⡀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢒⣺⢤⠀⠀⢈⠆⢇⠀⣠
⠀⠀⠀⠀⠀⠇⠀⠀⠈⠓⠁⢸⠑⢤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠈⠒⡤⢤⠤⣤⣠⡤⠤⠢⠔⠒⠉⢸⠈⢄⠤⠋⠀⢸⠉
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠁⠉⠒⠤⠤⠤⠤⣄⣀⠿⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠣⣀⣀⢤⣀⠜⠁
⠀⠀⠀⣀⠇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠀⠀⠀⠀⠰⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⢤⠔⠂⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠓⢒⠀⠀⠀⢀⠞⣧⣄⡀⠀⠀⠑⠠⠐⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⣀⣀⠠⠤⣶⣊⠁
⠀⠀⠀⠀⠈⠓⠙⣦⡎⠀⢡⠙⠦⠟⣶⢖⣀⣨⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠙⠶⠚⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠫⠀⠀⠸⠀⠀⠀⡏⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⡄⠀⠀⢀⠈⣆⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠆⡇⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢀⠀⠀⣎⠀⠸⡀⠀⠓⠤⡀⢸⢄⠀⠉⠑⠢⢀⠀⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⢑⠂⠀⠤⡇⠀⠀⠀⢀⠠⠂
⠀⠀⠠⠂⠀⠀⠀⢰⠀⠘⠦⢀⡀⠀⠙⠒⠚⢧⡀⢄⠀⢙⡗⠦⣄⠀⠤⠁⡀⠀⠀⠀⠀⠀⠀⠐⢡⠤⠄⠂⠁⠀⡀⠠⠺
⠀⠀⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠉⠉⠐⠦⣠⣴⠾⠉⠁⠋⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠅⡀⢀⠄⢂⠉
⠀⠀⠀⡇⠀⠀⠀⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠁⠀⠀⠀⠀⠀⢀⡠⠵⠀⠀⠀⠁⠘⠀⠀⠉⡁⠔⠂⠉
⠀⠀⠀⡇⠀⠀⠀⡇⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⢠⡟⠤⡀
⠀⠀⠀⠁⠀⠐⠀⠁⠀⠀⠀⠈⠐⠄⠠⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠁⢀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣂⡉⠀⠂⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠐⢀⡈⠁⢀⣀⠭⠔⠒⠉⠀⠀⠀⠐⠀⠀⠈⠂⠀⠀⠐⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠒⠢⢄⠀⠀⠀⠀⢀⡤⠤⠤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠂⠀⠐⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡀⡠⣠⠤⠴⠐⠓⠒⠶⠶⠯⣀⢠⡀⠈⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⣀⠤⣄⢀⣀⣀⣀⣉⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠡⡈⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠏⢀⠤⠤⠤⠚⠁⠀⠸⡤⠤⠤⠤⠤⠤⣭⢦⡀⠀⠀⠀⠀⠀⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠑⢄⠀⠀⠈⢆⠀⠀⠈
⠀⠀⠀⠀⠀⡎⠀⠹⡄⠀⢠⠖⠓⠶⠴⠃⠀⠀⠀⠀⠀⠈⠢⣱⡀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⢤⣀⠉⠀⠒⡌⡆⠀⢀
⠀⠀⠀⠀⢀⡇⠀⠀⠙⠦⠊⢸⠦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡇⠀⠀⠀⠹⠄⣀⠀⣀⠀⠀⢀⣀⣄⣀⠤⠚⢹⠘⠀⢀⠜⠀⢹⠒⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠈⠑⠋⠲⠤⣀⣀⣀⣀⠀⠀⢶⠉⠀⠀⠀⠀⠀⡇⠈⠀⠈⠉⠀⠀⠒⠀⠀⠀⡉⠀⠉⠁⠀⠀⡶
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡌⠀⠀⠐⠂⠀⠀⠀⠀⣀⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⢇⠀⠀⣀⠀⡰⠃
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⠀⠀⠀⠀⢠⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠠⣀⡠⠄⠀⠀⠀⠀⠀⠉⣉⠜⠉
⠀⠀⠀⠮⢤⠀⠀⠀⠀⣰⢇⠀⠀⠀⠀⠢⣀⡠⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣈⠀⠀⠀⢀⣀⡠⠔⠊
⠀⠀⠀⠀⠘⠦⠶⣄⡜⠀⢋⠫⣑⡦⣤⠤⠤⢐⣲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠍⠫⣄⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⢀⠀⠀⠀⡟⡌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠈⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡜⠀⠰⠀⠀⠧⣀⠀⢸⡀⠈⠑⠠⢀⠀⠀⠀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠄
⠀⠀⢠⠈⠁⠀⠉⢰⠀⠡⣄⠀⠀⠁⠺⠬⠶⢆⠀⡀⠉⠲⠦⣄⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠃⣀⡀⠀⠊⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠒⠒⠠⢀⠀⣩⣵⠙⠂⠜⠁⠀⠙⠢⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⡀⠄⠂⠈
⠀⠀⠀⡇⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠉⠋⢀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠠⠀⠙⠒⠃⡀⠄⠚
⠀⠀⠀⡇⠀⠀⠀⡇⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠁⠄⠀⠄⠃⠀⠀⠀⠁⠠⡀⢀⡠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠉⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠈⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣒⡩⠥⠒⠈⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠥⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠄
⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠢⠤⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠤⢀⡀
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠄⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⢱⡄
⠀⠀⠀⡀⠄⠀⠈⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢣⡈⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⣠⠀⠀⠀⠀⠀⠃⠀⡙
⠐⠀⣧⡼⣴⠡⠖⠎⡡⠐⠀⠀⠀⠀⠀⠐⠐⢁⠀⠀⠀⡀⠰⠍⠵⡔⠞⠿⢣⠟⠀⡷⡂⠀⠉⠒⠀⠀⠁⠀⢁⡐⣼⡂⠐⠂⠀⢃
⠀⠆⠀⠁⠘⠈⠀⠀⠁⠀⠁⢀⠀⠀⠃⠀⠀⠈⠀⠀⢠⠄⠀⠀⠀⠇⠁⠈⠈⠁⠉⠁⠇⠀⠁⠀⠀⠘⠀⠀⡞⠀⠑⠉⠘⠀⠀⠈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠭⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠂⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⢽⣧⣤⡤⠤⣥⢤⣶⠖⠄⠐⠃⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠂⡰⠶⠆⠈⢀⡀⠠⠶⡃⠂⠐⢠⠀⢠⡄⢄⠀⠁
⡈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠭⠤⠽⠬⠤⠤⠤⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠂⠤⠤⠤⠤⠤⠤⠤⠷⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠉⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁

⠀⠀⠀⠀⠠⠈⡁⠀⠀⠀⠀⠀⡒⠒⠂⠀⠀⠀⠀⠀⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠀⠀⠀⠀⠀⢐⠒⢒⠀⠀⠀⠀⠀⢈⠁⠄
⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠨⠁⠨⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⡗⠰⢒⣂⣠⠤⠄⡄⢰⠒⡖⢒⢶⡲⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⠒⣲⠒⡆⢠⠠⠤⣄⣐⡲⠖⣯
⠀⠀⠀⠀⠀⠻⠈⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠈⠡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀

⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠠⠤⠤⠄⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⢀⣀⠤⠐⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⡇⠀⠀⠰⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⠞
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠶⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣠⠴⢶⡴⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠦⣴⠶⢦⣄⠀⠀⠐⠿⣭⣽⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡼⠁⠀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢹⠀⠀⠙⣦
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡿⡏⠀⢀⡴⣿⠀⠀⠀⠀⠐⡿⣦⠀⠀⢹⠾⣄⠀⠀⢸⡆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣠⠞⠁⣇⢀⡟⠀⠙⡒⠒⠶⠶⣖⠋⠘⣇⠀⣼⠀⠹⣆⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠛⠓⠒⠋⠁⠀⠀⢹⡛⣧⠀⠈⣤⠀⠀⠀⢨⡄⠀⣾⠛⡇⠀⠀⠈⠓⠦⠤⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⣿⣄⠀⠀⢀⣀⡀⠀⢀⣰⣷⣚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠓⢲⣤⢤⣤⡶⠋⠁⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⠀⠀⠀⠀⠀⢀⡿⠦⣄⡀⢀⡀⢿⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿
⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⢀⡞⠀⠀⢈⣽⠞⠛⢛⣳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠘⢧
⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⡀⣀⣀⣸⠁⠀⠘⠉⠀⠀⠀⢐⣾⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠄⠀⠘⡇
⠉⠛⠉⠙⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠙⠷⢤⣤⣤⣤⠴⠶⠶⠛⢦⡿⠒⠒⠲⢶⣒⣋⠉⠙⠛⠉⠀⠀⢀⣰⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣩⠅⠀⠀⠀⣠⢴⠞⠋⠁
⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠙⢻⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣫⣖⡴⠚⠁⠘⣿⠛⠒⠒⠒⠖⠶⢶⣄
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡼⠛⠛⠉⠉⠙⠛⠛⠶⢤⣤⠶⠖⠛⠛⠛⠛⠓⠲⠶⣤⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣠⣤⣀⣀⣀⠀⠀⣸⠁⢀⣀⣀⣀⣀⣀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠴⠶⠶⠶⠾⢭⣝⡓⠟⢛⣩⣭⣭⣭⣭⣭⣙⡳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⡭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠇
⠀⠀⠸⡀⢅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢘⠂
⠀⢠⢾⠥⠤⠦⠄⠐⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡤⠦⠤⠤⠤⠀⠂⠀⠀⠈
⡀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠌⠀⠀⠈⠁⠀⠈⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣋⣉⣒⣞⣓⣉⣉⣉⣉⣑⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⢈⣉⣑⣒⣝⣓⣉⣉⣉⣉⣑⣶⡀


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡄⠛⠒⠛⠹⠈⠙⠒⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠿⠒⠆⠠⠆⠖⠲⠿⢍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠔⠉⠉⠑⣄⠀⠀⠀⢀⠔⠚⠑⠢⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⠀⠈⠈⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⢒⠮⠒⠚⠉⠉⠉⠉⠉⠛⠲⠠⢢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡠⠚⠑⡤⠒⠒⠒⠒⠈⠦⡀⠀⠀⠀⠀⠀⠀⣀⣧⠜⠁⠀⠀⠀⠀⠀⠀⢀⠔⠢⡀⠀⠣⠤⡀⠀⠀⠧
⠀⠀⠀⠀⠀⡜⠀⣞⠉⠉⢉⣡⣀⠀⣻⠊⠉⠉⠉⠉⠑⡛⢆⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠐⠠⠄⣀⠹⡄
⠀⠀⠀⠀⢠⡅⠀⠘⢆⢀⡎⣄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠚⠦⡄⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⡭⡷⠀⠀⢀⠇⢣⣀⠴
⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠀⡏⠑⠤⠴⢄⡀⠀⠀⠀⠀⠀⠀⣈⠧⠀⠀⠀⠈⠙⡖⠖⠲⠤⠤⠒⢊⡒⠉⠁⢠⠁⠣⠔⠁⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠈⠑⠒⠚⠒⠲⠄⠚⠀⠀⠀⠀⠀⠀⡇⣠⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⣰⠀⠀⠀⡄⠀⠀⠀⠀⠒⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⡀⠀⢀⠀⠀⠀⠀⠈⠢⠤⢒⠦⠊
⠀⠀⠠⡔⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⢠⠀⠀⡀⠈⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠈⠛⠉⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠡⣀⣄⠀⡜⠻⠳⡂⢄⣀⣀⣈⠈⢠⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢒⠶⡆⢈⡽⡲⠂
⠀⠀⠀⠀⠀⠀⢈⡟⠁⠀⡇⠈⠉⢹⢗⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠆⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⢁⠀⠀⠘⠈⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡌⠀⠆⠀⠘⡀⠀⠀⡀⠈⠰⠄⣀⠀⠀⠀⡀⠠⠦⠀⠀⠀⠀⠀⠀⠄⠀⠈⢐⠀⠀⠀⠀⠀⢈
⠀⠀⢀⠂⠈⠈⠑⡄⠘⢄⡀⠈⠑⠢⢏⣢⣤⠀⠀⠑⠢⡤⣀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⡽⢀⠀⢀⠄⠊⠀⠀⣠⠂
⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠉⠐⠢⠠⢄⠀⠈⣷⠜⠢⠴⠃⠈⠑⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠔⡋⠀⠀⡠⠄⠒⠁
⠀⠀⠈⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⠀⠠⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠠⠈⠃⠖⢒⡡⠔⠃
⠀⠀⠀⡇⠀⠀⢰⠇⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⣴
⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠈⠀⢄⢀⣀⠤⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠉⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⡈⠡⠀⠀⢁⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠂⢄⣐⠈⠀⣒⡨⠭⠒⠈⠁⠀⠀⠀⠀⠀⠁⠤⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠒⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠿⠿⢻⠃⠀⠀⠡⠀⠀⠀⢀⣠⣒⣂⠄⠀⢸⡀⠘⣰⠀⠀⠀⠀⠀⠀⠀⠀⣇⣻⠀⠀⣒⣃⣈⡲⠆⠈⠀⠄⠀⠁
⠀⠈⠢⠄⠁⠀⠈⠻⠈⠩⠆⠀⠖⠀⠆⠰⠄⠈⣶⣴⣜⡆⠀⠂⠐⠲⠚⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⠀⠀⠅⠀⠅⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⠀⢀⠄⠀⠀⢠⠀⠀⠠⠢⠄⠀⠀⠀⣤⠄⡀
⠀⠀⠀⢳⠀⠀⡇⠀⠠⠀⠀⠀⠀⠆⠠⡎⠉⢰⡀⠀⠀⠀⠆⠀⠀⢀⢆⠀⠂⠀⠀⠘⠀⠀⠀⠨⠀⠀⠀⠀⠂⠀⠀⢸⣁⠀⡹
⠀⠀⠀⠘⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠠⠧⠤⠀⠀⠀⠈⠁⠀⠉⠀⠈⠈⠁⠀⠀⠁⠀⠐⠂⠀⠀⠀⠀⠤⠄⠴⠀⠀⠀⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⡄⡥⠠⠁⠀⠀⠐⠀⠀⡤⠀⢀⠌⣀⡆⠵⠀⠁⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠂⠨⠀⠀⡇⠤⡄
⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⣰⠀⠀⠰⠒⣶⠒⠾⠀⡀⡀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠨⠰⠀⠇⠀⠀⢇⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠂⠀⠀⠀⠀⠀⣠⠖⠲⣄⠠⣖⠒⠒⠒⢒⡆⠀⠀⠀⡦⠴⠤⣄⢀⠤⣄⣀⢶⡄⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡇⠀⠺⠥⠤⡄⠹⠀⠏⢩⡄⠀⡤⠄⡇⢠⢤⠈⠇⠑⡌⢡⠊⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⠀⠙⠛⠒⢲⡀⢈⡀⡇⡆⢣⠱⠴⠃⡄⡆⢸⡤⢀⡆⠀⡇⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣰⡒⢒⣊⡠⠞⠀⠧⠇⠈⠓⠶⠚⠁⠷⠤⠔⠋⠀⠀⠙⠚⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣇⢸⠩⠀⢰⠋⣉⠆⢰⠋⡉⠳⡠⡖⠒⠲⢤⡀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢅⠀⡆⢸⠀⣉⠘⡌⠀⠋⣴⠃⠀⢘⢢⠀⢣⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⢸⠀⡇⢸⠀⡟⡄⢻⠀⡷⡈⢢⡇⠘⠋⢀⡎⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠈⠳⠃⠘⠚⠁⠘⠋⠓⠃⠙⠊⠱⠶⠖⠋⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠴⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⢶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣄⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣑⠲⠦⠤⠤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠉⠚⠒⠒⠒⠒⠲⠶⠄⠀⠤⠤⠄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠤⣤⣤⣤⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠶⠶⠾⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣄⠀⠀⠀⠀⠀⣀⠴⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠖⢉⣀⠀⠀⠀⠀⠀⠀⠑⢤⣄⡀⠀⢴⣂⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡐⠆⠀⢠⠃⡴⠉⠈⢦⠀⢶⡀⠀⠀⠀⠈⣿⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢰⠃⠀⠀⠀⠑⢬⣯⠲⣄⠀⠀⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⣀⠀⠀⠀⠈⡁⠀⢙⠒⣼⠀⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠉⠀⠠⠀⠀⠁⠀⢸⡞⠓⢤⡈⢃
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠢⣄⠀⠀⠀⢀⣠⠔⠣⣀⠀⢀⡧⠃
⠀⠀⣖⣩⡄⢨⣑⣩⣭⣍⡒⡄⠀⡸⠁⠀⠀⠈⠛⠝⠁⠀⠀⠀⠈⢆⠀⠀⢸⣉⣉⣉⣉⣉⣹
⠀⠀⠈⢎⣀⣀⣀⣀⣀⣱⣈⠁⠀⡇⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡧⠤⠤⠤⠤⠤⢼
⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⣀⡇⠀⣟⢀⣪⣆⣀⡀⠀⠀⣀⣀⠤⠤⢄⠇⢀⠋⠉⠉⠉⠉⠉⠹
⠀⢀⣠⠚⠒⠒⠒⠒⠒⠒⠒⣇⣀⣻⣲⠫⠝⠀⠈⡉⡉⠤⠹⢯⣂⣸⣀⣀⠗⠀⠀⠀⠀⠀⠰⣄⣀⡀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠊⠉⠀⠉⠒⠊⠉⠉⠉⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠠⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠁⠀⠀⠀⠀⠈⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⡀⠘⡄⠀⠀⠀⠀⠀⢀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠄⠂⠀⠁⠀⠃⠨⠐⠀⠀⠒⠚⡑⠈⢤⠊⠡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣈⠀⠀⠀⠐⣄⡄⠀⠀⠢⡀⠀⢀⠀⠀⠀⠔⠀⡀⠁⠐⣰⠃⣀⣀⣡⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠉⢁⠃⠠⣌⠉⡀⠠⠀⠈⠂⠤⢠⣤⠤⠔⠊⠀⠐⠊⠉⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠤⡂⢀⠲⣌⠓⣷⡦⠴⠦⠤⠀⠠⣀⠦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠙⠊⠡⠄⠀⠀⠀⠈⠁⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⣒⢒⣒⣒⣀⣀⣈⡁⠀⠐⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢓⡦⢄⡠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣿⣿⣧⡀⣍
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠻⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢿⣿⡿⠋⠁⠀⠀⠀⠀⢻⡋⡻⠿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⠅⡩⠗⠀⠖⢬⠹⢄
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣾⣿⢦⡠⡬⠌⢒⣣⡀⠈⢻
⠀⠀⢠⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⢰⢠⣥⣄⠍⠉⢘⠣⣤⡀⠑⢄
⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠻⣿⣿⡿⠀⠀⠈⢓⡿⡟⠿⠔⠁⢰⣿⣿⡄⠀⠑⢄
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⢅⠀⢐⣤⠜⢁⡷⢦⣄⣠⣞⠀⡇⠀⠀⠀⣼⢿⡟⢹⡀⠀⠀⢳
⣀⣶⣿⣷⣆⣀⣀⣀⣀⣀⣀⡀⡋⠀⣩⣟⣶⡤⠤⢮⣷⣀⢀⡾⢀⠉⣿⠙⢹⣉⡿⠀⠙⠟⢼⡀⠀⠀⡇
⠻⠿⣏⣉⣙⣛⡛⠛⠛⠛⠛⡱⠚⡾⠿⠿⠿⠿⣿⣷⣶⣦⣭⣝⣒⠦⡼⠦⣞⣓⣀⣡⣭⣭⣭⣭⣿⣶⣥⠤⠤⠤⠤
⣀⣀⣈⣉⣉⣉⣉⣉⣉⣛⣛⣒⣈⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣛⣛⣻⣧⣟⣛⣛⣓⣒⣒⣒⣒⣛⣛⣛⣛⣃⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⡀⠶⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠒⠲⡖⠀⡀
⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠊⠁⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠖⠓⠒⠒⠒⠿⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠐⠆⠀⠖⠈⣦⠠⡄⠶⠴⠲⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢄⣀⠜⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⢠⠀⠀⡤⠀⢰⡇⠐⠟⢠⠦⡀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⡆⠀⡄⡛⠉⠉⠙⠛⠛⡟⠒⠒⠒⠒⠒⠀⠐⠚⡇
⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠂⠀⠘⠀⣈⣤⣤⣶⡄⠘⢧⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠐⠾⣄⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠿⠍⡉⠛⠛⢳⠲⠶⠤⠤⠤⠄⠀⠀⡏
⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⡔⠉⠙⣿⣿⣿⣿⣿⣿⣇⠐⠂⠈⠁⣀⡠⠂⠑⡀⡀⠀⠀⠀⡀⠃⠀⠘⠀⢘⠁⠀⠀⠀⠻⣦⣄⡘⣄⢂⠀⠀⠀⠀⠀⠀⢃
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⢿⡀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡄⠐⠡⠀⠀⠀⠀⠀⢁⠀⢰⡆⠠⢘⡇⠀⠀⠀⢠⡏⠀⠈⠹⠃⠠⠠⢤⡜⣉⠀⠉
⠀⠀⠀⠀⠀⢶⠀⠀⠀⣀⣘⣧⠀⣴⣿⣿⣿⣿⣿⡟⢂⣠⡀⠀⠀⠀⠀⠄⠂⠀⢠⣴⠀⠈⡀⢸⣇⡔⠋⠀⠒⠒⠂⠈⠀⠀⡀⡀⠀⠀⠀⠤⠀⠀⣀
⠀⠀⠐⡀⠀⠈⠇⠀⠀⠀⠉⠙⡆⣿⣿⣿⣿⣿⣿⢀⡀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⢀⢧⡽⠂⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠉⠒⠂⠒⠀⠀⠉⣤
⠀⣴⣿⣿⣦⠀⠈⠀⠛⢲⠀⠀⠡⢈⣿⣿⣿⣿⡇⠈⡀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠈⠁⠒⠀⣤⣀⡀⠀⢹
⠰⣿⣿⣿⣿⣷⠀⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡿⠽
⠀⣿⣿⣿⣿⣿⣿⠀⡸⢃⣠⠀⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢣⠃
⠀⠟⠛⠛⠛⢻⣉⢱⣧⣬⠛⠋⠉⠉⠉⠉⠛⠟⣿⣷⣶⣾⣿⣾⣿⣿⣻⣿⣶⣶⣸⣿⠀⡄⠚⢼⠀⠀⠰⠃⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⣼
⠀⠠⡄⠡⠀⢀⡛⠉⠘⠙⠀⣀⠀⠀⠀⠀⢀⣀⠉⠋⠛⢻⣿⡶⠒⠛⠻⡿⠿⠶⢿⣿⠀⠘⠀⢸⠷⠠⠃⠘⡎⡐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡏⣞⠁
⠀⠀⠚⠓⢶⣤⣄⣤⣦⡤⠞⠛⢪⡵⡟⠻⢿⣿⣿⣶⡤⠞⠙⡁⠤⠀⠀⠀⠀⠀⠈⠉⠐⡂⠐⠿⠃⠀⠀⠄⠘⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣼⠿⠁
⠀⠀⠀⠰⠹⢿⣟⣿⡿⠓⠈⠑⠀⣠⣄⠀⠤⠦⠀⠈⠚⠓⢀⠀⠀⠀⢠⣢⠄⠀⠶⠖⠂⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠄⠀⠀⠀⠀⢠⣿⡦⠤⠶
⠀⠀⠀⢢⡀⠏⢡⡏⠵⠀⠠⡄⢀⣉⠀⠀⠀⠀⠀⠀⠀⠉⠏⠀⡀⠀⠀⠐⠂⠀⣼⡟⠀⣤⣄⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠶⠆⣁
⠀⠺⠊⠉⣭⡄⠁⠐⠀⠤⡀⠁⠀⠀⠉⠀⠀⠀⠀⢠⣀⢠⣄⠀⠀⢀⣀⠀⠀⠀⠈⠉⠀⠻⢿⣯⡛⠦⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⢋⣀⣀⡤⢤
⠀⠀⠀⠀⠛⠘⠛⠲⠦⠄⠀⢹⣶⣶⣤⣀⣀⢀⣠⣤⡞⠁⠉⠍⠉⠉⠉⠀⠤⠠⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⣶⢤⣄⣠⣶⠟⠿⠶⠶⠖⠋⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠛⣿⠛⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣿⢿⣥⢀⠀⠀⠀⠀⣀⣨⠥⠆⠒⠛
⠀⠀⠀⠀⠀⢤⠤⢄⣀⠩⠁⠒⠀⠀⠀⢀⠏⠐⠀⠀⠀⠀⠓⠒⠒⠒⠒⠀⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠀⠈⠙⠖⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠤⠄⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠆⠄⡦⠆⠆⠰⠠⠰⠱⠰⠴⠴⠤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠘⡯⠍⠙⠟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⠍⠻⠟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠽⠉⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⣤⡀
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣧⣄⣀⡀
⠀⠀⠀⠴⠿⠿⠿⠷⠤⠤⠤⠾⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠈⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠟⠻⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠛⠿⠻
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠠⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⣿⣆
⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⣄⣤⢰⢰⣶⡆⡦⣤⣀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠐⠃⠛⠛⠚⠘⠛⠃⠓⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⠀⠀⠀⠀⣠⠔⠒⠋⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠞⢀⡠⠶⣄⠀⠀⡀⠀⠀⠀⠀⠈⢻⣿⡦⣄⠀⠛⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠬⠓⠀⠀⡞⢀⡞⠀⠀⠘⢦⠀⢻⣆⡀⠀⠀⠀⠀⢿⠃⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠙⠦⣳⡙⢦⡀⠀⠀⢸⡄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡾⡀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠈⢳⠶⣼⠇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠛⠀⠀⢀⠀⠀⠛⠀⠀⢸⣴⠿⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠤⠄⠀⠀⠀⣠⠟⠁⠀⠈⢳⢀⡇
⠀⠀⠀⣀⡤⠤⠤⣀⣀⡤⢤⣀⡀⠀⠀⠀⢠⠎⠈⠓⠦⢤⣀⣠⡤⠔⠋⠀⠉⢢⡀⠀⠼⠋⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢾⡡⢖⣋⣑⣦⣥⣖⣲⣦⣍⡱⠀⠀⡏⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣯⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣸⣀⡀⠀⢸⠁⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡦⠤⠤⠤⠤⠤⠤⢼
⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀⡇⠀⢸⡞⠀⠭⣧⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡇⠀⢰⠋⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⢠⠼⠭⠭⠭⠭⠭⠭⠭⠭⢇⠀⠸⣷⢌⡽⢛⣏⣉⠑⠲⠒⠋⠙⣧⢂⡄⢈⡇⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠒⠓⠲⠶⠶⠶⠶⠶⠖⠲⠶⠚⠒⠒⠛⠻⣨⠴⠒⠒⢬⣒⣪⠥⠤⠬⢽⡶⠛⠒⠒⠺⠤⠤⠤⠤⠤⠤⠤⠤⠗⠒⠒

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠉⠛⠟⠋⠁⠀⠀⠀⠈⠻⠛⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠈⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⡶⠀⠀⡤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⠀⢀⡠⠀⢀⣀⣀⡀⠀⠀⠀⢠⠞⠀⠁⠒⠄⠒⠀⠉⠉⠐⠢⣀⡀⠐⠂⠈⠉⠐⠂⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠈⠛⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡀⠀⢀⣀⢀⣀⠀⢀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠁⠀⠀⣨⣅⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢏⣀⣀⣀⣰⠊⠀⠀⠑⣦⣀⣀⣀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠐⠒⠂⠀⢀⣤⣌⣥⣤⣄⣀⠀⠀⠒⠂⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⡏⠀⠂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠀⠙⠋⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿⣿⣿⣿
⣿⣿⡿⠛⠁⠀⠀⠀⠒⠠⢄⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⠤⠐⠃⠀⠀⠙⠻⣿⣿
⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣶⠟⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢶⣶
⣿⣿⣤⣾⠏⠀⣰⠆⠀⣴⣄⠀⠀⢿⣷⡞⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠑⠀⠲⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢲⣾⡿⠀⠀⣠⣄⠀⢠⡄⠀⠻⣦⣀⣿
⣿⣿⣿⣿⣤⣼⣷⣤⣾⣿⣿⣷⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣤⣴⣿⣿⣧⣀⣿⣦⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣤⣤⠐⠒⠒⠒⠒⠒⠶⣶⠄⣴⡆⠲⣶⠶⠶⠶⠶⠶⠶⢶⣤⣤⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣉⠙⠿⠿⠛⠛⠛⢿⡶⣦⠀⢸⡇⠀⣽⠿⠿⠛⠿⠻⠷⠊⢉⡁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢂⡴⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣒⣂⣀⣀⣀⣀⣐⣒⣤⣴⣿⣷⣤⣔⣒⣀⣀⣀⣀⣀⣐⣒⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⣀⣀⣸⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣟⠛⠻⣷⣶⣤⡘⠀⠀⠀⠀⠀⠘⠲⣿⡛⢻⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣷⣜⠿⣿⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⡄⠙⠟⣻⣿⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣾⡟⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⠩⣍⠛⠿⠃⠀⠄⢤⠆⠀⠀⠀⠀⠀⣤⠀⠀⠀⡿
⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠈⢎⡓⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⡀⠉⡉⠉⢏⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠻⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠒⠀⠀⠀⢁⣁⣠⡴⢚⣩⣼⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠯⣄⡀⠈⠳⡝⢦⡀⠀⢄⡀⠀⠀⠀⠌⠀⠀⣉⣀⢚⣋⣶⣶⣾⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⣙⣦⣀⡙⣆⠙⠢⠄⠁⠈⠡⠦⠅⠂⢀⡻⠷⠈⢘⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠤⠤⢄⣈⠑⢦⣹⠈⢧⣀⢻⢀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠸
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠈⠙⢦⡹⣆⠈⢿⡿⣀⣀⣀⣀⠤⣄⠀⠀⠀⢸
⠀⡀⠂⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣧⡈⢧⢯⠀⠀⠀⠀⢸⡆⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢤⣀
⠀⠀⠀⢠⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⢳⠘⣿⠀⠀⠀⠀⠀⡇⠀⠀⠸⢸⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠈⠓⠠⢤⡀
⠀⠀⢠⠟⠀⢀⠀⠡⡀⠀⠀⠀⠠⠤⢀⣀⡀⠲⢄⡿⠸⡄⣹⠀⠀⠀⠀⠀⣇⠀⠀⢀⢈⡀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠲⢀
⠀⢠⡟⠀⢀⠈⠲⢄⠙⣄⠀⠀⠀⠀⢀⣀⣉⣛⠒⠚⢳⣁⣿⣄⠀⠀⠀⠀⢹⢰⣊⣀⣵⣮⠆⡀⠁⠖⠰⢧⢀⠔⠁⠀⠀⠀⠀⠀⢀⡴⠋
⣰⠋⠀⠀⠈⠳⢤⣀⠙⠪⢿⣟⠛⠋⠉⠉⢉⣉⡡⠤⠼⢷⣿⣍⡃⠀⠀⠀⢸⠶⠶⠖⠋⠁⣀⠜⠀⠀⢀⠔⠁⠀⠀⠀⠀⢁⠀⣰⠟⠒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠽⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧⠉⠀⠀⠀⡜⠀⠀⠄⠐⢮⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⡠⣣⣎⡙⠒⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⡟⠠⡤⠒⠚⠓⠒⠒⠒⠲⣦⣀⠀⠀⡞⠀⠀⠀⠀⡠⣪⡎⠙⢿⠷⠆⠀⠤
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⣛⠴⣿⠻⠀⣠⠆⠀⠀⠀⠀⠘⡎⢳⠔⠙⢷⡄⠠⣪⢴⣫⡞⢢⠈⠀⠰⣶⣴⡆⠤
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⣦⡀⠀⠶⠛⠁⠸⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⣻⡄⡇⠀⠀⠙⠚⠁⠠⡝⠴⡆⡠⠊⡴⢠⣦⡌⢢
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠋⠙⢦⣄⠀⠠⠔⠋⠁⠀⠀⠀⠀⢀⣀⣀⣀⡝⠈⢁⡀⠤⠀⠐⠠⡀⠈⠳⣄⠑⠒⠠⠬⠍⠅⠼
⠀⣘⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠉⢻⡖⢶⡚⠛⠛⠉⠉⠉⢉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⢄⠈⠁⠀⣀
⢰⠘⠧⢅⣒⠒⠂⠀⠀⠀⠀⢉⡉⣀⣄⣛⣚⠛⢲⣲⠤⣄⠙⢦⠙⢄⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠈⠳⣄
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠌⠃⠈⢳⡀⠣⡀⠀⠈
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡂⠀⠠⠂⠂⠀⠀⢀⠆⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡈⠀⡈⢉⣂⡃⠉⠉⠁⢀⡘⠚⢙⠋⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠤⠁⠘⠿⠛⠛⠛⠀⠀⠀⠘⠛⠻⠷⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⡀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠂⠀⠁⠀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠁⢢⡄⠀⠘⣒⠌⡀⠀⡠⠔⠁⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣖⢃⠉⠀⠥⠀⠐⠈
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⡐⠁⠀⠀⠹⣆⢡⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠈⢁⠦⠀⠀⠒⠚⠂⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⡚⠛⠒⠒⠒⠶⠶⣤⣤⡄
⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡪⠗⠀⠀⠀⠀⡈⠁⠀⣀⡘⠿⠉⠉⠉⡉⠉⢙⡖⢲⣛⡭⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠒⠄⣀⠀⠀⠀⠰⠛⢬⡂⠈⠀⡊⠄⠀⢰⠊⠁⡑⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⠀⠃⠀⢪⣠⣤⣤⣊⡁⠴⢉⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠢⠤⢆⣀⡄⠀⠀⠀⠀⠀⠂⣂⣠⠄⠀⠀⠨⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠉⠉⠙⠒⠒⠚⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠛⠂⠠⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⡆⠀⠉⠋⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⡀⠀⠀⠀⢰⣿⠁⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀⠀⠀⢸⣷⣶⣤⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⣾⡟⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢻⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣤⡄⠀⠀⣤⡄⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⢿⡇⠀⠈⣿⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢹⡇⠀⠀⢻⡇⠀⠀⠀⠀⢸⣷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣷⠀⠀⠀⠀⠘⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣼⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⣧
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡟⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⠀⣠⣤⣶⣶⡇⠀⠀⢿⡀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠿⠀⠀⠸⠇⠀⠀⠀⠐⠛⠛⠛⠋⠹⠿⠾⠿⠿⠻⠿⠃⠀⠀⠘⠃⠀⠀⠘⠃⠀⠀⠀⠀⠸⠇⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠶⠾⠂⠉⠚⠙⠒⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠠⢞⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⣀⡤⠤⠤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⠁⠀⠚⣉⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢦⠀⢠⠚⠁⢰⠋⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡀⠀⠀⠀⠀⢞⠰⠹⠸⠆⠼⠆⠀⠸⢄⡘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⣀⠀⠀⡨⠓⠤⣄⣀⢨⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡡⠔⠉⠀⠉⠚⠳⢄⠀⢀⠜⠫⣀⣀⣀⣀⠤⠤⠤⢖⣋⠀⠀⣔⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠑⠯⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⣽⠛⡟⠐⠂⠤⠄⢀⡀
⠀⠀⢀⡠⠄⠐⢲⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠢⠤⣀⡠⠀⠈⠀⢀⠤⢰⠃⡎⠀⠁⠂⠀⢀⡀⠀⠉⠁⠒⠒⠢⠤⢀⡀
⠀⡎⠉⠉⠉⢹⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠚⢆⠙⠋⣨⡀⠀⠀⠀⠀⠀⢁⡆⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⢤⡀
⠀⢡⢀⣀⠠⣱⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣴⠃⣀⠤⠒⠂⠉⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠒⠊⠉⡏
⠀⠀⠀⠀⠀⡟⠈⠓⠶⣤⣁⠀⠀⠀⠀⠀⠀⠀⢻⠒⠒⠀⠉⠐⠶⠦⢤⣤⣤⠤⠚⠒⠂⠥⠊⠀⣀⠠⠤⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⡜
⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠉⠙⠲⠶⠤⣤⣤⡤⠼⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⠒⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⣺⠉⠉
⠀⠀⠀⠘⠁⢼⡧⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠦⠤⠤⠤⣄⣀⣀⠀⡸⢀⣀⣀⣠⠤⠀⠶⠚⠛⠉⠉⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠂⠀⠀⠈⠑⠤⣈⠓⠦⣤⣠⣀⣀⠀⠀⣀⣠⣤⠤⢀⡇⠀⠀⠀⠀⠀⠀⡏⠉⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⢸⠒⠒⢤⣄⡀⠀⠙⠃⠈⠉⠉⠉⠉⠉⠁⠈⡏⠁⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⢸⠀⠀⢸⠀⠈⢱⣒⠒⡖⠒⡖⠖⢲⠒⠒⡞⠃⠀⡟⠒⠒⠶⠤⢤⣀⣀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠃⠀⢸⠀⠀⢸⡧⠀⡇⠀⡧⠀⢸⡇⢐⣇⣦⠴⠋⠉⠙⡄⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢸⠄⠀⢸⠀⠀⢸⡇⠀⡃⠀⡇⢸⢸⡇⢸⡅⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⣼⠄⠀⢸⠀⠀⣼⡄⠀⡇⠀⠿⡼⢸⡇⠘⠟⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠘⠒⠒⠋⠀⠀⣿⠂⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣥⣼⠃⠀⠀⠀⠈⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⣠⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠶⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣹⣦⣄
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣶⣾⣿⣿⡿⣆
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣀⣀⣈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⢻⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⢸⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠸⣿⣿⡿⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣌⣛⣦⡤⢤⣀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣳⣿⠻⢷⣽⠭⣿⠼⣯⣉⠉⠳⣦⠀⠀⠀⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣿⠉⠻⢦⣉⠲⣄⡀⠀⠉⠓⠒⠛⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣹⠆⠀⠀⠀⠉⠳⣬⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢻⡄⠀⠀⠀⠀⠀⠀⠙⠶⣬⡑⢦⡀⠀⠀⠀⣤⡄⠒⢲⣬⣭⡵⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢾⠛⡛⢻⣿⢦⡀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣌⣩⣭⣵⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠀⣽⠀⢃⠸⡇⠙⢧⣙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠙⢦⣈⣹⡄⠀⠀⠙⠳⢦⣝⣛⣡⠤⠤⣤⣤⣛⡿⠛⢳⣄
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠙⠉⠉⠀⠀⠀⠙⣦
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠰⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢢⠀⣿
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣅⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣸⣿⠀⢸⡇
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠻⣆⠀⠀⠀⠀⠀⠈⢿⣿⠏⠀⢸⡇
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠉⢻⡿⠛⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢧⡉⠛⠛⣷⠀⠀⠀⠀⠀⢻⡋⠉⣠⡶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⡎⠙⠷⣾⣧⣦⣀⣤⣀⣀⣌⣷⡞⠋⡆⠰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠁⠀⠀⠈⠉⠈⠛⠈⠉⠉⠉⠉⠀⠀⠁⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠻⣷⡶⢤⣀⣀⠀⠀⠀⠀⣀⣠⣷⣶⡿⣋⣀
⠀⠀⠀⠀⠀⠀⣠⡴⠲⠶⠶⣶⠛⠉⠁⠀⠀⠀⠈⠉⠑⢲⡖⠋⠉⠁⠀⠀⠀⠉⠉⠓⣶⠶⠶⠶⢦⣄
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠀⠘⢷⡀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⣷
⠀⠀⢀⡼⠃⠀⠀⠀⠀⠐⢷⡄⠈⢉⣉⣉⣉⡀⠶⢀⡀⠘⠃⢀⡀⠤⣄⣉⣉⣉⡉⠁⢠⣾⠀⠀⠀⠀⠀⠘⢇
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠛⠛⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠟⠛⠿⠿⠿⢾⡇⠀⠀⠀⠀⠀⠀⠘⣦
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠙⠶⢤⣤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡤⠶
⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢉⡏⠁⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠁⠈⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣴⠿⠓⠉⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠓⠚⠿⣦
⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣶⣮⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣵⣶⣶⣾⣭⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⠟⠻⠿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣠⣀⣤⣤⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⢋⣝⣛⡒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢿⣃⢀⣾⡿⠋⠉⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⣿⣿⢫⣍⡀⠀⠉⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠟⠁⠁⠀⢹⣿⣶⠋⣟⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠉⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡀⠈⠙⠇⠑⠶⢄⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⣠⡖⠂⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠑⠀⠈⠙⠒⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣉⠀⠤⠀⢀⠄⠀⠀⡀⠀⠀⠀⠀⡄⡰⠋⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣞⣠⠔⣿⡦⠀⠘⠁⠀⠀⠀⠀⢀⠃⣀⠀⠀⠠⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡏⢹⡄⠀⢀⡀⠀⢀⠀⢰⣌⠺⠕⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠺⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣇⠀⣾⠁⢀⡌⠀⡼⢋⠄⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡖⠂⠴⠀⢠⠀⠨⠳⠦⣝⣿⣿⣿⣿⠿⣿⣿⣿⡈⣿⣸⡏⢀⡞⢠⡾⠒⠁⠀⠀⠀⠀⠀⠀⣠⢐⠜⡇
⠀⠀⠀⠀⠠⠚⡄⠛⠀⠀⠁⠀⠀⠸⡄⠘⣿⣿⡟⠋⠀⢿⣿⣿⡇⣿⣿⡇⣼⣴⠯⠐⠀⠀⠀⠀⠀⠀⠀⡴⡤⠀⠀⣿
⠀⠀⠀⠀⠶⣄⠹⠖⠀⠀⠀⠀⠀⠀⣹⠋⡙⠙⠀⠀⠤⠬⠿⠿⠷⢿⡿⠒⢻⣐⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠛⣓⠂⡀⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠋⠒⠒⠲⢼⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⢤⣤⣀⣀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⣀⠼⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠶⠬⠿⠶⠦⠤⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠩⠭⠝⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⢁⣀⠀⠀⠤⠠⣐⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠄⢻⡍⣙⠛⢛⡋⠉⢻⠀⢀⣴⣾⣿⣿⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠗⠋⠀⡙⠀⠈⢁⠀⣼⢰⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣦⡀⠑⠒⠒⢁⡴⠃⣿⣿⠉⡉⠀⢙⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠿⣛⣒⣛⠿⠛⢦⣿⡇⠈⠋⡀⠘⠃⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⣀⡤⠖⠒⠦⠤⡴⠊⠹⣿⣿⣄⠁⠤⠘⢀⣴⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⢦⡿⣿⠖⣆⠀⠀⣿⢀⡤⠖⢺⡏⠙⠟⠛⢉⡷⢭⣍⡁
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡞⠀⠀⢀⣯⡀⠀⢸⡋⠀⠀⠘⠶⠋⠳⣤⡼⠁⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠘⠉⠀⣤⠖⢺⠉⠁⣠⠊⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣤⣾⣁⡀⢘⣶⣶⡁⠀⠲⣿⠀⠀⠀⠀⠀⠀⣴⡄⢸⣷⠛⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣼⣆⢩⠻⣇⠀⣙⣢⢄⡈⠛⠓⢦⠤⡄⢰⡿⠤⣼⡽⠛⠀⢀⡗
⠀⠀⠀⠀⠀⠀⢀⠞⢹⣾⡃⠘⢣⠃⠀⣟⣚⡿⢡⠎⠷⢤⣀⡿⡰⣟⠛⠁⠀⠀⣀⡤⠴⠺⣅
⠀⠀⠀⠀⠀⢠⡿⠐⠚⠒⠒⠠⡧⠄⠒⠚⠛⣲⣃⣎⣎⣎⡛⡑⡝⡿⠛⠲⠖⠺⣅⣀⣠⣤⣌⣧⡀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠓⠷⠞⠛⠋⠙⣇⣈⣉⣉⣉⣰⠼⣦⠖⠛⠉⠉⠉⠛⠉⠀⠀⠀⠈

⠀⠀⠀⠐⠂⣐⣒⣒⣂⣐⣒⣂⣂⣒⡒⠒⢒⣒⣀⣀⣀⠀⣀⠀⠀⣀⣀⣀⣀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠈⠁⠀⢻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣧⢿⣿⠸⣿⠿⠿⠛⠿⠏⣉⠀⣿⣿⡾⣿⠽⠿⣿⣗⣒⣿⡏⠁⢸⣶⠠⡤⠀⠀⣀⡠⠤⠤⣤⡖⢻
⠀⠀⣦⣀⠀⢸⣿⣿⠿⠶⠀⠐⣶⣶⡇⠀⢸⠉⢹⣿⣷⢲⣿⣷⣶⠒⣶⣾⣶⠀⠟⢻⣿⣿⣦⣤⣤⣤⠤⣀⣴⣦⢸⣽⣿⣿⠖⠋⠁⠀⠉⠀⠐⢿⣿⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣶⣄⠀⣀⣿⢽⡇⠀⢸⠀⣸⣿⣿⣿⣿⠛⠛⠒⣛⣛⣻⠀⠀⢸⣿⣿⡾⠿⠿⠷⠤⠿⢿⣿⢸⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠋⠉⠉⠉⠛⠉⠛⠛⠛⠛⠻⠿⠇⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠀⠿⠿⠿⠿⠲⠶⠶⠶⠰⠿⠿⠿⠘⠿⠿⠿⠿⠞⠃⠀⠀⠐⠒⠚⠛
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⡄⠀⠀⠀⣠⠀⠀⠀⠄⠀⣄⣤⣤⣤⣤⠀⣤⣤⡄⣤⣠⣤⠀⠀⠀⠠⢤⣤⣤
⠀⠀⣄⣾⡃⠀⠀⠀⠀⠀⢀⣤⣛⠋⠀⢉⡇⠀⠀⠈⣹⡿⠖⢓⡿⠻⢿⣿⣿⣿⣿⠀⣿⣿⠆⣿⣿⣯⣄⣀⠀⠀⢿⣿⣿⠷
⠀⠀⣾⣿⣷⡤⠶⣀⢀⣀⣾⣿⣿⣤⣀⣾⡇⠀⢸⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⣿⣿⡀⠛⢋⣿⣷⡯⠅⠐⢘⣉⣽⣶
⠀⠀⣿⣿⣿⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠀⠚⣿⣿⣿⣷⣾⣿⣽⣿⣿
⠀⠀⠿⠿⠿⢷⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⡟⠀⠀⢀⣿⣷⣷⣾⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠶⠄⢰⡶⡖⠀⠀⠂⠐⠒⠒⠒⠲⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⢠
⠀⠀⡿⠦⠀⠀⣽⣿⣿⣿⡿⠿⠿⠿⠆⠀⠀⠀⠰⠿⡋⠁⣿⣿⣷⡆⢸⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠃⢸
⠀⠀⣇⣠⣴⣶⣯⣭⣉⣉⣡⣤⣤⣀⡀⠐⡖⢻⣿⣿⣧⣴⡿⣿⣿⡇⢸⣿⣿⣿⣿⣧⠶⠄⢠⠔⢾⡇⠀⢸⣿⡇⠉⡻⢿⣿⣿⠿⠿⠿⠛⠀⢸
⠀⠀⣋⣹⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⠀⣤⣿⣿⣧⣽⣿⣿⣿⣿⡇⢸⡿⣿⣿⣿⣷⡠⣤⠰⣾⢋⡇⠀⢸⣿⡇⢠⠉⢶⣼⣿⣦⣴⣦⠶⠿⢿⡀
⠀⠀⠀⠠⠿⠛⠛⠛⠛⠛⠷⠖⠒⠒⠂⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠘⠋⠙⠛⠛⠛⠛⠛⠒⠚⠛⠃⠀⠸⠿⠇⠸⠦⠼⠿⠿⠿⠿⠿⠄⠀⠸
⠀⢀⣀⡀⢀⡀⣀⣤⣤⣤⣤⣤⣤⠀⡤⠠⠄⣄⡀⢴⡶⠶⢂⣰⣶⠀⠀⣀⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⢤⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⢸⣿⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣾⣧⣬⣴⣶⣿⣿⣿⣿⣹⠀⣦⣍⣯⠉⠉⠉⢹⣿⡶⠒⣦⡤⣬⠀⢸⣿⣿⣿⣭⣽⣿⣿⣿⠟⠋⢀⣏⣈
⠀⠈⠉⣾⡄⢿⣿⣿⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⢫⣴⣿⣟⣛⢿⣿⠀⣿⣿⠉⣴⣶⣶⣾⣿⣤⣤⣿⣇⣿⠀⢸⡍⣏⠀⣿⣦⣄⣠⣤⣤⣴⣿⣿⣿
⠀⢀⠐⠒⣿⢿⡧⢴⠥⢶⣾⣋⣩⡄⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⣿⣿⣤⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠀⠘⣧⣿⣤⣿⣿⣿⣏⠉⠉⠉⠉⠉⣿
⠀⠈⠛⠙⠁⠐⠘⠛⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠚⠀⠈⠋⠙⠨⢝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣪⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠰⠫⢶⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠤⠶⣒⢖⠒⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢈⡤⠶⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢠⠊⣍⢳⠀⢎⠀⠀⡎⠀⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⢤⠀⠀⠀⢰⡌⠈⠈⠁⠘⠀⠀⠈⠂⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡱⠶⠦⢤⣔⠁⠙⠓⢲⡼⠀⠀⠀⠀⠀⠀⢀⣠⠖⠐⠁⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠉⠀⠀⠀⠀⠀⠙⢦⡰⠁⠈⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⣼⣧⠎⣀
⠀⠀⠀⠀⢀⡀⢠⠔⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠉⢦⢄⡀⠀⠀⠀⡀⠀⠊⠀⣀⣹⢁⠞⠠⢀⡈⠉⠐⠂⠀⠠⠤⢀⡀
⠀⡤⠖⠋⠤⢤⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠉⠚⠣⠤⠤⠤⢼⡀⢧⠞⡂⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠄⣀
⠀⠇⠀⠀⠀⣇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣐⡣⠀⠀⡀⠄⠀⠐⠈⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠓⠆
⠀⠘⠂⠉⠉⡏⠳⢦⣀⠤⠀⠀⠀⠀⠀⠀⠀⢻⠀⠭⠐⠠⣤⣤⣄⣀⣀⣀⡀⠷⡀⠐⡡⠀⠁⠀⢀⣀⡠⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠸⡇⠀⠀⠈⠙⠓⠦⢤⣀⣀⣀⣀⣸⣀⡀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠰⠦⡤⠴⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⡶⠖⠋
⠀⠀⠀⡐⢊⡳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠒⡤⣤⣀⣀⣀⣀⠀⠀⠀⠇⠀⠀⠀⣀⡀⠤⠤⠒⠒⠈⠉⠀⠀⠀⢠⠃
⠀⠀⠀⡇⠀⠈⠑⠩⢉⠓⢤⣄⣀⡀⠀⠀⠀⠀⣀⣠⣄⠀⡇⠀⠀⠀⠀⠈⢩⡓⢺⡃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢑⠒⠤⣄⡀⠀⠉⠲⠚⠋⠉⠛⠛⠛⠉⠉⡏⠃⢸⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢸⠀⠀⡏⠈⠉⢶⡰⢤⠄⢦⠴⠠⡆⠒⣶⠇⠀⡟⠒⠶⠤⠤⣀⣀⣸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢸⠀⠀⡇⠀⠀⣿⠄⢸⠀⢸⠘⠀⡇⠀⣇⣦⠴⠋⠉⠳⡄⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣸⠀⠀⡇⠀⠀⣿⠀⢸⠀⢸⢀⠀⡇⠀⡇⠀⠀⠀⢀⣠⡇⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣿⠀⠀⡇⠀⠀⣷⠀⠘⠀⠸⠴⠀⡧⠀⡟⠛⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠙⠛⠛⠁⠀⢸⣿⠀⣀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠟⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⢀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⢀⣼⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢠⣿⣿⣿⣿⡟⠙⠿⣿⣿⣿⣿⣿⣶⣦⡀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠈⠉⠛⠻⠿⠿⠟⠁⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣴⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⡉⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠉⠉⠉⠉⠙⢿⣿⡿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢻⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢳⡄⠀⠀⢀⣠⡶⠟⠋⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡈⠉⠳⣾⠛⠉⠀⢠⡤⠶⠤⢤⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⠷⡀⠀⠈⠳⣄⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⣸⠃⠀⠀⠀⠈⡠⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⢀⡟⠀⠀⠠⠀⡐⠀⠀⠀⠀⡀⣽⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠻⣔⣾⠐⠀⠀⠄⠀⠀⠀⠀⢰⣿⠘⠀⠀⠀⠀⠀⠀⣦⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⢡⠻⣿⠟⢛⠛⠿⢶⡆⠀⠀⠀⡾⠉⠐⠶⡀⠀⢀⡀⠀⠉⠉⠉⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⠚⠉⢖⡉⠡⣠⡜⡇⠀⠀⣸⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢤⠈⡆⢈⡾⠁⠀⠰⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⣁⡅⢸⡇⠀⢰⣶⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠾⠾⡄⠀⠀⠴⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣤⣭⡵⠿⠅⢀⣼⣟⠀⠀⠀⢳⡄⡀⠀⠀⢀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠘⠀⡠⢤⡅⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠻⢯⡁⠀⠀⠘⠛⠁⠀⢸⠇⠀⢹⠟⠒⠚⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⣼⣇⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠐⣶⠀⢀⣴⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣠⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣜⣇⢧⢼⠶⠖⠋
⠀⠀⠀⠀⣰⡖⠉⠁⠉⠹⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⢸⠌⣧⣳⡾⡆⠀⠀⠀⠀⣰⡀⣀⡄⠀⠀⠀⠿⢿⡋⠉⡍
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣷⣇⠀⠀⠀⠐⠋⠉⠋⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⢸⠃
⠀⠀⠀⢀⣟⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣄⣼⣳⣴⠚⠉⠡⢼⣿⣿⣿⢽⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⢸⠀⠀⠿
⠀⠀⠀⠀⠉⠛⠛⠋⠉⠙⠒⠶⠶⠶⠖⠒⠒⠋⣽⣿⡓⠒⠒⣀⣈⣉⣉⣟⠾⠋⠀⠉⠓⠢⢀⢀⣤⣤⠴⠖⠛⢲⠦⢼⠒⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠦⣄⡀⠀⠀⠉⠉⢉⣠⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠒⠒⠋⠉⠢⡀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠔⠠⠠⠔⠉⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠢⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠄⠀⠀⠘⠀⠀⠀⠀⠀⠸⠀⠈⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡁⠔⠒⠀⠤⠤⠊⠉⠒⠉⠈⠂⠒⠈⠁⠢⢄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡖⠀⠀⠀⠀⠀⠀⠀⢐⠀⣐⠀⠀⠀⠀⠀⠀⠀⠑⠽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⢦⡀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⢀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡅⠀⠑⣄⠀⠀⠀⠀⠈⠑⠠⢀⡀⠀⢀⣀⡄⢀⣀⡤⢊⣁⡀
⢰⢷⠂⠀⠀⠀⢤⡤⠠⠤⠤⠤⠤⢤⢤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⢚⢦⡀⠀⠀⠀⠀⠀⢸⠒⠀⠀⠒⠊⠉⠀⠹⠈⢂⠘⠆⢂
⢸⠾⠆⠀⠠⠤⠴⠷⠤⠤⠤⠤⠤⠴⢴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⢁⡱⣤⡀⠀⠀⠀⡀⠀⠀⠀⢀⠤⠄⣀⢰⠀⠘⠀⢠⠈
⢸⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢠⡯⡄⠀⠒⠒⠒⠒⠒⠒⡆⠛⠑⢄⠀⠀⢹⣷⡄⣌⣧⡢⢀⣀⠃⠀⢀⠔⠁⠀⠀⠀⢹⡄⠀⡇⠀⣶
⡼⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠸⠧⠧⠤⠤⠤⠤⠤⠤⠤⠧⠤⠴⠧⠤⠤⠼⣽⠿⠛⠃⠈⠢⣨⠀⠀⡘⠠⣀⠀⠀⠀⡌⡇⠀⠁⠀⣿
⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⡱⠒⠀⢀⠀⡀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣱⡂⠀⠂⠠⢀⣀⢀⠜⠀⠀⠀⠘⠀⡇⢀⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠉⠀⠒⠀⠤⠄⠀⣀⣀⠀⠀⣠⠁⡈⢠
⠈⠂⠀⠐⠂⠀⠀⠀⠀⠖⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⡆⠀⠀⠀⠀⠆⠀⣈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠩⠓⠾⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠇⠠⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠐⣈⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠂⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢴⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠛⠂⠀⠀⠀⠀⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢤⠀⠀⠀⠀⠀⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⣀⢀⠀⣀⡅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣄⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⣠⣴⡶⠶⠶⠶⣦⣄⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⣿⠁⠀⠀⠀⠀⠈⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⣿⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⠛⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⢶⡏⠀⠀⠀⠀⢻⣶⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡇⠀⡥⠉⠐⠒⠒⠊⠁⣿⠀⢸⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⠀⣈⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⣓⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠉⠉⣽⠀⠀⠀⠀⠀⠀⣯⠉⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⣠⣤⡴⢏⠀⠀⠀⠀⠀⠀⣽⢦⣤⣄⠙⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠋⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣷⡀⠙⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠁⠀⡰⠃⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠙⢆⠀⠈⠻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠞⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠳⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠈⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⡇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠿⠆⡾⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢴⡤⢾⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣤⣑⣂⣾⣇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⣶⡙⡞⢦⣈⣿⡟⣿⠖⠊⠉⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⢀⢹⣧⣀⡀⠙⠢⣿⣷⣄⠀⠀⠀⠈⠦⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣓⢎⠂⠢⣼⣿⣿⠘⠧⣀⡀⠈⠳⣻⣦⠀⠀⢸⠄⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⠫⠀⣄⢹⠛⣯⣵⡴⠠⠭⠝⠲⡿⠧⢷⣤⣤⣝⡶⠶⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣦⣴⣶⣶⣼⣾⣤⡿⠋⣠⣴⣴⣶⡶⢶⣶⣬⣤⣁⢫⡉⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠐⡒⢤⡀⣾⢶⠋⠁⠐⠋⠁⠈⠁⢸⡗⠛⡉⠍⠁⢀⣠⣶⣿⣅⡸⣿⡟⣧⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠀⣼⡌⢏⠛⢌⡾⣿⣷⡆⠀⠀⠀⢸⡶⢻⣿⣷⣷⣾⣿⣿⣿⣿⣿⣏⠻⣿⡷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⣏⠻⣌⣦⡎⠆⢿⣦⣷⠀⠀⠀⣸⢿⣿⣿⣿⠙⠻⠟⠋⠘⡽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢰⣦⣬⣭⣍⣈⣉⣉⣉⣁⣾⡕⢻⣿⣿⣿⠁⢰⠀⠀⠀⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠈⠉⠉⠙⠛⠛⠛⠋⠈⠣⡘⠋⣿⣷⡦⠖⠀⠀⠀⠘⠶⠀⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⡤⠒⠒⠠⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠼⠀⠒⠋⢔⠈⠢⣄⣀⡀⠀⠀⠀⠀⣀⠀⠀⣀⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠙⣺⡉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠈⡀⠀⡠⣤⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⠘⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡠⣒⠄⢐⠁⠐⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠒⠄⣀⡑⠀⠈⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠑⢄⠎⠁⠀⠀⠒⠒⠋⠀⢴⡤⠀⡀
⠀⠀⠀⠀⣀⠄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠠⢰⠠⠁⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠈⡄⢐⠆⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠐⠆
⠀⠀⠀⠀⠀⠀⡏⠑⠲⢤⣀⠀⠀⠀⢳⠀⠀⠐⠒⠶⠤⠀⢓⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⠴
⠀⠀⠀⠀⠀⠖⢳⣄⣀⠀⠀⠉⠉⠉⠉⠀⠐⠤⠀⠀⣀⣀⠀⡁⠀⢀⠀⠀⠀⠐⠀⠈⠁⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢑⠲⠦⠤⠤⠤⡶⠂⡄⠀⠀⠀⢸⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡆⠀⠁⠐⡄⠠⢠⠄⢄⢠⠆⢰⠂⠤⠤⠄⢨⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡇⢸⠀⢀⡇⠀⠰⠀⣿⢸⠛⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⣇⣈⠀⢸⡅⠀⠘⠆⢸⠘⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠸⣄⡆⠀⠀⠺⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡠⠄⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠀⠀⠀⠉⠉⠉⠛⠲⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡠⠴⠚⠛⠉⠉⠷⢎⡄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣤⡠⠞⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠹⣄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡗⠀⠀⢀⠀⣴⣋⣉⣠⡀⠀⠀⠀⠀⠐⠛⠋⠉⠉⠁⠀⠀⢹⡀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡾⡾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣠⣖⣾⡖⠢⠄⠀⠈⣇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠸⡁⠀⢀⣤⡶⢶⢦⢠⡄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘⣪⣍⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡇⠀⠁⠈⠛⠋⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢿⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣇⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠠⠤⠖⠒⠈⠉⡉⠉⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⣠⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠙⠳⣄⡀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⣿⢱⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠞⣻⠹⡄⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⣼⠃⠘⣇⠈⠛⠲⢦⣤⣄⣀⣀⣀
⠀⠀⠀⠀⢀⣀⣠⡴⠞⠉⠉⠀⠁⠀⠀⣿⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⢦
⢀⣠⡴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠙⠳⣄⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠳⢦⡀
⠉⠀⠀⠀⠀⠀⠀⣄⡠⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⢙⡶⠤⢾⡁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⠿⡀⠀⠀⡼⢦⡀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢰⠏⠀⠹⡆⠀⡇⠈⠳⣄⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡠⠋⠀⠀⠀⡔⠒⢢⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠰⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠒⠒⠒⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠦⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠲⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣦⣶⣶⣾⠿⠿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⣤⣀⣀⣠⣤⣤⣴⣶⣶⡶⠶⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣖⠼⠄
⠀⠀⠀⠀⠀⠀⠀⢐⣤⡀⠀⠀⠀⠈⠛⠲⢦⣄⡀⠀⠀⠀⢸⣿⠆⠀⠀⠈⠁⠀⠀⠀⣀⣀⣠⣤⠤⠴⢖⣚⣟⣛⣻⣭⣭⣷⣾⠟
⠀⠀⠀⠀⠀⠀⠰⠋⠒⠬⣙⠲⢤⣀⠀⠀⠀⠀⠉⠙⠲⢤⣀⣿⣿⣶⣶⣶⢶⣒⣛⣯⣭⣭⣴⠶⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣤⣷⡤
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣈⠑⠢⢄⡀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⢖⣚⣯⣭⣭⣶⣾⠃
⠀⠀⠀⠀⠀⠀⠈⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡈⠑⠠⢄⣻⣿⣯⣀⣀⣤⣤⠤⣶⣞⣿⣯⣿⡶⠾⠟⠛⠋⠉⠁⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡀⢈⣉⣩⣭⣿⠷⠾⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠒⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⢸⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠞⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⢸⣿⢋⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠼⣿⣿⣄⣠⣤⣶⠶⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⡿⠻⠟⠋⠀⠙⠿⠻⣿⣷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⠋⠈⠐⠀⠀⠀⠀⠀⠂⠀⠹⣿⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠉⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠋⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⢀⠈⠉⠁⡀⠀⠀⠀⠀⠹⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣤⣶⣿⣄⠀⣠⣷⣦⣤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣞⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡛⠛⠛⣛⣛⣛⣛⡆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣥⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣠⡀⣀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣄⣀⡑⠑⠁⠀⡇⠀⠀⠀⢁⠀⠀⠁⠈⠉⠐⠀⡡⠁⣠⡀⡈⠉⢉⡁⠀⠀⢀⡐⠆⡇
⠀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⡄⠀⢃⠀⠀⠀⢈⠀⠐⠀⠀⠠⠆⠀⡇⠈⡄⠀⢁⠀⠸⠤⠤⠤⠤⠃⠀⠃
⠀⡇⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⡇⠐⠌⠀⠀⠙⠀⢰⠂⠀⠀⠉⠇⠀⠇⠄⠉⠉⡁⠴⠦⡀⢸⠀⠉⢱⢸
⠀⠘⠢⠄⠇⢰⡖⠀⠀⠀⠀⠒⠄⠂⠀⠀⠀⠤⠤⠅⠸⡀⣉⠁⠀⠔⠀⡀⣀⠀⠀⠳⠤⠤⠃⠸⠀⠀⠌⠘
⠀⣀⡀⢠⠀⠀⢀⠄⠀⠀⠀⠀⠈⢄⡆⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠓⠒⠒⠒⠒⠒⠒⠂⠀⠒⠁
⠀⠱⠖⢃⠠⠔⢊⠓⠀⠀⡀⠀⠐⠉⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⡀⠤⠤⠒⢂⠰
⠀⠀⣮⠁⠀⠀⠀⠡⠀⠘⠂⡔⠀⠀⠆⠀⡠⠀⠀⠀⠀⠘⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠰⠠⠤⣀⠠⡀⠀⠈⡀
⠀⠘⢿⣧⠀⠀⠀⠀⠡⠀⠸⠁⠀⢀⠀⠈⠈⠀⠀⠐⠀⠀⠀⠐⢄⠆⠀⠀⢀⠌⠀⠀⡖⠀⠀⠀⠀⠘⡄⠀⢡
⠀⠀⠈⣿⣧⠀⠀⣀⠼⠀⠀⡆⠀⢪⠀⠀⢼⠐⠆⡀⠀⡀⠀⠀⠀⠁⠀⠈⠀⠀⠄⢠⠘⡄⠀⠀⠁⠀⠸⡤⠚
⠀⢠⠄⠈⠻⠛⠉⠀⢄⠀⢰⢰⠀⠀⠀⠀⢐⠀⠀⠀⢡⠖⠉⠁⠀⠀⠀⠀⠀⠁⠀⡈⡄⢱⠀⠀⠀⠀⠀⣱
⠀⠠⠼⡀⠀⠦⡀⠀⠈⠀⠀⡘⡀⠀⠀⠀⠈⣄⠀⢀⡌⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠉⠀⠚⢧⠠⠐⠂⠁⡄
⠀⠈⠀⠀⠀⢆⡀⠁⢉⣛⠄⠁⠃⠀⠐⠀⠀⠘⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠀⢤⡀⠀⠀⠠⠤⠤⠄
⠀⠀⠠⠀⠀⠈⠓⠃⠍⠀⠀⠈⢁⡤⠖⣀⣀⣠⡘⡎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡀⠘⡀⠀⠀⠀⠀⠀⡄
⠀⠐⢒⣽⠧⣲⣋⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠛⠉⠉⠉⠉⡀⠀⠄⡲⠃⢀⣉⣉⣀⣀⣀⡀
⠀⠀⠀⢀⠤⠤⢤⠀⠀⠀⠀⠒⠀⠀⠤⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠩⠄⠀⠂⢉⡀⠀⢫⠀⠀⠀⠀⠀⡇
⠀⢠⠲⡉⠉⠉⠉⠉⠉⠳⠀⠀⢀⠀⠄⠒⢆⠠⠄⡄⠀⡀⡰⠀⢀⣀⣠⣠⣤⡄⠈⠁⡠⠚⢀⠀⠀⠀⠸⠳⡄
⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⡇⡄⡄⠀⠀⠀⠘⡄⠀⡇⠀⠈⠁⠸⠏⠁⠀⠀⠂⠘⡄⠰⡥⠀⠀⠀⠤⠦⠀⠀⢼
⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⡀⣇⢱⠀⡔⠒⠂⠉⣉⣉⡩⢇⠀⠄⠈⡀⠀⠀⠀⠀⠰⠀⢹⠐⡒⠒⠒⢒⣲⢲⠁
⠀⠀⠀⠉⠒⠀⠀⠈⠉⢉⠅⠾⠀⠄⢧⠀⣀⣀⠀⠀⠀⠜⠀⠂⠀⠳⠤⠀⡀⠂⣤⠁⠸⡀⠛⠀⠃⠋⠛⠈
⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠉⢀⠠⠈⠙⠓⠂⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⢠⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⢀⠌⠡⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠱⡀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣀⣀⣀⠤⠤⡴⢖⠡⡀⠀⠀⢀⠄⠈⠲⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠌⠀⠀⡈⠀⡠⠠⠀⠀⠀⠁⠔⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⢁⡲⠤⠞⠀⠀⠠⠇⠀⣠⣶⡇⠀⠠⢨⢴⣶⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⠀⠀⠀⠀⠀⠀⢄⠙⢛⠅⠀⠀⡁⠙⣋⠀⢸⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢭⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣌⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⡉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠞⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣇⣀⠀⠈⢀⣴⠀⠀⢀⡀⠀⠤⠄⠒⠊⠁⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⠃⠀⢠⠔⠉⠈⠒⠤⠊⠕⠢⡀⠀⠀⡀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⡾⡀⠀⠀⠀⠀⠂⠂⠈⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⣅⠀⠈⠁⠂⢠⠆⠀⠺⣉⡀⡠⠃⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠈⠁⠒⠦⠓⠆⠀⠀⠀⠀⠀⠀⠄⢀⣀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⡦⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⠈⠪⡪⡢⠀⡀⠨⠦⠀⠒⠂⠀⠀⠀⠉⣀⢀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠂⠀⠈⠛⢠⣠⠄⠠⢤⠀⠒⠒⠈⠛⢝⢄⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣕⢄⠀⢀⠰⢤⣎⠸⡠⠶⡇⠀⠀⠀⠑⢍⡢⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡣⡀⠐⠶⠶⠃⠉⠋⠁⠀⠀⠀⠀⠀⠈⠢⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⠀⠀⠈⠙⠻⠿⠿⠿⠿⢛⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⢀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠀⠂⠁
⠀⠀⠀⠀⢀⡀⢀⡀⠀⠤⠄⠀⠒⠂⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣩⣉⠀⠀⢻⠓⠒
⠂⠈⠉⠁⠀⠀⠀⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡎⡟⢶⠐⠀⠐⠀⣶⡦⠤⠤⠤⠤⠼⠉⠛⠲⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠛⠛⡡⠤⢤⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠟⠙⠓⠶⢤⡼⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢤⡀⠀⠀⠀⠀⠀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠉⠤⣀⣀⠤⠵⠤⠤⠤⢤⡏⣀⢀⠀⠈⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡥⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢎⡑⢂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣰⠋⢀⣀⣀⣠⡴⠋⠀⢹⡊⣉⣉⣉⣉⣁⣛⢢⡀⠀⠀⠀⠀⠀⠀⣤⡵⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠢⡀⠀⠁⠘⣄⠀⠀⠙⢆
⠀⠀⠀⠀⠀⢠⠃⠠⡏⠀⠈⢡⡤⢤⣀⣀⡏⠁⠀⠀⠀⠀⠈⢫⠱⡄⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠉⠦⠤⢀⡈⣆⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠘⢆⢀⡞⢠⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢤⡄⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡠⢿⠊⠀⠀⢀⠃⢸⣀⠤⠊
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠉⠀⠘⠙⠢⢄⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠆⠀⠀⠀⠀⠙⠒⢲⠒⠦⠤⠴⠒⢚⡓⠚⠉⠀⡜⠘⠤⠔⠁⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠈⠑⠂⠤⠶⠲⠤⡤⠬⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠣⡀⣀⠴⣄⠴⠁
⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢢⡤⠒⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠙⢶⠀⠀⠀⠀⣠⢞⣤⡀⠀⠀⠀⠓⠤⠄⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⣀⣀⡀⠠⢠⣔⣂⠁
⠀⠀⠀⠀⠀⠓⠒⢢⣠⠃⠀⠎⠲⢭⠶⣤⣄⠐⢒⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠣⠠⠞⢡⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠐⠀⠀⠀⡏⠄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠇⠈⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢠⠃⠀⡃⠀⠐⣄⠀⠀⢀⠀⠉⠲⠢⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⡔⠈⠁⠉⠐⡄⠘⢄⡀⠀⠈⠒⠼⡉⢢⣄⠀⠀⠉⠂⢤⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠕⢀⠀⢀⠀⠀⠀⠀⢀⣠⠁
⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠉⠐⠦⠄⢀⠀⠀⠘⣂⡜⠦⣠⠞⠀⠙⠢⢄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢀⡀⠄⠂⠁
⠀⠀⠀⡇⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠒⠟⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠐⠮⡴⠀⢂⡀⠔
⠀⠀⠀⢳⠀⠀⠀⢸⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⢀⡀
⠀⠀⠀⢸⡀⠀⠀⡸⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠅⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠊⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⠤⠒⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣈⠁⠀⣀⡨⠥⠒⠊⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⡿⢿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣻⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢈⣠⠤⢄⠀⠑⠪⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠁⠀⠀⠃⠀⠀⠈⠙⠳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠶⠀⠴⣤⣤⢀⡀⠀⣀⠁⠉⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠙⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢀⡄⠲⢗⠀⠀⠀⠀⠛⣳⠂⠀⡀⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⢰⠀⢸⡁⠀⠀⠷⠛⠒⠆⠀⣏⠀⠀⢘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢤⠘⠳⢤⡠⠂⠀⠀⠀⠀⠚⠀⣤⠞⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠀⠀⠀⣠⣀⣀⣀⠀⠉⠉⠀⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⣀⡀⢠⣼⡿⢧⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣼⠛⠒⠶⠶⠶⠶⠖⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣀⠀⠒⠒⠂⠀⣰⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣦⣀⣦⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠂⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠒⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⢻⣿⣷⣦⣤⣤⣤⣤⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⣠⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⠁⡀⠀⠀⠀⢙⠋⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢀⠀⠀⠐⠀⡀⠀⢂⠙⡄⠠⠀⠶⠋⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⠀⣾⠀⠀⡄⣳⢀⡶⡀⢡⡈⠀⠀⠐⢛⣁⣤⡤⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣀⣅⡆⢸⣿⣿⣿⣿⣿⠀⣿⠀⠀⢁⢮⢇⡿⣿⡀⠙⠂⠀⠙⢁⣽⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⡀⡇⡆⠀⢢⠀⠀⠑⣿⣷⣄⡀⠀⠀⠈⢁⡀⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠇⠀⢀⠀⠀⠀⠈⠻⣯⡁⠂⠂⠄⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⠀⠀⠀⠀⠀⠙⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⢸⣧⠤⢤⣶⣶⢶⣶⣤⠽⠛⢿⣆⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣿⠀⠀⠘⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⡾⠛⠉⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠁⠀⣠⣤⣭⣭⣭⣭⣭⣭⣭⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⣿⣻⡿⠉⠉⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⣿⣇⣀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⢀⠠⠀⠴⠀⢸⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⣹⣿⣿⣳⡄⠀⠀⠀⠀⠉⠳⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣭⣌⠙⠿⢷⣮⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣶⣿⡿⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠛⡗⡮⠙⠋⢀⣂⠖⠀⠀⠀⠀⠰⣆⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡚⠀⠀⠀⠑⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⢀⣀⡵⢾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣎⠀⠙⢿⢢⡀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠤⢟⣭⣥⣶⣟
⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢙⣦⣀⣳⡙⠢⠌⠁⠀⠤⠀⠀⣘⠯⠈⠙⠀⠉⠉
⠀⠀⠀⠀⠀⢀⠖⠁⠄⠀⠀⠤⣙⢦⡝⠹⣤⣻
⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠑⣝⣆⠹⣟⡤⠀⠒⠒⢲⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢧⢹⡅⠀⠀⠀⢸⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⢄⣀
⠀⠀⡼⠃⠀⠀⢄⠀⠀⠀⠄⠀⣀⡀⢤⣹⠃⡈⡃⠀⠀⠀⠘⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠤⡀
⠀⡰⠃⢀⠈⠢⢈⢢⡀⠀⠀⣀⣀⣭⣓⠚⢳⣁⣷⣄⠀⠀⠀⡇⠚⣡⣵⡶⢠⠀⠒⠘⢄⠀⠀⠀⠀⠀⠀⢀⠖⠁
⠞⠁⠀⠀⠙⠢⢤⣁⠻⣯⡉⠀⠀⠠⠤⠐⠚⠻⣷⠬⠀⠀⠀⡞⠂⠀⢁⠠⠄⠀⠀⠀⢀⠀⠀⠀⢀⢄⢴⣉⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢳⣄⠀⠀⠀⠀⠀⠀⢘⡇⣀⣀⣠⣁⣀⠡⣌⡃⠀⠀⠐⠀⠀⠀⠀⣀⠴⢧⣎⡀⢀⡀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢞⣰⡿⠀⢠⠀⠀⠀⠀⢫⠢⡄⠳⣄⠀⢀⣢⣛⠆⡀⠀⢠⣄⣤⢀
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠴⠚⠁⠎⣠⠔⠁⠀⠀⠀⠀⠈⡇⠁⠀⠈⠐⠋⠠⡙⠴⢀⠄⠔⣭⣭⠢
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⠳⢦⣀⠐⠊⣁⣀⣀⣀⣀⣤⡤⠤⠁⠀⠀⠀⠀⠐⠄⠈⠱⡄⠐⠂⠊⠁⠐
⠀⢾⡒⢒⠀⠀⠀⠀⠠⠠⠄⠀⢁⣀⣀⣀⡀⠙⢍⠣⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠢⡀
⢰⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠒⢯⡳⠄⠣⡈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠄⠀⠀⠠⠴⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⠙⢦⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⢸⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⣾⣿⣿⣿⣿⡿⠿⠿⠷⠖⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠟⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣯⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⣲⡿⣿⠻⣶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠇⠀⠉⠀⠀⠹⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⡇⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢐⡇⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⡗⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡇⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢐⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢠⣀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠑⠤⣉⣉⡠⠞⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠤⣀⠀⠀⢀⡠⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠺⢄⠀⠀⠀⠀⠀⠀⣀⠕⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠊⠉⠁⠀⠀⠀⠀⠉⠒⠤⠤⠐⠊⠁⠀⠀⠀⠈⠉⠑⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣉⣉⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢰⠀⠁⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠉⠁⣰⣾⡿⢿⣶⣦⠀⠀⠀⣆⢆⠠⠤⠀⠀⡀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠈⡟⠀⠀⠀⠻⣦⡑⠲⠖⢚⣡⡿⠃
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠏⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠙⣟⠀⠈⠓⠒⠛⢤⡀
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢹⡞⡗⢸⠀⠀⠀⠙⠦⣄⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⠀⠀⢠⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠸⣷⠀⠀⢀⡾⠁⠀⠀⣠⠎⠀⠀⠀⠀⢸⣿⡏⠀⠀⣿⠳⢤⣄⠀⠈⢿
⠀⠀⠀⢠⡶⠿⠟⠀⠀⣾⡇⠀⠀⣰⠟⡆⠀⠀⠀⠀⠘⣿⠃⠀⢸⡏⠀⠀⠹⣇⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡇⠀⠀⢻⡄⢳⠀⠀⠀⠀⠀⠉⡄⠀⣿⠁⠀⠀⠀⣿⣤⣼
⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠻⣆⠀⠀⠹⣄⢀⣀⣀⣠⣤⣤⣤⣴⣿⣤⣤⣤⣴⠏⢸⡯⠴⠶⠶⠶⠶⠶⠤⡄
⠀⠀⠀⠀⠘⣷⣀⣠⣤⠤⠶⠾⠓⢦⢀⣼⢿⣉⣹⡇⠀⠐⠲⠤⣄⣀⠀⠼⠱⡤⠠⢹⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⢠⠄⠀⠿⢧⡀⠰⣟⡗⠀⠀⠀⠀⠀⠈⠙⠲⢤⡃⠀⠃⠀⠀⠀⠀⣠⠖⠲⠦⢀⡙⢷⣄
⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠹⠔⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠷⠀⢀⡠⠴⠒⠫⠓⠒⠲⡄⠉⢳⠙⢷⣄
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⠲⢤⡀⠀⠀⠀⢀⣠⡴⠚⣏⠁⠀⠀⠀⠈⡳⣄⠀⣀⣨⠴⠂⢻⣤⡼⠳⡄⠙⠓
⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠙⢷⣠⠖⠋⠁⢀⣀⠼⠃⠀⠀⠀⠀⠹⣌⠉⠉⣀⣠⠶⠋⠁
⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣉⣁⣠⣤⣤⣤⣤⣤⣶⣦
⠀⠀⠀⢻⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣀⣀⣀⣤⣤⣤⣤⣶⣶⠶⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠀⢸⠁
⠀⠀⠀⢸⡇⠹⡄⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⡶⠿⠿⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣇⠀⠙⠛⢻⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⡶⠾⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⢰⡶⠾⢶⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠠⣶⡟⠉⠈⠘⣿⡶⠀⠀⠀⠀⣿⠋⠁⢻⡆⠀⠀⠀⣾⡟⠋⠉⢻⣧⠀⠀⠀⠀⣥⠼⠽⢤⡀
⠀⠀⠀⠀⠀⠀⠹⠉⠉⠉⠙⠀⠀⠀⠀⠀⠁⠠⠶⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⣿⣏⠀⡀⢹⣿⠀⠀⠀⠘⠇⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠾⢶⣖⣿⣳⠀⠀⠀⠈⠻⠆⠀⠿⠃⠀⠀⠀⠀⠀⠆⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠓⠀⠀⠀⠰⠀⠐⠀⢉⠠⠀⠀⠆⠀⠀⠈⠉⠙⣍⢻⠁⠀⠀⠀⡀⢤⠀⠀⣰⠄⡀⠀⢀⠀⠈⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠠⠠⠀⢀⠔⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣽⣘⠓⠀⠀⠀⠀⠀⠁⠊⠁
⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⢿⡄⠀⠀⠀⠀⣾⠏⠙⢿⡀⠀⠀⠀⠀⣿⠛⠛⢿⡄⠀⠀⠀⠀⠸⡇⠉⠙⠻⠀⠀⠀⠀⠀⣿⠿⠟⠛⡇
⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠈⠇⠀⠀⠀⠀⠁⠁⠀⠀⡁⠀⠀⠀⠀⢅⢀⣀⢸⠃⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⣼⣿⠀⠀⠀⠀⠈⠻⠿⠏⠀⠀⠀⠀⠀⠀⢀⠁⠈⣀⠀⠀⠀⠀⠀⣀⠰⠀⠂⢀
⠀⠀⠀⠀⠀⢀⣠⣤⣀⣄⣴⣄⡀⠀⠀⠠⢰⠀⠀⢙⠻⣤⠀⠀⠠⣖⠁⠀⢀⡶⠀⠀⠀⠀⠈⣁⠘⠓⣯⠁⠀⠀⠀⠀⠓⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠈⠉⠉⠀⠀⠀⠀⢀⡌⠁⠐⠈⢡⠀⠀⠀⠀⢠⠉⠀⠉⠙
⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠘⠛⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⠀⠂⠀⠂⠰

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡟⠿⠻⢿⡆⠀⠀⠀⢰⣿⣿⠋⢿⣷⠀⠀⠀⠀⠔⡋⣉⡉⡓⡄⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⣴⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠈⠁⠀⠀⠀⢸⡉⠁⠀⠁⣽⠀⠀⠀⠀⠸⠉⠉⠉⠻⠁⠀⠀⠀⢸⡿⠿⠿⢾⠇⠀⠀⠀⢸⣿⠯⠀⠟⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⢸⣿⡄⠀⢼⣿⠀⠀⠀⠀⠀⣠⠀⢠⡀⠀⠀⠀⠀⠀⢳⣶⣷⡾⠀⠀⠀⠀⢸⣿⣀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠊⢠⡄⠑⠀⠀⠀⠀⠸⠟⠁⠀⠈⠻⠀⠀⠀⠀⠠⠀⠈⠁⠠⠀⠀⠀⢀⠀⠨⠉⠉⠅⠀⡀⠀⠀⠀⠉⠇⠀⠸⠅
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣼⣷⣦⡠⢄⣠⣾⣷⠀⢠⠀⠀⢠⣤⣆⠀⠀⠄
⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⣿⣿⣿⠟⠚⣿⣿⣿⡀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⡤⠄⠀⠤⠤⠤⣀⡀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠊⢀⡠⠶⠠⠀⠀⢀⣀⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡾⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⢄⣀⣠⠠⠄⢀⡠⠄⠠⠆⠠⡟⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡊⢁⣀⠀⠀⠈⠀⠀⢀⣀⠀⠨⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⠀⠐⢏⡀⠤⠁⠀⠀⠀⠀⠉⠄⣈⠀⠃⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣤⠃⠀⠀⠾⠀⠀⡀⠀⠀⠐⠟⠀⠀⠸⣇⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⡀⠀⣠⠆⣼⠿⠞⠳⣄⠀⢀⡠⠃⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⢿⠏⢴⣁⠴⢀⣐⣤⣴⠞⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠈⠉⠉⠀⠉⠀⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⢠⡄⣠⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⢻⡀⠀⠀⢈⡷⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠤⢠⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⢰⡠⠐⠊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⢡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠘⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⢙⡟⠀⠀⠀⢙⠀⠀⠈⣿⠁⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠘⠀⠀⠀⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠁⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢈⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣼⠀⠀⢪⣍⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⢀⣸⠀⠀⣆⣀⠙⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠁⠀⠀⠈⠉⠛⠛⠛⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣛⣹⣏⣹⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣿⡟⣻⣽⣾⣿⣷⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣾⣿⣷⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡆⢀⣿⣆⠀⠀⠀⠰⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⣿⡇⣸⣿⣿⣷⡄⠀⠨⠭⠭⠭⠭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠙⠁⣿⣿⣿⣿⣿⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢀⣾⠿⠛⢉⣿⣿⣿⣧⠀⢰⣿⣿⣿⡏⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡍⠀⠀⠀⢸⣿⣿⣿⣿⡀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⠙⣿⣿⣿⣷⣿⣿⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠃⠿⠿⠶




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠛⢻⣿⣿⣿⣿⡷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣯⠀⠀⠉⠙⠛⠛⠋⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡏⠀⠈⢀⡈⠁⠀⠀⣘⡛⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡹⡇⠀⠀⠉⠁⠀⠀⠈⠉⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠃⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠙⠪⠍⠩⠍⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠘⠀⠈⢳⣤⡀⠀⠀⠂⢀⡰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⠁⠀⠀⠙⢿⣿⣷⣾⣿⠟⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⡇⠀⠀⢰⠀⠀⢀⠀⠀⠈⠛⢻⠟⠀⡇⠀⠀⠉⠉⠀⠒⠂⠠⠄⢀
⠀⠀⠀⠀⠀⡀⠠⠘⠉⠀⠀⠀⢰⠁⠀⠀⠘⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠐⠉⢦⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⠀⠀⣠⣿⡄⠻⣆⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠓⡴⠉⣿⣦⠶⠈⠛⠅⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⡤⠀⠀⠱⠀⠀⠰⠶⠦⡤⢀⠀⠀⠀⠀⠀⠰⠿⠃⢾⡀⠐⠀⠀⢀⣤⡄⠞⠶⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡟⠁⠀⠀⠀⠑⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣾⡆⢀⠀⡟⠀⡀⠔⡄⠀⠀⠔⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠙⣄⠀⠀⠀⠀⠀⠸⣿⠇⠙⢠⠆⠀⠀⠀⠀⢀⠊⠀⠀⡀⠀⠀⠀⠀⣤⠀⡇
⠀⠀⠻⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢣⣤⡄⠀⠀⠀⠑⠒⠀⠉⠀⠀⠀⠁⠀⠀⠀⢠⠏⠀⡇
⠀⢠⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡇
⠀⠀⠀⡠⠂⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠌⠀⠀⠀⠀⠀⣀⠠⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠁⠀⠀⣧
⠰⠂⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡌⠀⠀⠀⢿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠊⡇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠸⣄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⣿⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⠀⠀⠀⠀⠏
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢀⠀⠀⠈⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡇
⢇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠛⠰⠶⠶⠄⠚⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠲⠀⠀⠀⠀⠀⠈⣅
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠉⠉⠁⠒⠒⢢⠀⠀⠀⠈⡿⠦⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣄⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⡀⣀⣠⡄⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢱⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡠⠔⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣀⡉⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢤⣀⢀⣴⣖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢄⣀⠈⢻⠻⣛⣀⣷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⢰⠒⡒⠋⠽⠁⠱⡜⢢⠀⢟⠁⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⠦⣇⠈⣥⠀⠈⠃⠀⠀⡜⠀⢈⣷⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⢿⢻⡄⠀⠘⣄⠀⠰⡞⢉⡇⣰⠥⡔⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⢾⡄⠀⣠⢼⢒⡤⣼⣭⡜⡹⣆⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠗⠉⣀⡤⣼⣾⠟⣶⠿⣥⠼⠃⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡳⣄⣀⣀⣠⡵⠤⣠⣤⡾⣃⠴⠮⡀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠉⠉⠉⢻⠉⠁⠀⣰⡛⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⡀⠀⠀⠀⠈⢇⠀⡸⠅⠁⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡍⠑⣢⣄⣀⣀⠉⠧⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡺⠋⣀⡔⠁⠙⢄⠀⠉⠙⠒⠒⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⡾⠋⠀⠀⠀⣨⠷⢄⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢻⠀⠀⠙⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣇⣠⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⠄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠈⢀⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠌⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡈⠁⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡁⠀⠀⠁⠀⠀⢠⠃⠀⠑⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠒⠐⠒⠐⠀⠀⠂⠰⣰⡦⡐⠈⡉⡆⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⣒⣻⣀⣀⢀⢠⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡏⠉⠙⠃⣤⡼⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⣿⠁⠀⠉⠓⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶⠒⡖⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢮⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣀⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢡⡾⠤⢄⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠾⠁⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠋⠁⠁⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠤⠔⠀⠐⠠⠀⢢⠐
⠀⠀⠀⠀⠀⠘⢁⠀⠀⢠⠀⠀⠀⣤⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡄⠀⠀⠴⠀⠀⠐
⠀⠀⠀⠀⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠣⣀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠰⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⡆⠀⢁⡹⠁⢈⡄
⠀⠀⠀⠀⠀⠀⠤⠐⠀⠘⠲⠤⠗⠂⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⢃⠀⠁⠑⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⢁⡠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣐⠀⠀⠀⢠⡄⠀⢤⠀⢀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡀⡀⠒⠨⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⠤⠤⠤⠤⠀⠀⠀⠜⠀⠠⠀⠂⠈⠠⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢉⠁⠒⣀⡖⠒⢂⡉⠃⠀⠀⠐⠛⠀⠀⠀⠁⠀⠀⠁⠀⠈⠛⠓⠂⠘⠀⠀⣀⠰⡖⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⣀⡬⠖⠛⠛⢻⠦⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣤⠼⠛⠛⠿⣭⡀⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠂⠀⣀⠀⢸⠐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢿⠠⠄⢀⠤⠤⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢐⠄⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡇⣠⣆⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠨⣶⡠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⠸⠮⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠌⠠⠀⠀⠸⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⢀
⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⣀⣤⣾⣷⡄
⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⢹⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢻⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠘⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠛⠋⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃


⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣻⣿⣿⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠒⠂⠐⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢠⣉⣀⣀⡰⠁⡊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠎⠀⠐⢒⡒⣒⠬⠀⠒⠒⠊⠀⠀⢭⣛⡶⠤⡚⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⢀⣔⣅⡶⣶⣷⠀⠀⠀⠀⠀⣼⣱⢶⣬⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡖⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠁⠀⠒⢠⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢆⠀⠀⠀⠀⢀⣀⣀⡠⠤⣠⣀⠄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠣⣀⠀⠀⠀⠈⠙⠨⠭⠔⠉⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⡤⠤⠡⣦⢀⡀⠀⠀⠀⠀⠀⠀⣀⠄⢚⡤⢄⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⠔⠉⠀⠀⠘⡄⠀⠈⠓⢄⡉⠀⠒⠂⠈⢁⠠⠐⠁⠀⡠⠁⠀⠀⠀⠈⢂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⢈⠔⠲⢂⡉⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⣄⠠⠊⠈⡚⠀⠈⢦⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡂
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠸⣧⠈⠆⠀⠈⠚⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⣀⢀⡠⠋⠀⠀⠀⠀⠹⣧⠘⡄⠘⠙⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠤⠄⠂⠒⠐⠢⣐⡀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⣠⠖⠒⠚⠙⠑⠛⠒⠶⠶⠶⠶⢤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠢⣙⢦⠀⠐⠒⠒⠒⠒⠚⠒⠒⠒⠒⢲⣿⠋⠉⠛⠛⠛⠣⠤⠶⣶⣆⣶⠶⢛⣉⡽
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠉⠉⣲⣄⢱⣀⡀⠤⠀⢒⡀⠉⠩⠍⠡⣒⠪⢉⠉⠀⠀⠒⠒⠠⠤⠴⠧⠠⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⢙⠒⠂⠠⠄⠀⠀⠬⠁⠈⠢⡇⠐⠀⢀⠤⠒⠀⠉⠩⣁⣈⠁⣄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠄⠭⠀⠀⢧⣀⣤⣤⣐⢊⣁⠤⠶⢉⢣⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠠⠉⠁⣀⠀⠉⠡⠄⠀⠀⠈⢅⠠⠀⠒⢂⣀⡀⠀⢈⣉⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡭⠥⠒⠒⠶⠶⠶⠦⣬⣥⣀⣀⣠⠤⠒⠉⠑⠀⠀⠀⠀⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠰⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⡀⠀⠀⠀⠠⢢⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⠄⢠⠀⠀⠀⠞⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⡑⠈⡋⠉



⠀⠀⠀⠀⣀⠀⠀⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠲⠖⠀⠀⠀⠀⠀⠤⠤⠴⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⣀⣀⠄⠐⠳⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠐⠂⠄⠀⠀⠀⠀⠐⠲⠀⢠⡀⠀⠀⣤
⠀⠀⠀⠀⠀⣀⠁⠀⠈⡄⠂⠀⠀⠀⠘⠋⠉⠀⠀⠀⠘⢛⠀⠂⠀⠀⠐⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⢸⠁
⠀⠀⠘⣿⡀⠀⠠⣤⠌⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢈⠀⠀⠀⠀⠀⠀⡀⠐⠆⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⡈⠁⢀⡶⠒
⠈⠓⠘⠋⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⢀⡀⣤⠀⠈⠀⠀⠀⠀⠀⠠⣤⡄⣧⡴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⠀⢀⣤
⠀⠐⠀⠀⠀⠀⠀⠀⠂⠁⠘⠀⠀⠀⠀⠋⠁⠈⠙⢃⠀⠀⠂⠀⠀⠐⠋⠀⡏⠁⢀⡀⠀⠄⠀⠀⠀⠂⠀⠁⡎⠉⠀⠀⠀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⢄
⠀⠀⠀⣀⣁⡀⠀⠼⡄⠀⠀⠀⠀⠀⢀⢤⡄⣀⠀⠀⠀⡄⠀⠀⢀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⣛⠀⠀⠀⠤⣀⣀⠀⠀⠀⢀⠈⣀⠘⠁⠇⡄⠈⠀⠀⠀⠀⢀⣠⡄⠦⠤⢠⡂⠕⠀⠀⠀⠀⠰⠱⢆⠼⠤
⣀⠘⢠⡟⠓⢦⠀⣀⠀⢠⠘⠀⠀⠀⠖⠈⠀⢐⣀⡞⠐⢆⣠⠀⠰⠠⠰⡆⠀⠀⠀⡟⢀⠐⠀⠀⢰⡤⢰⣄⠀⠀⠀⢀⣀⣠
⠐⠄⠁⠀⢀⠘⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠃⠀⠈⢡⡀⠀⠀⠀⠀⠐⢂⡀⠁⠘⠀⠀⠀⠈⠁⡴⡌⠀⠀⠐⣾⡇⠙⢷⡀
⠐⠀⢠⠇⠀⠶⠴⠣⠀⢡⠀⠀⠀⠀⡶⠦⠹⠎⡻⠀⢀⣆⢉⠅⠀⡶⢤⡜⠋⢉⡁⠀⠀⠀⠀⠀⠀⣀⡷⢏⠐⡶⢰⠇⡇⠀⠐⠷
⣀⣀⣀⣀⣈⣀⡀⢂⢀⣀⣀⣀⡀⣀⣀⢐⣀⡀⣰⢀⣀⣀⣀⣀⣀⣀⡀⣂⢀⣀⣴⡀⢂⣀⣀⡀⣈⣈⠳⣊⣉⣁⣀⣤⣈⢀⡀⠃⣀
⣿⠿⡿⠿⠿⠿⠟⠻⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣻⢟⣻⠿⣿⣿⡿⠿⣟⡿⠿⠿⠿⢿⣿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠛⠛⠀⠚⢿⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⣠⡄⠀⠘⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠘⠗⠂⠀⠀⣸⣿⡻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠐⠛⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⠒⠄⠀⠀⢀⢸⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠠⡴⠿⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆⢀⠀⠀⡀⢀⡾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠋⠁⠀⢣⠈⠊⡀⠀⠀⠋⡠⠋⠋⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡀⠀⠀⠀⠀⠀⠀⠱⢄⣉⠀⠀⠈⠀⠀⠀⠀⠀⠙⠉⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⢠⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠎⢁⢆⠠⢃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠱⣔⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⣷⠀⠀⣊⠽⠓⠒⠒⠒⠦⣄⡠⢤⣤⡤⠒⢲⣄⣀⣠⣼⡿⠀⠀⠀⠀⠈⢸⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⡀⠀⡇⢀⣀⠨⣧⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠖⠛⠚⠁⠀⠀⠀⠎⠳⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⣤⣤⠤⣴⣾⣟⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣡⠀⠀⣀⡌⠉⠉⠉⠉⠙⠛⠶⠯⢵⣿⣿⣾⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠿⣶⣿⣟⣤⠤⠖⢛⣿⠿⠛⣁⣠⣤⠤⠤⠶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢠⠀⠀⠄⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡝⠻⣿⡿⠿⣿⣷⡀
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣟⣻⣿⠙⣧⠀⣂⣶⠀⠀⠀⠈⣽⠿⠆⠛⠀⠀⠙⡿⣿⣆
⠀⠀⠀⠀⢸⣿⣇⠀⠀⣢⠱⡀⠀⣠⡀⡀⠀⠀⡀⣍⣿⣹⣿⣿⣿⢿⣿⣷⠾⣇⠀⠀⢀⠁⠀⠀⣰⠀⠀⠀⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠸⣿⣿⡄⡀⠁⠀⢷⡈⠉⠁⠛⠒⠂⣷⣃⣻⣿⣿⣿⡿⠾⣏⣟⣻⡿⠂⠀⠘⠀⠀⠀⠋⠀⠀⡀⢻⡿⠟⠁⠀⠀⠀⠀⠀⢀⡄⢫⡀
⠀⠀⠀⠀⠐⠹⣿⣿⡔⡀⠀⠀⡿⠄⠀⠀⠀⠀⢿⣟⣉⣉⠛⠃⠄⠀⠀⠉⠀⠀⠀⢶⠿⡀⠀⡌⠀⠀⠈⢁⡿⠁⡆⠀⠀⠀⣠⣂⣼⡟⠀⣾⡗
⠀⠀⠀⠀⠀⠆⠹⣿⣿⡀⠈⣴⠁⠿⣄⣤⣶⣶⣞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠁⠉⡥⠴⠒⢃⠸⡀⠀⠀⢀⠄⠀⠀⢀⠀⠀⣀⣴⣿⢟⡄⢠⡿⠁
⠀⠀⠀⠀⠀⠒⠊⠻⣿⣿⡔⠍⣀⡀⠘⢎⠋⢉⠛⠁⠁⠀⠀⠀⠠⣤⣾⠀⠀⠀⠁⠀⠀⠀⠀⠈⣄⣠⠎⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠃⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⢨⣥⣄⢤⡄⠂⢿⣷⣄⣾⣷⣿⣿⡿⠤⠀⠀⠠⠤⠄⣀⡀⠀⠠⠏⠀⠄⠀⠀⡠⠒⡀⣀⣿⣿⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠀⠀⠈⠉⠛⢻⣇⢸⡟⠛⣿⠿⣿⡿⠃⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢾⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡛⢟⣙⠛⣻⢛⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠍⠦⠺⠦⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⣀⡠⠤⡤⢤⣤⣤⡤⠀⠀⣀⡀⠀⡠⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⣴⣭⣤⠤⢤⣼⣧⣄⣀⣉⣒⣖⣒⣛⣲⡄⠀⢀⣀⢹⠤⠛⠗⠉⠺⠲⠤⣀⡎⠀⣿
⠀⠀⠀⠀⢹⣟⣿⡇⠘⡏⠛⠛⠛⡟⠋⠉⢫⢰⠀⢘⣿⣘⣢⡰⣭⠆⠀⢮⡣⣉⠇⠀⢿
⠀⠀⠀⠀⠸⣿⣿⣧⣐⣇⣀⣀⣀⣵⣄⣀⡼⠞⠩⢼⡇⡄⠀⠙⠒⠧⠤⠖⠚⠉⠉⠒⠾⡀
⠀⠀⠀⠀⠀⠈⠛⠻⢿⢿⣿⠚⠛⠛⠋⢋⡇⢀⣤⡾⠷⢇⠀⠀⠀⠀⠀⠀⢀⡠⣠⣶⠒⠈⠢⡀
⢀⣀⣀⡴⠶⠾⠷⢶⣶⣬⣿⣤⣤⠤⣶⣾⣧⣾⡏⠀⣲⣠⡗⠒⠒⠒⠒⠲⡷⣢⢄⠘⣷⠤⠤⢇⣀⠄⠀⢄⣀⠀⠀⠀⣀
⠀⠀⠀⠓⠾⠤⢤⣀⣰⡉⢹⡷⢿⣛⣻⡿⠿⠛⠓⡟⠉⠻⠃⠀⠀⠀⠀⠀⠈⢙⠟⠊⠁⠀⠀⢀⡈⠲⣤⡤⠚⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⢁⠜⠀⠀⠀⠘⠷⠶⠶⠶⣶⠶⠶⠶⠦⠴⠾⣭⣢⡠⠔⠊⢁⣀⣀⣤⣧⣤⠶⠶⠶⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢤⣤⣄⣀⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⠉⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⠖⠉⠉⠑⢦⠀⠀⠀⠀⢀⡤⠒⠒⠒⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡀⢔⣒⠤⠴⠒⠚⠓⠚⠒⠒⠾⢤⡔⢠⣀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⡤⣄⠀⣀⣀⣀⣀⣉⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢥⠞⠂⠀⠀⠀⢨⠂
⠀⠀⠀⠀⠀⠀⢀⠞⠁⣀⣤⣤⡤⠞⠁⠀⠘⣏⣉⣠⣤⣤⣤⣌⣉⣳⡀⠀⠀⠀⠀⠀⠀⣠⠤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠈⢢⡀⠀⠉⠉⢦⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⡎⠀⠸⡅⠀⠀⢠⡤⠦⣄⣀⡏⠀⠀⠀⠀⠀⠀⠈⢧⡙⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⢉⠒⠠⢤⡈⢇
⠀⠀⠀⠀⠀⢰⡅⠀⠀⠻⣄⢀⡏⢠⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⡄⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡥⡟⡇⠀⠀⢀⠆⠸⣄⡠⠞
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉⠀⢸⠙⠢⣄⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡧⠀⠀⠀⠀⠉⠓⡖⢲⠒⠤⠤⠤⠔⢒⡓⠒⠋⠁⠀⡇⠰⠤⠔⠁⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠙⠒⠤⠤⠴⠤⢄⣀⣈⠧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⣄⠀⢀⣤⡀⣠⠃
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠄⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢄⣀⡰⠄⠀⠀⠀⠀⠀⠈⠉⡩⠔⠉
⠀⠀⠀⠲⣋⡀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠴⣀⠀⡀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣈⠉⠀⠀⠀⠀⠀⣀⡠⠴⠊
⠀⠀⠀⠀⠀⠣⣀⣤⡀⢠⠋⠰⡻⣖⠢⢄⣀⣀⣀⡀⠤⢤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢒⠶⢶⠉⢉⡝⡒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠚⠀⠀⡇⠀⠉⠉⢿⡒⠦⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡛⠀⠀⠉⠁⠀⡆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⡇⡆⠀⠀⠛⠀⠀⠀⢰⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠒⠒⢸⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡀⢀⢀⡟⠀⠈⡄⠀⠀⠣⢄⡀⢸⣄⡀⠀⠋⠒⠤⣀⠀⠀⠤⠀⠎⠉⠀⠀⠀⠀⠀⠀⠀⠓⠂⠤⠀⣸⠠⢀⠀⠀⠀⣀⠔⠀⠀⠀⡀
⠀⠀⠀⡬⠀⠀⠀⠀⢸⠀⠈⢢⣀⠀⠀⠈⠙⠢⠭⠶⡄⠀⡀⠀⠙⢶⠦⣀⠀⠀⢄⠃⣀⠀⠀⠀⠀⠉⠀⠀⠀⠎⢠⣀⡀⠔⠊⠀⠀⠀⡠⢮
⠀⠀⠀⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠓⠒⠤⢄⠀⠀⢭⣵⠚⠢⠴⠋⠀⠈⠑⠦⠀⠀⠈⠀⠀⢀⠀⠀⠀⡀⣠⢴⣃⠀⠀⣀⣤⠴⠊⠁
⠀⠀⠀⢸⠀⠀⠀⠀⣸⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢏⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠰⡅⠄⠀⠁⠛⠉⠴⠷⣞⣥⡼⠇
⠀⠀⠀⢸⠀⠀⠀⠀⡏⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠀⡀⠀⢀⡀⠤⠒⠊⠉⠁⠀⠀⠀⠁⠙⢀⣠⡄⠈⠋⠉⠁⠀⣀⣔⠒⠀⡦
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠈⠒⢄⠠⠀⠀⠀⠀⠀⠀⣀⠠⠜⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡠⠒⠲⠿⠒⠒⢍
⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠢⠴⠒⢋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠁⣀⠀⠀⠈⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⠤⠒⢈⡀⠤⠀⠀⠰⡀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠀⠀⠀⠁⠂⠄⡀⠒⠈⠀⠀⢒⣋⠥⠔⠂⠉⠀⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⠄⠁⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⡭⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠉⢀⡀⠄⠂⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣴⣦⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠋⠉⠉⠉⠛⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠡⠂⠈⠈⠁⠀⢀⡸⠻⠟⢉⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠠⠄⠀⠇⠀⠘⣶⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠒⠀⠀⠀⣿⡟⠈⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⣰⠀⠐⠻⠇⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠀⠀⢀⣄⠤⠎⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠉⢐⢲⣶⠂⡁⠀⢀⡄⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠐⢢⠄⠆⣸⡟⠀⠁⠀⠈⡆⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡀⠀⠀⠀⠘⠀⣿⣿⡗⠀⠀⡠⠂⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠃⠀⠀⠀⠀⠀⣿⠏⢀⠀⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⢀⢴⠀⠀⠀⠀⠀⠠⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⠦⣀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⢀⠔⠁⢸⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠁⢄⠀⠀⠀⡽⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠌⣂⠀⡀⢀⠔⠁⠀⠀⢸⠀⠀⠀⠀⠀⠏⠀⠀⠀⠐⠐⠐⠄⡀⠀⠀⠰⠀⠀⠀⠀⠀⠳⣣⡮⠈⠀⢠⠄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠦⠤⠔⢀⡜⢧⠔⠁⠀⠀⠀⠀⠀⡀⢀⣀⡠⠔⠀⠠⠄⣀⡀⠀⠀⠀⠁⠀⡠⠁⠀⠀⠀⠀⠀⠀⠈⠈⢲⠈⠀⠠⢄⣈⡁
⠀⠀⠀⠀⠀⠀⠤⠤⠀⢀⡄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠦⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠤⠐⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢦⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⢆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⣷⣾⠀⣄⣀⣸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⠛⠛⠋⠀⢼⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢛⣁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢋⣥⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⢰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣿⣿⠂⢸⣿⠃⢀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣿⣇⢸⡟⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣹⣧⣴⣿⣿⣿⣿⡿⠿⣤⣴⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣻⣿⣷⡜⣿⣿⣿⣿⠈⠋⠉⠉⠉⢉⣉⣉⣉⣉⡉⠋⠙⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣛⠁⢀⣠⣤⣾⣿⡘⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⠿⣿⢿⣿⡿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣛⣛⣛⠛⠛⢛⣛⣛⣀⣙⡛⣻⡛⡋⣛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣨⣭⣭⣭⣭⣭⣿⣿⣿⣿⣯⣍⣉⣭⣉⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⢤⡀⠀⠀⠀⠀⢀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⣩⢀⣄⡠⠤⠗⠒⠢⠤⢴⣁⡠⢄⠀⠉⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⣀⣄⠀⠈⣀⣀⣈⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡥⠚⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢠⠓⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡼⠁⣀⣤⣤⠤⠞⠁⠀⢯⣁⡀⠠⡤⠄⢉⣑⣄⠀⠀⠀⠀⠀⠀⡤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠈⢢⡀⠀⠀⠑⡄⠀⠀⠑
⠀⠀⠀⠀⠀⢸⠀⠘⡅⠀⠀⣠⠖⠦⣄⡼⠀⠀⠀⠀⠀⠀⠙⢌⢣⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⡄⠈⠒⠀⠤⠸⡀
⠀⠀⠀⠀⠀⡌⠀⠀⠘⢦⡰⠃⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⡆⠀⠀⠀⠹⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠔⡋⠃⠀⢀⡜⠀⡧⠤⠚
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠈⠒⠼⠦⣄⡀⠀⠀⠀⠀⠀⠀⡤⠓⠀⠀⠀⠀⠀⢹⠙⠉⠑⠒⠂⠋⠩⠉⠁⠀⠀⡇⠈⠒⠁⠀⠀⡇
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠃⠀⠀⠤⠀⠀⠈⠉⠈⠉⠑⡖⠒⠊⠀⠀⠀⠀⠀⠀⢸⠠⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡄⠀⠀⠀⠀⠐⠓⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠓⠤⠔⡻⠖⠁
⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡀⠀⠀⠀⠉⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠑⠚⠉⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠈⠹⡀⢀⠀⢀⠞⠹⢶⠠⢀⡀⠀⠁⠂⣁⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢐⢤⡆⠒⣸⠧⠄
⠀⠀⠀⠀⠀⠈⠁⢱⠞⠀⠀⠀⠉⠊⢹⡗⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡍⡆⠀⠀⡇⠀⠀⠘⠈⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠇⠸⠀⠀⢃⠀⠀⠀⡄⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢠
⠀⠀⠀⠀⠀⠀⠾⠀⠀⢇⠀⠈⠒⠤⡀⡧⢄⠀⠀⠑⠢⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⢤⠀⠀⠀⠀⠠⠐⠀⠀⠠
⠀⠀⠰⠂⠀⠀⠀⠘⠀⠀⠑⠤⢀⡀⠀⠉⠒⠛⠦⡀⣄⠀⢨⠉⠢⢄⠀⠂⠁⠤⠀⠀⠀⠀⠀⠀⠀⢁⡔⠀⠀⠁⠀⢀⠠⠒⠃
⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⠈⠉⠉⠐⠤⣠⠴⠋⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⣀⠀⠠⠐⡈
⠀⠀⠀⡇⠀⠀⠀⢸⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⡤⠴⠂⠀⠀⠀⠀⠁⠀⠈⠉⠀⠐⠉
⠀⠀⠀⢷⠀⠀⠀⡼⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠈⠒⠀⠒⠁⠀⠀⠀⠀⠁⠢⠀⠤⠖⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⢂⠁⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢐⣈⠭⠐⠂⠉⠀⠀⠀⠀⠀⠀⠑⠤⠄⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠄
⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠶⠖⠀⠀⠀⠀⠀⠀⠲⠶⠆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⣠⣄⠂⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠟⡀⠀⠤⠀⠈⠻⢃⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠠
⠀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠎⠉⡦⡀⠀⠀⠄⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠠⢄⡀⠀⠀⢀⠀⠀⠀⠀⠒
⠀⠁⠰⠐⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠠⠀⠀⠄⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢀⠈⠀⠀⠈⠀⠐⠃⠀⡄⠀⠀⠈⢀⠐⠁⠀⠀⡀
⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⠀⡇
⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡦⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⢀⡀⠱⠋⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⡀⠊⠈⠉⠁⠈⠁⠐⠚⠆⠀⠀⠀⠀⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠰⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠄⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠆⠀⠀⠀⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠘

⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠐⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠖
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀
⠀⠀⠀⣷⣤⣶⣤⣤⣄⠀⠛⠛⠛⠋⠉⣥⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠍⠩⠭⠉⠭⠤⠥⠤⠤⠆⠀⠀⡀⠈⠁
⠀⠀⠀⠟⠉⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠃
⠀⠀⠀⠶⠲⠶⠶⠶⠶⠖⠒⠒⠂⠀⠄⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣀⣀⡀⣀⣀⡀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⡦⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⢩⣉⣉⣉⣉⡁
⠀⠀⠀⣷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⣤⣄⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠛⠛⠛⠛⠛⢷⣶⣆⣉⠩⠤⠤⠄
⠀⠀⠀⣦⡤⠠⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⡃⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣉⣙⣛⣛⣻⣿⣿⣿⣯⣭⣽⣯⠙⠛⠛⠛⠛⠛⠛⠛⢓⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣈⣈⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⣀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⠴⣯⠉⡠⠀⠀⠀⢄⠉⢿⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠊⠀⠀⠀⠀⠈⠑⠠⠄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠹⠛⠍⠉⠉⠛⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⡾⡀⠀⢤⣀⢀⣐⡖⠀⡀⢠⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡼⠁⡉⠓⠒⠊⠉⠓⠲⢿⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣴⠇⠀⣤⡀⠀⠀⠀⣤⡀⠀⢇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠛⠀⠀⠀⠀⠛⠁⠀⠈⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣀⠀⠀⠠⠄⠐⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡴⢻⢈⣗⠶⠤⠤⠖⣆⢹⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⡌⢸⠈⠉⢳⡖⠊⢹⡈⡆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡟⠢⣠⠇⡇⠀⠀⠀⠀⠇⠚⣇⣧⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣰⣿⣼⠁⠀⠀⠀⠀⠂⠐⢻⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⢇⢘⠇⠀⠀⠀⠀⠀⠀⠀⠘⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢘⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠴⢿⡏⠓⠒⠶⠶⠶⠖⠚⢽⠋⠸⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⡃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢤⣠⣼⠛⣧⢄⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⡟⠀⡟⣭⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡀⣸⣤⣷⡋⢀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠉⠉⠁