Dwarf planet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠖⠒⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣋⣡⡤⠤⠤⢤⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣚⡭⠖⠋⠉⢀⣀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠛⠶⠯⣤⡴⠒⠋⠉⠉⠉⠉⢢⠀⠀⠀⡞⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢀⡠⠞⠁⠉⣳⣄⠀⠀⠀⠀⣸⠀⠀⡼⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣀⣤⠤⠖⠚⠉⠀⠀⣠⠔⠁⠈⠳⡄⠀⣰⠃⢀⡜⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣠⠖⠋⠁⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⢹⡼⠁⣠⠋⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣧⠞⠁⠀⣠⠤⠶⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⢺⡇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⢀⠞⣡⠞⣡⠞⣷⠋⠀⠀⣀⡤⠤⢤⣄⣀⣀⣠⣤⣤⠖⢉⡴⠊⠁⣠⡾⠁
⠀⠀⠀⢀⡴⠋⡴⠃⣰⠃⠀⢹⡀⢀⡞⠁⠀⠀⠀⣀⣀⣠⠴⠋⣡⠖⠉⢀⣴⣿⣿⠃
⠀⠀⢠⠞⠀⡼⠁⢰⠃⠀⠀⠀⠱⣏⠀⣠⠖⣚⡩⠟⢋⣡⠖⠋⢀⣠⣾⣿⣿⡿⠃
⠀⢠⠏⠀⢸⠁⠀⠘⢦⣀⣀⣀⣀⣨⠿⠖⠋⣁⡤⠖⠋⢀⣠⣶⣿⣿⣿⡿⠋
⢠⡏⠀⠀⢸⡀⠀⠀⠀⠈⠉⠉⣀⣠⠤⠖⠋⠁⣀⡤⠾⠿⠿⠿⠟⠋⠁
⢸⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠉⠉⠀⣀⡤⠖⠋⠁
⠘⢦⡀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠁
⠀⠀⠉⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⣠⠔⠚⣉⠛⠲⢄⠀⠀⠀⠀⠀⢀⠴⡚⡙⠑⠒⢄⠀⠀⠀⠀⠀⢀⡴⠒⠛⡛⠲⢤⡀
⠀⠀⠀⠀⡼⢁⠈⠀⠍⡀⣘⠀⢣⠀⠀⠀⢰⠃⠀⠀⡌⢀⢀⡌⢱⠀⠀⠀⢰⠋⠄⠀⠀⠄⠃⠀⣱⡀
⠀⠀⠀⠀⣇⠐⠔⠀⡔⣢⠙⠀⢸⠀⠀⠀⢻⣀⡀⣈⢀⠨⠄⠁⢨⠃⠀⠀⢸⠀⡀⠠⠀⢀⡐⠨⣼⡇
⠀⠀⠀⠀⠘⢖⠃⠠⠈⣀⠀⣡⠏⠀⠀⠀⠈⢯⡁⠀⠀⣠⠀⣤⠟⠀⠀⠀⠈⢣⡀⢀⠤⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠓⠒⠚⠁

⠀⠀⠀⠀⠀⣀⠤⠂⠀⠒⠢⣄⠀⠀⠀⠀⠤⣤⡴⠖⠒⠲⠦⣄⠀⠀⠀⠀⠀⢀⡤⠒⠒⢒⠂⢄
⠀⠀⠀⠀⣰⠉⠐⠄⠀⡀⠀⠊⣣⠐⡐⠀⢀⠫⣐⡒⠒⠒⣒⡚⣳⠀⠀⠀⢠⢯⡄⠁⠀⠛⠄⠶⢳⡀
⠀⠀⠀⠀⡏⢁⡐⠀⠀⠀⠀⠀⢸⠀⠀⠀⡙⠓⣨⠁⠒⠠⠐⠐⢸⣷⣄⠀⢸⠀⠠⡀⠁⠀⠂⢋⠀⡇
⠀⠀⠀⠀⠘⣌⠀⠀⠀⢀⠠⢠⠏⠀⠀⠀⠘⢇⡢⣌⡁⠀⠀⠀⡬⠡⠂⠑⠈⢦⠊⠈⡀⠈⠀⢀⡜
⠀⠀⠀⠀⠀⠈⠑⠲⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠙⠒⠩⠷⠒⠀⠀⠀⠀⠊⠀⠀⠙⠒⠦⠴⠒⠉

⠀⠀⠀⠀⠀⢀⠤⠖⢖⠒⠦⣀⠀⠀⠀⠀⠀⢀⣤⡶⡖⠖⠦⣄⠀⠀⠀⠀⠀⢀⡠⠐⡒⠲⢢⣄
⠀⠀⠀⠀⣰⠁⢀⠠⠘⠀⣸⡌⣦⠀⠀⠀⢠⡋⠀⡔⣀⠘⢨⢌⢣⠀⠀⠀⢠⡏⠩⢉⡀⡈⠄⠊⢳⡀
⠀⠀⠀⠀⡇⠑⢨⠒⠢⡜⠥⡀⢸⠀⠀⠀⢸⢌⠂⠈⠐⠹⠘⠦⢸⠆⠀⠀⢸⢂⠭⠀⣀⡠⠬⢹⢼⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠠⠀⠀⢡⠎⠀⠀⠀⠘⣖⠀⠁⠂⣀⢈⢡⠞⠀⠀⠀⠘⢦⠀⠈⠉⠐⠈⣀⡼⠁
⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠒⠁⠀⠀⠀⠀⠀⠈⠓⠦⠴⠼⠞⠉⠀⠀⠀⠀⠀⠈⠙⠢⠤⠤⠖⠋

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

⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣮⠀⠘⢸⡆⠀⠀⠀⠀⡀⠈⠡⠊⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⢀⠉⢀⠰⡠⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠛⠂⠀⠢⠃⠀⠀⠀⠐⡙⠛⠈⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠠⡀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠐

⠀⠀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠠⢀⠠⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠈⠄⡀⠁⠀⠀⠀⠀⠐⣒⠒⠀⠀⠀⠀⢰⢸⠀⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠂
⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⡠⠒⠒⠢⠀⠀⠀⠀⠰⣤⠀⡀⠄⠀⠀⠀⠀⠀⣶⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠄
⠀⠐⠁⠀⡄⠀⠀⠀⠀⠀⠀⠘⢣⣭⡀⠀⠀⠀⠀⠠⡾⣹⡆⠀⠀⠀⠀⠀⠀⡴⣑⡀⠀⠀⠀⠀⠂
⠀⠀⠽⠷⠱⠿⠇⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠼⠳⠀⠀⠀⠀⠀⠀⠀⠁⠀⠍⠀⠀⠀⠀⠀⠆⠀⠈

⠀⠀⠀⠤⠠⣄⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⢢⡀⠀⠨⠀⠀⠀⠀⠀⢏⣐⣦⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠐⠂⢤⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⠆⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠲⠤⡀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠘⣆⡴⠊⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⢹⠀⣤⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠻⡄⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⢀⡏⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠙⠦⣤⣤⠴⠋⠀⠳⢤⣠⡤⠋⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⡴⠛⠳⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠀⠀⡇⠀⢠⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢏⠀⠀⠳⠤⣍⠁⠊⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢹⡆⠀⠀⠀⠀⠀⠈⡇⠀⠀⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠂⠀⠀⠀⡏⠉⠉⠉⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⣿⠀⠀⠀⠀⠀⡼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠇⠀⢐⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢹⣆⣀⣠⠴⠚⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡜⠁⠀⢀⣸⡔⠊⠀⠈⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡣⠄⠀⢀⡤⠒⠢⢼⣏⣀⣀⣤⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠱⡄⠐⠀⠰⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢀⡤⠖⠋⢹⡇⠀⠀⠀⠙⠒⠒⠒⠂⠤⠤⠤⠤⠏⠀⠀⠀⠀⠀⢀⠖⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡿
⠀⠀⢀⡴⠋⢀⡴⠚⠉⢻⡄⠀⠀⠀⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⣼⠃
⠀⠀⡾⠀⢠⡏⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⢠⡇⠀⢸⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠈⠀⠀⠀⢄⢱⡾⠃
⠀⢈⡇⠀⠘⠳⡄⠀⠀⠀⠀⠀⠘⢷⣄⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡼⠋
⢠⠏⠀⠀⠀⠀⠳⠦⡄⠀⠀⠀⠀⠀⠉⠳⣧⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⡾⠀⢠⡾⡗⠦⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢾⣄⣀⣀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠋⠁
⣇⠀⢸⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠉⣿⢹⡏⢹⠉⠁
⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣤⣀⡀⣿⠀⣿⢸⡇⢸⠀⣀⣤⣤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⣿⢸⡇⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣟⣸⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠤⠤⠠⠄⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⣠⠖⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠿⠷⠶⠶⠚⠁⠀⠀⠀⡴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⣄⢀⠀⠐⠀⠀⠈⠧⡀⠀⠀⠀⠀⠐⠉⠀⢸⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣧⢠⣄⢀⡀⠀⢠⣀⠄⠀⢐⡄⠈⡿⠋⠀⠀⠀⠀⣤⠀⣿⣦⣶⣀⡀⠀⢵⡄⠀⠉⣿⣿⣿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠈⠁⠈⠁⠂⠤⠠⠷⠷⠀⠀⠤⠤⣄⠀⢤⣴⡌⣿⠋⣻⡇⢠⣨⣿⣄⡀⢨⣿⠃⠀⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠻⠷⠦⠾⣯⣿⣿⠃
⠀⠀⠀⠀⠐⡄⠀⠰⠠⠄⠀⢐⣆⠤⠀⠀⠐⠀⠒⠚⠛⠲⣖⣂⣀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢨⣱⣿⠏
⠀⠀⠀⠀⠀⠐⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣉⣶⠀⠀⠠⣠⡀⢠⡅⣠⡄⠶⠖⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠈⠣⣍⣁⠀⠀⠲⢶⡖⠃⠒⠂⠀⠀⠀⠰⠀⠈⠉⢙⠛⠚⠻⠓⡋⠛⣻⢉⡿⣿⣷⣶⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣤⡀⠀⠁⠦⠐⠄⣀⣆⣴⡖⠂⠀⠀⠂⠀⠀⠐⢛⣏⣾⣿⣾⣿⣿⣿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣤⣤⣄⣤⣉⣛⠃⢁⣤⠀⣼⣯⣯⣴⣛⠛⣛⣛⡛⠛⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣭⣷⣾⣿⣿⣞⣙⣛⣉⣻⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⢖⡰⢂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⣠⣴⠶⢀⢄
⠀⠀⠀⠀⠀⠀⢀⡾⢟⣛⣭⣭⣾⠿⣫⣴⣆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣤⡾⠛⡡⣊⣴⣿⡷
⠀⠀⠀⠀⠀⠀⢐⣪⣭⣽⣷⡶⠶⣟⣛⣛⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⡋⢔⣡⣼⣿⢟⣫⣾⠇
⠀⠀⠀⠀⠀⠀⢸⣿⢟⣭⣶⣾⠟⣫⡭⠯⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⣪⣴⣿⡿⣋⣵⡿⠛⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠡⣿⣯⣩⡿⣼⢫⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢟⣩⣾⠿⣉⡴⣋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠑⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⠞⠁⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣟⡶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⣶⣭⣛⠿⣿⣿⣷⣯⣟⡆⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠀⠀⠀⠀⠀⠀⠛⠿⣿⣉⣻⠀⠉⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣿⣯⣅⡲⢤⣀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠻⢿⣷⣮⣝⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⠀⠀⣬⣷⣤⣼⡀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣶⡾⣍⢀⣿⣿⣵⣶⣶⣤⢐⠶⠁⡀⠀⠀⠀⠀⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡿⢿⡏⢤⡷⠊⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⢟⣵⡿⠱⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣶⢿⠀⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣠⡤⣤⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⢰⠆⠀⠀⣠⡚⠩⠉⡛⡒⠤⣈⠳⣄⠀⢠⡀⢁⣀⣀⣈⠀⢤⡿⠃⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⡠⠔⠂⠄⠀⣀⡠⢨⣷⣦⡀⠀⣠⣰⠦⣄⠀⡜⠉⠛⠻⢷⣦⣤⡐⠢⣙⠮⡆⠀⡟⠉⠈⠷⣄⠙⢆⠀⢀⠄⠀⠲⢦⡀⠀⣠⢔⣲⠤⡀⠀⡠⢤⣄
⠀⢀⢀⣷⢰⣀⣄⠠⢘⠄⣿⣿⣿⣿⣿⡆⢰⠋⠉⠀⠘⠀⣷⣶⣤⣤⣄⡈⠉⠙⢶⣌⠑⣽⠀⡅⠀⠀⠀⠙⣷⣾⠀⢈⠀⢀⣿⣷⣿⠰⡷⣷⣶⡿⡇⠀⣏⣾⣾
⠀⠈⠉⠁⠀⠓⠩⠅⠊⠀⠙⢿⣷⣿⠿⠁⠈⠳⠤⠄⠊⠀⢛⠙⠛⢽⣿⣿⣷⣦⣀⠈⠻⡏⠀⢣⡀⢐⡀⢐⣾⡝⠀⠘⢷⣼⣿⡿⠋⠀⠑⠤⠴⠖⠁⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠳⣄⣀⠀⠉⠙⢿⣿⡷⠊⠀⠀⠀⢉⡛⠛⠛⠻⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠇⣀⠀⠉⠓⠒⠒⠚⠉⡀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡄⠆⠀⠀⠀⠀⠀⠠⡥

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣠⣾⣿⣿⣿⣷⣖⣶⠆⠀⢀⡤⠖⣚⣻⣿⡆⠀⡀⠀⢀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣴⠊
⠀⡠⣿⣿⣿⣿⣿⣿⣟⠁⢀⡔⢉⣴⣿⣿⣿⠟⢁⠔⠁⠀⢸⣧⣿⣿⣷⣾⣿⡕⠀⠀⢀⣤⣾⡿⠃
⠺⠷⠾⢿⣿⣿⣿⡿⠃⠀⠈⠀⠸⢿⣯⡭⠴⠚⠁⠀⠀⠀⠀⠛⢿⣿⣿⡿⠟⠀⠀⢸⣿⣿⠏
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⣀⣤⣀
⠀⠀⠀⠙⠛⠓⠛⠉⠂⠀⠀⠀⣴⠃⠀⢈⣭⣿⣧⠀⠀⠀⠀⢀⡀⠚⠀⠀⢰⣿⣿⣿⡇
⠀⢸⠓⢶⠶⣶⠶⠶⣺⠀⠀⢸⣿⣷⣽⠿⠿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠛⠫⠄⠈
⠀⠈⠛⠛⠿⠿⠿⣛⠋⠀⠀⠀⠻⣿⣿⣦⢀⣠⠟
⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣤⣀⢀⣤⣄
⠀⠀⠀⠀⠀⢤⢾⣿⠟⠀⠀⠀⠰⣶⢖⣴⣾⠟⠀⠀⠀⠀⠀⢈⣽⣿⣿⣏⡀⠀⠀⠀⢀
⠀⠀⣰⡟⢾⣿⣿⠃⠀⠀⠀⠀⣤⣴⣿⢟⣵⠀⠀⠀⡀⢄⠠⣌⠻⠟⠁⠈⠙⠃⠀⢠⣧⣤⣤⠊
⠀⠐⣫⠾⣧⠿⠃⠀⠀⠀⠀⠀⠈⠻⡇⠈⠻⠀⠀⠀⠙⢦⣑⠦⠅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠔
⠀⠀⠁⠊⠁⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉
⠀⢤⡀⣀⠀⠀⢰⣤⣶⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠙⣿⣦⠀⠈⠉⠈⠀⠀⠀⠀⢿⣦⡶⠋⠀⠀⠀⠀⠀⣿⣶⣤⢤⡾⠀⠀⠀⠀⠀⣠⣤⢶⡿⠛⠋⠁
⠀⠀⠀⣿⡏⠙⠃⠀⠀⠀⠀⠀⠀⢨⡟⠿⠦⠀⠀⠀⠀⠀⢹⣿⣿⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡟⠛⠻⠿⠷⠀⠀⠀⠀⠀⠀⣸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡟⠁⠘⠗⠐⣲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠛⠙⠉⠀⠀⠀⠀⣴⠿⠁⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⣛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢴⠃⠀⠀⠀⠀⠀⠀⠈⠁⢠⡾⣡
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠃⠀⣠⢏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠐⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠔⠀⢀⣴⣶⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢞⡼⠻⠋⣰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢈⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⣴⡷⠟⠀⢀⣹⡿⠟⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⢀⡴⣭⠟⠀⠀⢀⡜⠋⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠹⣿⢄⡀⠀⠀⢀⣤⣶⡟⢁⣀⡴⣫⡾⠁⠀⢀⡴⠏⠁⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠸⣿⣿⣶⣿⣿⣿⣃⣼⡿⣫⣾⠟⠀⢀⣤⠞⠁⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⠟⣫⣾⣿⣡⣴⣶⡟⠁⢀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⠂⠐⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠀⠀⠒⠤⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢘⠀⢠⠄⠂⠀⢀⣾⢱⠀⠀⠀⠀⠀⠀⠀⣼⠇⠠⠞⠁⠀⠀⠀⢈⣧⣄⣀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⡗⠐⠀⠀⢀⢑⣡⢂⣾⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⠀⢀⡀⠀⠠⠈⢹⠄
⠀⠀⠀⠀⠀⠀⡅⠠⣀⠀⣀⣀⣤⠶⢟⡞⠁⣼⠏⠀⠀⠀⠀⠀⠁⠀⢻⡍⠀⠒⠋⠀⠀⢀⢈⡤⠀⠐⠂
⠀⠀⠀⠀⠀⢄⠷⣄⢉⣉⡥⣜⣶⡾⠋⢀⠾⣉⡰⠂⠀⠀⠀⠀⠉⠀⠀⠘⠶⢭⣈⣬⣥⠴⡋
⠀⠀⠀⠀⠀⡇⢀⠈⠉⠓⠺⠟⠉⠀⢠⠋⠌⠹⣿⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠣⠈⠃⠀⠈⠀⠀⢀⠔⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠁⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠤⠦⡀⠀⢀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠰⠂⠀⠀⠀⠂⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠠⣿⡼⡧⠀⠀⠠⠛⠓⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡄⢀⠕⣄⡠⠖⠰⠀⠀⣀⢤⠃
⠀⠀⠀⠀⠀⠉⠀⠯⠵⣅⣤⠴⠀⠐⠒⠠⠡⠄⠀⠀⠀⠀⠀⠀⠀⠘⠎⠠⠄⠀⡇⢀⠒⠫⣺⠏
⠀⠀⠀⠀⠀⠃⠀⠠⠒⠀⠀⠲⠀⠒⠂⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠠⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠱⢤⡀⣀⠀⢈⠁⣁⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠜⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠁⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⡀⢘⡃⠠⠀⠐⠄⣠⠐⠇⠀⠀⠀⠀⠀⠫⢤⢧⣠⣤⣽⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢤⠁⠈⢰⠀⠀⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠤⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠥⣀⣀⠹⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂

⠀⠀⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⠀⠀⣠⢴⠆⠠⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⢀⣸⣭⡖⠀⠀⡂⠁⠀⠀⢸⡷⠎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣤⠀⠀⠀⠀⠀⢨⢭⠉⠉⠁
⠀⠀⠀⠈⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⠷⠶⠊
⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⣀⣤⠄⡀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⠀⠀⠀⠀⠀⠀⣤⡶⠒
⠀⠀⠀⠀⣼⣿⡇⠀⠈⠀⠀⠀⠀⢸⣿⡟⠀⠀⢠⠀⠀⠀⢀⣾⣿⠖⠚⠋⣻⠀⠀⠀⢸⣿⡀⠤⠂
⠀⠀⠀⠀⠙⢿⣷⣶⠞⠀⠀⠀⠀⠘⢧⣴⣄⡀⠀⠀⠀⠀⠻⠽⢿⣦⡄⠀⠁⠀⠀⠀⠀⠙⠿⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢀⣀⠀⣠⣀⡤⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⠀⠀⠀⢀⣠⡤⠄
⠀⠀⠀⠀⢰⣛⣿⠣⢐⠁⠀⠀⠀⢡⡌⠀⡉⣉⡀⠀⠀⠀⠀⠀⠋⣠⠚⣹⠎⠀⠀⠀⣾⣿⠓⠀⠐
⠀⠀⠀⠀⠈⠿⠿⣉⡁⠀⠀⠀⠀⣼⠇⠀⢣⠀⠹⠆⠀⠀⠀⠀⣰⠟⠿⠕⠁⠀⠀⠀⠘⠿⠿⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⡴⠶⣚⣛⠋⣁⠐⢢⢱⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⠿⠿⠛⠋⠁⢠⠈⣆⠀⣬⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⢜⡜⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⢿⣿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⡅
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠉⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠋⠁⠀⠐
⠀⠀⠀⠀⢀⡴⣫⣾⠟⠁⠀⠀⠈⢀⠀⠀⣀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠐⠁
⠀⠀⢀⡴⡁⠀⡍⠸⣀⣀⠀⣀⣤⣴⣷⣿⡿⠛⠉⠁⠀⠀⠀⠀⢀⠄⠊
⠀⠠⢱⠰⡀⠐⠀⠒⣒⣒⣭⠿⠟⠛⠉⠀⠀⠁⠀⠐⠒⠂⠀⠈
⠀⠐⠠⠅⠤⠉⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⡿⠿⢿⠛⠿⣿⣿⣷⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢿⣃⡾⠀⡐⠌⠐⠋⠈⠀⠙⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢛⡛⣉⣉⣁⣄⣀⣤⣀⣀⣀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣬⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⠛⠃⠒⠟⠛⠹⠟⠟⠻⠿⠟⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠹⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⣤⣤⣤⣄⠀⠀⠀⠀⢀⢛⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠝⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣿⣿⣿⣿⣷⣾⣿⣿⣧⡄⠀⠀⡤⢈⢩⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣉⠛⠂⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⢎⣉⣉⡿⠿⠷⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣘⣛⣿⣷⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡠⡀⣀⢀⣤⢀⣄⡄⣠⠾⠆⠤⠐⠐⠒⠊⠁⠆⠀⠀⠀⠉⠛⡿⠉⠋⢭⣿⣿⣧⣍⢋⡉⠹⣿⣿⣷⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⠟⠙⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠈⠙⠧⡄⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣾⣿⣿⣭⣤⣴⣤⣶⣶⣶⣶⣶⣾⣷⣶⣪⣴⣶⣶⣆⠴⣦⡶⣦⣤⣄⣀⣐⣠⣤⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⣨⣴⣿⣿⣿⣿⣿⣿⠿⡛⠛⠙⠉⠋⠉⠉⠉⠉⠛⠉⠀⠁⠀⠘⠻⠻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣡⢀⣂⣤⣠⣤⣴⣶⣶⣶⣤⣤⣴⣤⣀⣀⠀⠀⠀⠀⣹⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⢻⣿⣿⣷⣾⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠏⢛⣿⣛⡛⠻⠙⢟⢿⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣽⣀⡆⠠⠦⡌⠠⡝⢛⡚⢢⣮⣾⣿⣿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣥⣶⣷⣿⣿⣷⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠒⠸⢿⣷⣶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠶⠋⠀⠀⠀⣺⠟⣩⣿⣿⣿⣿⣟⠛⠛⠻⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⣾⠋⠁⢘⣿⣿⣿⣧⡀⣰⢇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠀⠐⠉⠁⠀⣰⣿⣿⣿⣿⣿⡷⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣾⠿⣋⣿⣿⡿⢋⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⢁⣴⣿⡿⣋⠔⣡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⣾⡿⠟⡡⢊⣥⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⣡⠔⣉⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⣩⣖⣤⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⢤⣀⣀⣠⡬⠥⠖⣚⣩⣴⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠀⠃⠈⠃⠈




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

⠀⠀⠀⢀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⡴⣔⡁⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢃⠀⠀⠄⠀⢀⠠⠀⠀⠀⠀⠀⠀⠔⠖⠚⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⡀⠂⠃⠀⠀⠁⢢⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐
⢀⠑⠚⠰⠦⠖⠁⠲⡤⢮⡆⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢀⠰⣠⠃
⠘⠈⠰⠐⠠⢀⠠⢶⠄⠄⠋⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡉⠰⠂⠂⠈⠒⠀⡈
⠸⡷⠄⠄⠀⠀⢲⣦⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠀⡄⠊⠠⠔⠁
⠀⠘⢤⡠⠔⠂⠀⢤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡄⠒⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠖⠀⠀⠀⠂⡀⢀⠱⡄⠒⠄⠤⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠁⠀⡠⠏⠀⠒⠀⠈⡠⣜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠔⠀⠡
⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠁⣐⢠⠀⠠⣅⣉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⢀⠀⠀⠄⠀⠀⠀⠉⠉⠉⠀⠃⠀⠀⠀⠀⠉⠔⠆⠀⠘⠄⠀⠈⣁⠋⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠔⠃
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠓⢲⣄⣠⠖⢛⣹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⡿⣿⠿⠿⢿⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠉⢀⣠⡾⠛⠁⣱⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⣀⠈⠭⠤⠐⠀⠈⠁⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⣀⣠⣴⡞⠛⠉⣀⡴⢞⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠋⠉⠀⣠⠴⢚⣥⠖⢋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⢰⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣵⣶⣯⠵⠞⢉⣠⣾⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠘⢦⡍⣄⢠⠤⠤⠤⠄⢒⣲⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠀⠀⠑⠒⠺⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣖⡲⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⡀⢀⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⣸⣫⡿⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠦⠐⠃⠈⠀⠉⠁⢅⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣇⣤⠀⢀⣴⣟⢕⣷⡆⠈⣆⠀⡀⠀⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠐⠀⡀⢀⠀⣈⠠⠀⢔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣣⠈⠚⢱⣿⣿⣿⠀⢸⠁⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠀⠀⠌⠠⠀⡱⠈⠆⠀⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠙⠤⡄⠀⠈⢹⢛⠿⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⡀⠘⠤⣉⡀⠜⠀⠀⢈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢷⡁⢠⣿⣦⣰⢋⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⠌⠂⠄⠀⠠⠄⢂⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠘⠛⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢱⢠⠢⠔⠖⠢⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠔⠂⢉⠟⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣤⠖⠀⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠠⠀⢂⠀⢬⣿⡄⠀⣠⠊⢀⢀⣀⠅⠀⠀⠤⢈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⢃⠀⡟⢦
⠀⠀⠀⠀⠠⠒⢉⠄⠀⠀⠀⠀⠀⠏⣀⠁⠀⠀⢀⡠⠀⠀⢎⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡏⠀⢠⠀⠸⣀⠤⡠⠀⠎⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠅⢪⠀⠀⠀⠀⠀⣀⢤⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠁⠀⣀⢄⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠬⠇⠀⠀⠀⢀⠑⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣉⠀⠀⠁⢲⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⣠⠀⠀⠾⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣖⣯⣼⣟⢲⣦⣽⣤⡀⢠⠀⠀⠈⠀⣠⣦⡙⣅⠀⠙⠷⣦⡀⠀⠀⠀⠀⣠⡴⠖⣲⢤⡀
⠀⠀⠀⠀⣰⣶⣯⡿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡌⠄⣄⠀⠐⢅⠀⠑⢤⡐⢄⡀⠈⢑⡀⠀⠀⠐⠋⡀⠈⢁⣼⣿⡀
⠀⠀⠀⠀⣿⢄⣽⣷⡌⠻⠿⢿⣿⠭⣭⣁⣿⣷⡠⠏⠀⠀⠀⠑⢄⠀⠉⠲⢌⡑⠺⡇⠀⠀⠘⣁⠀⣠⠔⡻⣿⠁
⠀⠀⢀⣈⡟⢻⡿⣛⣿⣿⣷⣾⣧⡴⣿⣿⡟⡿⠃⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⣨⡿⠀⠀⠀⠀⠈⠛⠿⠷⠚⠁
⠀⢠⡼⢃⣀⣘⣿⡏⠙⣋⠈⠛⢋⡄⠈⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠵⠈
⠀⠀⠈⠑⠻⢏⠙⣻⣿⣧⣦⣿⣼⡳⢾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠿⣿⠟⠋⠑⠁⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠂⣐⣦⣤⡀⠀⠀⣤⣄⡰⣧⢠⡇
⠀⠀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣚⣃⣀⡀⠐⣒⣀⡀⣘⣻⣦⠀⠀⠲⠥⠤⠚⠁
⠀⠸⣏⣉⠉⢉⠀⠀⠀⢀⣴⣯⣤⠀⡟⣳⣦⡀⠀⠀⠉⠉⠙⠇⠈⠈⠉⠉⠛⢨⠙⠩⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠛⠛⠋⠀⠀⠀⢶⣶⠿⣏⠛⣉⡿⢿⣷⠀⢰⣶⣦⣤⡤⣤⣶⣄⠠⢤⣤⣤⣼⡧⠀⠀⣤⡾⠿⠿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣷⣾⣿⡀⣠⡟⠀⠈⠋⠛⡛⠿⠿⠓⠛⠛⠙⠉⠉⢿⠇⠀⢸⣏⠤⠴⠛⠿⠶⣿⡆
⠀⠀⠀⠀⣴⣞⢦⠀⠀⠀⠉⠉⣉⣿⣿⣿⠟⠀⠀⠀⠈⠺⣉⣛⡛⡛⢛⣛⣛⣿⡿⠋⠀⠀⠘⣷⣶⣶⣶⣖⣲⡾⠁
⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠖⠛⢋⣉⠙⠓⠦⣄⠀⠀⠀⢀⣆⠀⠀⠀⢀⡤⠶⡟⢹⠋⠛⠲⢤⡀⠀⠀⢤⡞⣦⠤⠀⠀⣠⡴⡺⢛⠟⢉⠗⢶⣄
⠀⠀⢠⠞⡁⠶⠀⠻⠞⠀⠀⣶⠈⢷⡀⠙⣯⣨⡟⠁⣰⢛⢒⢒⠁⠘⠤⠤⠤⠤⠽⢆⠀⣼⠛⠻⠀⢀⡾⠉⢁⠀⠄⠒⠁⡰⠁⣨⠷⡀
⠀⠀⡟⢠⠔⠦⠀⠘⠂⠆⢠⢤⠐⠀⣧⠘⠋⠈⠓⢰⠏⠉⠈⠀⢉⡇⢠⣦⠠⣖⣒⣛⡆⠀⠀⠀⠀⣾⡤⠊⢁⠔⠂⠈⢉⠤⠊⣀⠴⢻
⠀⠀⡇⠘⠲⠚⠀⢠⠚⢲⠈⠉⠀⠀⣿⠀⣀⣀⡀⢸⣋⣉⡉⠉⣉⠀⣀⠤⠤⠤⠤⢤⡇⢀⠤⢄⠀⣿⠔⣒⠥⠐⠒⠬⠅⢒⣊⢅⡮⣿
⠀⠀⢻⡄⣞⡆⠀⡈⠛⠋⠀⠰⠆⣰⠇⢰⠋⠬⢳⠀⢷⡐⠋⡈⠋⠀⠑⠒⠒⠒⢒⡾⠁⠺⣘⡺⠀⠘⣯⣊⠕⡀⠬⠄⠉⣀⠠⡀⢭⡟
⠀⠀⠀⠙⢦⣀⠀⠁⠀⠰⢂⣠⠾⠃⠠⡈⠓⠒⠋⠀⠀⠻⢭⣭⠭⠭⠭⠝⢀⣯⠟⠁⠀⠀⠀⠀⢄⠀⠈⠳⣏⡴⢊⠩⠤⠀⣂⡴⠋
⠀⠀⠀⡰⠀⠈⠙⠛⠚⠛⠋⠁⠐⠄⠀⠀⠄⢀⣤⢠⣄⠀⠀⢉⠙⠛⠛⠛⠉⠀⠜⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⢋⡁
⠀⠉⢊⠁⣉⠈⠀⠀⠀⠀⣴⢶⡄⠐⠉⠐⠀⣾⢤⣻⢾⠀⠢⠀⠀⠀⠀⠀⠳⡈⠀⠈⡀⠒⠂⠠⠀⡒⢀⠀⠠⢿⡿⠆⠀⠻⠟⠠⠶
⠀⠀⠄⠉⠑⠄⣀⣀⣀⣀⡈⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠐⠀⣀⣀⣀⡀⠀⠤⠒⠄⡇⠀⠐⠂⢿⡽⢀⠀⠀⢉⣋⣀⣀⡀
⠀⠀⠀⢀⡴⠾⢉⡐⠀⠈⠉⣳⣤⡀⠀⢠⠂⡡⠐⠶⢶⣶⡶⠛⠩⠭⠭⠟⠻⢶⣄⠀⠈⠀⠀⠘⠀⠂⢀⡴⠞⠉⠉⣉⠉⣉⠓⢦⡀
⠀⠀⣰⠋⠙⠢⢀⡀⠀⠀⠀⡔⡤⠳⡄⠸⡀⢆⠡⡀⠻⡛⠒⠒⠦⠤⠤⠤⠤⠖⠚⢧⠀⠀⠺⠒⠀⢠⣞⡀⡈⠁⠈⡐⠯⣊⠂⣶⠹⣆
⠀⠀⡿⠤⣀⡀⠀⠈⠉⠒⠒⠒⠒⠒⣷⠀⠑⢄⠑⢬⣦⣈⠙⠶⣒⣒⣒⣒⣒⣉⣉⣹⣧⡀⠀⠀⠀⣾⠘⠭⠀⠀⠶⠀⠀⡀⢀⣤⠀⢹
⠀⠀⣇⢠⣶⡄⠉⠉⠀⠒⢂⣀⡉⠉⡿⠀⠀⠀⠑⢤⡉⠋⠭⡦⢄⣉⠙⠲⢄⣈⡀⢠⣿⢿⣷⡄⠀⢿⠀⢠⠫⠕⡄⠀⠀⣁⠀⠠⠄⣸
⠀⠀⠹⣄⠉⠄⠒⠈⣀⠀⠀⣤⠄⣼⠃⠀⠀⠀⡀⠀⠻⡑⠦⣌⡙⠂⠌⠐⡢⠤⢀⣈⢁⡴⢈⠜⡆⠘⣧⠰⠉⠊⠁⠀⡎⠡⢱⠄⣰⠏
⠀⠀⠀⠈⠳⣆⣉⡀⠆⢀⣉⡶⠞⠁⠀⢋⠐⢨⠁⢠⠀⠙⠷⣤⣛⡓⠦⣤⣄⣈⡉⠁⠀⠀⢁⡠⠃⠀⠈⠳⢤⣀⣛⠀⢈⣁⣥⠞⠁
⠀⠘⠃⠠⠆⠀⠉⠉⠉⠉⣁⠔⢀⠀⠠⠆⠒⠲⠆⠀⠀⠄⠀⠀⢈⡉⠉⠉⠡⠄⠀⠈⠉⠉⢠⣲⡀⠺⡗⠀⠀⠈⠉⠉⠉⠁⠀⠀⣴⡄
⠀⠀⠀⡁⠈⠐⠀⠀⠀⠈⠂⢀⠠⠁⠀⠀⡜⢢⠀⠈⡀⠀⠀⠐⠄⡐⠀⠘⢄⡀⠓⠠⠄⡤⠒⠁⠓⠠⠠⠄⠐⣶⠆⠀⠀⠀⢠⠀⠉⠁
⠀⠀⠀⠘⠀⢀⣠⣤⣤⣤⣈⡀⠈⠠⡔⠊⠀⠀⠑⣠⠀⠀⠀⣀⣨⣤⣤⣄⣀⠠⢶⠀⠀⢀⠀⡀⠀⠐⠁⠀⢀⣠⣤⣤⣤⣀⡀⠀⠺⠂
⠀⠀⠀⣠⠞⠉⠓⠒⢱⠄⠀⢹⢦⡀⠀⠑⠄⠠⠋⠀⠀⣠⠞⡉⢃⠵⠸⣄⢉⠿⣦⡀⠀⠆⠁⠐⠢⠠⣠⣞⣛⣀⣀⣒⣊⣠⠝⢳⣄
⠀⠀⣰⡇⠀⣀⣠⠔⠚⠀⢀⣻⣂⣿⡄⠀⠘⠁⠀⢀⣾⡁⠀⢠⢖⢠⡐⠋⢼⢰⡉⢳⡀⠀⠀⠀⠀⣰⡇⠒⠤⣄⣀⣀⣀⠤⠒⠁⢘⣆
⠀⠀⡇⠑⠌⣓⠤⠤⣀⠀⣏⣀⠀⠈⣿⢀⡖⢦⠀⢸⣅⠸⠤⢌⡢⠥⠖⢲⠀⣇⢉⣹⡇⠀⠈⠀⠀⡿⢭⣙⡒⠒⠰⠶⠶⣒⣒⣿⣗⣻
⠀⠀⣧⠀⠀⠘⡄⠀⠀⡑⠀⠈⡇⠀⡟⠀⠙⡋⠀⢸⡄⢹⡆⢤⠃⡀⠀⠘⠤⠬⠅⢾⠇⠀⠀⠀⠀⢿⡒⠲⠮⢭⡽⢿⣛⣉⡭⠖⢋⣿
⠀⠀⠘⢦⡀⠀⢸⢀⡔⠁⠀⠀⢹⡜⠁⣴⢋⡍⣷⠀⠻⣬⠥⠤⠤⠃⠠⡄⢒⠴⣴⠏⠀⢠⣼⣧⡄⠈⢷⡩⠍⣂⠒⠤⠤⠤⢆⣈⡽⠃
⠀⠀⠀⠈⠙⠦⣬⣚⣀⣀⡤⠖⠋⠀⠀⠙⢶⡴⠟⠀⠀⠈⠲⢶⣄⣐⣤⣹⠾⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠙⠷⢦⣐⣒⣂⣴⠶⠋

⣿⣿⠿⠿⡿⢿⠿⢿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡀⠈⠈⠙⠂⠀⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠘⠳⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⣠⠀⠈⠏⠀⠀⠀⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠄⠀⠄⠒⢁⠀⠀⠀⠐⠊⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⠀⠀⠀⠀⠐⠔⠀⠤⠋⠀⠀⠊⠙⡇⠀⠐⠰⣦⠸⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠠⡄⣀⠀⠈⠃⠀⠜⠒⠃⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠱⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⣁⠙⠃⠀⠀⠀⡠⠀⠀⠀⢤⡆⠀⠀⠀⡀⠒⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘
⠀⠀⠀⠀⠀⠘⣦⠀⠐⠁⠈⢧⠀⠀⠀⢰⠇⠀⠀⠈⠁⢿⡄⠀⠀⠀⣀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⡇⠀⢻⣀⡀⠀⠀⢀⡴⢚⠁⠀⠔⠋⠀⠈⠉⠻⣻⣄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡑⠂⡊⠀⠢⠟⠫⠉⠁⠊⠐⠻⠁⠀⠀⠀⠀⠀⠁⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⢀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡀⠆⠀⠀⠉⠛⠃⠠⣤⡐⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⣁⠀⠈⣀⠀⠠⣀⠈⠂⠀⠀⠀⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢸⡉⠙⢿⢥⡀⠀⢀⣀⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⠀⠀⢙⠟⠀⠐⠠⠉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠈⠉

⠀⠀⠀⠀⡠⠖⠚⠛⢻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡓⣦⣄⠀⠀⠀⠀⠀⠀⠀⣰⣒⠫⠛⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⡀
⠀⠀⠀⢈⠁⠀⠀⠀⠀⢲⢹⣿⣆⠀⠀⠀⠀⠀⠀⠐⠀⠘⠗⠛⣿⣷⡀⠀⠀⠀⢠⠏⠉⠛⠁⢄⠈⣙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢿⣿⡄
⠀⠀⢸⠌⠀⣀⠀⠂⡀⠉⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⣭⠸⠇⢔⣽⣿⡇⠀⠀⠀⢷⣀⡈⠀⠀⠀⣹⣿⣿⣿⡄⠀⠀⠀⠀⣀⣄⣐⣦⣤⣠⣾⣿⣿
⠀⠀⠰⠀⠀⠉⠀⠀⠉⠧⣨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⡈⣵⣯⣿⣿⠇⠀⠀⠀⠘⠿⣿⡇⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⢍⣍⣿⣯⣽⣿⡟
⠀⠀⠀⠁⢂⠀⠐⣠⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠆⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠐⢻⣧⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠆⠀⢘⡋⣡⣿⠟
⠀⠀⠀⠀⠀⠁⠁⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⢲⢶⣤⣄⣴⣶⣶⡀⠀⠀⠀⠀⠐⠂⠂⠲⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣷⡄⠀⠀⠀⠀⠀⠀⠀⠔⠡⠋⣹⣿⣦⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⣿⣷
⠀⠀⠀⠀⠒⠶⢶⣶⡖⢶⣟⣿⡿⠀⠀⢀⠀⠀⠀⠀⠈⣠⠞⢋⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣠⣨⣵⡿⠁⠀⢠⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠐⠂⠉⢛⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠁⠀⠀⠀⠀⠁⠈⠉⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠩⠁⠀⠀⠉⠉⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⠀⠠⠣
⠀⠔⠂⢈⠭⠍⠩⠥⠴⠆⢐⡖⠀⡀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢣
⠀⠑⢄⠈⠢⢄⠀⠀⠀⠀⢀⠅⠈⢀⠁⠀⠀⠈⠪⠿⠁⠈⠉⠁⠻⠧⠃⠀⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠁⠢⢄⡉⠒⠤⣀⢸⠂⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠂⠀⠖⠀⠠⠁⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡈⠑⠂⠤⣄⡠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠠⢄⣈⠁⠒⠢⠄⣀⡀⠀⠀⠊⠀⠈⢀⠀⠀⠀⠀⠰⠁⠒⠭⣒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠂⠀⠉⠒⠂⠤⣄⣈⠉⠙⠛⠠⠄⣀⡀⠀⠁⡰⠃⠀⠀⠀⠀⠉⠒⢅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠠⠄⠀⠤⢀⠀⠈⠛⠒⠒⠠⢤⣀⣉⠉⠑⠒⠂⠠⠤⠤⠀⠀⠀⠕⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀⠀⠀⠀⠤⠄⠀⣀⠤⠊⠁⠀⠉⠁⠀⠐⠒⠒⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁

⠈⠓⠂⠀⠀⠛⡯⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⢠⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⣀⣀⡀⢠⡤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢢⠀⠀⠐⠂⠄
⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀
⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠂⠀⠒⠀⠀⡀
⠀⡀⠀⣀⡀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⡡⣤⡀⠈⠉⠉⢠⠉⠳⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⢟
⣥⣰⣀⣉⣁⣀⣞⣋⣲⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣿⣲⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⣠⣿⣦⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣶⠄⠠⣤⣀⠀⠀⠀⠀⢀⠉⠀⠉⠀⠀⠀⠀⠀⢤⣴⣿⣧⣄⠀⣀
⠀⠀⠉⢻⣿⣿⡯⣔⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⢀⢔⢮⠛⠃⠀⠀⠀⠀⠐⠄⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⢀⡀⠀⢈⠄
⠀⠀⠀⠚⠹⢿⣏⣤⣍⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡞⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⢀⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢳⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠀⠈⡆⠈⣆
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠋⠀⢀⡇⠀⠸⡄
⠀⠀⠀⣤⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠢⢤⣤⠴⠊⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠬⠉⢿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠘⠃⡀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡹⡆⠀⢀⡀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡻⣮⢳⡻⣿⡀⠀⠀⠀⠀⠀⠹⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠋⡀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⢧⡹⡍⢷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⡀⠀⠀⡀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡳⡌⠄⠣⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠐⢖⢒⡡⣌⠂⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⢨⠀⣓⠃⠾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠷
⠀⠀⠀⠘⢿⣿⣯⡓⠘⣏⢿⡀⠀⠀⠀⠀⠀⠘⣷⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡄⢀⡀⠀⠀⠀⠀⢀⣤⣾⣦⣀
⠀⠀⠀⠀⠀⠙⠿⡿⢦⡈⠄⢳⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠟⢀⡀⣔⠲⣤⠀⠀⠀⠀⣿⣿⣿⡁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⢄⠀⠣⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⡳⣄⠀⠀⠀⠀⠀⠀⣼⡇⣿⡌⢷⡈⡄⠀⠀⢸⡏⣇⠈⠁⠀⠀⠀⠈⣆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⡹⡌⠣⠀⠀⠀⠀⠀⠀⠀⢹⣧⠘⣿⡄⠀⠀⠘⣿⡘⢦⡀⠀⠀⠀⢠⡟⢰⡇
⠀⠀⠀⠀⠀⠀⣻⣿⣿⣄⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠁⢿⣇⠑⠀⠀⠀⣶⣤⣶⠀⠀⠀⠁⠂⣿⡷⠀⠀⠀⠘⢿⣦⣙⠳⠶⠞⢋⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠛⠹⠏⠀⠀⠀⠀⠀⠚⡿⣛⠀⠀⠀⠀⠀⡌⠈⠀⠀⠀⠾⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢫⢔⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢐⢪⡓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⢹⠧⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣦⠻⣷⠄⠀⠀⠀⠀⠀⠀⢰⣿⣏⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠳⠄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⢿⠆⠀⠉⢁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⢠⡄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢤⡀⠀⠀⠀⠄⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣽⣿⠂⠀⠀⠀⣰⡄⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⡤⠀⢀⢠⡜
⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠁⠀⠀⠘⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠃⠓⠋⠁
⠀⠀⢀⢀⡀⠀⠁⠀⠀⠀⠀⣀⢘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠒⠲⠖⠊
⠀⠀⠼⣿⠷⠀⠀⠀⠀⠀⢨⡀⢰⠹⡄⠀⠀⠀⠃⢐⡄⠀⠀⢤⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢻⣖⠚⠖⠓⠉⠀⠀⠀⠸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠈⠁⠄⠀⠀⢀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢽⡿⠄
⠀⠨⠄⠀⠀⠀⠀⠆⠀⠈⠛⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⢤⠀⠁⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄⡐⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⢹⠀⠀⠀⠀⠘⣄⠀⠀⠀⡀⠀⢀⣄⠀⠀⣿⡟⠡⣾⣿⣷
⠀⠀⠀⣼⣿⣅⠀⢀⠄⠀⠀⠀⠀⣀⡖⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈⠙⠁⠀⠱⣦⣄⠀⡉⠁
⠀⠀⡜⠘⠁⠀⢰⠁⠐⣄⣀⡤⠚⡡⠀⠀⣤⡤⠀⠀⠀⠀⠀⡄⠀⢸⠉⠐⢢⣤⡀⠀⠀⠈⠀⠀⡀
⠀⠀⡂⠀⢂⠀⠈⠓⠒⠋⠉⠈⠁⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢸⣠⠖⡋⢀⠙⢄⠀⠀⠀⠿⠃
⠀⠀⠠⠀⡂⠀⠀⠀⠀⠀⡔⠉⠈⡁⣐⡀⠀⠀⠀⠈⠀⠀⠀⣠⣀⠈⠣⡀⠀⠊⠀⡈⠢⣀⣀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠐⠀⡀⡀⠀⠀⠀⠰⠆⠀⠀⠛⠇⠀⠀⠙⢆⠈⠢⢃⣔⠁⠈⢢⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⡨⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠚⠹⡀⠙⣄⡠⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢶⣾⣄⠀⠀⢰⠉⠢⡀⢈⠦⠜⡆
⠀⠀⠀⠐⠦⣠⡠⠔⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠑⠢⢬⣣

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠐⠚⢻⣯⠀⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⣤⣄⣹⡾⠛⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⣀⠀⠀⢼⣿⠖⠀⠀⣐⠻⣮⣿⢹⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣿⠴⠁⠰⣿⣶⠀⠿⠗⠉⠀⠻⠁⠛⠯⠹⢿⣿⡿⣷⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣝⣯⣟⣏⣔⣠⢦⣼⡿⡄⠀⠀⠀⠀⠀⠆⠀⢀⠀⠉⣉⠂⣽⣷⣤⣤⣆
⠀⠀⠀⠀⠀⠀⢰⡿⣼⡿⢾⣿⣿⣿⣿⣿⣿⡯⠎⠈⢠⣶⢊⠜⠀⠀⠀⢈⠅⠀⢸⣧⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠒⠁⡯⣀⣼⣿⣿⣹⣿⣿⡿⠀⡀⠀⠈⠁⠈⠀⠀⠠⠈⠁⠀⠀⣴⠎⠙⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⢢⡈⣹⣿⣿⣿⣿⣧⡀⠀⠀⢀⣶⣄⣠⡴⡆⠀⣤⠒⠂⠀⠘⠀⠁⣤⣿⠁
⠀⠀⠀⠀⠀⠀⢷⡞⠻⣿⢟⡺⣿⠿⣿⣷⣧⣴⢲⣬⣽⣿⣿⠁⢁⡚⠀⠀⠀⠀⠁⠀⢀⣽⡏
⠀⠀⠀⠀⠀⠀⠸⣟⠆⠺⣮⢱⣊⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⢂⣶⣿⣆⡀⠀⢐⣧⣄⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠁⠛⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⡿⣭⠟⠉⠀⠀⠀⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣁⠀⠀⠁⣜⡛⢿⡿⠐⠀⠀⠀⠘⣿⡷⠁⠆⠰⠀⠤⠀⣀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡃⠈⠙⠑⠻⠿⣄⡀⠀⢐⣶⣿⣤⣐⣤⢀⣂⣤⣿⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣒⣦⠠⣰⣦⣥⢉⣼⣿⣟⢻⣿⣿⣯⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠺⠯⠍⢟⣶⣿⡫⠴⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄
⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣦⣬⣉⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣠
⠀⠀⠀⠀⠀⠠⠿⠛⠉⠉⠁⢀⣠⣬⠭⠽⠂⢁⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠛⣿⠿⡆⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠄⠀⠐⣿⣷⣶⣶⣤⣄⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⠓⠦⣈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠂⢀⣸⢶⣶
⠀⠀⠀⠀⠀⠀⢀⣀⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡾⠛⠂
⠀⠀⠀⠀⠀⠀⠠⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢛⣋⣩⣭⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⣚⣛⣋⣉⣉⣛⣛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣄⡀⠀⠉⠉⠉⠉⠉⠛⠻⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⣀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⠛⠁⣼⠁⠙⣧⡀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⢴⣞⣉⡀⠀⠀⠀⠙⠶⣄⠈⢻⡄⢻⡓⠦⡴⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⣴⠛⠛⠉⠉⠁⠀⠻⣆⣷⠀⠀⠀⠈⠛⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠀⠀⠀⠀⣴⣏⣥⣤⣄⠀⢰⡛⠉⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣴⣦⡀⠀⠀⠀⠻⣧⡀⠀⠈⠳⣼⡇⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠻⣦⣤⠶⠞⡿⢻⣆⠀⠀⠈⠁⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠀⠀⠀⠀⢀⡾⠁⠀⠙⢷⡀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣥⣄⡀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠈⢻⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣤⠶⠦⣤⣬⣿⣆⠀⠀⠹⣦⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⢻⡄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⢻⡄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢻⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢿⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠾⠿⠿⠛⠻⠿⠿⠷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠋⠁⠈⠙⠛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⢀⣤⣶⠶⠿⠛⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣠⡾⠟⠉⢀⣠⣤⡶⠾⠟⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣠⡾⠋⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⣴⡿⠃⣼⡇⠸⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⣠⡾⠋⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄
⠀⠀⠀⢀⣼⠟⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡾⠟⠁⠀⣠⣾⠏⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠈⢿⣆
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⢀⣴⠟⠁⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⢻⣆
⠀⠀⣾⠃⠀⠀⠀⢀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡏⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⢀⣀⣤⡾⠋⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⢀⡿⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⢉⣩⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣤⡶⠾⠷⣦⠀⠀⠀⠀⢠⣾⠏⠘⣧
⢸⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⢠⣿⠁⠀⠀⢠⡿⠃⠀⠀⢿
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⡿⠁⠀⠀⣰⡿⠁⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⡿⠋⠀⠀⢀⣼⠟⠀⠀⠀⣠⡿⢻
⣿⠀⠀⣀⣤⣶⠶⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣿⣀⣀⣤⣶⠟⠋⠀⠀⠀⣠⣾⠋⠀⠀⠀⣴⡟⠁⢸
⣿⣠⣾⠟⠁⠀⣠⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⣠⣾⠋⠀⢠⣿
⢹⡟⠁⠀⣠⡾⠋⠁⠀⠀⠀⠈⠉⠛⠿⢶⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⣠⡿⣿
⠘⣧⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⠀⣴⡟⢁⡿
⠀⢻⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣠⣶⠟⠁⠀⠀⣠⣾⠋⠀⣼⠃
⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁⠀⢀⣤⡾⠛⠁⠀⠀⣠⡾⠟⠁⠀⣰⡏
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠁⠀⣀⣤⡾⠟⠉⠀⠀⣠⣴⠿⠋⠀⠀⠀⣰⡟
⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠉⠀⣀⣤⣶⠿⠛⠉⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⣀⣴⡶⠟⠋⠁⠀⣀⣤⣶⠾⠛⠉⠀⢠⡀⣠⡄⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢀⣿⠃⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣠⣶⠿⠛⠉⠀⠀⢠⣦⢠⣿⠱⠿⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⡇⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⣿⠃⠈⠁⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⣼⡏⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⠀⠀⠀⣰⡿⠃⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢾⣿⣤⣤⣤⣤⣿⣥⣤⣤⣤⣤⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⠀⠀⠀⠈⢉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣤⡀⠀⠈⠛⠂⢱⣤⠔⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣧⢀⠀⠒⠀⠈⠀⠀⠀⡔⣰⠄⠀⢱⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡠⢾⣿⡄⠉⠀⢰⠉⠙⣷⠀⠀⠀⠀⣆⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁
⠀⠀⣴⠟⠁⠸⣿⣿⣂⣀⡈⠃⡚⢃⣤⣶⣤⣿⠿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢘⠉⢄⠀⠀⠛⢛⣛⣩⣭⡲⠖⠛⠋⠉⢱⡄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣤⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⣠⣤⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠃⣀⣴⣿⠁⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣯⠓⡀⠉
⠀⠀⠀⠀⢃⡐⠙⠀⢿⣶⣿⣷⣿⣿⣿⣿⡉⠀⢉⣄⡀⠁⠀⠀⢠
⠀⠀⠀⢀⡄⠀⠀⠐⢿⣿⣿⣿⠹⢿⣿⠟⠛⠂⠈⠛⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣾⢠⣶⡀⠀⠈⠙⢻⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⣾⣿⣿⣷⣠⣤⢈⣿⠉⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⢿⣿⣿⣿⣿⠙⠟⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠐⢀⡻⣿⡏⠀⠀⠀⠈⠀⠀⠒⠒⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⣾⣅⠀⢳⠤⠀⠀⠀⠀⠳⣾⠣⠟⣹⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⢿⣷⣤⣤⣤⣾⣶⡤⠖⢃⣄⠉⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠟⠓⠄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠾⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠠⡤⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠴⠾⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠀⠴⠀⣀⣢⣄⣄⡀⠀⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⢀⣽⡏⠉⡀⠀⢀⣨⢿⣶⣄⣤⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠖⠒⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢈⡟⠙⢦⣤⡄⢻⠇⠡⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⠀⠀⠂⠀⠀⠀⠀⠘⢦⠀⡀
⠀⠀⠀⠀⠀⢠⣼⡃⠀⣿⠉⠀⠀⣷⣄⡀⠀⣨⣿⣷⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣚⡆⢉⠠⠤⣈⡳⠾⢧⡀⡀⠀⠘⢂⠀⠀⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⡶⡄⣤⣼⠁⠉⠻⣯⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠑⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠳⣤⡀⠻⢄⣀⣀⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠉⣷⠀⠀⠘⡿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⠠⡀⠉⠿⣀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢏⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠆⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⡄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠂⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠁⠐⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⠀⢀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡇⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢴⡀⠀⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢨⠀⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠚⠀⢰⠶⠂⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⡠⢔⢢⠉⢤⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⠰⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠠⣀
⠀⠀⠀⠀⠀⡣⠗⠁⠀⠀⠀⠀⠱⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⡇⡅⠀⠀⠀⠀⠀⠀⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣇⠀⠀⠀⠠⠀⠀⣍⠹
⠀⠀⠀⠀⠀⠰⡙⢄⠠⠀⠀⣰⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠰⠎⠒⠥⠤⠍⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠯⠇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐⠞⠁⠀⠀⠈⢱⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠃⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠁⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⣀⠼⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣄⠤⠛⠛⠄⣀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠒⠒⠂⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢞⠅

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⠃⠀⠀⠀⠈⠑⡴⠂
⠀⠀⠀⠀⠀⠞⣿⣤⡄⢀⡠⠀⣤⣼⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢽⢄⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠓⢢⡴⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⠀⠀⢻⡍⠉⠉⠙⡧⠀⠈⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⠀⡞⠹⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠶⣦⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⣐⠰⣟⠀⠀⠀⢰⠉⢻⠇⢠⠀⢀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣰⠋⠙⣿⠀⠀⠀⠀⠐⠪⠃⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠠⡀⠳⡴⠛⠀⢀⡈⢁⣀⡪⢊⣠⠾⠛⠟⣻⣿⡷⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣖⣫⣿⣶⣮⣝⢿⢜⣋⣠⢦⣿⠁⠀⠀⠀⢱⣿⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡆⢿⡘⣿⣧⠻⢆⡀⣀⣠⣬⠁⠃⠂⠀⠀⠀⢀⣴⢿⣿⣦⠀⠀⠀⠀⣀⠁⠈⡇
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣇⣛⣽⣿⣿⣿⣿⣿⣿⣏⡚⠋⡁⡘⠉⠁⠁⢀⡀⠀⠀⣼⠀⠀⠘⡿⢃⠀⡄⠀⠘⢆⠀⡄⠰⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣷⡔⠜⠆⣤⠝⠳⠟⠀⠀⠈⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣀⢄⣀⣠⣤⣴⣄⣤⡤⡄⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠙⢿⣿⣿⣿⣿⣿⣿⣅⠹⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠰⠆⠀⢠⠉⢸⠟⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡄⠀⠛⠁⠀⣀⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣒⡔⣄⣶⣶⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣿⣿⣿⣿⣿⣿⣆⠹⠛⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣛⣉⣩⣭⣽⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠠⠐⠊⠉⠉⠀⠀⢄⠀⠀⠀⠀⠀⡠⠀⠊⠉⠉⠀⠠⡀⠀⠀⠀⠀⡠⠐⠀⠉⠁⠀⠀⢄⠀⠀⠀⠀⢀⠄⠀⠈⠉⠀⠀⠠⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠄⠀⠀⠀⠀⠀⠔⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠂⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠂


⠀⠀⠠⠒⠀⠉⠁⠐⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⢑⡶⢔⠊⠉⡗⠀⠀⡀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠊⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠁⠀⠀⡢⠞⠁⠀⠀⢢⡞⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢐⡵⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠀⢀⠀⠀⠤⠒⠁⠀⢀⡞⠀⣀⡦⡀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠢⠀⠀⠀⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡂
⠀⠀⠀⠀⠀⠐⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠈
⠀⠀⠈⠀⠀⢠⡀⣠⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠁⠠⠖⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⡀⠐⠐⢲⢤⡀⠀⠀⠀⠀⠀⠔⠀⠀⠤⠒⠖⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠚⠶⠆⠚⠛⠷⠛⡀⠀⠀⠀⢁⠄⠈⠀⠀⣠⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢿⣶⣾⠷⠹⠞⢻⠁⠀⠀⡠⠁⣀⡤⡲⠋⠁⡘
⠀⠈⠀⠈⢀⠄⠁⠈⠀⠀⠈⠫⠭⠭⠭⠟⠃⠀⠠⠊⠀⡢⠕⠂⠒⠐⠈⠀⠀⠀⠈⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡀⢴⣒⣶⣤⣄⠀⠀⣀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⡤⠖⠒⠂⢄
⠀⠀⠀⠀⢀⠉⠉⠉⢐⣓⣏⣉⡤⠂⠄⠀⠀⠀⠀⠀⠀⡀⠰⠓⠰⠂⠀⠀⠀⢀
⠀⣀⠤⢦⢂⣴⣾⣾⠭⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⡞⠉⠈⠈⠂⡀⠂
⠨⠗⠒⠛⠻⡏⠁⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠲⠀⢀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠂⠀⠀⠀⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠕⠈⠀⠈⠁⠂⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠠⠤⠤⠥
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡀⠀⠀⠀⠑⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡁⠀⠡⠀⠀⠀⠀⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡦⠀⢀⡉⠉⠐⠠⠄⢀⠀⠀⠀⠀⢳⠀⠀⠑⠄⠠⠀⠀⠀⠀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠂⠀⠁
⠀⠀⠀⠉⠢⡀⠀⠉⠀⠐⠂⠄⢈⡁⠒⠠⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠐⠂⠀⠀⡁⠠⠀⠤⠤⠤⠀⡄
⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⢀⡠⠔⡠⢁⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠁⠀⠀⠀⠀⢀⡀⠄⠐⠂⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⡠⠐⠂⠉⠀⢈⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠒⠒⠊⠉⠀⡠⠔⠁⢀⠔⠁⠀⠀⢀⠠⠐⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠈⠂⠐⠒⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⢔⠒⠠⠄⢀⣀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠂⠉⠉

⡀⢀⣀
⣀⠈⠁⣆
⣿⣿⣦⣼⠂⠔
⣿⣿⣿⣿⣆⠰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⠠⠉⢀⢠⣶⣄⢰⣶⣦⢠⣶⡄⣴⣶⣆⠀⠀⠀⠀⠀⢘⡆⠀⠴⢃⣶⡂⠀⣴⣶⡄⢠⣶⣦
⣿⣿⣿⣿⣿⢀⣛⡀⠈⠛⠃⠘⠛⠋⠈⠛⠁⠙⠛⠃⠀⠀⠢⣤⣤⡼⠃⠀⠒⠿⠟⠁⠘⠿⠟⠃⠈⠛⠋
⣿⣿⣿⣿⠯⠈⠃
⣿⣿⠟⢛⠄
⡍⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠓⠢⠤⣄⣀⡴⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠂⠛⠉⠉⠉⠉⠓⠒⠳⡀⠀⠀⠀⠀⠀⠀⠸⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⣀⡤⠤⠒⠒⠘⠉⠉⣉⣉⣉⣍⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⡠⠔⠊⠉⠀⢀⣀⠤⠒⠚⠉⣉⡠⠤⠐⠒⣂⠞⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⢀⡠⠚⠁⠀⠀⣠⠴⠊⠁⢀⡠⠔⠊⠉⢀⡤⠖⠊⡡⠃⢀⣀⠤⠔⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣠⠔⠉⠀⠀⣠⠔⠋⠀⢀⡠⠒⠁⠀⣀⠴⠊⠁⠀⠀⠘⠛⠉⠁⠀⠀⠀⠈⠣⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⠁⠀⠀⡠⠊⠁⠀⢀⠔⠁⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠜⠁⠀⠀⡠⠊⠀⠀⢀⠞⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡰⠃⠀⠀⢀⠞⠀⠀⠀⡔⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⣠⠋⠀⠀⢀⠜⠀⠀⠀⡰⠃⠀⠀⢠⠊⠀⠀⢀⡜⠁
⠀⠀⠀⠀⡰⠁⠀⠀⢠⠎⠀⠀⠀⡜⠀⠀⠀⡰⠃⠀⠀⢠⠎
⠀⠀⠀⡰⠁⠀⠀⢠⠂⠀⠀⠀⡜⠀⠀⠀⡰⠁⠀⠀⢠⠃
⠀⠀⢰⠃⠀⠀⢀⠏⠀⠀⠀⡜⠀⠀⠀⣰⠁⠀⠀⢀⠇
⠀⠀⠃⠀⠀⠀⡎⠀⠀⠀⡸⠀⠀⠀⢠⠃⠀⠀⠀⡎
⠀⡴⠀⠀⠀⡼⠀⠀⠀⢠⠃⠀⠀⠀⡞⠀⠀⠀⣸
⢀⠃⠀⠀⢠⠃⠀⠀⠀⡜⠀⠀⠀⢰⠁⠀⠀⠀⡇
⠸⠀⠀⠀⣸⠀⠀⠀⠀⠇⠀⠀⠀⡼⠀⠀⠀⢰
⡟⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⣸
⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣇
⠀⠀⠀⢲⠊⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⠉⠀⠘⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡛⠉⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠸⠒⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡜⠁⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣩⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣲⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⣀⠠⠄⠒⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⡠⠔⠂⠉⠀⣀⠠⠤⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⠤⠂⢁⡀⠤⠒⢈⣁⡠⠤⢤⡞⠀⠀⣀⣠⠤⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⠊⣁⠔⢊⡡⠄⠒⠉⠁⠀⠀⠀⠸⠓⠋⠉⠁⠀⠀⠈⠓⢤⡀⢸⠅
⠀⠀⠀⠀⠀⢠⢎⠔⡡⢔⡩⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺
⠀⠀⠀⠀⣴⢕⣵⡪⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄
⠀⠀⢀⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⡤⠞⢆⣀⠀⠀⠀⠀⠀⠀⠀⢈⡇⣠⠋
⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢄⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⠇⠸⣆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠁⠉⠲⣄⠀⠀⠀⠀⣠⣴⡏⠘⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡏⢸⣆⣀⣀⣀⠀⠀⠘⠀⠀⣼⠁⣠⣄⠈⢿⣿⡇⡇⠀⠀⣀⣀⣀⣠⡟⠸⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⢀⡴⠟⠉⢇⠀⠀⡀⢰⡷⠚⠉⣿⣷⣾⣿⢡⠁⠀⢰⠉⠙⢦⡀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢃⡤⢤⡘⣿⡀⠀⠸⡄⠀⠀⢺⠀⠀⠀⣿⣿⣿⣿⠘⠀⢀⠇⠀⠀⣰⢇⣤⢦⡘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠀⠈⢿⣿⣷⡀⠀⢳⠀⠰⢸⡀⠀⠀⣿⣿⣿⡏⡇⠀⡼⠀⠀⣰⣿⣿⠋⠀⠙⢻⠄
⠀⠀⠀⢀⠿⣦⡀⠀⠀⠘⢄⠀⠀⠈⢿⣿⣷⠀⠘⣇⠀⡟⡇⠀⠀⣿⣿⣿⣿⠀⢰⠇⠀⢠⣿⣿⠋⠀⠀⣠⠋⠀⠀⢀⣴⣿⡀
⠐⢆⡐⠚⠀⠛⢛⡲⠶⡄⠈⠣⡀⠀⠈⢿⣿⣧⠀⠹⠀⠁⠇⠀⠀⢿⣿⣿⠟⠀⡞⠀⢠⣿⣿⠃⠀⢀⡞⠁⣠⠖⢶⣟⠛⠁⠳⢲⡶
⠀⠀⢹⠀⣀⠀⣯⣄⠀⠈⠢⡀⠑⢄⠀⠀⢻⣿⣆⠀⠁⠀⠀⠀⠀⠉⠗⠋⠁⠰⠁⢀⣾⡿⠃⠀⣠⠋⢀⠔⠁⠀⢀⣽⢇⣤⡘⡏
⠀⠀⣶⡛⠉⠓⢾⣿⣷⣄⠀⠘⢦⡈⠂⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⢀⡜⠁⠔⠁⠀⣠⣾⣿⠿⠋⠀⠉⠻
⠀⠀⠈⠙⠲⢄⡀⠉⠻⣿⣷⣤⠀⠑⠄⠐⠄⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⣠⠔⠈
⠀⠀⠀⠀⠀⠀⠉⠂⠀⠈⠉⠘⣒⠢⠀⠁⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠙⠈⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁