Furious Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠀⣠⠀⠙⠀⡀⠀⠄⠀⠘⠀⡀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠐⠀⡍⠢⡉⠀⠁⢀⠈⠢⠘⠀⡀⠀⠁⢃⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⢄⠂⠐⢦⡐⢄⡰⢸⢢⡀⠆⠃⠤⣀⠡⡀⠀⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⠢⡉⠀⠒⡈⠢⠀⣌⢀⠱⡠⢮⠞⠉⠳⡘⠈⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠒⠀⠁⣈⣲⡄⢰⡄⢹⡄⠝⢦⡹⠁⠀⠉⢠⠃⠀⠂⡠⠂⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⢁⣻⡈⠉⠻⡌⠋⡹⠀⠈⠇⠈⢀⣴⠁⠁⠠⠦⠶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣬⡝⠓⠀⠀⢀⠀⠀⠀⠀⢀⠀⠁⠘⡶⠨⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡀⠀⢰⡕⠀⠀⠀⣠⡂⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠉⠀⠀⠀⠉⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢀⠀⠀⠀⠀⠐⠂⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢆⠢⠀⠤⠄⢌⡤⡁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠉⠂⠄⠀⠈⡰⠑⠀⠀⠈⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠕⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠨⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⢊⠄⠀⠈⠆
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠂⠄⡰⢑⠀⢀⠀⢠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠤⠀⢸⠁⡠⢀⠀⠘
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢤⢜⡉⠀⠈⠄⠀⣀⠀⠀⠤⠷⠃⣴⣄⣠⠀⠀⠀⣾⡵⣶⢗⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠒⢔⠀⡠⣿⠶⠶⠢⠂⡄⠾⠀⠀⠀⠀⠒⠘⠿⢓⡽⡂⢸⠁
⠀⠀⠀⠀⠀⢄⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠵⠚⠁⠀⠳⣀⠓⠄⠀⠀⠀⠀⠐⠘⡗⢊⠇⠘⡄
⠀⠀⠀⠀⠀⠀⠡⡀⠀⡀⠁⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠀⠀⠀⠀⠀⠀⢩⡄⡠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠄⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⡀⠀⠀⠀⠀⠈⡇⠒⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠢⠤⣀⣀⣀⠀⠀⠀⠁⠀⠀⠂⠂⠀⠀⡔⠁⢂⠄⠔⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢂⠀⡠⠀⡀⠀⡠⠈⠀⠐⠂⠀⠐⢊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠈⠔⠁⠠⠀⠠⢊⠔⠀⠔⢁⠔⠠⠁⠌⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠁⠠⠀⠄⠀⠊⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠶⠋⠟⢻⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠛⠛⣻⣿⡛⠁⢠⣤⣤⣉⡛⠿⣷⣤⣄⠈⠉⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⡵⠚⠉⠀⠀⠞⠋⠁⠐⢛⡛⠛⢿⣯⣉⠁⠠⠿⣿⣦⡀⠐⠶⣮⡙⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢃⡼⠁⢀⡄⠤⠶⠶⠚⠴⣾⣿⣯⣁⠲⠿⠿⠛⠃⣢⡀⠻⣿⣿⣆⠀⠈⢿⠂⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠈⠛⢢⣿⣾⣶⣶⠶⠖⠀⠀⠠⠾⠟⠛⠃⠀⠀⠈⢻⣷⠦⠀⠙⣿⣷⣦⡀⠀⠀⠀⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠒⢦⣤⢈⣫⣿⣿⠟⣇⠀⠀⠀⠈⠉⠛⠳⢦⣀⠀⠀⠀⠀⣿⣦⣀⠚⠻⠿⠟⠃⠀⠀⠀⠀⠠⡘⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠋⠉⠁⠾⠷⠦⢍⠒⠾⠃⣠⠀⠀⠀⣀⣀⣀⣀⣙⣦⠀⠀⠀⣿⣿⣿⣧⡀⠘⣷⠞⠁⠀⠀⠀⠀⢷⠸⡆
⠀⠀⠀⠀⠀⢀⡼⣷⣋⣤⠴⠒⣁⣤⣤⣤⡗⢠⣌⣙⠛⠶⢤⣿⡞⠛⠿⠀⢨⣭⡤⢀⣴⠟⢸⣿⡏⠃⠀⢹⠀⠀⢀⡀⠈⢶⣼⡇⠃
⠀⠀⠀⠀⢀⡾⠁⠈⠉⢀⡴⠛⠉⠀⠒⠈⠁⢤⡌⠙⠿⣤⣀⡈⠉⣀⣶⡾⢛⣿⠁⣾⠃⠀⢸⢻⠁⠀⠀⣾⠀⠀⠀⢷⣀⠈⣿⠓
⠀⠀⠀⠀⢸⠻⣶⣶⡶⠛⣠⣴⣾⣿⣿⣿⡆⠈⣁⣀⣀⡀⠉⠛⣿⣿⠁⢀⣸⣿⡄⣿⡀⠀⠀⠸⠀⠀⠀⢸⢰⠀⠀⠈⢿⣷⣽⡆
⠀⠀⠀⠀⠸⣦⣨⣿⣦⣴⣶⣿⣿⣿⣿⣯⣤⣤⣬⣍⣀⣡⡴⠂⠸⣿⠀⢸⣿⣿⡇⢹⣧⠀⠀⠀⣷⢠⠀⠀⠸⣇⠀⠀⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠈⠻⡖⢒⣋⣭⣴⣎⠉⢻⣿⣿⣿⡿⣿⡏⢥⡤⠀⠀⡿⠀⠘⠁⣿⡇⢾⡏⢀⠀⣀⡏⢸⠀⠀⠀⢿⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢄⢫⠉⠻⣿⣆⠘⣿⡇⢻⡇⣿⣷⡄⠁⠀⣰⡇⠀⠀⠀⡟⢀⡾⠁⣼⠀⢹⠇⣾⠀⠀⢰⡜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⠉⢿⠹⣧⣽⣿⠘⡇⢸⣿⣿⡀⠀⢹⠇⠀⠀⠀⢀⡾⠁⣴⠏⠀⠀⢰⡏⠀⠀⣼⠇⣿⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢱⣿⡝⠿⠀⠁⣼⣿⣿⡇⠀⠀⠀⠀⠀⣠⠞⢀⡼⠋⠀⣠⢀⣿⠁⠀⠚⡟⠀⣿⠇⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡙⣛⣿⣤⣤⣾⣿⣿⣿⢃⡜⠁⠀⠀⠀⠀⠀⡜⠁⠀⣠⣿⡾⠃⠀⠀⠀⠀⣼⣿⡾⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠉⠉⠀⠀⠘⠻⢫⣾⣀⡾⢸⣠⣾⡇⠀⣀⣴⣾⣿⠟⠁⠀⠀⠀⠀⣼⣿⠟⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣤⣀⡀⠀⣀⣴⠏⠈⡿⠁⠸⡿⢿⣷⣾⣿⣿⠟⠁⡀⠀⠀⡀⢀⡾⠋⠁⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠛⠛⢿⡟⠀⠀⠀⠀⠀⠁⠈⠻⣿⠟⠁⣠⣾⣴⡶⠞⠁⡜⠁⠀⢠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⡴⠂⠀⠀⠀⣠⠀⠀⠉⠀⡼⠋⠀⠁⠀⢠⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣁⣀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⣽⣿⡞⣠⡾⠀⣠⣶⣿⣾⠟⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠿⣿⣿⣿⣥⣾⢻⣿⡿⠋⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⡿⠁⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠋⠀⠀⠀⠀⠀⢀⣠⣴⢶⣿⣿⣯⣷⣶⣶⣶⣾⣿⣿⠿⠿⠿⠿⠿⠿⠛⠿⢿⣷⣤⠀⠀⠙⢶⣤⡀
⠀⠀⠀⢀⣤⡾⢛⣩⡶⠛⠛⠉⣩⡽⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣀⠀⠀⣿⢿⣷⣄
⢀⣤⠶⠛⣡⡴⠋⠉⠀⣀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠰⣿⢿⣢⡀
⠟⣁⣴⡞⠁⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄⠀⠀⠀⠘⢿⣧⣿⡛⣄
⣾⡟⠁⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⣻⣿⣿⣿⣿⣷
⠏⠀⠀⢀⡴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠉⠉⠉⠙⠳⣦⣆⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠀⡰⣷⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⠀⠀⠀⠀⠀⣌⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⣿⣿⣿⣿
⣼⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⣛⠁⣀⣠⡤⠀⠁⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢙⣷⣿⣿⣇⣠⣴⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣿⣿⣿⣿
⣿⡿⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠛⠘⠲⠿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⣠⢀⠔⣄⣠⠀⠀⢈⣿⣿⣿⣿⡟
⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢼⣮⣅⣾⣿⡟⠉⢻⡆⠀⣠⠄⢀⡼⣱⠏⠎⠀⠀⠀⣀⠈⣼⣿⣿⣿⠇
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠹⣿⠉⣣⣔⣧⣨⣧⣼⣿⣴⣿⡿⡃⠂⠀⠀⠀⠈⠛⠆⣿⣿⣿⡟⠘
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⡰⠃⣴⣿⣿⣿⣤⣿⣿⣿⣿⣿⡿⠁⡀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣶⣿⡿⠁⢀⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣯⠞⠁⠀⡀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⡿⠋⡀⢠⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⢂⠀⠀⢀⡼⢃⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣷⡿⠛⡟⠀⠈⢙⣦⡙⣿⠃⠙⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⢠⡔⣴⡟⢱⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢸⠃⠀⠀⠈⠻⣿⣿⠀⠀⠀⣿⣿⠀⠉⠛⠻⣿⣿⣷⣶⣶⠏⠘⣾⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⡍⠨⠃⠀⠀⠀⠈⠛⠀⠀⠀⣙⠘⢄⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠾⠀⠀⣸⣿⠛⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣶⣾⡿⢃⣰⣿⣿⣿⡟⢻⣷⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣴⣿⣿⠏⣹⠏⠀⢨⣿⣾⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠐⢀⠀⣴⣦⠄⠀⠀⢀⣈⣤⣾⣿⣿⣿⣿⣿⡿⣿⣴⠊⠁⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣽⣿⣿⣿⣷⣀⣠⣴⣿⣿⣿⢿⣻⣿⣿⡿⠋⢐⡁⠀⠶⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣼
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣴⣿⣿⠟⣿⣦⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣟⣏⣥⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠐
⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⡿⢟⣩⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣩⣾
⣄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠟⠀⠀⠀⠀⣀⣤⢸⣿⣿
⣿⣷⣤⡀⣀⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣶⣿⣿⡿⠛⠁⢀⣤⣶⣾⣿⠿⠃⠻⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠈⠓⠎⠻⠁⠔⡥⠉⣁
⠀⠀⠀⢀⠔⣉⢀⣀⠄⠀⡀⣀⠤⣀⡀⠀⠀⠚⠫
⠀⠀⠰⠟⠉⣤⡊⠤⢒⠁⠀⠀⠀⠀⠠⡄⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⢢⡀⠈⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠲⡆⢠⠤⡀⠀⠙⣄⢼⠀⠀⠀⣀⣀⠀⠀⡠⠉⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡇⠀⠘⠄⠀⠈⢎⢧⢀⠊⠤⠈⠣⠘⡀⠀⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠸⡄⠀⢸⠀⠀⠈⠿⠋⠘⠁⢀⡄⠀⡇⠀⠙⠃⢐
⠀⠀⠀⠀⠀⢀⡠⠐⠀⠉⠢⠤⣴⠋⠓⠓⠀⠀⠀⢀⡀⠘⢇⠉⠀⠀⠈⠑⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⢤
⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠈⠄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⡌⠀⠀⠀⠀⠚⢢
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠁⠘⠁⡀⣀⣶⣿⡄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡠⠀⠄⠀⠀⢤⠀⠀⠀⠐⠂⡇
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢠⡡⠖⠂⠈⠁⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣁⢎⠀⠀⠀⠀⠀⠀⠦⣀⠤⢧⡨
⢇⠀⠀⠀⠀⢀⣀⠤⠔⠂⠁⠀⠀⠈⢁⠐⠈⠉⠉⠈⠉⠉⠛⠇⠀⡆⠀⠀⡠⢄⡀⠀⣐⠩⠃⠀⠈⠢⠕⢀
⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⣀⠠⠐⠚⢦⡀⠘⠀⢰⠀⢠⠉⣳⠉⠛⢄⠈⢄⠀⠀⡴⠎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⢰⢦⡸⠷⠤⡇⠀⠒⠈⠁⢀⢧⠀⣀⣁⡦⠑⠢⢄⣠⠀⠃⠒⠈⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠑⢄⣤⠆⠀⢀⣠⢊⣠⡘⢮⡁⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠉⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡨⠷⠦⠤⡤⠔⢉⡸⠋⠁⡟⠈⣳⠀⠀⠈⠢⣀⣀⣠⠴⠒⠒⠂⡏⠀⠀⠀⠀⠀⢹⡀⠀⢀⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠘⢊⠝⠃⠌⠀⢸⠺⡇⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⡎⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠘⠃⠐⡄⠀⠐⡄⠀⢐⠂⠒⢸⡀⢹⣍⠀⠀⠀⠀⢀⡀⠤⠐⠒⡖⠀⠀⠀⣀⣤⡞⠥⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠠⠰⡅⢀⡼⠛⠛⠛⠀⠀⡌⢣⡆⢹⡯⡑⠶⠈⠀⠀⠀⠀⣸⠀⡠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡄⢀⡀⢀⢒⠟⠁⠀⠀⠀⠀⠀⢈⠷⡆⠐⠀⠓⠈⠆⠡⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢧⠀⠀⠀⠀⠀⠀⠘⠓⠢⢌⠁⠀⠀⠀⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡆⠀⠀⠀⣀⣀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⢉⣭⠡⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠤⠤⠐⠲⠈⠙⠛⠛⠉⠃⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⠴⠤⠐⠀⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⡴⡋⠁⠀⠐⠋⠉⠀⠀⠀⠀⠀⣉⠁⢦⠀⠀⠀⠀⡀⠒⠊⣀⡩⢀⣁⡶⠊⠉⠉⠉⠳⠀⣍⠃⠬⣵⢦⡀
⠀⠀⢀⠞⠸⠁⠀⠀⠀⠀⠀⠀⠀⠄⣀⣦⡴⠖⣿⠀⠀⠀⢸⠀⢀⣀⠦⡄⠣⡿⠧⣀⠀⠘⣦⠀⠀⠀⢳⡀⠀⠀⠹⣆
⠀⠀⡖⢈⠁⡀⠀⠀⢀⣀⠴⠓⣻⡯⢟⠝⠀⠀⢻⠀⠀⠀⡸⠁⢀⣰⠚⠀⡘⠀⠀⠈⢷⣦⣘⢀⡀⠀⠘⢧⠀⠀⠀⡎⣇
⠀⣘⡔⠁⠀⠁⠀⡠⠁⣠⢶⣰⣿⠓⠀⠀⢹⣷⢀⠀⠀⠀⠀⠠⢴⡷⠈⠀⠱⣿⠍⠀⠀⠸⣟⣦⣽⣆⠈⠊⡀⠀⠀⠆⢸
⢠⣢⠀⠀⠀⠄⠠⠂⢾⣬⢮⣿⣿⠀⠀⠀⠀⠀⠈⠒⠒⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢫⠸⣭⡋⣦⠀⢷⡀⠀⠇⢸
⢀⢋⠐⣤⠀⠀⡞⠃⠀⢹⣿⡏⡿⠀⠀⡀⠀⢀⢣⠤⠀⠀⠀⠠⠒⠀⠑⢲⣔⡀⠀⠀⠀⠀⠀⠰⣧⡾⣿⠀⠘⢱⠀⢀⡾
⠸⠇⢀⠈⠉⠺⡇⢀⣴⢉⣿⣿⣄⡀⠀⠘⢰⠿⠟⠁⠀⠀⠀⠀⠀⠠⠀⠈⠘⢶⣌⠂⠀⠀⠀⠀⣿⡟⣿⡻⠀⠀⣸⡶⡇
⠀⢁⠘⠀⠷⣄⡀⠂⡹⡦⣽⡿⣿⣷⣷⣶⣉⡂⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠀⠀⠀⠀⣴⣿⡟⣿⣷⢀⣴⣷⣷⡇
⠀⠠⠤⠂⠒⠓⢩⠴⠾⠁⠀⢹⠿⠛⠛⠛⠛⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡔⢘⣟⣤⣿⣿⣇⣾⣥⢄⣇⣞⣇⡾⠉
⠀⠁⠀⠀⠀⠈⠈⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠲⠀⠒⠀⠀⢀⠀⠀⠳⠿⠛⠉⠉⠙⢿⠛⣩⢿⡿⣿⣉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠻⣦⡴⣶⠂⢲⢦⣶⠾⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠿⠿⠿⠀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⢠⣴⡶⣦⡄
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣸⣿⣿⣿⣷⣶⣶⣶⢂⣼⣿⠟⣿⣿⡇⢸⣿⣿⣯⣭⣍⠁⠛⣿⣿⡟⠛⠁⣼⣿⢿⣿⣤⡄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠿⠿⠿⠁⠀⠀⠀⠠⠿⠿⠛⠛⠿⠿⠇⠶⣾⢿⣿⡿⠟⠀⠰⠿⠿⠀⠀⠀⠙⠛⠛⠙⠛⠃
⠀⠀⣸⣿⣿⣿⣿⣤⣤⣤⣤⣤⡄⣾⣿⠇⢰⣿⡿⢠⣿⣿⠿⢿⣿⡷⢀⣾⣿⢂⣴⣾⡿⠿⣿⣷⡄⣸⣿⡗⢠⣿⣿⢂⣶⣿⣿⠿⡿⠟
⠀⢠⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⢸⣿⣿⣠⣿⣿⠃⣾⣿⠿⣿⣿⣍⠁⣼⣿⡏⢸⣿⣿⣀⣴⣿⡿⢠⣿⣿⣁⣼⣿⠏⣨⣛⣛⣻⣿⣿⠆
⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠀⠈⠉⠉⠀⠉⠉⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉










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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠚⠛⠛⠋⠉⠉⠛⠛⠛⠓⠲⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠶⠄⣀⠀⠸⠀⠀⠒⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠹⡇⠀⠀⠀⣠⡴⠯⠚⠉⠀⠉⠙⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⢤
⠀⠀⠀⣀⡀⡀⢀⣀⣰⠲⢾⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣷⣰⠶⢤⠴⠒⠲⢤⣀
⢀⣴⣭⣍⡑⠀⠉⠀⢡⠘⣾⠃⠀⠀⠀⢠⣀⣀⡼⢤⣤⠚⠀⠀⠀⠘⣿⠀⠈⠁⢀⠞⠉⠉⠙⡀
⠎⡠⠤⠤⣙⠀⠀⡄⠀⢁⣿⠀⠀⠀⠀⠀⡤⠈⠀⠀⠁⠐⠄⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠄⠠⢵
⠀⡆⠀⠀⠀⣁⣇⡇⠀⠀⠻⣤⣀⡀⠀⢀⡑⠚⠤⠤⠜⢁⡠⠀⢂⣿⠀⠀⠀⢀⣌⠐⠂⠉⠙⡞
⠀⢿⠀⠀⠀⡏⠁⠉⠀⠀⠀⠘⣇⠠⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡞⡿⠀⢠⠔⠉⠈⣧⠀⠀⢠⡇
⠀⢸⡄⠀⠀⣇⠀⠀⠀⠰⡀⠀⠹⣆⠫⠀⡀⠀⠀⣀⠨⠁⠀⠀⣹⠃⠀⣼⠀⠀⢀⡏⠀⠀⢸⠃
⠀⢸⠇⠀⠀⠈⠦⣀⠀⠀⠹⣄⠀⠘⢧⡉⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⢀⡇⢀⡤⠚⠀⠀⠀⢻⡀
⢠⠇⠀⠀⠀⠀⢀⠈⢣⠀⠀⠙⣦⠀⠀⠙⠚⢷⣤⣤⣤⡴⠞⠁⠀⢀⣾⠁⢀⠀⢄⠀⠀⠀⠀⢱
⠇⠂⠀⠀⢉⡀⠙⣤⠂⠀⠀⠀⠈⢷⣄⠀⠀⠈⠀⠀⠀⠈⠂⠀⢀⡾⠃⠀⠈⡧⠋⠀⠀⠀⠀⠀⡵
⠈⠲⠦⠑⠦⠜⠒⠋⠀⠀⠀⠀⠀⠀⣹⠷⢤⣤⣀⠀⠀⣤⡤⠴⣏⠁⠀⠀⠀⠈⠒⠅⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⢀⡤⠴⠀⠀⢠⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠁⠀⠀⠀⠀⠁⢄⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢠⠀⠀⠀⠀⠀⠈⣧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠉⠀⠀⠀⠀⠀⡀⠃⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣯⣽⣵⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣷⣶⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣀⣀⣀⣀⡠⠄⠒⠒⠛⠓⠢⠤⠄⣀⠀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠙⠳⠶⣶⣶⠊⢀⣠⣶⠆⢀⣠⣀⡱⡄⠀⡀⡀⠀⡀⣀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡵⡄⠀⢀⡄⠀⠚⠁⠀⡄⠉⢸⡅⢿⠗⠘⠶⠇⠟⠲⣣⣍⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡸⠆⠀⣀⡼⠀⠸⣇⠱⣌⠁⠀⣉⣉⠤⠴⠖⣙⢆⣩⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣸⠁⠀⠀⣨⠗⠀⢸⠃⠠⠃⠀⠜⡽⠉⠁⠀⠀⠉⢿⣿⣿⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⡇⠀⠠⠟⢻⠃⠀⢰⣅⠀⠈⠆⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⢻⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡇⠰⢲⠀⠈⠳⣄⠀⠀⣠⠏⣰⣿⣷⣶⡖⣶⣶⣶⡾⣤⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡎⢠⡄⠀⠀⠀⠀⢿⣄⠈⣆⡄⠀⠘⠄⠀⣵⢒⢻⣿⢻⢻⣷⣿⡿⠁⣸⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣤⡼⠧⠈⠃⠀⣠⠀⠀⠀⠈⠃⠹⠅⠀⠀⡄⢠⡏⠈⣾⣿⠇⢸⣿⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠴⠶⢶⡄⠀⢀⣿⣀⡀⠀⢀⠀⢀⠀⠀⣼⡁⠸⣧⣦⢹⣿⠸⢿⡉⣿⠇
⠀⠀⠀⠀⠀⠀⣠⠖⠠⠥⠤⠤⠖⠒⠳⡄⠻⢦⣌⠙⠻⣿⠀⠸⡆⠸⣠⡆⠀⢻⡀⠻⡇⢼⣽⣷⣿⣿⣥⣆
⠀⠀⠀⠀⠀⠸⣡⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠳⡄⢹⡇⠀⢿⣄⠁⠸⣄⡄⠁⢀⠉⢸⣷⣤⠤⠤⠤⡔⡴⠒⠐⠒⠲⠖⠀⠶⠚⣉⣑⣢⡴⠶⠶⣄⡀
⠀⠀⠀⠀⠀⣰⠇⣼⠃⢠⡇⢠⣤⠀⠀⢹⣆⡀⠀⠀⡀⠈⡇⠀⣾⠋⣀⣀⡙⠃⠀⠘⠂⠀⠻⠷⠤⠤⠔⠁⠀⠀⠀⠀⡄⢄⠀⠀⠬⣄⠀⠀⠈⢳⣤⣀⡬
⠀⣠⠶⠦⣾⣿⢀⣿⠀⣾⡀⠸⣿⡆⠀⢿⠉⠉⠙⠲⣣⠀⠃⠀⠁⡴⠋⠉⠉⠁⢀⣤⠖⢀⠼⠀⠀⣀⠀⢴⠀⢀⣷⢠⡗⢸⣷⠷⠶⠙⠿⢶⣄⢠⠦⣹⠟
⡀⡁⣠⠞⠛⢃⣼⣿⢰⣿⡇⠀⡏⡄⠀⠈⡇⠀⠀⠀⠸⣄⣀⣀⣀⣁⠀⣀⡤⠶⠿⠏⠀⠀⠒⠒⠚⠉⠁⠈⢶⣾⣷⢂⢄⠸⠟⣤⡀⢠⡖⢤⠿⠿⣦⠟
⠷⣷⢃⡀⡔⠉⠁⢰⠟⠋⠀⠀⠈⢮⠚⣨⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣸⣥⠾⠛⠿⠿⣇⠎⠀⠘⠉
⠀⠸⠺⢶⠇⣄⠀⢸⣀⠀⠀⣠⣼⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠘⠃
⠀⠀⠀⠀⣶⠿⣶⣾⣏⢿⣻⣛⡵⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⢲⣤⣬⣭⣍⡉⠉⠉⠉⠉⣉⣭⣭⣤⣤⠒⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠼⣇⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠈⠒⠄⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣀⣀⠔⢤⠲⡚⠉⠹⢻⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠘⢧⡀⠀⣤⣀⠀⠀⢸⡆⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠉⠙⡖⢢⠔⢄⣀⡀
⡔⠃⠀⠈⠆⠈⡧⠀⠞⠂⠸⡇⠀⣠⡶⠋⠁⠀⠀⠀⠀⢀⣀⠀⠀⠙⠶⠏⠉⠛⠲⠾⢃⣀⠀⠀⠈⠙⠓⠶⠦⣤⠤⠀⡿⠀⠚⠆⠀⡋⠀⠎
⠧⠤⠄⠤⠈⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣉⠻⠂⠀⠀⠀⠀⠀⠀⠺⢋⣁⣀⡀⠀⠀⠀⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠈⠠⠀⢤
⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⡇⠀⠀⠀⠀⠘⠋⠙⠋⠙⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠉⠙⠀⠀⠀⠀⠀⣿⣀⡏⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⢹⠀⠉⠓⠲⠤⠤⢤⢀⠀⡞⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⡆⢀⡀⠤⠤⠴⠒⠛⠁⢸⠂
⠀⠀⠈⡷⢄⠀⠀⠀⠀⠀⠈⠑⡙⠦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠞⡑⠁⠀⠀⠀⠀⠀⠀⠴⡏
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠰⡀⠈⣧⠀⠀⠀⠀⠀⠀⡤⠰⢤⣤⡤⠤⠤⣤⣤⠴⠢⡄⠀⠀⠀⠀⠀⢠⡏⠀⡴⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢄⠘⢧⠀⠀⠀⠀⠀⠹⣠⠎⠀⠀⠀⠀⠀⠈⢦⡸⠁⠀⠀⠀⠀⢠⠟⢀⠜⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠲⣆⣀⣀⣀⡀⢀⣙⡾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣞⡁⠀⣀⣀⣀⣀⡴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⠝⠋⠀⠀⠀⡾⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⠋⡀⠀⠀⠈⠛⢅⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠈⠉⠀⢤⠒⠘⢺⠃⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠒⠚⠛⠉⠁⠀⠘⣦⣗⠐⠋⢢⠄⠈⠁⠘⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢂⠟⠂⢠⠜⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡄⠀⠘⠄⠀⠚⠑⢢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠰⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⣄⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠉⠛⠉⠙⠋⠉⠉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠢⠇⠀⠀⠂⠀⠀⠇⠀⠀⠦⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣁⣠⡀⣀⣀⣀⡄⠀⠀⣅⣀⣀⣀⣠⣀⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣀⣀⣀⣀⣀⡽⠀⠘⣅⣀⣀⣀⣀⣀⣀⡁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⡄⠁⠀⠀⠀⠀⠢⡅⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣅⡌⠀⠀⠀⢐⠋⠀⠐⢰⠐⢦⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠂⠀⠴⠋⠑⠒⠂⠈⠑⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠘⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠘⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⣄⢠⠈⠂⠀⢀⠄⠐⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⢈⢁⣼⡇⠈⡀⠈⢀⠀⠈⠁⠀⠀⠐
⠀⠀⠀⠀⠐⠁⢀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠉⠪⢙⡿⠀⠀⡀⠀⠀⠁⠀⠀⠈⡢⠀⠈
⠀⠀⠀⠜⠀⠐⠋⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠂⠀⠀⠀⡠⠂⠀⠀⠑
⠀⡀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⢀⢂⡀⡉⠲⡢⠤⡤⠄⠀⢀⠜⢀⡀⡘⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⢀⠀⡤
⡈⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠸⡀⠙⠄⢠⠋⠳⡅⠀⠔⠁⡀⠄
⠁⠀⠀⠀⠀⡰⠂⠰⠀⠀⠀⠀⠀⠀⠁⠢⢕⣄⠴⠋⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠒⠄⠤⠠⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠠⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢏⣁⢀⡀⣀⡀⠀⠀⠀⠂⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠈⠁⢀⣧⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣹⣦⣀⣴⠀⠀⠈⠀⠀⢰⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢙⡛⠛⠴⣶⣶⣵⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢡⠀⡀⠀⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢦⣀⠀⢣⣍⡙⠙⡄⠀⠲⠀⢀⠄⣀⢤⠀⠀⠀⠀⠀⠁⠀⠳⢄⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⢈⡇⠛⠢⣈⠖⠒⢧⠒⠀⢆⡠⠊⠀⢠⠀⠀⠀⠈⠋⢉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠛⠐⣀⡀⠀⠛⠀⠉⡐⠢⣀⠀⠰⢇⠀⢼⣿⠇⠁⢺⠈⡱⣞⢱⡆⢀⠚⠁⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⡀⠉⠀⠀⠀⠀⠀⠄⠀⠀⠐⠂⠐⠌⢂⣀⠈⣂⢷⣜⡧⡤⣼⡤⢕⣦⣶⢭⣛⡄⠋⠭⠁⣰⠆⢁⠀⠀⠄⠐⣆
⠀⠀⠀⠀⠀⠀⢀⡀⠁⠠⠀⠄⠈⠀⠂⠄⠀⠄⠀⠀⢌⠁⡚⢈⠻⣯⣭⠝⢣⠬⢈⣧⣁⠀⣈⣶⡧⢿⠊⠑⠈⡋⠤⠉⠓⢑⠄⡀⠈⠊⡀⠀⠃⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠬⠄⠢⢀⠀⢁⠠⠤⠧⠤⠤⢄⢡⠂⠀⠀⠄⠙⣧⠀⠴⠴⠲⢮⣭⣻⣿⢖⣳⠶⢧⠀⣀⠚⠓⠚⠢⠉⠀⠀⠻⣄⡁⢀⠈⠆⢻
⠀⠀⠀⠀⠀⠲⠠⠄⠄⠀⠀⠄⢈⠀⠀⠀⢀⠀⠀⠀⠈⠳⣤⠀⡀⠠⠜⠛⡆⠄⢨⣜⣍⠛⠋⣹⣀⠀⠤⠔⠈⠂⠀⠀⠀⠹⣆⠐⠀⠈⠀⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠾⠀⠀⡀⠉⠀⠀⠈⠳⡄⠐⠈⠣⣄⠀⠀⠀⠒⡮⢴⡡⠄⠰⠛⠛⠂⣹⠇⠀⠀⢺⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⢀⠁⠈⢦⡈⢸⡇
⠀⠀⠀⠀⣸⠀⠂⣁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⡙⠀⠀⠒⠀⠡⠄⠀⢈⠿⠁⠈⢻⡇⠀⠀⠀⠀⠀⡠⠀⠀⠀⠤⡈⠀⠀⢄⣀⡠⡄⢺⠁
⠀⠀⠀⢠⡇⠀⠁⠀⠀⠀⠉⠐⡟⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠤⠀⠀⠀⡰⢀⢀⠆⣟⠦⣤⡤⠬⣝⠐⣄⠀⠀⠀⠀⠀⡔⠣⢆⠐⠄⠠⠀⠀⠀⢩⣼
⠀⠀⠀⢸⠠⠂⠀⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠰⠤⠤⠘⣄⢀⠀⠀⢦⠠⡦⠌⠒⠂⡌⠉⠒⢈⡀⠃⠠⡍⠲⠀⠑⠧⠌⠀⠀⡀⠰⣄⣀⡀⢨⡟
⠀⠀⠀⢸⠀⠆⠀⠉⠉⠉⠉⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢦⠰⢦⡆⣄⠀⠀⠴⡇⠁⠐⠆⡀⠚⢄⡆⠀⢈⠀⠀⠐⠀⠀⠀⢀⣾⠁
⠀⠀⠀⢸⡁⡆⠀⠀⠀⠀⠀⡈⢣⡀⠰⢦⣀⠀⠀⢸⡳⣄⡀⠐⢧⡢⠄⠀⠀⠙⢂⠅⠋⢶⠘⢷⣹⠙⠷⣥⠡⠄⣐⡦⢤⠠⠃⠔⠚⢢⡤⣰⠩⡍⢆⢀
⠀⠀⠀⠈⡇⡔⠤⠄⠀⠤⢆⠐⠈⡈⢦⠉⠀⠉⠆⠀⠀⠈⠂⠀⠀⠱⡆⠂⠀⠘⠀⠀⡐⠀⠘⠷⠸⣄⢀⢘⣋⣋⣭⡴⢂⣙⣆⠀⠀⢚⣰⣨⣷⡞⣛⢡⣹⡄
⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢈⡀⡦⢬⠤⢕⣤⡀⣡⣹⠂⡲⣄⠀⠀⠀⠈⠙⠲⢤⡀⢂⡈⢀⣄⣀⣏⠙⠉⠋⠉⢁⡤⣼⣧⡘⣿⠳⣤⣨⣿⣿⠟⢿⡿⠞⠷
⠀⠀⠀⠀⠀⢻⣆⡀⣀⡀⠰⢄⠍⣃⠀⠀⠉⠻⠈⠙⠺⠀⡄⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣁⣺⡉⠁⣹⢈⣃⡐⣉⣛⣁⢰⣋⣉⣙⣉⣁⣁⢀
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢢⠀⠙⠉⡩⠉⠒⣄⠺⣄⠀⢤⠀⠈⠑⠒⠐⠆⢠⡀⣀⣀⡴⠿⢶⠚⢿⠀⠉⠉⠡⠙⢩⣭⠏⠂⢯⡓⠈⠩⠉⣿⣉
⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠈⠁⠲⣄⠒⠒⠴⠚⡄⠉⠑⣇⠲⢀⠁⠸⠄⠒⣀⢠⠀⠀⠀⠐⠀⠁⠀⣈⣂⣀⡤⢬⡦⣬⠙⢂⠈⠣⣢⣸⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢪⡀⠀⠀⠀⢀⠈⠓⠒⠶⣥⠱⣤⣤⠷⠈⠉⠩⠁⠈⢠⣀⠄⣀⠁⠀⢀⡠⠴⠒⠉⠁⠀⠀⣌⢆⠈⠻⢅⣇⡀⢌⡀
⠀⠀⠀⢀⣠⣤⣄⠀⠃⠙⢫⡷⢦⣀⠁⠀⠀⠀⠀⠘⠀⠓⠸⡇⠰⢤⣄⣠⣬⡁⠀⣀⣤⠴⠛⠉⠀⠀⠀⠀⣄⠀⠀⠈⠀⠠⠀⠘⡌⠇⢀⡈⠁
⠀⠀⠐⠓⡿⡕⠚⢷⠀⢀⡴⢉⠓⠠⢛⠿⡒⠶⢅⣀⣀⣀⣀⣀⣀⣀⣡⡤⠤⠗⠊⠉⠀⠀⢀⣠⠄⢀⡀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠇⢀⠈⠉
⠀⠀⠀⠀⠈⠻⢶⣦⣷⣭⣀⣠⠤⠚⢅⠒⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠔⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢽⣃⠒⠺⡭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⡶⢿⣿⣿⠿⢿⣟⣛⣛⡁⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢟⣵⣾⠟⣱⡿⡩⢖⣛⣛⣛⣻⣇⣤⢄⡸⣦⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡵⠿⠿⣗⣠⣿⢠⢞⣭⣽⣷⣶⣶⣿⠿⢟⢡⣿⡇⢹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⣛⣒⣚⣻⣿⣿⣿⣧⣵⣦⣄⣛⡛⠿⢿⣿⢿⣛⡍⣼⡿⠀⣟⣛⣛⠇
⠀⠀⠀⠀⠀⣛⣛⣿⣶⣿⣿⣿⣛⣉⣙⣻⣿⡟⣩⡛⠿⠿⠿⢛⣠⢹⣿⡟⣱⡿⢡⢸⡌⣿⣿⡇⣆
⠀⠀⠀⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣻⣿⣿⣿⣣⣿⢏⣼⠏⣠⡟⣸⠇⣿⣿⢡⣿⡆
⠀⠀⠀⠀⢼⠂⡶⢙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⢋⣾⣿⠟⠡⠚⠵⣾⣿⢣⡿⢸⣿⠇⣾⣿⡇
⠀⠀⠀⠀⠈⠀⠃⠈⣿⡮⢻⣿⣿⣿⣿⣿⣿⣿⡇⣸⡿⠿⢛⡅⠠⢞⡻⡿⣎⠋⣾⢃⣿⡟⣼⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⡏⣿⣿⠻⠏⢿⣿⣿⣇⣿⣷⣾⠏⣴⣾⣿⠿⡇⢈⣄⣿⢸⣿⢸⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⣿⣿⣿⣿⣿⣿⠿⠛⣿⣟⠇⣼⣿⣿⣿⠇⢀⣾⣷⠻⣌⠇⠋⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠘⢿⡿⢏⣼⣿⠘⠉⠉⢵⣒⡶⣾⣿⣿⠀⣿⡟⣼⡿⣰⡿⢟⠋⣁⠬⣠⣾⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⢿⡟⠀⠀⠀⠀⠈⢻⣶⡝⣿⣇⢻⡇⣯⠇⢉⡴⢣⡞⣡⣾⡿⢋⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡷⠈⢿⣎⢿⢹⣧⡾⣱⡏⠼⣛⣩⡶⣣⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢿⡌⢻⣎⢇⢿⢳⣿⣿⠿⣛⣭⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡙⢧⡈⠛⠵⡾⠿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣍⡓⠀⠉⢻⣶⣍⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣼⣷⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠛⠛⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⢀⣠⣤⡶⠞⠛⠋⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢫⢤⣹⠀⠀⣠⣴⣾⣿⣿⣷⣦⣤⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣀⠻⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡠⠴⠶⠶⠞⠀⢀⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣆⡃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢒⣛⡂⠀⡀⠀⡀⣄⠒⠁⠄⠀⣸⡵⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠘⠁⣽⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠁⠡⠶⠚⠀⠀⢠⢃⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣼⠏⠈⠛⠛⠛⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡻⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠙⣴⣏⠀⠀⠀⠀⠀⢀⡤⠛⠀⠀⠀⢀⠷⡄⠀⠀⠀⠀⠀⢠⣇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠠⣫⣿⠀⠀⠀⠀⣠⠚⣅⡆⠀⠀⠀⢀⣀⠽⡀⠀⠀⠀⠀⣾⠟⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣿⠀⠀⠀⠰⠃⠀⠀⠙⢦⣤⡴⠟⠁⠀⠃⠀⡄⠀⢠⢿⣒⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣴⣈⣹⣶⠠⢀⠀⠀⢀⠀⠀⠀⠇⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣿⣿⣧⢀⣴⣤⠴⠞⠇⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⣀⠀⠲⠄⡀⠄⠀⠀⠤⠔⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⡟⡇⠈⠙⡶⡀⠀⠀⠀⠉⠉⠀⠀⠀⣰⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡺⠛⠁⠀⡇⠁⠀⠀⢷⠟⠳⠶⠦⠤⠤⠶⣶⠋⠁⡟⣿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠐⠉⠀⠀⠀⠀⢧⠀⠀⠀⠈⠜⡄⠀⠀⠀⠀⢠⠃⠀⢠⠃⠛⠃⠀⠙⠲⢤⡀
⠀⠀⠀⢠⡶⠾⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢠⠟⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⢤⣀
⠀⣰⠏⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠢⠄⠀⣀⡀⠀⣀⣀⡤⢞⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠦⣄
⢠⡏⠀⠀⠀⠀⠀⠀⢸⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠙⢦
⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡇⠀⠀⠀⠀⠈
⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣛⣋⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⢔⠒⠒⠒⠛⠛⠂⠀⠀⠀⠒⠂⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⡑⡆⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⢣⣆⡔⠁⠀⠀⠸⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠣⡎⠀⣴⣁⡠⠤⡄⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠉⠑⠒⠦⠴⡀⠀⣅⠀⠀⠀⣸⠀⢰⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠉⠉⠁⠀⠈⠄⠀⠀⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠀⠀⠀⠤⠐⠂⡙⣀⠔⠦⡀⠀⣀⣸⠀⠀⠁⡠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⡫⠿⠥⠦⣶⣶⠀⡇⠀⠀⠀⠐⢀⣊⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠂⠉⠱⠾⢿⡇⠧⠤⠞⢄⡀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠒⠀⢰⣦⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⣄⣸⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⢄⡈⢙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠠⢖⡪⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣀⡐⠠⡑⠬⡑⠊⠀⠐⢄⡠⡒⡄⠀⠀⠀⠀⠀⠀⠁⠆⢣⢄⣀⠅⠴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢇⠠⡈⠇⠦⠀⠀⠁⠒⢠⣄⣁⡇⠘⡖⠂⠀⣖⡰⠂⠠⢌⠳⡀⡽⠤⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⢈⣟⢀⠭⠭⠤⠭⠅⢿⠁⠓⠘⠓⠦⠇⠀⢀⠇⠈⠀⠀⠠⠁⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⠀⠈⠂⠀⠸⡀⢆⠀⠀⠀⠙⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⡔⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠃⠀⡰⡙⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⡤⢤⣷⢎⠎⡵⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡄⠀⠀⠖⠁⠀⡇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⢤⠤⠼⠞⣄⠀⠀⠀⠀⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠠⠤⠐⠚⠻⠤⠬⠇⠀⠀⠀⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠳⣄⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣓⣒⣲⡤⣤⡘⣆⠨⡄⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⢉⣩⣤⡤⠬⠽⣷⣯⣿⣄⡵⠁⢀⣀⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣠⠞⠋⢁⣠⣤⣶⣶⡶⢾⣿⣿⠿⣿⣿⣿⣿⣭⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠁⢠⣶⠿⠛⠉⠀⠀⢀⡾⠉⢳⣄⡀⠈⢻⡆⠉⠉⠙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣴⡿⠁⠀⠀⠀⠀⠀⠘⣇⠀⢺⣼⠟⠦⣼⡏⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡟⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣦⣤⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡵⠟⢀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⣤⣤⣾⡿⠟⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣶⡆⠀⠀⣠⣾⠋⠁⠸⡍⠙⢶⡀⠀⠰⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠁⠀⠀⣼⠋⠘⡄⠀⠀⢧⠀⠀⢻⣄⠀⠀⠈⢹⣿⠛⠛⠛⠛⠿⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⠏⠀⠀⢣⠀⠀⢸⣀⣤⠾⠛⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡿⠀⡇⠀⠈⣤⠴⠛⠉⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⡇⠀⣠⡴⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠸⣷⠞⢉⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢰⣄⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⠟⣿⡿⠿⠿⠿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⡷⠶⣦⣤⣀⡀
⠀⣀⣠⣀⣠⣴⡿⠛⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⠈⢳⣄⠀⡠⠞⠉⢋⠉⠲⣄⠀⣠⠟⠹⣿⠀⠀⠈⠙⠻⣶⣄⡀
⣼⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⢸⠀⠀⢈⡿⠋⠀⠀⢻⣇⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⣄
⠸⢿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⢸⠀⣠⠟⠁⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠂
⠀⠀⠉⠘⠃⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢛⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⣿⡿⠿⠿⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠤⠼⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡤⠴⠶⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⢀⣆⣀⣤⣆⠙⣦⠀⠀⠀⠀⠀⠀⠀⣰⠋⢡⣤⣄⣀⣅⣀⣴⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣭⣥⣤⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣤⣬⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿