Green arrow Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢈⡤⣤⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠟⠉⠹⣼⡇⠈⠁⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢋⢣⠀⣢⣾⣫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡟⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣾⣿⣿⠸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠟⠋⢈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠐⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢟⢕⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠠⠆⠀⠈⠆⢀⣋⣀⡠⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣴⣴⡿⣫
⠀⠀⠀⠀⠀⠀⠀⠐⣱⣿⣿⡀⠀⠀⠀⠀⣀⣴⣶⡀⠀⣀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡙⢋⠜⠑
⠘⠁⠀⠀⠀⠀⢠⣴⣿⣿⣿⣧⠀⠀⠀⢿⣿⣿⣿⣧⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⡿⠟⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡔
⠀⠀⠂⢦⣍⣛⡛⠻⠿⠿⠛⠃⠀⠐⠀⠃⢂⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠂⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⣾⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⣧⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣼⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣾⣷⡄⠘⣩⣤⣾⣿⣿⣿⣿⣿⣿⣦⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⡀⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣿⣿⣫⣿⣾⣿⢏⣿⣿⣇⢰⡄⠓⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⡵⠊⣱⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣡⣿⢙⣀⡀⠘⣿⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⡉⢽⡟⠺⠉⠉⠀⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣄⣾⡇⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣽⣇⣽⢠⣷⡄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠈⣾⣿⡅⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣻⣿⣿⡆⠈⢻⡁⢰⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣉⢹⣿⡿⣿⣿⡇⠌⢢⢼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⢻⣦⣿⣿⣷⣜⠛⢢⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠃⣀⠈⢿⣿⣿⣿⣿⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣽⣿⡏⠀⠁⠈⠩⣿⣿⡿⠿⠃⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠈⠓⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣇⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⢻⡄⢿⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⢷⣾⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⢰⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⢻⠤⠄⠀⣤⣾⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣼⠈⠀⢀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⡀⠀⠙⢷⡀⠀⠀⢀⣇⠀⠀⠀⠀⠼⢿⠆⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠸⢁⣴⣾⣿⣿⣿⡟⠛⠛⠿⢛⣿⣿⣶⣤⡀⠁⠀⠀⠀⠀⢽⣇⠀⠀⠈⠳⣄⢀⡌⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠲⣶⠶⠖⠊⠁
⠀⢀⣠⠄⠐⣤⣿⣿⣿⣿⣿⣬⣽⣦⢿⣾⣟⡋⠛⠡⣿⠟⢦⡀⠈⠳⣀⠀⠙⠳⢤⡀⢀⡜⠁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣧⣀
⠀⠐⣴⠎⢳⡟⣻⣿⣿⣿⣯⠛⢿⣧⠘⠛⠛⠓⠀⠀⠁⢀⠠⣽⣦⣤⠈⠽⠷⠶⢒⡋⠙⠀⠀⠈⠀⠈⠓⢦⣄⡀⠀⠀⠉⢟⠛⠿⡋⠀⠀⠀⠁⡀
⠀⠀⠘⢿⣿⣿⠋⠘⣿⣿⣿⣀⠉⣁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⢊⠄⡄⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠈⣇⠠⠅
⠀⠀⠃⠀⠻⡏⠀⠀⣿⣿⣿⣿⡄⣹⡖⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⣸⣄⡀⠀⢠⡀
⠀⠀⠀⠀⠀⢻⣷⠀⣿⠸⣿⣿⡿⣟⢻⣁⣀⠀⠀⠀⠛⢄⡀⠀⠀⠀⢀⣀⣠⣾⢂⣼⣷⣿⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⠀⠙⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠁⠀⣿⡀⠹⣿⡗⣿⣧⡌⠀⠀⠀⣠⣶⣾⠟⠉⢀⣿⣿⣿⡿⣻⣿⣶⣾⣿⣋⠀⠀⠀⠲⢦⣄⠀⠀⠀⠀⠀⣇⠀⠀⠀⢿⡟⢦⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠿⢧⠀⠙⠳⡘⢿⣿⣶⣶⣿⠟⠛⠀⠀⣔⣫⣿⣿⣟⣿⣿⠋⣿⡿⡛⠯⡉⠁⠀⠀⠐⠚⠻⣶⣶⣶⣾⡟⠀⠀⠀⢸⠃⠠⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠙⠂⠀⠀⠀⠹⠈⣿⡻⠄⢀⣴⣾⣿⣿⣿⣿⠟⢩⠋⢰⣿⡀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠠⠭⢽⣿⢀⠀⠀⢸⡎⠀⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢷⣶⠲⢶⣶⣦⣍⢿⣄⣾⣿⣿⠟⠋⠉⠀⠀⣠⣤⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⢸⠃⠀⠀⢀⡴⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣾⣿⣿⣿⣿⠉⣿⣿⢃⡴⠃⢀⠀⣾⡿⢿⣛⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣀⠀⣀⣾⣶⣿⣶⢏⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣼⣿⣿⣿⣿⣾⢸⣿⡃⠈⢀⣠⢤⣿⠃⠀⠈⣿⢩⣿⣿⣷⣄⡀⠀⠀⠀⠠⠤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⡷⣛⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣧⣽⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣼⣿⠀⠀⠀⠙⣻⣯⡿⣿⣿⣯⣕⣲⠤⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⣟⣉⣿⣿⣿⣿⣿⡿⢹⠃⠀⠀⠀⠀⠀⢾⣿⡄⠀⠀⠀⢝⠃⣀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⢀⣾⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣏⡾⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠈⠻⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⡹⠿⣿⣁⠈⣿⣿⣿⣿⢻⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢿⣿⣁⣠⣿⣿⣿⠿⡉⠁⢈⣿⠿⠟⠛⢉⣿⠁
⠀⠀⠀⠀⠀⠀⣷⣦⡇⠴⢿⣿⣿⠿⠃⢸⢹⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣽⣟⣭⣿⠟⠁⠀⠀⢨⠃⠀⠀⠀⢨⡟
⠀⠀⠀⠀⠀⡼⣿⣿⡅⣤⣾⠉⠁⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⢿⡍⠃⠀⠀⠀⠁⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠞⠀⢸⡿⠀⣿⠄⠀⠀⠀⠀⠀⢠⠁⣿⣧⡀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⣠⠿⣧⡸⣟⢠⠀⠀⠀⠀⠀⠈⣦⣼⢿⣿⣦⣀⣠⣤⣾⠟⡻⠏⣰⣿⣿⠟
⠀⠀⠀⢠⡎⠀⢰⠿⠳⠲⠿⣿⣿⣿⣶⣤⣴⣿⣿⠻⠛⠛⠉⠉⠀⠀⣀⣤⣼⣿⠟⠁⠀⠀⠀⡠
⠀⠀⠀⠀⡀⠀⠁⠀⠀⠁⠰⣾⣉⠁⠀⠀⠤⠿⡿⠀⠀⠀⠀⣀⣤⠼⣻⣛⣿⡷⠆⠀⠀⢀⣾⠃
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣹⠛⢿⣿⣶⣦⣄⣷⣢⣴⠞⠟⢉⣤⣾⠿⠋⡝⠀⠀⠀⣰⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠉⠻⢶⣍⡿⣿⡉⠁⡘⠋⠁⠀⠀⠀⠀⠀⠀⠼⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣶⣷⣀⣠⡔⢈⣐⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠀⠀⠀⢻⣿⣭⣽⣿⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⣦⣶⡼⠋⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⢦⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⠀⢠⣭⣿⠟⣿⡟⣿⡿⠗⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣯⣈⣈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⣿⠀⠀⣿⡿⢷⣿⡷⠋⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣿⣧⡐⣿⣿⠿⠋⠀⠀⠀⠀⠀⠔⠈⠁⠀⠉⠛⠛⢷⣄⠀⠈⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⡿⠋⠀⠀⣴⠀⣴⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⢰⣿⣿⡏⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠈⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣾⣿⣿⡇⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢿⣿⣿⣇⣿⣿⣆⠀⠀⠀⠀⠀⣠⡇⢠⡄⠀⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣾⣿⣤⣿⠃⠀⢻⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠚⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⣿⡟⠛⠉⠉⠉⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣶⣿⠟⠀⡀⠀⠀⠀⠸⣿⣇⠀⠀⢈⡀⢲⣾⣿⣿⣿⣿⣿⣿⠿⢣⡄⠀⢰⡇⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠁⠀⣰⣬⡀⠀⠀⠀⠈⠉⠉⠀⠉⠁⢸⡏⢺⣿⣿⣟⠁⠀⠀⢾⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣶⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⢠⣿
⠀⠀⠀⡄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠋⠁⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⢀⣠⢸⣿⣿⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣦⡄⠀⠀⠀⢦⡀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢰⣶⣿⣿⠟⠋⠀⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡿⢫⣿⣿⡇⠀⠀⠀⠈⣿⣆⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠁⠹⣤⡀⠀⠀⢹⣷⣤⡀⢀⣴⣾⠃⣠⣶⣿⣵⣿⣷⣿⠁⠀⠀⠀⢠⣿⣿⣆⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⡈⢛⠶⠷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡿⣛⣽⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣮⣷⠀⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣤⣾⣿⣿⡟⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⣶⣶⣶⣤⣽⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⠃⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⣿⡿⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⣿⣿⣦⡀⢀⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣹⣿⣿⣿⣿⢿⡿⣿⣿⠿⠃⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀⣀⠀⠀⣸⣧⢠⣶⣿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠉⠉⣏⣿⠸⣿⡏⠉⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣠⣿⣿⡀⣿⠷⣠⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣻⣯⡥⢿⡷⣿⣿⣧⣤⣤⣿⣿⣿⡇⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠐⠂⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⠁⠀⠀⣀⡠⠂⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣶⡉⠉⢻⡦⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠞⠛⣠⢿⡟⠁⢊⣅⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣀⠔⠈⠉⠛⠋⢉⡧⠠⠄⠀⠀⣿⣧⣌⠀⡹⠊⠀⣠⡶⢶⠦⢄⡀⣀⢀⣀⠀⢀⣄⡤⢂⡒⣡⣴⢄⠠⠄⣀⡄
⠀⡘⢷⣿⣿⠿⢿⣦⣬⢷⣤⣤⣥⠠⣍⡩⠞⠁⢀⠀⣰⣿⣶⠀⠀⠈⣁⡀⠀⠉⠻⠋⠉⣿⣾⢿⣿⠋⠀⠀⠈
⠀⠰⠿⣆⣈⣿⣶⣿⣿⠂⠛⠛⠟⣻⠟⠀⠀⠠⠏⣾⣯⣗⣊⡁⠠⢀⣿⡟⢻⣿⣧⣄⣸⣿⠂⢹⡏
⠀⠀⠀⠀⠈⠻⠿⣿⣯⣿⣤⣀⠀⠁⠀⠀⠀⠀⢦⡿⠿⠟⠿⠛⠃⠈⠉⠉⠉⠈⠙⠛⠋⠂⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣀⠀⠀⠀⠁⡿⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠛⠛⠻⠒⠀⠐⡇⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⡜⣶⡀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣿⡈⢿⡆⢿⡀⢺⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣣⣾⣿⠀⠛⠊⠀⢠⣆⠀⠀⠀⠀⠄⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢈⡴⢿⣍⠁⠀⢀⠔⠁⠀⠱⠀⡠⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠓⠋⠰⢤⣽⣿⣖⠁⠀⠀⠀⠑⣎⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠐⣶⣿⡟⢻⣷⣄⠀⠀⠆⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢀⣿⡟⠀⠀⠑⢽⣷⣤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⣼⠟⠠⡄⠀⠀⠀⠙⢿⣿⣿⣾⡷⠾⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣧⣤⣴⠟⠉⣁⣀⡱⠀⠀⠀⠀⠀⠉⠛⣋⣥⣶⣷⠉⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣧⣀⠙⠟⣻⣿⣦⣴⠉⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⣭⠟⠀⢷⡆⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⡾⠿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣶⡀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣄⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣅⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠰⠏⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣃⠀⠀⠒⠂⠀⠐⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⣭⡀⣀⣀⣀⣈⣦⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⢻⠿⠟⠋⠿⠿⠉⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⠃⠀⡐⠦⣀⡀⠈⢻⣿⣏⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣵⡖⣶⠄⣹⠛⠉⡀⡄⠁⠄⠀⢀⠄⠻⠏⡛⠈⠃⣿⠲⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⢘⢓⣙⣇⠘⠠⣴⣿⣿⣷⣦⣴⠏⠀⢧⡀⠁⠠⣿⣿⣄⣛⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠟⠁⡼⠛⠢⣌⣹⡿⠙⡃⠀⠀⡴⠛⠀⠀⠀⢴⣆⠈⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⣴⣻⣆⣤⣤⡈⡛⢦⣘⣠⠜⣁⣶⣾⣾⣷⣿⣿⣆⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠿⢻⣿⡟⠛⠛⠻⠿⣿⣶⣬⣥⣶⣿⠿⠟⠛⠻⢿⣿⣿⠛⡗⢸⡂⡀
⠀⠀⠀⠀⠀⠀⠰⣾⣿⣶⣾⣼⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⠀⠀⠀⠀⠀⣸⣿⣟⣸⡿⢿⣿⠃⠆
⠀⠀⠀⠀⠀⠇⠀⠘⣿⡟⢹⣿⣿⡧⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⠙⣿⢃⠀⠈⠆
⠀⠀⠀⢀⣀⣀⣀⣰⣿⡇⢸⣟⣿⡁⠀⠀⠀⣶⣄⠀⢠⡄⢀⢀⣄⠀⠀⠀⠀⣚⣿⣗⠀⣿⣷⣶⣾⣿⣆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢸⣿⡿⢧⣴⡶⠖⠋⠁⠀⠀⠀⠀⠈⠉⠲⠾⣴⣾⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⡿⠛⠻⢿⣿⢿⣿⠀⢸⡏⠁⠀⢠⣦⣀⣠⣧⣄⣠⠀⠀⠀⡸⠙⢿⣿⠙⣿⡿⠛⠉⠀⠹⣿⡄
⠀⠀⠀⣿⣿⠁⠀⠀⠀⠈⠘⣿⡇⠰⡀⠀⠄⠀⢹⡿⠉⠉⢉⡟⠉⠀⢀⠀⠀⢸⡟⠀⠘⠄⠀⣠⠀⠀⣿⣇
⠀⠀⢰⣿⣇⣀⣀⣲⠂⠀⠀⠙⠃⠘⠳⣤⣦⣀⣀⣿⣷⣶⣿⣤⡀⣸⣇⢀⡴⡶⠁⠀⠀⠀⣀⣀⣀⣀⣿⣹
⠀⠀⠸⠞⢿⣿⣿⣿⡆⠀⠀⠀⡀⠾⠀⠙⠀⠀⢿⣿⣿⣿⡿⣛⡁⠸⠋⢸⠃⠀⠀⠀⠀⣸⣿⣿⣿⡿⢟⠏
⠀⠀⢰⣷⠀⠉⠛⠉⠅⠀⠀⠀⠀⡿⠀⢀⠰⣌⣾⣿⣿⣿⣿⣿⠀⠀⠀⢻⠃⠀⠀⠀⢠⡏⢙⣋⣉⣠⣿⠁
⠀⠀⠈⣿⣷⡖⠀⠀⠂⠀⠀⠀⢴⡟⠀⢘⡄⢻⣿⣿⣿⣿⣿⣿⡃⣾⡆⢺⡇⠀⠀⠀⡙⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠸⣿⠇⠀⠀⢈⠀⠀⢀⣞⣿⡀⣻⣿⠺⣿⣿⣿⣿⣿⣿⢱⣿⡷⣾⡇⡆⠀⢀⠃⠠⡾⠃⣼⠃
⠀⠀⠀⠀⠹⣤⠀⠀⠀⠄⠂⡀⠀⠉⠑⠛⠿⠧⠿⠛⠛⠛⠻⣯⡿⠟⠓⠉⠁⢀⣀⡼⢠⣿⢀⣼⠃
⠀⠀⠀⠀⠀⠹⣇⠀⠀⢳⡎⠽⠶⠄⠀⣀⣄⣀⠀⠀⠀⠀⠀⢀⣀⢀⣠⠄⠐⠛⣛⢳⡾⢧⡿⠃
⠀⠀⠀⠀⠀⠀⢹⣦⣤⡶⠻⠇⢠⣀⣢⣿⠟⠉⠙⠒⠀⠀⠐⠉⠻⣿⣡⡆⠀⢀⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⡀⠘⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠈⣠⣿⡏⢠⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⢤⣄⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣼⢋⣽⠈⠀⠸⠇⠀⠻⠽⠯⠝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⢞⠋⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⣠⣆⠀⠁⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠿⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠐⣀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠶⠶⠦⡤⣠⢠⠀⠀⠀⠀⠰⣿⣷⠃⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠛⡄⠀⠀⠀⣩⡌⠀⡠⢤⡀⣦⣿⣿⣷⣭⡄⢴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⢀⡀⣰⠇⢀⣠⡝⠱⣿⣿⣿⣿⣿⣶⢇⡀
⠀⠀⠀⠋⠀⣠⡆⠀⠀⠀⠠⠂⠀⠱⠀⠀⠀⣀⠍⠸⠂⠈⡉⣵⣦⣿⢿⣿⣿⡯⠛⢨⠟
⠀⠀⡐⠠⠤⠘⠀⠀⠀⠀⠀⠐⣀⡀⠀⠻⡿⠁⠀⠀⠀⡼⠋⣹⣦⣽⣶⡯⠍⠁
⠀⢀⡀⢂⠀⡀⠀⢀⣀⠀⣀⠀⢻⡇⢈⠀⠄⠀⠀⢀⠊⣠⣾⣿⣿⣷⣾
⠀⢠⣿⣦⣴⡅⢀⠀⠙⠇⢨⡄⠀⠀⢀⠁⠀⠀⣴⢃⡼⢿⣿⣿⣿⣿⠇
⠀⠀⢿⣷⣯⠿⡇⠀⢸⠷⠐⣧⡀⢀⣿⣷⠀⠚⠁⠁⠀⠸⢫⣿⡿⠋
⠀⠀⠀⠉⠀⠀⠐⠚⠋⠀⠀⠈⠁⠀⠀⠘⢿⣤⡀⠀⠀⢀⢋⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⣴⣿⣿⣿⣿⣷⣷⣯⣾⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠉⠁⢀⡍⠙⠻⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠉⠉⠁⠀⠠⠀⢦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⢢⡀⡿⠀⠀⢠⠀⠀⠀⠀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠉⡉⠀⠀⠀⠀⣄⠀⠻⢿⣷⣄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠶⣀⠀⠺⣤⡄⠀⠀⢹⣇⠀⠀⠉⠛⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⢻⣿⣶⣾⣿⣶⡾⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠑⢻⣿⠋⢀⣾⣿⣿⣿⣿⢿⣧⣙⢿⣿⡷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⣾⣥⣶⣿⣿⠿⠟⠋⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠸⣶⣿⠀⣒⢂⠰⣾⣿⡏⠀⠀⠀⢀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣇⣀
⠀⠀⠀⠀⠈⢿⣾⣋⣩⣍⣉⣉⠁⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠁⠀⠀⠀⠀⣼⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄

⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣀⠀⠀⠀⠀⠀⠀⠈
⠘⣿⣷⣦⣀
⠀⠹⣿⡿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠿⣿⣷⣶⣦⡄
⠀⠀⣿⣧⠈⠙⠻⢿⣿⣶⣤⡀⠀⠂⠀⠀⠀⣀⣄⡸⣿⠁⠀⠀⠀⠈⠻⣿⣧⡀
⠀⠀⢻⣿⣆⠀⠀⠀⠈⠛⠻⣿⣷⡀⠹⣶⣿⡝⢣⢱⣿⢰⣦⣀⣀⠀⠀⠙⣿⣿⣄
⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⣳⡄⠘⢫⣿⣿⣼⣿⣻⣿⡿⠛⣷⡄⠀⠈⠻⣿⣧⡀
⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠁⢘⣄⠀⠙⢻⣿⣏⣟⣩⣤⡼⠿⠿⠀⠀⢀⡈⠹⣿⣦⣤⣀
⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⢀⡀⣹⣦⡀⠈⢻⣿⣿⣿⣮⡷⣾⡇⠀⠀⢈⣿⡖⠛⠻⣭⣿⣷⣄
⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⡤⠃⣀⣠⣿⣿⡿⢿⣆⠀⠻⣿⣧⣤⣴⡿⢃⡤⣺⣿⡏⠠⠁⠀⠈⠻⣷⣿⣧
⠀⠀⠀⠀⠀⠸⢿⣿⡆⢸⣷⣾⣿⣿⣿⣿⠷⣿⣿⣳⣾⣫⡌⢛⣿⣷⣾⣶⣿⣷⣌⠐⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢿⣿⣿⣿⣿⣼⣷⡾⣿⣿⣿⣿⣗⢡⣾⣿⣿⠻⣿⣿⣯⣏⣀⡀⠀⠀⡈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠉⠛⠛⠿⠛⠁⠀⠘⢋⣿⣻⣯⣷⣾⣯⣛⡷⢸⣿⣿⡙⢿⣿⣿⣄⡇⣴⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠉⢿⣿⣿⣿⣷⡿⢿⣦⣿⣿⣿⣻⠈⠉⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣷⡈⢿⣛⣿⣿⣷⣦⡻⣿⣿⣿⡏⠀⠀⠀⠀⠈⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣘⣿⣷⠀⠹⣟⠘⣿⣩⣽⣯⣾⡟⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⡄⠙⣷⣿⠿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⠈⢿⣾⣿⣿⣿⣿⠇⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣄⠘⣿⣉⣿⠏⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡆⠀⠀⠀⠀⠀⠆⢶⣌⣻⣿⣿⣿⣿⣿⡿⢆⠈⢿⣧⠀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⣿⡄⠀⠀⢸⣆⠻⣦⣿⣿⣿⣿⣿⣷⣶⣧⡾⢳⣄⠹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⢀⣼⣿⣿⣷⣿⣿⡏⠛⣹⣿⡿⣛⣷⣾⣿⣿⣷⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⠀⢉⡀⠀⣽⣿⣿⣿⣷⠀⣿⣷⡶⠟⠉⠁⠀⢻⣿⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡶⠿⠿⣻⣿⣿⣿⣿⡿⡾⢟⡟⠀⠀⠀⠀⠀⢀⡿⠇⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⡰⣮⣤⣶⣾⡿⠟⠛⠉⠀⠀⢁⠘⠀⢀⡀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣬⣿⣿⣯⣿⡆⠛⠀⠹⣷⡄⠀⠀⠀⠀⠘⠀⠀⠻⠃⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⠀⢀⣼⣧⡀⠀⠀⢠⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠛⢻⣿⣦⣀⣙⣛⠵⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⢿⣿⣿⣿⣿⣾⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠸⣿⣿⣿⣿⣿⣄⠀⠀⠀⢼⡿⢿⣿⣿⣿⣿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⢘⣻⣷⣬⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢀⣤⣴⣀⢀⣤⣄⣀⣴⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⣈⣉⣉⣈⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⠍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⢶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡂⠀⠈⢀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣃⠄⢦⠈⠀⠹⣿⣟⠂⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠚⣦⡄⠐⠶⠆⠀⠄⠀⠀⠀⠉⢻⣿⣶⠀⠀⠀⢸⣿⡂⠀⠂
⠀⠀⠀⠀⠀⣷⠖⢿⡄⠻⣷⠸⠿⠛⣤⣴⣧⡀⠀⣿⠟⣙⡡⠄⡀⠀⠸⣿⡇⠀⡀
⠀⠀⠀⠀⠀⣿⡀⠈⠍⢀⣸⣧⣤⡀⢹⣿⣿⣿⣆⠋⣼⠠⣿⢾⠀⣦⣀⣟⠃⠀⠃
⠀⠀⠀⠀⠀⢻⣷⣾⠷⠈⠛⠛⠻⠟⠲⣿⠛⠛⠛⠐⣻⡄⣦⣀⠀⠈⠁⠛⠛⠖
⠀⠀⠀⠀⠀⠀⠻⣯⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⠃⡀⠠⡄⠀⣀⣀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⣤⡀⠶⠀⠀⣿⡄⠀⠁⠀⠀⠀⠓⣲⣾⠀⠉⢸⣻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢀⠀⠀⢀⣿⠛⠀⠀⠀⠀⠀⠀⠈⠉⣿⠟⠁⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡌⣤⠀⣄⢙⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃⠚⠉⠛⣠⠀⠀⠀⠀⠀⠀⠲⣄⢳⢀⣀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠄⠘⠀⠀⠀⢀⣠⣶⣿⣿⣧⠈⠉⠉⣁⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣀⣀⠀⠈⠻⠛⠿⠛⠛⠿⣇⣴⡌⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠙⠷⣴⣙⣦⣄⣀⠘⠀⠀⠀⢻⣷⡀⠈⢃⠐⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢱⡄⠈⠁⠀⠣⠊⢁⠂⠀⠁⣙⠻⢶⣿⠞⣷⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⠒⠀⠀⠄⠀⠟⠀⠀⢀⠃⠀⠀⣿⣷⣿⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣙⠀⠀⠀⠘⠁⠒⢀⡌⠀⠀⠀⢹⣿⣿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⢀⡀⢀⣠⣄⠇⠀⣸⠀⠀⠙⣿⡇⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⣌⢿⣇⠙⠻⢤⣿⡿⠀⠀⠀⠈⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⡸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⣦⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⣿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠒⠲⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠘⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⡴⠞⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⠇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣻
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠠⠜⠃⠉⡡⠁⢀⠀⠀⠀⠀⠀⠀⣲⣀⠋⢡
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣴⣶⡾⠷⠐⠐⠂⠀⠀⣠⣤⣤⣄⠀⠀⠀⠃⠛⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⠄⠐⠒⢾⣹⣿⡷⣦⣥⣀⡀⠀⢀⣠⣶⡿⠫⣹⡿⠋⠀⠀⠀⢰⠇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⣿⣘⣿⣭⡿⠛⠛⠻⠿⠿⠿⠋⠀⠀⠀⠀⢔⣿⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⠿⠋⠹⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡠⠈⠋⠈⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡠⢶⡷⠀⠀⠀⠉⠀⠀⠀⠒⠆⣾⠁⠀⢠⠀⢸⣷⣦⡀⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠹⠁⢸⣷⣀⣠⠔⠃⠀⢀⣀⡴⢾⠃⠀⢀⡞⠀⠘⠋⠉⠀⠀⣼⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⡇⣻⣟⣶⣾⣽⢏⠉⠲⠚⠛⡛⠜⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡼⠋⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣿⣿⡯⢻⡇⢈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠋⠀⣠⢶⣿⣿⣦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠜⢿⡎⢳⡶⠖⠀⠂⠂⠀⠀⠢⣴⠂⠀⢀⠀⠀⣠⠁⣠⠞⢀⠚⢫⣿⠿⣟⣯⠿⠋⠉⠙⠓
⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣏⠀⢠⣶⡀⡾⠃⠀⡄⠀⠀⠀⠀⢰⡘⠛⠀⠀⢀⡴⠃⣠⠇⡰⠁⠒⠀⠀⠞⠋⠁
⠀⠀⠀⠀⠄⠀⠀⠈⠙⠛⠿⣿⠟⠹⢿⣿⡇⠹⠤⠛⠑⢣⠏⠀⠀⠃⠀⠀⠀⠄⣸⠁⠀⣀⡴⠋⢁⣴⢋⡘
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⣸⣿⡁⠀⢦⠀⢰⣷⣾⡶⡀⢲⣾⣤⠺⠖⠉⣠⡼⠋⢀⣴⡿⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⡏⠚⠀⠀⣿⣿⣇⠀⠀⠀⠀⠙⠋⠁⣀⠭⠭⠀⠐⠒⠛⠉⣠⣾⣿⠟
⠀⠀⠀⡇⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠛⠋⣡⣾⣻⡿⠋
⠀⠀⠀⠹⡆⢀⣠⣾⣿⣿⠀⡀⠀⠀⠹⣇⣿⣿⡷⠀⠀⢠⠀⠀⠉⠀⠀⠀⢀⡾⢫⣾⠟⠁
⠀⠀⠀⠀⠻⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⡇⠈⠧⡄⠀⠀⠀⠀⠀⠀⡾⢡⣿⠋⠀⠀⠀⠀⠐⠂⠐
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⡇⠀⠈⠳⡄⠀⠀⠀⠀⢀⣧⣿⠃⠀⠀⠀⡀⠀⠀⠒⠀⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⡄⠆⠀⠇⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠘⡄⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠁⠀⠀⠀⠀⢸⡀⠀⢈⣿⡇⠀⠋⠀⠻⠀⠀⠓⢀⡀⢠⣤⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⢳⡶⣦⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡄⠈⠃⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠶⠶⠦⣤⣤⣄⡙⠀⢷⣿⠻⢿⣤⣿⣻⣿⣟⡟⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⡿⠀⠀⠈⣷⣾⡿⠛⢿⣥⣼⠏⣿⣿⢠⡦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠟⠁⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣰⣿⣿⢸⡇⣿⡟⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠛⠫⡈⣰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣧⣿⡇⣿⣼⡇⣴⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣿⠿⠃⠀⠀⡀⢻⡟⣿⠁⠀⠀⠀⠀⠉⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⢰⢷⣿⢸⡏⣿⠆⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣀⢀⣴⡄⠀⠀⢀⠀⢰⣾⣿⠀⠀⢀⠈⣼⡿⣧⡈⠛⠂⠀⠀⠀⠀⠀⢰⣿⠿⠙⣿⣿⡿⠿⠷⠿⠞⣋⣭⣶⠏⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢙⡛⣼⡿⣿⠀⠀⠀⣤⣬⣿⠟⠀⢀⣤⣦⣿⣷⠘⢷⣴⣾⠷⢦⣀⣤⡀⠀⠁⠀⠀⠿⠟⠁⠀⠀⠠⡘⢻⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠿⣏⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠈⠑⢶⡶⠾⢋⡾⠁⣸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣁⣴⣿⣷⣰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⢹⣿⣿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⢽⢿⣿⣧⡰⠄⣠⣿⣿⣿⣿⡟⢀⠛⠛⠛⠂⠤⢤⡀⢀⠀⠤⠤⠈⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⣿⣿⣿⣿⡆⢠⡛⢿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣾⣷⣦⣴⣤⠤⢀⠀⠀⢀⣴⣿⣄⣤⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀⠁⠈⢙⠿⣿⣿⣇⣸⡉⣿⣿⣿⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠈⠅⠄⣸⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠶⣶⣿⣷⣶⣿⣿⣿⣷⣤⣝⣈⡛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣷⡿⠟⠻⣿⡛⠃⠀⠈⠀⠀⣹⣿⡿⠋⠉⠉⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⣌⣠⢉⡔⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠉⠉⢻⣿⣿⣄⠀⠈⠀⠂⠀⠀⠀⢴⣿⡏
⠀⢴⣶⣶⡀⠀⢸⣷⠿⡝⠶⠚⠒⠲⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠿⠟⠉⠀⠀⠀⢀⠀⠀⢰⡟⠙⠃
⠀⢸⣿⣿⣿⣿⣾⣷⠶⣿⣖⣳⡚⠛⠛⠉⠀⠀⠀⠟⠙⠛⠀⠈⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣴⣿⣿⣆⣠
⠀⣸⣿⣿⣿⣿⣿⣿⣶⣾⣿⠠⢤⣠⣤⣴⣶⣶⣶⣿⣿⢷⣤⣴⣮⣀⣀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣟⣿⠃
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠈⠉⠉⠻⣿⣿⡧⠀⣶⢹⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⣿⣿⣄
⠀⠀⠀⠀⠛⠛⠃⠀⠙⢺⣿⡀⠀⠀⠀⠸⣿⣿⣿⡟⢿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠙⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣿⣿⡟⠀⠘⢿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠈⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠘⣿⠀⠀⠀⠸⣧⠉⣼⣿⣿⣿⣿⠿⡿⢿⡟⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠁⠈⠹⡻⢿⣿⣿⣿⣧⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣾⡟⠹⢦⣠⠀⠀⠀⢀⠙⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠂⠀⠀⠀⠀⠘⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠻⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣿⣷⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣶⠾⠋⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⡀
⠀⠀⣠⣾⡿⣿⣿⡟⠛⠋⠉⠙⢢⣾⣿⣿⣟⣯⣭⣿⣷⡄⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠻⣿⡇⢿⣿⣿⣦⠀⠠⣘⠲⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢳
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣶⣶⣿⣿⣟⢻⣿⣿⣿⣿⣿⡄⠘⠿⢿⣿⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠻⣿⣿⣏⠿⣾⣿⣿⣷⣮⣿⠿⣷⣾⡿⠯⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⣦⡙⣿⣿⠋⢹⣿⠷⠞⠉⠛⣄⣀⣠⣤⣾⡖⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠈⠹⣿⣿⣄⣀⣿⣶⣦⣴⣶⣿⡿⠉⠀⠈⢝⡶⠶⣦⡀⠀⠀⠀⡟⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣞⣛⣄⣠⠝⢢⣄⡀⣅⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠻⣿⣿⣿⣿⣿⣶⣾⣿⣿⠛⣿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡙⢿⣿⠉⠋⠻⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⢿⣧⡙⠻⣯⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣼⣿⣿⣿⣾⣿⣧⣤⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠿⢶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣭⡡⣨⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠻⡄⠀⠀⠋⠻⣿⣿⣿⡄⠀⠀⠀⠹⡶⢄⠀⢠⡤⠤⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠀⠀⠀⠀⠘⣷⣏⣿⣦⡄⠀⠀⠹⡀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣿⠙⠿⣿⣏⠳⢤⡀⠹⡀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣰⡀⠈⢻⡇⠀⠈⠻⣆⠀⠉⠂⠁⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣾⣿⠀⠀⠀⠙⣧⡀⠀⠀⠀⠘⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠈⠛⠳⣦⣴⡀⠙⢻⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⠛⠶⢤⣀⡀⠀⠘⣿⣷⣤⡀⢢⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠈⢹⡄⠀⠙⠿⣿⣿⣎⡸⡁⠀⠀⣷⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠁⠀⠀⠀⠈⠉⢻⡆⣷⠀⠉⠋⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠞⢾⣁⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣻⣿⣿⠿⠳⡄⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⡀⢀⣤⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠠⠖⢿⡅⣸⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢨⠠⠄⣠⠆⣣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢠⣿⢂⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣤⡀⠀⠀⠀⠀⠤⢿⠏⢀⡠⣾⢗⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣵⡄⠀⠀⠒⢦⣴⡷⠫⠚⣁⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⢿⡼⣭⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⢴⣿⣿⣅⠈⠋⠉⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢀⣘⣦⣿⠟⠋⠀⠀⠷⢦⣈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡽⠇⠀⠀⣸⣤⣿⣟⠀⠀⠀⠀⠀⠀⠀⠉⢿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⣟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠷⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⣄⠀⠀⠀⢸⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⢀⡈⢻⣿⣿⡇
⠀⠀⠀⠠⠀⠀⢀⠌⠀⠀⣀⡀⢀⣼⣿⣿⣿⣿⣤⣴⣶⣶⣀⠀⠀⠀⠔⢀⢸⢿⣿⡇⠁⠶
⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠙⣻⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣧⣄⣀⠈⠁⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠹⠻⣿⣿⣿⣾⣷⣶⣿⣿⣿⣟⡻⢿⠿⣿⣶⣾⣿⣿⣿⣤
⠀⠀⠀⠀⣀⠐⠂⠔⠂⠐⠀⠀⠀⠀⠀⠉⢩⠙⠗⣈⢻⣿⣿⣿⣿⣷⣟⡻⢿⣿⣿⣿⣿⣿⣷⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⣠⣿⣻⣶⣷⡄⢿⡰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢰⣿⣿⢯⡀⣽⠿⣾⣣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⠀⢀⠀⣨⣿⡁⢸⡇⠀⠀⣸⣧⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡓⠉⣹⣾⣿⣿⣷⡈⠦⠂⣰⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠙⣿⠱⠈⠙⢿⣦⡼⠊⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⣤⠀⠸⠂⢻⣶⣦⣤⣤⣩⠆⠀⠀⠀⠀⠀⠀⣤⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠟⠱⠁⠀⠀⠀⡘⠿⠛⠋⠠⣧⡀⠀⠀⠀⠀⠀⢣⡼⢀⡈⢁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢳⣾⣤⠂⠑⢀⠀⠶⣏⣽⣤⡄⠀⠀⠀⠀⡘⣣⣿⣦⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡂⠀⠙⣿⢃⣬⡴⠉⢲⣶⡁⢿⠀⠀⠀⠀⠀⣀⠙⣿⡿⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢀⣿⠟⣡⠀⠀⣶⣿⣇⠀⠀⠠⣤⡄⠀⢀⣌⣿⡇⠀⠸⠏⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠶⣾⣿⣿⠗⢀⣾⡛⣛⡋⣷⣦⡄⠀⠀⠶⢿⣷⣿⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠙⠛⠾⢯⣭⣭⣭⣥⣤⣤⣾⣿⣦⣄⡀⣹⡟⣷⡄⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⣉⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠿⠇⠀⣠⣤⣤⣄⣉⠀⡛⢠⡀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠾⠿⣤⣦⣠⣀⠀⠀⠀⠀⠀⣼⠁⠀⠲⠄⢐⡋⠀⣹⠀⣾⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣼⣿⣧⠀⠀⠘⢻⣷⠀⣿⢠⡟⠁⢢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⣉⠉⠉⣉⣽⣿⣻⣟⣠⠐⠀⠁⣈⠿⠀⠛⣈⡁⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣿⠷⣿⡛⣂⠈⠙⢿⡿⠛⣁⠀⠐⠾⠿⣿⡄⠇⠺⠟⠁⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣼⣛⣀⣿⣿⡙⠻⠷⠦⠷⣮⣽⣿⣿⣶⡄⢸⣇⣶⣶⡆⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣿⠋⢡⣿⢿⣷⠀⠀⠀⠂⠘⠛⠉⠀⢈⣿⣾⣿⣅⣈⠑⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⠛⠿⠗⠀⠒⠀⠀⣴⡮⣴⣶⡞⢩⠾⢋⣿⠛⠉⣷⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠙⠂⠀⠀⠲⣤⣴⣶⣶⣿⣏⡀⠀⠀⠉⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣿⣯⠀⠀⠀⠀⠀⣶⣿⠟⠉⢻⣿⣭⣤⣀⠀⢷⡀⠰⠞⠋⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡚⠯⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠋⢸⣧⡙⠀⢀⡀⡺⠷⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠚⠂⠀⠀⠀⠀⠀⣼⢣⠈⠛⠋⠁⠋⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠈⠁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠎⠉⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣀⢐⣭⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠛⠛⠁⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡄⢴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣿⣗⣤⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⠀⢈⡀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠉⠛⠃⡀⠺⡄⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣤⠛⣀⣿⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⢿⠆⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡄⠈⠩⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣌⠀⠀⢾⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠚⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⣏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠁⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠅⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣁⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⡬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠛⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠱⠶⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⣿⣆⣡⡀⠀⠀⣰⣦⡀⣀⠀⠀⠀⣴⣿⣧⡝⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⡀⠴⢾⣁⣼⣿⣿⣾⣿⣿⣿⣖⣆⠀⠀⣛⡀⠙⣿⠀⢀⣾⣟⢻⣷⠤⣶⣿⣿⡟
⠀⢀⡠⠶⠊⡀⠐⣶⣿⣿⣿⣿⡿⣿⣿⣍⠛⠿⠋⠀⢠⣿⠁⠀⠈⢠⣾⡿⠋⠁⢀⠀⠈⣿⣿⡇
⠀⢹⣶⣶⣤⣽⣿⣿⣿⣿⠟⠁⠀⠀⠈⠉⠁⠀⠀⠀⣿⣿⡀⠘⢷⡆⢿⣧⢀⣠⡬⣲⣶⣿⣿⠁
⠀⠀⢹⣷⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⡇⠀⠀⠀⣿⣃⠀⠀⠀⠚⣾⢿⡀
⠀⢀⣼⣿⣿⣿⣿⠏⠀⠠⠄⡀⠀⠀⠀⠦⠀⠀⠀⣾⣦⣽⣿⣧⡄⢰⣿⣿⣦⣤⣶⣲⣼⡀⠰
⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⢀⠀⠀⠘⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠇⣸
⠀⠀⠀⠀⠀⠀⠀⠒⠢⣤⣶⣀⣤⠠⣿⣾⣦⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠟⣠⣼⣷⡄⠀⠀⠀⠀⠀⠀⢀
⠀⢸⣿⣷⣏⠀⠀⠀⣀⣈⣿⣿⣿⣤⣿⣿⣿⣿⠘⠁⠀⠙⣿⡿⠟⠁⠉⠣⣠⣼⣏⠐⠛⠉⠀⠉⠀⣄⣤⠄⠀⠀⠚
⠀⠀⠈⠙⠻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⢽⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⡀⢸⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢆⠈⡆⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⠘⠀⠠⠀⠀⠀⠀⠀⢻⡁⠀⢰⣄⡀⢰⣴⣿⡁⣠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠈⣿⣼⡿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣾⣿⣧⢹⣿⣿⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⢀⣠⣤⣤⣤⡤⢴⣾⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡏⠀⢿⣿⣦⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣿⣿⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣿⣿⠃⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⠀⠿⣿⡇⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡿⠁⠀⠀⠘⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣇⠀⢹⣿⡀⠘⣷⠸⣿⢿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡅⠀⠀⡜⠂⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣄⣮⣿⡇⣄⢹⡄⣿⣼⣿⣿⣿⣿⣿⣶⡆⠀⠀⣿⠛⠘⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⡏⠉⠛⢛⣽⠿⣿⣿⣿⣿⣃⣥⣘⡿⣿⣿⣿⣻⠿⠛⣷⠀⠀⠹⣿⣿⣆⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣼⡶⢆⠀⠇⠹⠆⢿⡛⣹⡟⣩⣿⣾⣟⣿⠉⣿⢉⣗⡠⢾⡆⠀⠀⢻⣿⣿⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣄⠀⡄⣴⡶⠞⡛⠛⠻⣿⣿⣿⠛⠛⠛⣻⣧⣈⣵⡎⠀⠀⠀⠸⣿⣿⣇⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣾⡿⢿⣧⠋⠀⠀⡁⠀⠄⣿⣿⡏⢠⠀⣠⠉⣹⠛⠿⠃⠀⠀⠀⠀⢻⣿⣏⣻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢿⢿⡄⢹⡆⠀⠀⢸⣇⢀⣿⣿⣯⣱⠚⠀⢀⡄⡀⠸⣧⠀⠀⠀⠀⠾⠋⣉⣻⣷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠲⠷⠤⠖⠘⠉⢻⣿⣿⣿⡏⠘⠃⢼⡧⢀⣷⣾⠄⠀⠀⣾⣶⣄⣙⣻⣿⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠛⠚⠻⢿⣧⡀⠀⠀⠀⠀⠉⠀⠀⣸⣿⣿⣿⣇⠀⢀⡏⡀⣞⠈⠁⠴⢤⠄⢠⣺⣿⣿⣿⣿⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣮⣉⠒⢤⣂⣀⡀⢀⣼⣿⣿⣿⣿⣿⣷⣾⡴⢧⢁⣰⣇⠂⠈⠉⠛⠻⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣭⣉⡛⠻⠿⠿⠿⠿⠿⠟⢛⣡⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣠⣤⡄⢰⣿⣷⣦⡬⢉⣒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡈⠻⢼⣯⡛⢷⣤⣹⣿⣿⣿⡟⠶⢬⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣽⣿⣶⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠿⠿⢿⣽⣿⣿⣿⣿⣿⣍⢻⣿⣿⣿⡙⢿⣦⡀⠀⠀⠂⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⣀⣤⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⠛⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠰⣍⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⠿⣄⠈⠻⣵⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠺⣷⣶⣿⣤⣹⣿⣿⣿⣿⣿⣿⣷⡈⠂⠀⠌⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣾⣿⣾⣾⣿⡟⠀⠀⣠⣶⣾⣿⣾⣿⣾⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣷⡯⢄⠀⠃⠘⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⣰⣿⣿⡿⣻⣽⣿⣛⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁⣸⡆⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⡀⠀⠀⣸⡯⠚⣁⣴⣿⣿⣿⣿⣿⣿⣿⣦⣝⢿⣿⣿⣿⡿⠀⢿⣷⠸⣿⣿⣿⣿⣿⣿⣷⠙⣿⣀⡠⠒⣧
⠀⠀⠀⠀⠱⡀⠀⠀⣞⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠻⢋⣀⣤⣞⣿⡇⢿⣿⣿⣿⣿⣿⣿⡀⢸⣿⢷⡄⠈
⠀⠀⠀⠀⠀⠈⢀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⣿⠃⠈⣿⣾⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠑⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⡆⠀⢿⣿⣖⡛
⠀⠀⠠⠀⠀⠑⡄⠰⢄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢻⡟⠃
⠀⠀⠀⠐⢀⡀⠘⢦⣌⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠁
⠀⠀⢄⠠⡀⠻⣆⠈⠉⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡀
⠀⠀⠀⡑⢿⡂⠘⣷⣄⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣅
⠀⠀⠈⢣⡆⠻⣄⠈⠳⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⣉⠛⠿⣿⣿⣷⡀
⡀⠀⢂⠀⠛⢦⡈⠣⡀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣿⡿⣉⣡⣶⣿⣿⣿⣷
⠈⠀⠈⢧⡀⠀⠙⢢⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢣⡀⠙⢆⣰⢟⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⢻⣿⣿⣿⣿⠟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⣠⡾⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⣿⣿⣿⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣸⢿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⠆⠀⠈
⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣆
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⡿⡿⣿⣯⣥⣉⡉⠀⠛⠈⠀⠉⠑
⠀⠀⠘⠙⠛⠛⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠛⢿⣿⠿⣿⣿⣿⣿⣿⡛⢿⣾⠷⠶⠶⢶⠶⣿⣟⠟⠿⠀⠀⠀⠀⠀⣀

⡇
⡇
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣶⡀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠻⢿⡄⠻⡀⠀⠀⣠⣠⡀
⡄⠀⠀⠀⠀⠀⠒⠠⢄⡀⠀⠀⠀⢠⠆⠀⠀⢠⠀⠙⢦⡙⣶⣦⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠉⠀⠀⠂⠛⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⣦⣙⢿⣿⣿⠃
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⡀⣤⠄⠠⠶⠶⠿⠟⢻⡿⠃
⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣷⣤⠀⣀⡀⠀⠀⣄⡰
⠀⠀⣠⠞⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣖⡈⠁⠲⠊
⠀⠈⠁⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣜
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣤⠀⠀⣀⣶⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣛⣂⡀⠀⠀⣀⣀⣀⣀⣉⣻⣿⣼⣿⣿⣿⡿⣤⡿
⠀⠀⠀⠀⢀⣶⣶⣤⣀⣀⣶⣿⡍⠉⠉⠀⠀⠀⠀⠠⣄⢹⣿⣿⣇⣨⣿⣥⣭⣰⣿⣷⡀
⠀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡿⢿⣿⡿⠋⠁⠈⢿⣄
⠀⠀⢀⡉⠛⠛⠟⠉⢙⣿⣿⣿⣿⣿⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢀⣴⣿⣥⣤⣾⠀⣠⡿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠧⠙⢇⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠛⠻⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠢⡀⠀⠀⠀⠉⠓⠦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣾⣦⡀⠀⠀⠀⠀⠁⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⢦⡄⠀⠀⠀⠙⣆⠠⣤⣤⡀⠀⢢⠀⠀⠀⠀⠈⢧⡀
⠀⠀⡠⢾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣝⢆⠀⠀⠀⠀⠠⣼⣏⠙⠓⠈⠇⠀⠀⠀⠀⠀⠳⡄
⠀⠘⣿⠆⠈⣞⠛⢌⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⠳⣶⣤⣤⡀⢈⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠘⢦⠀⠁⠀⠈⢳⣬⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣷⣌⠛⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠈⠷⠤⣂⡀⠋⠀⠈⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣶⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣿⣦⡴⠚⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⢶⣶⡆⡀⢀⠐⠂⠀⠀⣀⡀⠀⠙⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣋⣁⡀⠙⢆⠀⠙⢦⣤⣶⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡙⠳⢄⠻⣦⡤⠋⠁