Birthdays Emojis & Symbols

⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠔⠈⠁⠀⠉⠐⢄⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡠⠒⠉⠀⠈⠁⠢⠀⠀⣀⠀⣀
⠀⠀⢀⠔⠁⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠈⠢⡀
⠀⠀⠆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠐⡀
⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠃
⠀⠀⢃⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⢲⠄⣀⣀⠠⡔⠊⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠙⢢⢄⣀⡀⢤⠐⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠈⠑⠀⡤⠀⠐⡁⠐⠀⠒⠐⠟⠂⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠉⠒⠀⠤⠀⢊⠀⠈⠀⠂⠒⡛⠂⠀⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⢆⢠⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⢎⠘⠓⠂⠀⠀⠀⠀⢰⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡰⠦⠀⠀⠀⠀⠰⡂⠛⠠⡀⠀⠐⠛⠯⡀⠹⠋⠓⠀⠀⢔⠒⠇⢀⠀⠀⠀⠀⠀⠤⢆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠗⠂⢀⡀⠀⠀⠀⠁⠐⣦⠤⡀⠆⠰⠆⢸⠀⠴⠀⢄⠀⢼⠑⢰⠂⠀⠀⠀⢀⡀⠐⠺⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠲⡤⢚⠁⠀⠇⠀⢸⣤⣀⣀⠀⢀⣀⣀⣼⠀⣨⠀⠠⠏⠲⣤⠶⠋⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠉⠁⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⡿⠀⠉⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠴⢤⠀⠙⢧⠀⠈⠀⣠⠟⠁⠀⡠⢤⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⠀⠈⡆⠀⠀⠀⡏⠈⢳⠀⠀⢀⠇⠀⢣⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣀⠇⠀⠀⠀⢇⠀⠀⢀⠇⠀⠈⢦⣀⠜⠀⠀⠀⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠤⢤⣀⢀⢀⣠⠤⠤⠤⠴⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣾⣧⠀⠀⣿⣾⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢡⡀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡙⢦⡽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂⠀⠁⠛⢻⣿⣷
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠒⠁⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠠⣿⣿
⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⢠⡰⢖⡖⠊⢻⠈⠀⠉⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⢶⣤⣤⣤⠴⠺⠏⠙⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠙⢿
⠀⠀⢀⡄⠀⠶⠸⣯⠑⠁⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⢳⡀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡦⠆⣒⣶⠖⣻⠏⢡⡦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠙⡄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠀⢢⣥⠽⡰⠋⣴⠋⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠁⠂⠀⡞⣰⣧⡜⣣⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠾⡀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣽⡆⠀⠀⠀⠏⠀⢚⣿⠅⠶⠱⡃⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡐
⠀⠀⠀⠀⠀⠀⠈⢆⠹⠿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⣻⡀⠀⣞⠭⣦⢚⠁⠈⠁⠀⢀⣥⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠴⠖⠋⠩⠤⢀⠀⠀⣠⢤⢖⡡⡤⠶⢾⣥⠼⢫⣾⣏⠄⢐⣂⢢⠀⠘⡈⢏⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠑⠤⢘⡇⢘⣛⣄⡀⠀⠷⢀⣈⡩⣶⠚⠛⢯⠀⣆⠠⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠈⠛⠋⠡⠶⠞⠙⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠂⠈⣧⠀⣀⠀⢀⢲⡘⡧
⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡄⠀⢀⠠⣦⠸⣿⢁⡠⣿⡀⢿⡻⣜⠾⢻⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢹⠀⣾⣆⡘⣆⠘⣮⠳⠏⠳⠬⠀⠈⠀⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⢲⡟⠆⠹⠿⣆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢺⡄⠀⠀⠀⠀⠙⠘⠃⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣷⠀⢀⣤⡀⣄⢤⡘⣾⠱⡜⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡁⠘⣇⠸⣯⢳⣽⡄⣷⢹⡟⠃⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣧⠀⠙⠖⠀⠀⠉⢿⡀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠄⡀⠀⢤
⠀⠀⢏⢀⠀⠀⠀⠀⠀⠒⠁⠀⠀⣀⠀⠀⡼⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠠⠘⠆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠙⣆⠀⠀⠀⠠⡠⡄⠀⠀⠀⠘⠉⠂⠀⠀⠀⢇⡠⠀⠈⠉
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠅⠤⠒⠁⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠂⣤⠁
⠀⠈⠀⠀⣴⠀⠀⢀⡀⢰⡆⢢⠀⠀⢠⠀⠀⠀⡤⠠⡀⢰⡄⣀⢀⠀⢤⠄⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠙⡀
⠀⠀⠀⠀⡟⠀⠃⣼⢡⠀⡇⠁⡆⠀⠈⣧⠀⠀⢿⠐⠄⢸⠀⣿⠀⠀⢸⠀⡏⢀⠸⡆⠀⢠⠄⢳⡐⠀⠀⠄
⠀⠈⠀⠀⠁⠀⠘⠃⠀⠀⠁⢠⡇⠈⠀⠇⠀⠀⠸⠤⠂⠈⠀⠟⠀⡀⠈⠀⠃⠀⠀⠃⢠⠟⠂⠀⡇⠀⠰
⠀⠀⠀⠈⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠆⡄⡈⠀⠐⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⡄⠀⠁
⠀⠈⠀⠀⠀⠆⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢗⡂⠨⠈⠐⢱⠀⠀⠀⠎⠑⠊⢁
⡀⠀⢀⠀⢀⠖⠁⠤⡀⠀⠀⡤⠀⠀⠈⠂⠐⠄⠄⠀⠀⠀⠀⢠⣤⠴⠦⠒⠛⠁⠀⠀⠈⠢⠠⠁⠀⣀⠀⠊

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠈⠢⠀⠀⡀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠡⠄⠀⠁⠐⠀⠄⠀⠘⠀⠀⠀⠉⠀⠄⠀⠈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠠⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡴⠀⡈⠉⠀⢱⠀⠀⠀⠰⠀⡈⠀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠐⠀⠃⠂⠀⠀⠁⠐⠂⠀⠀⠀⠀⠂⠀⠀⠠⠤⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠖⠂⡀⠀⠀⠀⠐⢈⠀⠢
⠀⠀⠀⠀⠐⠖⠆⠀⠀⠀⠠⠀⡀⠀⠀⡠⠄⢁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢴⢱⠂⠱⠀⠀⠀⠀⠄⠐⠀⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢅⠁⠀⠁⡖⠁⠄⢀⠀⠀⠀⠠⠉⡐⠀⠀⠁⠀⠄⠈⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⢡⠄⠰⠀⠀⠀⡂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⠤⠀⠂⠈⢁⡈⠀⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠐⠀⠀⢀⠉⠀⠑⣄⠠⠀⠀⠀⠀⡄⡨⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⡅⢋⠠⢀⠰⠠⠈⡀⠀⠀⠀⡠⡀⠀⢂⣁⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠧⠜⠀⠀⠀⣁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠈⠃⠀⠁⠀⠈⠡⠄⠀⠀⡼⠈⠀⠈⠈⠀⠀⡀⠀⣀⠂⠈⢂⠈⢀⠀⠀⠂⠀⠀⠈⠀⠀⠐⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁⡠⠀⠀⠀⠀⠀⠁⠁⠀⠀⣀⠘⠀⡀⠠⠡⠈⢆⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠡⠄⠆⢠⠀⡦⡀⠁⠀⡀⠄⠀⠀⠀⢀⢀⠀⠀⠤⠄⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐
⠀⠀⠀⠀⠈⠁⠢⡀⢀⠀⠂⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠤⢇⡑⠠⠄⡀⠀⠀⠀⠠⡂⠆⠰⢀⢀
⠀⠐⠀⠀⠐⠀⠐⠃⠀⠓⠀⠘⠀⠀⠠⠀⠀⠠⠀⢂⠀⢀⠓⡰⢤⠃⠒⡀⠀⠠⠍⣤⠘⠃⠚⢀⡐⢃⠀⠀⠀⠀⠀⠘⠁
⠀⠠⡄⠀⠀⠀⠠⠄⠀⡤⠀⠀⠀⠀⠜⠀⠀⠀⠁⠀⠀⠀⠀⠅⠒⠈⠀⠀⠀⡕⠠⡆⢀⡀⣀⠀⡄⠠⡀
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢔⠂⢀⠠⠆⢀⠑⠁⠀⠠⢄⣉⠀⠄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠁⠴⠀⠆⠔⠈⠀⠀⠈⠤⠈⠒⠁⡄
⠀⠀⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠂⠀⢀⣀⠡⠠⠂⡀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⣈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠀⠐⡈⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠤⠀⠄⠁⡠⠀⠄⠀⠈⠑⠠⡄⠈⠂⠤⠐⠉⠀⠈⠀⠀⠀⠐⠁⠹⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⢀⢀⠀⠀⠀⠦
⠀⠀⠀⠀⠐⠂⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠂⠰⠊⠀⠀⢸⠁⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐
⠈⠀⠀⠀⠀⠀⠠⠼⠁⠀⡀⠀⠄⠀⠰⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠈⠧⠄
⠀⠀⢄⠰⢀⢀⠀⠀⠀⡀⠀⠀⣀⠀⡀⠀⠀⠀⠠⢀⠀⢨⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠐⢂⠀⠀⠒⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠑⢈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠂
⠀⠈⠀⠁⠈⢀⠀⠠⠀⠀⠀⡀⠐⠂⠐⡀⠀⠀⠀⡒⠒⠚⠓⢒⠂⢀⡐⠀⠐⠂⠐⠂⢢⠀⠄⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠰⠀⡆⠂⢈⠐⠂⠆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣂⠀⠀⠒⢉⠀⠂⠁⢈⡈⠀⠀⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⠘⠂⠀⠀⠘⠃⠀⠀⠐⠃⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠄⠀⠀⡠⢠⠐⡄⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢬⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠠⠐⡀⠐⣀⡖⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠠
⠀⠀⠀⠀⠀⠠⡁⣀⠅⠀⠨⢀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠁⠈⡠⠠⠈⠀⠉
⠀⠀⠀⠀⠀⠈⢒⣀⠴⠀⠣⢀⡐⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠀⠀⠰⠄
⠀⠘⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠐⠆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀
⠀⠀⠁⠂⠉⠐⠉⡀⠀⠀⠀⠀⠀⡀⠴⠐⠀⠠⣀⠀⣰⠄⠠⠰⠀⠀⢀⠄⢠⠀⠀⠠⠀⠀⠀⠀⠘⡌⣰⠢⠌⡀
⠀⠈⠀⠄⠀⠠⠁⠁⠀⠄⠀⠀⠀⠥⠐⠀⠐⢀⠀⠀⠀⢈⢁⠀⠀⠀⠈⠐⠀⢆⠁⠀⠀⠀⠀⠀⠘⠠⠈⡈⠠
⠀⠀⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠀⠃⠀⠐⠀⠐⠘⠀⠈⠀⠀⠐⠘⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠁⠀⠒

⠀⠰⡀⠀⡐⠀⠀⠀⢠⠀⠀⠀⠀⢔⠀⠀⢤⠀⠀⣀⠠⡄⡀⠤⡀⠀⠀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠄⢠⢀⡄⣠⢀⡀
⠀⡔⠃⠠⢊⡐⠄⢀⠰⠄⡀⡄⡂⠊⠀⠐⣓⡦⠘⢆⠁⣸⠀⡠⠃⢢⠀⣿⢠⡝⣘⢃⢼⣶⣯⢹⣿⢀⠔⠀⠂⣀⠠⠄⣀⠤⠄⣀⠔⠀⠢
⠀⠀⠀⠈⠁⢂⠂⠈⠄⠃⡐⠇⣐⡁⠀⠂⢡⠐⠀⡮⡹⠇⠹⢦⡄⠰⠁⠻⠿⠿⠿⣿⡿⠿⠿⠛⠋⢘⠀⢧⡄⠃⡠⡆⠘⣠⣄⠘⠀⡦⡆
⠀⠃⠘⣀⠁⠀⣞⠰⠁⠁⠀⠀⣁⠉⠀⠑⠐⠀⠀⢀⡧⠁⢠⠊⠁⢀⠔⡤⢀⠀⠀⠋⠀⢋⠀⠀⠔⠈⠢⣉⡠⠄⠙⢁⣌⠉⠉⡰⢄⣈⠔
⠀⠀⡀⠎⢀⡀⠂⢀⠀⢘⠆⠂⡄⠌⠂⠀⠰⡣⠀⠀⢀⢀⠃⢠⠂⠁⠀⠀⠀⢲⠀⠀⢰⠝⠆⢀⡲⣁⠀⠀⠀⠀⠙⠁⠀⠈⠃
⠀⠊⠐⠣⡀⢨⢃⠂⠐⡩⡕⡇⡀⠖⡈⠐⠪⢅⢢⠀⠀⠁⢀⢼⡆⠁⠀⠀⣀⠨⠁⡂⢸⠀⡄⠸⠀⣸⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⡠
⠈⠢⢁⠡⠃⠀⠆⢀⢡⠤⡄⠄⢁⣈⡀⠄⠃⠠⠠⠀⠉⠁⠐⠠⠉⠉⠩⢤⠀⠂⠈⠀⡄⠀⡇⢀⠅⢸⠀⠂⢛⠀⠈⠒⠁⠀⠀⠃⢣
⠀⠀⠀⠀⠀⠄⡀⠠⢅⠒⢈⣆⠀⠐⠁⠈⠐⠂⠁⠀⠈⠁⢀⣀⠀⠄⠤⢸⡇⠀⠀⠀⢈⠉⠠⢘⠆⠓⠀⠄⠀⠐⠀⠐⠀⠀⡞⡄⠀⠣
⢰⠂⠀⠐⢂⠌⠀⣠⣤⣥⠁⠛⠘⣍⠉⠝⠩⠉⢉⠝⢍⠁⡹⠑⢄⠀⠆⠀⡀⢠⠀⡐⠁⠀⠀⠀⢁⠀⠠⠀⠲⣀⠐⢆⠀⠘⠠⠀⠄⠂⢁
⠠⣶⣶⣶⠀⠐⠜⢿⣿⣿⠀⠀⠀⠈⠊⢤⠀⠑⠊⠀⠀⠑⠁⠀⠀⠉⠀⠀⠁⠈⠀⡁⠀⠀⠀⠀⢠⡀⡀⠦⠠⠀⠀⠈⠁⠛⠀⠀⠀⠒⠈
⠀⢻⠿⡿⠀⠀⠀⠈⠉⠙⢦⡀⠀⠀⠀⣿⠀⠀⠀⠂⠀⡠⠒⠚⠙⠉⠉⠋⠓⠰⢢⡀⠄⣀⣀⠐⠃⠀⠀⠈⢣⠂⠠⡘⠀⠀⠀⢠⣤
⠀⠀⢸⠀⠀⠀⢀⠚⠐⡀⠎⠕⠠⠐⠒⠾⠒⠀⠀⠀⢐⠃⠀⣀⢀⢀⠘⡀⡇⢠⠈⠕⠀⠉⠀⠀⠀⠀⠀⡄⠀⢳⠀⠇⠀⠈⢀
⠀⠂⠙⠉⠂⠀⠨⠀⠀⠘⠄⢀⠔⡀⠀⠀⠀⠀⡆⠀⢘⠀⠘⠀⠄⠁⠈⠀⠃⠘⠀⠀⠀⠀⠈⣤⠄⠀⠊⡀⣀⠀⠀⠀⠀⠙⡀⠁⠀⠈
⠀⠀⠀⢠⣆⠀⢇⠀⠐⢀⡃⢸⠠⠔⢑⠈⣀⠉⢄⡃⠘⣁⢐⠀⠐⠔⠢⠄⠀⠬⢀⡸⠀⠀⠀⠀⠀⠀⡦⠀⠠⢆⠀⠀⢀⠀⠙⠂⠙⠆⠁
⠈⡡⠀⠜⠘⡄⠘⡀⠀⢨⠀⢶⠀⠄⠀⠀⠀⠀⢀⠆⠀⠈⠃⠄⠤⠤⠤⠠⠤⠄⠋⠁⠀⣶⠀⣶⣶⡖⠂⠀⠀⠘⢶⣶⡆⠀⠀⠒⢂⠀⠂
⠀⠁⡼⠀⠀⠈⡄⠑⠒⠈⠀⠓⠌⢀⡀⠀⣀⡀⠥⠊⢀⢀⠀⠀⠀⠀⡀⢀⠒⠒⡠⠆⠀⠀⠀⢈⠿⠀⠄⠀⠀⠀⢸⠏⠀⢀⡠⠀⠄⠠⢄
⠀⢰⠃⠀⠀⠀⢱⠀⠀⣔⠘⠛⠀⠺⠂⠄⠀⠀⡰⠂⢪⠃⠐⠀⠄⢘⣐⡠⢤⢊⠔⠃⠸⠵⠀⠀⠘⠀⠀⠀⠀⠀⡘⠀⠀⠁⠢⠠⠤⠓
⠀⠈⠐⠃⠚⠁⠈⠁⢠⠇⢀⠠⠠⠠⠀⠂⢀⡜⠁⠈⠄⠐⠰⠏⠁⠀⠃⠈⠉⠇⠀⠸⠀⢀⢨⡄⠀⡊⢑⣆⣶⠋⣀⠀⠀⠓⠀⠀⠀⠀⠊
⠀⠀⠀⠠⡶⠄⠀⠀⢤⡀⠌⠀⠨⠘⠀⠀⡎⣀⣠⠤⠆⠉⠁⠀⠀⠀⠀⠢⠄⣀⡠⠀⣰⡆⠁⠈⠈⠛⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⢀⣶⠄
⠀⣠⠆⣤⣤⠈⣃⠀⠀⠈⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⡤⠒⠂⢆⣠⠤⠤⠀⠀⠀⢀⠀⠐⠃⢸⠉⢩⡏⠃⠁⠐⢰⢒⠒⠋⠃⠀⠩⠀⠈
⢀⠭⠒⠊⠚⠝⣂⢹⠀⡀⠁⡡⠀⠠⡄⠁⢀⠄⠀⡛⠤⣀⡀⠉⡇⠀⠀⢀⠀⠀⠂⠰⠀⠀⠰⠒⠲⠀⡄⠤⡘⢸⠴⠦⠀⠠⠐⠠
⢀⠄⠀⢸⠂⠁⠀⢸⠀⣀⠈⠀⠀⠀⠸⣔⡖⠀⢠⠁⠁⠀⠀⡭⢡⠫⡄⠈⢠⠀⠀⠀⢀⣀⢀⡀⢀⡀⠀⠀⢀⡀⠀⣀⢀⡀⣀⠀⢀
⠀⠙⠆⣀⡀⠥⠖⠂⠈⠈⠉⠀⠀⠁⠀⠀⠀⠀⠈⠨⣉⠑⠰⠀⠰⠀⠧⠀⡺⠀⠀⠀⠀⢐⠂⡇⠄⠠⠀⠀⡃⠅⢈⡣⠋⠎⠁⠀⢀
⠀⠤⠀⠀⠀⠀⠐⡄⠀⡰⠆⠀⠀⠀⠀⠸⠀⠀⠠⢀⠁⠠⠁⠀⠀⢙⠀⢀⡅⠀⠀⠀⢀⠀⠀⠁⠀⠀⠁⢈⡁⣀⠉⡀⠀⠃⢀⡀⠀⡀⢀
⠀⠀⠀⠢⡈⠁⠀⡅⠀⠀⠈⠀⠀⠠⠀⠀⣀⠀⣀⣀⣀⣀⣀⣨⡵⠄⢢⡰⠀⠀⢩⠀⡄⠀⣘⢠⠀⠀⠚⠀⡓⠈⠄⠀⠑⠀⠀⠄⠀⠣⠁
⠀⠓⠀⠀⠀⠀⠐⠁⠀⠑⠂⠀⠁⠁⠀⠀⠋⠀⠑⠒⠒⠒⠒⠒⠐⠂⠀⠀⠀⠉⠀⠀⠙⠀⠋⠘⠁⠘⠀⠐⠁⠈⠉⠓⠁⠈⠀⠈⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⣠⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣱⡞⠀⠀⠀⠀⠀⠀⠈⠢⠃⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣓⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡼⠅⢀⣐⡇⠀⠀⠀⠐⠢⡄⠀⠀⠀⠢⣀⣸⡕⠀⠀⠀⠀⠀⡠⠄⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⣉⡀⣒⠒⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⠁⢀⣀⠆⠚⡆
⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠈⢉⠉⠀⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⢁⣀⡤⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡜⠀⢠⣄⠀⠈⣷⠀⢀⡇⠀⠀⠀⠸⣆⠀⠀⡄⠀⠀⠙⠧⡀⠀⢀⠆
⠀⠀⢠⠒⠢⠔⠈⢢⠀⠀⢸⡗⠒⠒⡇⢀⡾⠙⡄⠀⣿⠊⠉⢰⡖⠒⢄⠀⢻⣄⡜⠀⠀⠀⠀⠀⠀⠹⣣
⠀⠀⠀⠣⡀⠀⢀⠇⠀⠀⢼⠇⠀⢸⠁⣼⠋⠉⢣⠀⢸⡄⠀⢸⡇⢀⡼⠀⠈⡟⠀⠀⠀⢎⢒⡅⠀⠀⠘⡄
⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠈⠂⠀⠀⠀⣼⠉⠁⠀⠀⠸⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠐⣖⠂⢀⡤⢤⡀⠠⠤⣶⠒⠂⠀⠉⠀⢰⡖⠢⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⢿⠀⢀⡇⠀⢰⡇⠀⢸⡇⣠⠇⠀⠀⡿⠀⢸⡇⠀⡆⢸⡇⠀⢹⠀⠀⡀⠘⣧⠀⢰⠁⠀⡆
⠀⠠⢄⣄⠀⢸⡏⠉⢲⠀⢸⡇⠀⢸⡟⢄⠀⠀⠀⡇⠀⣿⠦⠤⡇⠘⣧⠀⡼⠀⣾⢣⠀⠸⣧⠃⠀⠀⢃
⠀⠀⠀⠀⠀⢸⡇⠀⡰⠀⠉⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⡿⠀⢠⠃⠀⠛⠋⠀⣼⠓⢺⠀⠀⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠀⣖⡄⠀⠘⠁⠀⠘⠀⠀⠙⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠉⠂⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠓
⠀⠀⠀⠘⠁⠀⢸⠑⡖⢤⣀⠘⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡸⠤⠄⢢⠀⠈⠢⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠕⠒⣒⡒⠥⠘⡄⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠛⠀⠀⠀⠈⠀⡰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠁⣀⡀⢤⢤⣷⠄
⡠⠔⠒⢄⠀⠀⡰⠋⠀⠀⠀⠀⠀⣶⠠⣄⠀⠀⠀⠉⠀⠀⠀⠸⠝⠚⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠠⠤⠚⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢠⣀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠂⠀⠤⠋
⠀⠀⠀⠀⠀⠀⠐⠤⡔⠓⠁⡮⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢒⠒⠒⠂⡁
⠀⠀⠀⠀⠀⠀⠐⠀⢙⣄⣰⡁⢉⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠡⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠠⠀⠀⠀⠀⠀⣀⢠⡤⢐⡒⠒⡲⣶⠈⠱⠎⢉⡡⡋⢐⡶⡒⠒⣠⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢸⠀⠡⠀⠀⡰⡫⡀⢯⡾⡕⠼⡨⣋⢡⢲⠘⡧⡈⠉⢰⢢⠑⡫⡼⠕⡩⣦⠗⣩⡳
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⢡⠀⡷⣱⠃⡨⡄⠠⢲⠈⠪⢟⣉⠰⡟⢻⡪⢂⣁⠯⠚⢱⠲⡙⢺⢄⠱⡸
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠆⢠⣧⠤⡘⠚⡥⡓⠃⡰⡒⠳⡪⡈⡗⢆⡴⡌⣪⠗⡖⡄⣓⠃⣈⡑⡡⢤
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠄⠀⠀⠈⠀⠀⢧⡉⢱⢹⠙⣚⢠⢻⢁⢴⣄⠋⢋⡁⣍⠕⢅⢣⢺⠹⠵⡧⡈⣥⡩⣅
⠀⠀⠀⠀⠀⢠⠁⠀⠌⠀⠀⡰⠁⠀⠀⠂⠩⢹⠘⣼⢽⡇⢸⡼⡍⢸⠀⠀⠑⠋⠀⠸⣪⢗⣶⠳⣑⣋⠀⣞⡾
⠀⠀⠀⠀⠀⠂⠀⠌⠀⠀⡐⠁⠀⠀⠌⠀⠀⢸⡀⠈⠉⠀⢸⠒⢽⣹⠀⠀⠀⠀⠀⠀⠙⠓⠃⠀⡓⠚⣶
⠀⠀⠀⠀⠐⡠⠂⠀⡠⠀⠀⠀⠀⡔⠀⠀⠀⠀⠣⡀⠀⠀⢸⠰⣳⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡿⡏
⠀⠀⠀⢀⠋⢀⠄⠊⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠘⠁⠀⠀⠀⠀⡠⠔⠁⠀⠀⢀⠠⠊⠀⠀⠘⠦⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⡌
⠀⠀⠀⠂⠀⣀⠀⠔⠈⠀⡀⠄⠐⠈⠀⠀⠀⠀⠀⣀⠜⠦⠤⠤⠤⠤⠤⢤⣤⣤⠤⠤⠤⠤⠤⠤⢴⠃
⠀⠀⣸⠁⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⣀⠠⠄⠂⠈⠀⠀⠜⠁⠐⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁
⡔⠀⠀⠑⠢⠅⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠤⠐⠀⠁⢀⠄⠀⠜
⠈⠐⠒⠢⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⡄⣀⣀⠔⠂⠐⠁
⣤⣤⣤⣤⣬⣥⣬⣴⣦⣬⣬⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⡟⣳⡦⢘⡃⢀⢀⡀⣠⡄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⢴⡶⠳⣦⠸⣧⣸⡇⠀⠀⣿⠛⢻⣧⢸⡇⣿⠋⠁⣿⡟⢸⡿⠶⣦⠀⣀⣀⣠⣶
⠀⠀⢀⡀⠀⢀⣤⢶⣆⢻⡏⢈⣿⢸⣷⣴⠟⠀⢹⣿⠀⠀⠀⠛⠛⠛⠁⠘⠃⠛⠀⠀⠻⠇⠾⠃⢰⡟⢰⡏⠉⣿⠇⣠⣤⣀
⣤⡀⣸⣿⣄⠸⣧⣨⡿⠎⣿⡛⠁⠈⠿⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⢸⣏⣀⣿⠃⣶
⠘⢿⣏⠀⠻⠆⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⣶⣆⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⢰⣯⡴
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⡜⠉⢸⠀⠏⠀⢁⠂⠌⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⢠⠁⠀⠈⢆⠘⢌⠢⡁⠂⠠⢈⠐⠂⠖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡀⠀⠔⠀⡔⠠⠂⠀⠀⠀⠀⠣⣄⠑⢌⡀⠒⠤⢀⠀⠐⠤⡙⢆⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⡏⠐⣔⣀⢗⡴⠀⠈⠄⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄⡈⠑⠂⠄⣈⠑⠂⢈⠠⣄⡖⠂⡌⠳⠂
⠀⠀⠀⠀⠀⠀⠸⣀⠒⢣⠀⠠⢺⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠈⠁⠀⠛⢿⠤⡈⠀⠞⠑⡦
⠀⠀⠀⠀⠀⠀⠀⠏⢀⠋⡑⢺⣃⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠒⠠⣾⢠⠧⠀⡞⢋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠛⠉⠆⠀⠙⠁⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⢀⠛⠰⠦⢀⡀⠋
⠀⠀⠀⠀⢀⠄⠐⠒⠠⣀⠔⠀⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠐⠁⠀⠀⠀⠐⠭⠂⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣈⣉⣱⣀⡀⠀⢩⠁
⠀⠀⠀⠀⠀⠈⠒⢤⣀⠀⢀⠜⠓⠀⠀⠤⠤⠄⠀⠠⠰⠇⢸⠀⠀⠘⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢛⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⡄⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⢘⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠊⠀⠀⠀⠒⠀⠤⠀⠈⠀⠉⠐⠒⠒⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠔⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⠁⠀⡊⠘⡄⢀⠤⠀⢀⠔⠢⠀⡉⢡⠈⡲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠵⢎⠀⠘⣄⡄⠈⣤⣈⣀⠤⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠀⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣷⠀⠀⠀⠀⠀⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⠀⠀⠀⠀⠀⢻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠸⠟⠏⠀⠀⠀⠀⠀⠀⠸⣶⡆⠉⠱⠆
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⢠⡁
⠀⠀⠠⠄⠀⠀⠰⡀⠀⠐⠂⠀⢀⡀⠃⣀⠀⠄⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉
⠀⠄⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠆⢀⠀⠀⡐⠀⠀⠀⠈⢑⡈⠁⠀⠀⠀⠐⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠈
⠀⠈⠀⠀⠈⠀⠀⠀⠀⠠⠀⠈⠁⠸⡀⠂⠀⠁⡀⠀⠀⡀⠓⠩⠒⢄⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠄⠁⠁⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⡄⡀⠀⠀⠀⠀⠠⠄⠴⡆⠒⠧⠀⢈⡷⠂⠀⠀⠀⠀⠀⠊⠀⠀⣤⠀⢰⠀⠐⠂⠠⠀⠤⠊⠐⠂⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⣈⠢⢴⠀⡰⠄⠊⠂⠐⠢⠇⠐⢪⠀⠄⠰⡁⠀⠀⠠⢀⠀⢠⠁⠀⠀⠳⠀⡆⠄⠀⢠⠎⠀⠤⠘⠠⠖⠀⠀⡀⠀⠠⢀
⠀⠀⠀⢀⠤⠀⠀⠀⢀⠈⠲⠍⡱⠞⠀⠁⠚⠓⠂⠘⠈⠓⠀⠒⠀⠀⠂⠁⠐⠂⠀⠛⠀⠂⠀⠀⠀⠐⠤⠇⠀⠀⠸⠀⠤⢀⠀⢀⠒⠐⠆⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢕⡤⠤⡄⠀⠀⠀⢀⠀⠴⢰⢐⠰⠀⣆⠀⢰⠀⠀⠀⠂⠀⡄⡆⠐⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠰⠐⣉⣠⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠖⠠⡇⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡍⠋⢀⠂⠈⣑⠦⣅⠀⡀
⠀⠀⠀⠄⠣⠓⠛⠆⡀⡤⠠⠖⡳⠖⠀⠐⢲⠀⠀⠐⠒⠒⠀⠒⡖⠒⡒⠀⠀⠀⠀⠀⠀⠀⣤⠤⡤⠠⢤⣤⣤⣤⠀⠀⡰⠇⢃⠀⡙⠀⠀⠃⠉⡄
⠀⠀⠀⢀⡀⠀⠀⠥⢦⠈⠠⠊⠀⠀⢀⠃⣾⡄⠀⠂⠠⠀⠀⠀⣤⠀⠧⡤⠀⠀⠀⠀⠠⠴⠃⡸⠂⠤⡀⠈⠈⠀⠀⠄⠀⠘⠄⠉⠑⡀⠔⢣⠄⡋
⠀⠈⠉⠀⡀⠀⢠⠒⡎⠀⣇⠀⠀⠀⠂⡴⠖⠁⠀⠀⠀⢀⣠⠞⡻⣄⠀⠘⢤⡤⠦⣀⠼⠁⡰⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠒⠸⠥⠀⠌⠋
⠀⠀⠀⠀⠑⠒⠁⠈⡱⡀⠙⠓⠈⣀⠐⠃⠀⠀⠀⠈⣁⣹⠤⠐⠃⢈⣳⣄⣀⠀⠀⡀⡠⠔⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠁⠈⠀⠀⠀⠀⠀⠀⠫⡕⠄⣼⠛⠨⣮⠌⠀⠀⠁⠀⢀⠀⠀⠀⠚⢀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠴⠒⠂⠀⠉⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠉⣠⠔⠊⣀⣀⣈⢉⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠞⣁⡴⢧⣄⠠⠶⠶⠤⠰⠶⣄⡀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡾⢁⠀⢀⣿⠷⠆⠀⠤⣭⠏⢴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣿⠸⠋⠀⣀⣉⣫⡥⠩⣟⣓⡉⠙⠓⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢳⠈⢸⠘⠀⡄⠀⢀⠐⢒⡂⣄⣓⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠸⠰⣇⠋⠰⠈⡀⠡⠍⠰⠸⢀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⠁⡀⡀⠃⠘⠧⠙⢳⣤⣤⣤⣤⡾⢋⡹⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠸⡀⢃⡅⢰⡘⠦⠠⠀⡿⠁⠈⢻⠧⠠⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠁⣸⣿⣄⠉⠂⡴⠀⡇⠀⠀⠨⠗⠄⠞⢃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠻⣷⣾⠁⠀⠐⢦⡴⠂⠀⣸⣾⠛⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣾⣿⡉⢦⡀⠈⠳⢦⠀⠚⠃⢠⡴⣋⣠⢊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡟⢳⡄⠁⠀⠀⠈⠛⠾⠟⢩⡾⠋⢉⡡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠘⠻⣦⡀⠠⣀⣀⠀⠠⠏⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⣄⡀⠀⠙⢦⡈⠙⠛⠃⠀⠀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠢⡄⠁⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⠀⠀⠀⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢰⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣈⣠⡿⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣿⡌⠂⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢣⣸⠀⠈⠙⠃⠀⠐⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠴⣍⡆⠀⠀⠀⠠⠀⠀⠈⠀⡏⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠉⢸⠆⠀⠀⠀⢁⡦⠀⠀⢇⡏⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡤⢿⡷⠐⣏⣠⣖⡒⠉⡁⠀⣠⠊⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡖⢠⡾⢋⠅⡼⢟⣡⣄⠄⣰⠃⡀⠀⡀⠉⠳⣄⠐⠁⠀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣮⡰⣇⠈⢧⠸⢊⣴⢋⡜⠁⣼⠃⢸⠀⠀⠈⠛⢆⠈⠢⠄⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡲⣆⠹⣿⠇⢸⢠⢺⡎⢸⢀⢸⡎⢀⡟⠀⠈⠉⠒⠄⠀⠀⡀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⡉⠟⣸⠇⠠⠟⠈⢯⠃⣟⢸⠸⡆⠸⠁⠀⠀⢀⠀⠀⠀⠴⣿⠏⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣀⢤⠞⠁⠀⠀⠓⣀⠀⠈⣦⠀⠀⠀⠈⢧⠙⠮⠧⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⣤⣦⠀⠶⠆⠛⠛⠋⠀⣤⣤⡤⠀⠙⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⢀⣄⠤⠠⠖⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢠⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡘⢀
⠀⠀⡤⢌⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡡⠃
⠀⠀⠑⠢⢽⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⢻⡄
⠀⠀⠀⡠⡾⠀⠈⢉⠋⠑⠒⢒⡶⠤⡤⠤⠤⠤⠤⢤⠤⠤⠤⢤⠤⠤⠤⠤⠔⠒⠒⠞⠉⣉⠀⠀⢀⡘⡀⠀⠀⢊⠓⠄
⠀⠀⠈⠐⠁⠀⠀⡘⢐⡆⠀⠈⠂⠀⠇⠀⠀⠀⠀⢸⢀⡀⠀⠐⠃⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠁⢃
⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⢠⣢⠀⢠⠀⠀⠀⠀⠀⢸⠈⠁⠀⡠⠀⠀⡇⠀⠀⠀⠀⠀⡄⣀⠋⠃⠀⣖⠜⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠚⣀⢄⠀⠶⢮⠀⠀⠀⠀⠀⠀⢰⡆⠀⠉⠠⡲⠅⠀⠀⠀⠀⠀⢚⠚⢀⠊⠐⠠⢀⣃
⠀⠀⠀⠀⠀⠀⠸⠔⠈⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠈⠢⢄⣀⠀⠀⠀⠀⠀⠘⡔⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⡇⠠⠀⠂⠐⠀⠂⠐⠀⠒⠐⠂⠐⠀⠂⠰⠀⠂⠐⠀⠂⠐⠀⠒⠐⠂⠒⠐⠂⠐⠀⠆⠰⠀⠆⠰⠀⠆⠐⠂⠂⠐⠄⢸
⠀⠀⠀⠐⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸
⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡃⢸
⠀⠀⠀⠀⡇⢘⠀⠀⠀⠠⠇⠀⡇⢠⢲⠆⡇⢂⣰⢰⣠⠆⠴⠀⠀⠀⠀⣾⠁⡄⠀⠈⢠⠁⠀⢠⢀⢐⠃⡤⡄⢰⠀⠄⠀⠀⡅⢸
⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠇⠀⠀⠀⠈⢰⠇⠃⡆⠊⠀⠀⡖⠀⠀⠀⠀⠻⠀⠃⠂⠰⠘⠀⠃⠘⠀⠀⠈⠀⠁⠁⢠⠂⠀⠀⠆⢸
⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⢸
⠀⢀⡄⠀⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⢠⡀
⢠⣾⣧⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠰⠰⠆⠸⠷⠰⠆⠶⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠆⣼⣷
⢾⣿⣧⣴⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣦⣼⣿
⡌⠾⠿⢛⣧⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣼⡛⠿⠷
⠏⢀⣶⣿⡟⣈⠀⠠⢾⣇⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣸⡷⠄⠀⣥⢻⣿⣶⡀
⡠⠈⠉⡩⠿⠿⠂⣤⡀⠈⠉⠻⠀⠀⠀⣀⢀⣾⡀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⢀⣷⡀⣀⠀⠀⠀⠟⠉⠉⢀⣤⠐⠿⠿⢍⠉⠁
⠀⣀⡠⡤⡤⢲⣿⠛⠙⢦⡀⢀⣤⡄⣼⣿⠸⣿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣿⠇⣿⣧⢠⣤⡀⢀⡴⠋⠛⣿⡖⢤⢤⢄⣀
⣿⣡⡀⠁⣵⢿⣷⣀⡴⣿⡿⡀⠙⡇⢿⣿⠀⢉⣐⣥⣶⣶⡶⠄⠀⠀⠀⠀⠠⢶⣶⣶⣮⣀⡉⠀⣿⡿⢸⠋⢀⢿⣿⠦⣀⣾⡿⣾⠀⢨⣌
⣤⡈⣧⣾⠟⣃⣾⢥⡒⣿⠵⠹⡄⠁⠀⠁⠰⣫⣴⣿⣧⣄⠀⠀⠀⠀⠀⣶⣄⢰⣿⣿⣿⣦⣝⢆⠈⠀⠀⢠⠋⠺⣿⢒⡬⣷⣘⠛⣷⣼⢁
⣯⠀⠉⢳⣶⡽⣏⡢⡈⣿⠀⡀⠘⡆⢠⣿⣙⣿⠉⠉⡟⠉⠑⡄⠀⠀⢶⣜⢿⣿⡿⠟⠉⠛⢉⣈⣷⡄⢰⠣⢄⡀⣿⢑⢔⣹⣮⣷⡞⠉
⢿⣧⡤⢼⡇⠘⢹⠟⠲⠿⣉⢙⣻⣿⠶⣿⠷⣤⣤⡀⢿⣾⣟⣹⢢⢄⠘⢿⣨⣵⡶⢂⣀⣀⡤⡿⣿⠾⣿⣟⡋⣉⠿⠖⠻⡏⡃⢸⡧⢤⣼
⠁⢙⣧⣾⣷⡟⢻⣀⣠⣤⣿⣥⠀⠸⣷⣼⣿⣿⣿⣆⠸⠀⠙⢿⣅⣾⠧⣬⢤⡆⠤⢠⣽⣟⣿⣶⣵⣹⠃⠀⣭⣿⣤⣄⣀⡟⢻⡾⣷⣼⡋
⣠⣟⣵⠋⢮⡗⠛⢛⣿⣿⣿⣿⢿⣿⣿⣿⣊⠟⠃⠀⠈⠛⢻⠟⣛⠁⣀⣴⠖⠻⣗⣣⣴⣿⡿⠄⣍⣻⡀⠀⣿⣿⣿⣟⡛⠛⢺⡤⠝⣮⣻
⢹⡿⢃⣝⣵⡏⠀⠈⣛⣿⣿⠏⠻⣩⣿⣿⣭⣥⠖⢛⣦⣼⣿⠂⢹⣿⡿⣿⣶⠀⡨⣿⣷⡎⠀⠀⠸⣟⠙⠟⠱⣿⣿⡛⠁⠀⢹⣮⣋⡙⢿
⠛⠿⡿⡟⣽⣿⣏⡙⡏⠉⠁⢀⡰⠛⠉⣾⠟⠋⠀⢩⣛⣁⣨⣧⡀⢙⡟⠿⠷⠛⢦⡟⠁⠀⠀⡄⠀⠈⠛⣆⠀⠈⠁⢹⢋⣽⣿⣏⢟⣿⠿
⡿⢿⠿⠿⡿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠛⠛⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣿⣷⠀⠀⠀⣴⡟⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⢀⣿⠏⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣤⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣀⣤⣼⣟⠀⢀⣴⡶⣤⡀⠀⣼⣟⡤⣶⡄⢀⣿⢋⠴⣦⠀⣴⣿⡟⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣻⡟⠉⠉⢹⣿⠁⢰⡿⠋⣰⡟⠀⣰⣿⠋⢠⣿⠃⣾⡿⠁⣸⡿⠀⣾⡏⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⡏⠀⢿⣇⠞⣿⣇⣤⣿⢿⣽⡿⠃⣸⡿⣯⣽⠟⠁⠸⣿⡠⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠀⠀⠀⠀⠈⠻⠄⠀⠀⠘⠷⠄⠀⠁⠀⠈⠀⣾⠇⠀⠀⠀⢠⣿⠁⠀⠀⠀⢀⣀⣈⣠⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⣡⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠤⣰⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣠⣤⣤⣤⣤⣀⣀⣀⠀⠀⣠⣶⠆⢠⣾⠟⠀⠀⠈⣷⡄⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⢀⣶⡿⢛⣿⠏⠉⠉⣧⠀⠀⢀⣤⠀⠀⠈⠉⠉⠛⢻⣿⠷⣶⣿⣧⣤⣤⣤⣴⡿⠃⢠⣿⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠧⢀⣾⣏⣀⣠⡴⠋⢀⣠⣤⠉⢠⣟⣷⠀⠀⢠⣿⠃⢰⡿⢁⣤⣤⡍⢉⣡⣤⣤⣾⠃⠀⠀⣠⣶⠶⣤⠀⢀⣴⡗⠀⣴⠆
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉⠉⠉⢱⡄⢩⡿⠁⠀⣠⠟⣻⠇⢀⣾⠃⢀⣿⡵⢋⣿⠏⣰⡿⠋⠀⣾⠃⠀⢀⣼⡟⢁⣼⠇⠀⣼⡟⢀⣾⡟
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣀⣤⡟⠁⣿⣧⡴⠞⠁⣾⣋⣴⣿⡏⠀⢸⡟⠁⣼⣏⣠⢿⣤⣤⠾⣿⣤⣴⠿⣿⡠⠊⣿⣤⢼⣿⡠⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠁⠀⠀⠈⠁⠀⠀⠀⠉⠉⢠⣿⠁⠀⠈⠀⠀⠈⠁⠀⠀⠉⠠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠐⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠶⠶⠶⠶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠁⣀⣀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⢛⣿⣿⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣠⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠀⠀⠠⠄


⣿⢿⠿⠿⢿⢛⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣛⣿⣿⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⢸⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⡀⠐⠇⠀⣦⡀
⠸⣿⠟⠋⠉⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡀⣄⠀⠀⠈⠙⣿⠃⠀⠘⣁⡀⣠⠶⠿⢶⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠉⠙⣆⠀⠀⠀⠁⠀⠀⠀⠘⠛⠿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠀⢀⠒⠂⠀⣠⣷⣽⠆⠀⠀⠀⠀⠐⠂⠺⠂⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠐⣂⠠⠀⠀⠀⠀⠀⠀⠤⠤
⢸⣦⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠁⣤⣾⣿⠏⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠁⠀⠀⠀⢶⡞⠀⠀⠀⠀⠀⠉⠐
⠸⢿⠇⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⢠⣴⣦⣄⠀⠀⠘⠿⢷⣦⣤⡆⠀⠀⠘⠟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂
⢠⣌⠙⠋⠀⠀⠀⠀⠀⠀⠀⠓⠠⣤⠀⣀⣀⠀⠄⠛⢻⣷⣤⣦⠀⠀⠀⠟⠓⠀⠀⠀⠀⠀⢀⠀⢰⡋⠗⠀⢰⣦⠀⠀⠀⠀⠀⢰⣦
⠈⠛⣿⣦⣼⠄⠀⠀⠀⠀⠀⠀⠀⠛⠈⠩⠀⠀⠀⢀⣿⠉⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠐⠷⠸⡇⠀⢡⠄⠀⣘⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠉⠁⡿⠧⡄⠀⣀⡀⠘⠳⣦⠀⢀⠀⣾⠛⠳⢌⣧⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣚⠉⢁⣀⣀⣋⡉⠁⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠐⠲⠾⠛⠙⠛⣿⣦⣁⠀⠎⠀⠹⢶⣶⣎⠈⢁⡄⠀⠀⠀⣠⣤⣀⢶⡶⠀⠲⡄⢸⢿⣀⠈⠿⣿⡿⢷⣀⠀⠀⠀⠀⠀⠘
⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠣⠀⠀⠀⠈⠉⢻⡆⢻⣤⡄⠀⠸⠋⢙⣦⣴⠀⠀⠈⣛
⢸⣿⣿⡇⠀⢠⡀⠀⠀⠀⣼⣿⡏⢴⣦⣤⡀⠀⢀⡈⠀⠀⠐⣧⠀⠀⢠⣤⢾⢷⣿⣿⡁⣠⣄⠀⠈⠏⢸⡗⡄⠀⣉⡀
⢸⣿⣿⡇⠀⠀⣹⣦⣤⣶⣟⠿⣿⣿⣿⣿⣿⣯⣽⠁⠐⠀⣴⣿⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣧⣼⠃⠀⠀⣸⣿⡀⢨⣷⠀⠈⠀⣠⣴
⢸⣿⣿⠇⠀⠀⠛⢿⠉⠀⠈⢡⣄⡉⠛⠁⠈⠉⠉⠀⠀⠀⣩⣿⠀⢰⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⠀⠀⠀⠈⢭⣭⠛⠀⠀⠀⢰⣿⡇
⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠘⢿⠏⠁⠀⢀⡀⠀⠀⠉⢻⡆⣰⡆⠀⠀⠉⣦⠀⢠⡄⠈⣿⣷
⢸⣿⣿⣿⣷⣶⣄⠀⠻⣦⣴⣿⣿⣿⣿⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣤⣴⣆⠁⠀⠠⠀⠜⢠⣿⣿⣦⡀⠀⣿⡄⠘⠃⠀⠙⢿
⢸⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⢀⠀⣀⣀⣀⣀⣀⠀⠀⠐⠻⠲⣶⠿⣷⡀⠀⡀⢀⣾⣿⡿⢿⣿⣦⣙⡇⠀⠀⠀⠄⠈
⠘⠻⣿⣿⣿⣿⣿⣿⡷⠀⢻⣿⣿⠿⢿⢿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠴⢉⣀⣤⣭⡀⠉⠋⠰⡦⢠⣿⣿⣷⣶⢢⡀⠀⣤
⠀⠀⠀⠉⠀⢹⣿⣿⠇⠀⠀⠹⠛⠿⠶⠂⣸⣿⣿⣿⣿⠏⡿⠟⠃⠙⠂⠀⠀⠀⠀⠈⠻⠃⠈⠙⠀⠀⠀⣀⣼⣿⣿⣿⣟⠀⠀⠀⣈
⠀⢠⢠⣤⡀⠈⠛⠋⠀⠀⢀⣀⠀⢀⠀⠀⣿⣿⣿⣿⠄⠀⠀⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣀⣤⡉⠛⣿⣿⣿⣿⣿⡀
⢠⣷⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣼⣷⣦⣼⠿⠛⠗⠆⠀⠀⠁⢀⣠⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠿⠟⢁⣾⣇⠀⣄⣀⣨⣿⣷⣶⣦
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⠿⢿⡷⠀⠀⠀⢰⠚⠲⣿⡞⣩⣿⠟⠛⣶⠂⠀⢀⣀⣀⠈⠀⠀⢸⡟⢿⠀⢸⣿⣿⣿⡏⠁⣀
⠀⠉⠻⣿⡆⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⢨⣧⠀⠀⠀⠿⡄⠀⠻⠈⠛⠙⠓⠀⢀⣤⣼⣿⡏⠙⡇⠀⣠⣾⣿⣿⡄⢈⣥⣶⣿⣿⣿⣿
⢈⣡⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠈⠀⠀⣠⣤⣤⣀⠀⢀⣄⠀⣶⣶⣶⡿⢻⣿⣿⣇⣴⡧⠎⢹⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣦⣤⣶⣶⣤⣤⣤⣿⣷⣦⣴⣿⣾⣯⣄⠙⢻⣿⣿⣿⡄⣹⣿⡉⠀⢾⣿⣿⣿⣛⠃⠀⢻⡏⣉⢙⡘⢻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⣤⣤⠄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠮⡥⠉⢡⡽⠷⡜⠁⣤⢾⣷⡈⠟⡃⣸⡷⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⢈⣧⣶⢶⡰⣟⣽⢳⣧⢻⣿⢯⣶⣷⣾⡽⣿⡿⠈⠽⠛⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣏⣏⡬⢿⣿⠛⠓⠈⠀⠀⢀⣀⣠⣤⣀⣉⡉⠁⠻⣿⣃⣴⣿⣼⠏⢤⡀
⠀⠀⠀⠀⠀⠀⣼⣃⡏⢰⣿⣶⠊⠁⠀⢀⣤⢞⡟⢋⣹⠯⣌⣿⣷⣿⣂⣦⠀⠐⡍⢻⣟⠁⢃⠷⡀
⠀⠀⠀⠀⠀⢸⡩⢮⡕⠆⣻⠁⠀⣠⡾⡹⢿⣭⡽⣶⣿⣿⡶⠟⡛⠈⠀⠁⠀⠀⠐⠀⠘⣿⣯⠚⡧
⠀⠀⠀⠀⠀⢺⣶⢄⡟⢈⣿⠀⠀⣿⣟⣷⢭⣍⡁⠻⣿⣿⣷⣋⢽⣀⡀⠀⢀⡔⠀⠈⠀⢸⡷⢾⡶
⠀⠀⠀⠀⠀⢨⡹⠾⣷⡈⠿⣦⡴⣿⡋⠀⠠⣄⠴⠷⣌⠳⣤⡘⢦⣈⠙⠓⠋⠀⠀⠃⠀⠐⡷⢶⡁
⠀⠀⠀⠀⠀⠀⢻⡄⠾⣛⠛⣫⣽⡏⠂⢀⣲⡃⠀⠀⠀⠙⠚⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⣼⡯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠨⢙⠘⠛⠛⠊⠁⠀⣤⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣸⡷⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠆⠐⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡞⣩⣹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣻⢯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⠆⠳⣿⣵⡸⠏⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣤⣴⣴⢶⣾⣾⠉⢿⣿⣣⣾⣾⣿⣿⣿⣿⣿⡶⢦⢤⣀⡀
⠀⠀⠀⠀⠈⠀⠀⢠⡤⣦⢦⣼⠿⢛⡻⠟⣷⣀⣪⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣟⡷⢼⠯⠇⢀⣦⣄
⠀⠀⠈⢀⣤⣶⠿⠿⠳⣷⣿⠝⠓⠉⠉⢁⡴⢻⡟⣿⣿⡿⠟⠋⠉⡁⠀⠠⠠⠠⠠⠡⠉⠛⠷⣤⣶⢿⣮⣛⣉⣡⡄
⠀⢀⠶⣿⠯⣍⢿⣿⠟⠉⠀⠀⠀⠀⢠⣯⣷⣮⣛⡿⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⡃⠛⠋⢩⣿⡆
⠀⣼⠲⠞⠧⠙⣼⡏⠀⠀⠀⠀⠀⠀⣾⡌⢻⣿⣿⣇⡀⠀⠀⢀⣀⣠⣤⡔⢲⣖⣶⣶⣶⡄⣀⠀⠀⠈⡿⣿⣿⡷⣿⢛
⠀⣿⠛⡿⢷⡞⢿⠃⠀⠀⠀⠀⠀⠀⢺⣵⡆⢥⡄⣿⣷⠶⢋⡽⠛⢛⣯⠒⣩⡭⣬⠉⣷⠀⣾⣗⣄⠀⣷⣮⣁⠸⢿⡞
⠀⢹⣺⢳⣿⢏⡐⣜⡦⠀⠀⠀⠀⠀⠈⢷⣶⣗⣲⢿⡶⢃⣴⣲⣮⣅⣀⡼⠿⠿⠯⢿⣯⠈⢀⣡⣥⣿⣭⣻⣭⣧⡍⣠
⠀⠈⢿⣿⣥⢾⣿⢩⢮⢀⣷⣄⡀⠀⠀⠀⠉⠻⠿⢮⢡⣼⠽⠿⠛⠉⠁⠀⠀⠀⠀⢀⣨⣿⢮⡽⢿⣿⣆⣫⣭⠟⢠⠇
⠀⠀⠀⠻⣿⢛⣏⡘⢫⡠⣽⡶⢶⣝⠒⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣯⠿⣉⡧⠔⠘⣇⢻⡟⠋⣰⠃
⠀⠀⠀⠀⠈⠙⡯⣿⣌⣱⣮⠿⣑⡛⢈⡳⢠⣾⢻⣿⠱⡴⢇⣾⣉⣻⣻⣿⣿⣿⣿⣿⣷⣯⣼⢀⡜⣿⣶⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠍⡙⠓⠾⢿⣿⣌⣡⣿⡴⢟⣙⡃⢀⣾⣟⣻⣿⣓⡿⣿⣿⣿⣿⠿⠞⢹⠌⢻⡾⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⢀⡉⠉⠁⠙⠛⠻⠿⠛⠿⠟⠟⠇⠃⠛⠉⢉⡀⠄⠒⡧⢀⣼⡃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠂⠀⠈⠈⠀⠀⠀⢜⡑⢿⢐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠃⡀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⢦⣤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢀⠶⣆⣰⣯⡿⠟⢻⣽⣿⣦⣅⠀⢀⡠⢲⣭⣵⣟⣻⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣿⢿⣁⣀⣀⣀⣀⣩⣥⡿⣸⡆⢣⣵⣟⣻⣾⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣻⣖⣎⣝⢣⠮⣝⣿⣿⡆⡾⣷⡸⣃⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⣉⡛⣩⣟⡿⠛⠉⣿⣿⢚⡷⠟⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⣀⣼⣫⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢰⠁⠀⠀⠈⣲⣤⠲⠀⠀⠘⡄⠀⠀⠀⠀⡰⣦⣡⡶⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠈⠁⠛⠉⠒⠀⠀⠘⠃⢄⣀⠀⠀⠀⠈⡍⠛⠦⣤⣀⣀⣀⣀⣀⣤⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠰⣦⣀⠨⢉⡒⠶⠴⠧⠤⠤⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠘⢹⡖⢤⡀⠁⠀⠀⠀⠉⠑⠦⣿⡠⠆⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⡏⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠠⠠⠜⠀⡆⠙⢦⠀⠀⠀⠀⠐⠛⠉⠑⠦⣄⣀⣀⠴⠁
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠠⡀⠀⣀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡸⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡾⠐⠀⠀⠀⠀⡴⠓⠆⠀⠠⡾⠀⢀⠄⢠⡄⠀⣤⠀⢠⡀⢠⡄⠀⣄⠀⡤⠀⣠⠀⠀⠀⠀⠈⢀⠘⡌⢆⠉⠒⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢤⣀⣀⣀⠠⠆⠀⠀⠀⠑⣴⠃⠀⣇⡀⣿⡀⢠⡇⣀⡼⠁⣼⢁⣠⠏⢰⡇⠀⡯⠀⠀⠀⠀⢀⠎⢠⢧⠀⠑⠤⢤⣀⣀⣀⣤⠚⠀⠁
⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠄⠃⠀⡖⢸⡆⠶⠖⠀⠦⠈
⠀⠀⠀⣾⠀⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠛⠀⠀⠀⠀⠐⠄⠃⠀⠀⠀⢀⠔⠀⢰⠇⠸⠇
⠀⠀⠀⣿⢠⡯⠐⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⡏⠈⠀⢂
⠀⠀⠀⢁⡾⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢸⠁⢠⡄⣜⡀
⠀⠀⡀⢰⠃⢠⣄⠈⠀⠀⠤⠀⠀⠀⠀⢰⠇⠀⡾⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢹⠯⣍
⠀⡐⢠⠏⡄⠄⠈⠻⠀⢠⠄⢀⡄⢤⠀⡟⠁⢸⣇⢤⠀⠀⡠⠀⣼⠁⢀⠤⢀⡄⠀⡤⠀⣠⠀⠀⠀⠀⠄⠀⠀⢸
⠀⡤⢋⣀⣉⣀⡠⠎⠀⣟⠀⢸⠃⠀⢸⡃⠀⡾⠁⣼⠀⢸⡁⠰⡇⠀⣏⡀⣾⠁⢠⡇⠀⡏⠀⠀⠀⠀⠇⠀⠀⠘⢆⡀⣀⠇
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠘⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⣄⣀⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣍⣙⣶⣶⣦⣤⣤⣴⣶⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⢶⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⣀⣀⣼⠃⠀⣄⠠⠤⢶⢀⡉⠀⠀⢀⣦⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⢿⣿⠀⢰⣿⠀⠀⠀⠋⠈⠁⠈⡤⠟⢻⣿⡇⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⡀⡙⣄⢼⣏⡀⠀⠀⠠⠑⢲⡁⠠⠾⠾⢿⡇⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠸⡇⠀⠘⣿⣦⣤⡀⠀⠨⠦⠀⠄⠀⠀⠉⠙⠁⠉⡏⣶⠂⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣭⣇⠀⢷⡀⠀⠘⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣤⣄⠀⠀⠀⢀⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⢸⣿⣤⣀⠹⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⢀⣠⡾⠟⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠄⠀⠈⠛⠷⣝⣟⠻⣷⣟⣷⣤⡀⠀⠂⠁⠀⠀⢀⣠⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠈⠛⠿⣿⣿⣏⣉⠀⠀⠀⢀⣠⣴⣿⣿⠋⠀⢀⣤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠑⢦⣀⡀⠈⠛⢿⣿⣷⣤⣀⣀⣀⣴⡿⢁⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠁⣽⣦⣤⣤⠛⣩⣿⡿⠿⠿⠛⠂⠉⡉⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠙⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠚⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢷⠀⠀⠀⠀⠀⠀⡟⠈⣷⠀⠀⠀⠀⠀⠀⢰⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡼⠀⠀⠀⠀⠀⠘⣇⣀⡿⠀⠀⠀⠀⠀⠀⢸⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⡀⠀⠀⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⡄⠀⠀⣿⠀⠀⠀⣼⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠿⠶⠶⠾⠿⠿⠷⠶⠶⠿⠶⠶⠶⠿⠿⠿⠶⠶⠾⠷⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣴⠶⢦⡀⠀⣴⠶⣦⠀⠀⢠⡟⠉⠻⣆⠀⣼⠏⢿⡀⠀⡿⠙⣧⠀⢰⡿⣆⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠃⠀⢸⡇⢀⡿⠀⢸⡇⠀⣼⠁⠀⠀⠙⠶⠏⠀⢸⡇⢸⡇⠀⠘⠷⠾⠃⠙⢧⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⠞⠁⠀⠀⣷⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡀⣀⢀⣀⢀⣀⣀⢀⡀⢠⣀⢰⢀⣀⣄⣠⣀⢀⣠⢀⣀⢀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠓⠟⢹⠾⢻⠿⠋⡿⠁⠘⠞⠛⠛⠁⠳⠛⠘⠙⠾⠒⠟⢸⠏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⣀⢠⡀⢀⢀⠀⡀⡀⢀⡀⡄⢀⢠⡄⣀⡀⡤⣀⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠀⠘⠁⠀⠁⠁⠈⠁⠁⠀⠈⠀⠉⠀⠁⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣷⡄⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢿⠋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⡌⢀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠄⠀⠀⡠⠄⢯⣷⠈⡴⢸⣇⢀⠀⡀⠀⣤⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢣⠈⠋⢠⡇⠸⠟⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠂⠐⠂⠸⡄⡀⠂⠘⣿⡆⢠⢏⡄⠄⠂⠐⠂⠀⠀⠀⠘⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⡀⠀⠀⠀⠀⠙⢞⣧⡀⣽⣿⢨⣿⠀⠀⠀⠀⠀⠀⠔⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⢷⠸⢃⡾⢣⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠒⠀⠐⠂⠚⠁⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠉⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠈⠉⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠀⣀⣀⣀⣀⣈⠑⢄⠀⠀⠆⠰⠀⠀⡠⠊⣁⣀⣀⣀⣀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢻⡈⠉⠉⠉⠙⢦⠃⠀⢀⠀⠀⠜⡴⠋⠉⠉⠉⢉⡟⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠙⢦⣀⠀⠀⣀⡵⠀⠀⠀⠀⢎⣀⠀⠀⣀⡴⠋⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠒⠰⠶⠖⠒⠂⠀⠂⠀⠀⠐⠀⠐⠒⠲⠶⠆⠒⢀⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠉


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣛⣻⣿⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠂⠑⢄⠀⠀⠉⠭⢭⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠳⢤⣄⣀⣤⡴⠋⠀⠀⠀⢀⡴⠁⠀⢠⠀⠀⣹⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠖⠚⠁⠀⢀⡴⠁⠀⢀⣿⠓⢮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠾⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⠤⠚⠁⠀⠀⢀⣾⡏⠀⠈⢷⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣠⣴⡿⠋⣿⠀⠀⢸⣧⢸⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠞⣋⣭⣥⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠛⠁⣠⣾⠃⠀⠀⣸⡏⢸⡇⠈⢧
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⠿⠛⢁⡰⠁⣰⡿⠁⣼⠃⠀⢸
⠀⠀⠀⠀⠀⣿⡏⠀⣀⣤⣶⣶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⢀⣠⠔⠋⣠⣾⠟⠀⣴⠏⠀⢀⡿
⠀⠀⠀⠀⠀⢿⣧⣼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠖⠚⢉⣠⣴⡿⠛⠁⢀⡾⠃⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⠛⠉⠉⣀⣀⣤⣴⣾⣿⠋⣁⣀⣤⣶⣯⣤⣶⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣿⠉⠛⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠋⣹⡇⠀⢸⠇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠸⡇⠀⢸⡇⠀⠸⣷⠀⠀⣿⠀⠀⢸⡇⠀⠀⡿⠀⠀⣿⠀⠀⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢳⠀⠀⣷⠀⠀⣿⠀⠀⢿⠀⠀⢸⡇⠀⢸⡇⠀⢠⡇⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡆⠀⢸⠀⠀⢹⠀⠀⢸⠀⠀⢸⠁⠀⢸⠁⠀⠸⠀⢀⣦⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣦⣤⣤⣸⣀⣀⣸⣀⣀⣸⣀⣠⣼⣤⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢠⡞⠁⠐⠂⠬⢍⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣋⠭⠄⠂⠈⠙⣦
⠀⠀⠀⢸⡖⠚⢋⣉⣓⡒⠦⢝⡮⠷⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠴⠭⣞⠥⠖⣚⣋⣙⠛⠒⣿
⠀⠀⠀⠈⢷⡉⣉⠀⠨⢭⣍⣻⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣼⣋⣭⠍⠀⣈⡉⣸⠇
⠀⠀⠀⠀⠘⢧⡠⠤⠖⠒⠒⠒⠛⠦⣄⠀⠀⠙⢦⠀⠀⠀⠀⣠⠞⠁⠀⣀⡴⠞⠒⠒⠒⠒⠦⠄⣰⠏
⠀⠀⠀⠀⠀⠈⢷⣐⠊⠉⢉⣉⣉⡙⠛⠛⠒⠦⣄⡳⣐⣢⡴⣁⡤⠖⠛⠛⠛⣉⣉⣉⠉⠉⢒⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠧⣤⣤⠬⣭⣭⣭⠯⠭⢽⣏⢘⣿⠭⠭⣯⣭⣭⡭⢤⣤⡬⠿⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣁⠤⠄⠐⣶⠤⠒⠊⡝⣿⢾⡿⡑⠒⠤⢴⡒⠀⠤⢄⣉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⣉⠤⠒⢈⡏⠀⠀⣠⢾⢀⡏⡘⡇⠹⢆⡀⠀⠙⣏⠐⠢⢌⠓⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠤⠂⡩⠳⡴⢺⠁⠀⣸⢀⢃⢹⠸⠀⢻⠲⡴⠫⡁⠢⣄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⢠⠊⠀⡜⠀⠇⠀⢰⠇⠈⠃⠈⣿⠀⠈⡄⠑⡀⠈⢦⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣇⠀⡘⠀⠀⡆⢀⡞⠀⠀⠀⠀⠸⣆⠀⠇⠀⢸⠀⢈⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠶⠚⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠒⠒⠀⠀⠐⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢀⠀⠰⡀⢠⣂⠄⣰⢠⠀⡀⠀⠈⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⢗⠙⠀⠋⠉⠈⠀⠀⠉⠀⠀⠏⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣀⣀⡀⠀⠀⣾⠋⣶⣄⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⡀⠀⢰⣦⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠰⠁⠀⠀⢸⣿⠏⠁⣨⡑⠂⠤⣀⣿⡿⠀⣄⠀⠀⣿⡆⢸⣿⠁⠀⣿⡆⢸⡿⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⢰⣿⠋⠀⣿⡆⢠⠎⣹⡧⠀⢩⡁⢠⣿⡇⠀⠀⣸⣿⠇⢰⣿⡧⠴⠟⠁⠀⠉⠓⣾⣿⡟⠋⠁⠸⣿⠁⠀⣹⣦
⠀⠀⠀⠀⠀⠀⠙⠁⣸⣿⣇⢃⡼⠛⠁⢀⣛⠋⠈⢿⣄⠀⢰⣿⡟⢀⣿⡿⢁⣀⠀⠀⣀⣤⣴⣿⡟⠀⢀⣤⡤⣭⡁⢠⣿⡿⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠈⣿⣦⠀⣾⣿⠀⠌⣼⣿⠃⣾⣿⠁⣸⣿⡧⢡⣿⠇⣴⣿⠏⣼⣿⠃⣴⣿⢋⣼⣿⠇⣿⣿⢁⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⠀⣿⣇⠎⠀⢿⣏⠔⢿⣧⠔⠹⣿⠁⣼⡿⠀⢿⡿⠎⠻⡧⠜⣿⡿⠎⢻⣿⠘⢿⡧⢊⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⣠⣾⠟⠁⣠⣬⣁⠀⠀⠀⠀⣀⣤⢄⠀⠀⠀⠀⢹⣧⣀⠄⢤⣤⠀⠀⠀⢀⣤⠴⢤⡀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠢⣄⢉⣸⣿⠀⠀⠀⣾⡏⢀⣸⡇⠀⠀⢀⡴⠻⣄⣀⣼⡿⠁⠀⠀⣾⡏⢠⣼⡗⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠉⠁⠀⠀⠀⠹⣧⣈⠛⣁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣉⡠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⠎⢠⠔⠄⠀⢀⢀⠀⡤⢄⠠⡀⢂⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠘⠠⠂⠀⠀⠇⠀⠦⠔⠀⠉⠁⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⢀⣀⣀⣀⡠⠤⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⠸⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠇⣿⡂
⠀⠀⠀⠀⠀⠀⢠⠖⣐⡋⠁⣸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⡈⢙⣂⠲⡄
⠀⠀⠀⢤⣴⣴⡴⢰⣦⢿⣷⠗⣶⣶⠈⣭⡭⠩⠩⠍⠭⢩⡍⠍⠭⠩⠍⠍⢭⡭⠍⠍⠭⢩⣭⠁⣷⣶⠻⣾⡿⣠⠆⢦⡦⣦⡤
⠀⠀⠀⠴⣶⡦⢁⣠⣽⠟⢁⣴⣍⣙⡴⠻⣿⣶⣾⣷⣽⢶⡼⠖⠀⠀⠐⠲⢿⡶⣯⣾⣿⣿⣿⣶⣋⣩⢦⠈⠻⣯⣄⡈⢴⣶⠦
⠀⠀⠀⠀⠀⠤⣿⣯⢸⣿⣏⢹⡿⠟⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⠀⠻⢿⡎⣸⣿⡇⣽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠆⣬⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⠰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡟⠩⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⡻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢟⢘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣦⠱⣫⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⡏⣬⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡍⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢙⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠞⣹⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣏⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⣱⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣎⢐⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢆⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠠⡇
⠀⠀⠀⠀⠀⠰⣶⣟⢰⣿⡏⣹⣷⣄⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣠⣾⣏⢹⣿⡆⣳⣶⠆
⠀⠀⠀⠤⡿⠗⠋⠹⢪⣤⠙⠳⣛⣙⠧⣴⣾⡿⣿⡯⢷⡭⢷⠤⠀⠀⠀⠤⡾⠯⡾⢽⣿⣿⣷⠶⣋⣛⡿⢋⣤⡗⠏⠉⠚⢿⠤
⠀⠀⠀⠞⠻⠺⠳⠰⠟⣿⣽⠦⠿⠿⠀⠛⠃⠒⠘⠀⠂⠘⠛⠂⠂⠐⠐⠂⠚⠓⠐⠂⠂⠘⠛⠀⠿⠿⡤⢿⣿⠻⠆⠞⠗⠟⠳
⠀⠀⠀⠀⠀⠀⠘⠦⠹⣍⠀⣹⣶⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⣶⣏⠀⣩⠟⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢁⣶⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣶⡈⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛

⡶⢶⢶⢶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⡶⣶⣶⡶⣶⠶⣶⡶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠵⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠙⠗⡴⠷⠀⠀⠀⠀⠀⠀⠀⢠⢧⡄⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⠀⡁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⣈⠔⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡠⢂⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠡⣦⠀⠀⠀⠀⠣⡈⠄⡠⠀⠀⠀⣰⢦⠄⠀⠀⠀⠀⠀⠀⢀⠤⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢷⠼⠧⠀⠀⠀⠀⠀⠀⠉⠒⣶⠮⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⢸⠀⢀⡈⠀⣠⠄⠤⡀⠀⣆⡆⠒⠒⢄⡖⡦⠐⠒⢄⢠⠀⠀⢰⡆⠀⠀⠀⢀⠄⠠⣤⠒⢢⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡔⢉⠠⣴⢆⢃⠀⠀⢸⠀⠀⢱⠀⠁⠀⠀⠁⠀⠀⣃⡀⠀⠈⠀⠈⣀⡀⠀⢸⠀⠀⢸⠁⠀⠀⠀⠈⠢⡀⠉⢀⠌⠀⠀⠀⠀⠁⡆
⠀⠀⠀⠀⢣⠸⠙⠀⠀⠏⠀⠀⠀⠀⠀⢸⣀⢢⡀⣀⠧⡈⠀⠧⡐⣁⠜⠀⡸⢄⣊⠔⠀⠄⠠⢻⠀⠀⣠⡀⠀⠀⠈⠲⠁⠀⠀⠀⠀⣄⠚⠛⠓⣠
⠀⠀⠀⠀⠀⠉⠣⡀⠀⠆⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⢸⠀⠀⢇⠈⡢⠀⠀⠀⠀⠀⠀⠀⣠⣅⣀⠉⡁⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠙⢠⠀⠀⡏⠐⠀⡄⠀⠀⠠⡠⠔⠀⢸⠀⠀⠀⠁⢛⢀⠖⢹⠀⠀⠀⠀⡧⠤⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⡄⢒⡀⠌⠀⢀⠔⡂⠐⠀⡠⢄⣀⠤⢄⠑⠒⠊⠀⠀⠑⠒⠊⠀⠀⠀⡀⠉⠐⠐⠁⠀⠀⡆⢐⠀⡼⠖⠊⢀⠀⠀⠀⠧⢀⣀⢀⣀⡠⠄
⠀⠀⠀⠀⠀⠈⠈⠙⠀⢠⠡⡠⠃⠀⠸⣀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠈⠈⡱⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣶⣭⠈⠋⠀⠀⠀⠀⠀⠀⠶⠖⠊⠢⡀⠂⠀⠀⠤⣠⠀⠀⠶⣴⣀⡀⠀⠀⡧⠀⢄⠀⠀⠀⡠⠤⠤⣸⠀⠠⠊⠉⢢⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⡠⣄⣢⠀⢸⣴⣆⠦⠀⠀⠀⢴⠃⢦⠀⠀⠇⡄⡠⢌⠀⡆⢠⠢⡀⠘⠀⡠⠠⠠⠀⠀⢘⠀⠀⠎⠀⢀⡀⡈⢢⠀⠀⠀⢸⠀⣀⠇⠀⠀⣾
⠀⠀⠀⠀⠀⠑⠊⠀⠡⣈⠀⠀⠀⠀⠀⠘⣄⡋⢊⡠⠊⠀⢅⣙⠜⠀⠆⢈⠕⠀⠠⣀⣑⠔⠀⠀⠀⠠⣘⠟⠢⡀⠃⡈⢇⡸⠐⢄⢀⠜⠠⠔⠑⠄⠜⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠒⡄⢀⣀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⢐⡈⠲⠋⢀⠅⠀⠤⠤⠀⠤⠀⠀⠀⠄⠀⢎⡛⡝⠀⠀⠘⡀⠤⠁⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠈⠑⠲⠁⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠈⠒⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⢉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⢻⢅⠀⠀⠀⠀⠀⠀⣠⠕⣶⠂⠀⠀⠀⠀⠀⠀⠀⢨⠀⡔⠂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠟⠉⠀⠀⠀⠀⠀⠈⠗⡰⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠠⠒⣉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠚⠳⠀⠀⠀⠀⠀⠀⡔⢁⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠴⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⠔⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡴⠶⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⡰⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⠒⠋⠉⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠬⠳⡀
⠀⠀⠀⠀⡼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡇⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢤⡀⠀⠀⣠⡇⠀⠲⣄⠀⠀⣠⡟⣡⡞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣇⢠⣀⠀⣀⣹⢦⡀⠻⣄⣴⠟⡇⠀⠀⠹⡳⡜⡝⡴⢹⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⣿⢀⣙⠻⡦⣹⣾⣌⡦⠾⠴⠴⠣⠶⣦⣄⣸⢠⡷⢁⠟⣿⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢹⡀⠉⢳⣝⣜⢿⠏⠀⠀⠀⠠⠊⠀⠈⢷⡇⢸⡇⡜⢸⣿⢡⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⢱⠛⠍⠉⢻⣾⡀⠀⠀⠀⠀⠀⠀⣀⣼⣇⣸⣷⠋⠉⠉⣹⠉⢹⡄⠀⡇⠀⢀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠉⠑⠚⠉⠉⠉⠉⠀⠀⠈⠁⠈⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⡀⡀⡀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠴⠚⡝⠉⠙⠍⠓⢂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠁⠀⡘⠀⠀⠀⠈⠀⠀⠑⢄⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢃⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠛⠛⡋⢉⣉⣀⣀⣉⣉⣉⡛⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⠭⠆⠒⠂⠉⠅⠀⠀⠀⠀⠀⡇⠀⠀⠉⡙⠒⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱⡀⠀⠀⠄⠀⠀⠀⢰⠀⠀⠠⠃⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⢄⠑⠄⠀⠀⠀⠀⠀⠄⠀⡠⢂⠔⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠢⠢⣄⣢⡀⣀⣠⠴⠐⠁⠠⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠁⠀⠀⠰⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠘⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠓⠾⠀⠀⠀⠀⠇⢀⠆
⠀⠀⠀⠀⠀⠰⠀⢄⠀⣀⢀⣀⣀⣀⣀⡀⢀⠄⠰⠘⡤⠇⠀⠀⠀⠀⠘⢾⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠁⠀⠁⠀⠀⠐⡀⠀⠆⢠⡄⠀⡄⢠⡔⢰⡖⠀⠀⣰⣆
⠀⠀⠀⢀⠊⠀⡰⠀⠀⠄⠀⠀⠀⡄⠀⠄⠀⠡⠀⠀⢴⠃⠘⠃⠈⠃⠘⡇⠀⢔⣿⣿⡢
⠀⡠⠔⠁⢀⠔⠀⠀⠜⠀⢀⠀⠀⢀⠀⠘⡀⠀⠑⢀⠀⠑⠆⡀⠀⠀⠀⠡⢂⠊⠃⠁⠁⠐
⠛⠛⠛⠛⠟⠛⠛⠻⠛⠛⠛⠛⠛⢛⠛⠛⠻⠛⠛⠛⠟⠛⡛⠛⠀⢀⠔⢠⠂⠌⠀⠠⢠⠀⡈⠢⡀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠁⡠⠁⠀⠀⡀⠀⠀⠂⠈⢄⠈⠂⢄
⠀⠀⠀⠀⢠⠀⠀⠀⣯⠝⠛⢻⣽⠛⠋⢍⡇⠀⠀⠀⠀⢰⣥⣤⣤⣮⣤⣴⣥⣤⣤⣤⣤⣬⣦⣤⣵⣤⣤⣥⣦
⠀⠀⠈⠀⠈⠀⠀⠀⣿⠀⠀⢸⣿⡀⠀⢸⡇⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠀⡀⠀⡆⠀⢀⠁
⠀⠀⠀⡇⠀⡆⠀⠀⣿⠀⣆⣿⣿⣇⡇⢸⡇⠀⠀⠇⠀⠃⠀⠘⠀⠆⠀⢸⡟⠋⢻⣟⠉⢻⡇⠀⠘⠀⠃
⠀⠀⠀⠀⠀⠃⠀⠀⣿⢀⣿⣿⣿⣿⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠈⡇⣐⣾⣿⣄⢸⠀⠀⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⣿⣿⣿⣿⡽⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⣿⣿⣿⣿⣼⠀⠀⠃
⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣞⡽⣳⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⡥⢴⡖⠻⢍⠻⣾⣵⣷⣾⣿⣇⢀⣀⠤⠤⢀⡀
⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣥⠏⣔⡩⣬⡗⡄⡃⢸⡾⠟⢿⣿⣽⡟⠀⠀⣀⡀⠈⠲⠗
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢄⢨⡙⣩⠇⡜⣧⠎⠆⣠⣤⠈⣉⡃⢠⠞⠉⠉⠱
⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠚⢳⣤⣙⣭⣍⡩⠜⣡⣾⣿⡛⠁⠺⡤⠈⠇⣰⣷⣀⡴⢁⡄⢠⣋⠉⢆
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠉⣈⣁⣪⡓⠶⠶⣿⣟⣏⣼⣽⡗⡿⠂⣀⠘⠦⣀⣀⠤⠛⠤⣉⣉⣀⡤⠀⠠⡀
⣿⠀⢸⡇⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⢩⣏⣀⣈⣉⡧⡙⢦⣿⢍⠚⢭⣶⠞⢣⡘⢂⡕⢀⡉⢀⠎⢉⢙⠀⠀⠀⠧⣴⠀⣽
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⣌⣯⣃⡾⢠⣇⡜⢹⣷⣿⡏⢀⣤⣀⠛⠁⠀⠏⣰⢹⠀⠈⢻⡆⠀⠀⠀⢢⣤⢳⠂⠴
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⢿⣤⣉⣉⣽⡀⣠⡾⢿⣿⠻⢟⡭⠽⣦⣀⣀⣀⠠⠊⠀⠀⠊⠀⡔⠉⠉⢧⠈⣎⠓⢤⠄⠤⡀
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⢻⡵⢻⣯⢝⣪⡟⠘⢿⡘⡹⣿⣿⡇⠀⠀⠀⠀⠀⢰⠀⠀⢣⡀⠚⠧⢀⠟⠃⠧⠩⠂⢹
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣻⣷⣾⠁⠀⠀⠉⠙⠛⠿⠇⠀⠀⠀⠀⠀⠈⣳⣄⣤⢈⠗⠈⠀⢴⡉⢢⡀⠀⢘⣠⣤⣤⡄
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⠇⣈⠂⠃⡾⠦⡄⠈⢁⡔⢟⣿⣿⣿⠁
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡓⣿⡹⣏⠀⠻⣷⣴⢝⣷⢼⢦⣸⣹⡾⠫⣽⠇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⢮⡿⠋⢙⣋⣬⡙⢿⣗⢿⡎⢜⣿⣿⣿⣯⣄⣀
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡿⢀⡟⢀⣀⡀⣀⢀⡀⡀⢀⢀⠀⡀⠀⠀⠀⠀⠑⢿⣵⢃⣴⣍⡐⡎⠆⢹⠟⢉⠿⠭⡉⠱⡷⢫⣩⣿⣷
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⣾⠓⡾⢡⡏⣼⢡⢏⡼⣿⢣⡟⡞⣰⠏⠀⠀⠀⠀⠀⠀⢻⢦⡨⡿⢚⣇⠼⣴⣀⡥⣔⣒⢶⠶⡷⡛⢍⡿⠁
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠈⠃⠈⠁⢩⡟⠈⢱⠏⠉⠀⢱⠏⠀⠀⠀⠀⠀⠀⠈⢌⠳⢍⣁⠠⠋⣼⡍⢼⠁⣿⠝⡵⢠⡟⠚⠋
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢲⣦⣀⣀⢠⣤⣆⢠⣸⣡⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠹⠀⢧⣈⡶⢮⡭⢷⢷⣳⡀
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠣⠜⠙⠃⠚⠊⠓⠛⠛⠑⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡞⠓⣶⠂⣻⡿⠿⠇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⠸⠷⢶⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⡷⠶⠿⠀⢸⡇
⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠿⠶⠶⠶⠾⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠇
⣶⣶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢛⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠅⡚⠟⢃⠇⠀⡆⡄⢣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢊⡔⠈⢀⠤⠊⢀⠔⢠⠁⣰⠛⢍⢣⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠭⢀⣒⠚⠙⠳⠴⠖⠷⠒⠓⢉⠔⡀⠊⠰⢀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠤⣒⣾⣮⠐⢈⠁⠠⠤⠀⠀⠀⠀⠐⠒⡈⠕⢊⣀⡔⣡⣪⠃⡜⢢
⠀⠀⠀⠀⠀⠀⢸⠭⠬⠉⢉⣙⠋⠥⠈⢛⣉⠨⠌⢚⡋⠭⠑⠋⣉⠠⠐⢉⠤⠊⡠⢊⡇
⠀⠀⠀⠀⠀⠀⠘⣈⢈⠡⠄⢀⣒⠀⠭⠀⠒⠈⣉⡀⠤⠐⢂⡉⠤⠒⣈⠤⠐⣈⣔⠅⠣⡀
⠀⠀⠀⠀⠀⢠⠊⠈⠂⠢⠭⠤⡄⠐⣒⣈⣩⡅⠀⣒⣈⢭⡀⠒⠬⠵⠒⠚⠉⠉⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠸⡖⢢⠄⢠⡀⢀⣀⠀⡀⡀⡀⠀⠀⠀⠀⢀⢀⣀⣀⡀⢀⡠⠠⡤⠀⠶⠈⣿
⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡇⠀⠉⠀⢸⠀⠸⠁⠘⠁⠈⠁⠈⠁⠈⠀⠀⠀⠀⠁⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠁⠀⢰⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠘⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡄⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⡃⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⣇⠀⡄⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⡀⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠁⠈⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢩⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢈⠀⠀⠀⠀⣀⠤⠒⠒⠂⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡀⠀⢀⡜⠀⠀⠀⠀⡇⠀⠀⠀⣠⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠉⠉⠒⠒⠀⠀⠀⠀⢠⡇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⣒⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢰⠇⣤⠀⠀⡇⠀⡿⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠀⣸⠁⠀⢸⡇⢀⢀⠀⡼⠉⣦⠀⢸⡁⢠⡟⠠⡇⢀⡼⠁⣸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠈⢧⡀⣀⠇⠳⠀⢿⠀⣾⠶⠋⠀⢸⡇⢈⠄⠀⠘⠂⢠⡏
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡠⠤⠶⠶⢬⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡴⢢⡇⠀⡀⠀⠸⢣⠏⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠎⠀⠀⢠⠆⠀⠈⢷⠀⠠⠄⠀⠀⠀⢀⠄⠀⣼⠁⠸⠇⣠⠆⠀⢠⡏⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⡏⠀⠀⠀⣸⠀⡤⢀⠀⠀⠀⣽⠁⢰⡟⠒⠂⠉⠀⡀⢀⡿⠀⠀⢀⠀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣾⠔⠢⠴⠚⠥⣼⠁⡟⢠⡇⢠⡇⠀⣼⠀⢸⡆⢠⠏⠀⣸⡇⠀⡴⠁⢰⠇⠀⠀⠀⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠤⠤⢄⡀⠀⢯⠹⡇⢸⠃⢸⡇⡠⡏⠀⢸⠀⣿⡠⠊⢸⠁⢰⡇⡠⣿⠀⢸⠀⢰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⡇⠀⡀⠀⢹⠀⠀⠀⣿⣾⢀⡄⠉⠀⠀⠀⠈⠃⠀⠀⠀⠘⠡⠈⠉⠀⢷⣀⠜⠓⢙⡇⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠀⠀⠀⣰⠟⡈⢉⢀⠀⠀⡀⡀⠠⠀⠒⠐⠒⠐⠒⠀⢀⡀⠊⠁⠀⠀⢸⠇⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠁⠀⠂⠀⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⣀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⠌⠙⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠆⠞⢤⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠙⢂⢀⡖⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠡⠀⠁⠀⠀⠀⢀⣀⡀⢄⠠⠤⡠⣤⠒⠲⡖⠂⣼⡃⢠⢤⠆⠤⣤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡁⢮⡽⣽⠵⣈⡓⢡⢶⢑⢇⡈⠊⠱⢎⢒⣃⠮⢜⣛⡍⠌⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⠀⠀⢡⠀⣴⣡⠇⣈⡗⢡⠲⠑⠮⢟⡃⡰⡗⢿⡺⢈⡛⠧⠊⢰⢢⠓⡧⡀⢎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠆⠀⠀⠀⠡⣇⡤⡘⠒⡡⡑⠃⡐⡲⢧⡫⡈⡗⢄⠤⠘⣬⢲⢢⠈⣚⠀⣉⠚⡠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢱⡌⢱⠉⡉⡚⢠⢻⢡⢴⢭⠋⢫⡁⣚⠦⢝⡡⡯⠮⠼⢦⢠⣄⡭⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⢀⠂⠀⠀⠄⠙⢹⠀⣶⢥⡇⢸⡼⡁⢸⠀⠈⠑⠁⠀⠘⣬⠃⡶⢫⣸⢸⢸⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡠⠁⠀⠀⡐⠀⠀⢸⡄⠈⠉⠀⢸⠋⢯⣿⠀⠀⠀⠀⠀⠀⠉⠒⠁⢸⡐⢸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡠⠈⠀⠀⠀⡐⠀⠀⠀⠀⢣⡀⠀⠀⢸⠸⣵⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠈⢣⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡠⠀⠁⠀⠀⡀⠔⠈⠀⠀⠈⠶⠂⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠠⠄⠂⢁⡀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠠⠘⢷⠐⠲⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣖⡐⠂⠀⠉⠀⠀⠀⠀⢀⡀⠠⠀⠂⠈⠀⢀⠠⠘⠀⢈⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠀⠀⠀⡀⠀⠀⢀⠄⠦⠴⠊⠉⠉


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

⠀⠀⠀⢀
⠀⠀⠔⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠂⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠀⠀⠘⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠡⣀⠀⠀⠇⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠉⠉⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⡀⡔⠑⡄⠀⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⢀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠌⣓⣃⠀⢀⠀⢄⣂⠀⠀⠠⠀⢀⠀⠀⠀⠌⠀⠈⠂⠊⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠄⣀⠀⢸⠀⠀⡋⢩⠇⠀⠈⠀⢿⣽⡗⠀⠀⠰⣯⣿⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠅⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠐⣌⠲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠦⢈⣑⡦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠈⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⣶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣴⣶⣦⣶⣦⣾⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⢶⡤⠀⣤⡄⣤⠀⠐⣠⣀⠤⣄⣀⠤⠀⠄⠀⠤⠤⡤⢤⠠⠤⠄⣶⣄⣢⣴⢄⣰⡖⠶⠶⠒⠒⠒⢒⣲⣶⣶⡶⢶⣶⠶
⠈⡈⡡⠀⠠⠁⠢⠄⠜⣠⠴⢫⠥⡀⠉⠺⣩⢈⢳⣃⠜⡀⠀⠀⠈⠋⠁⠐⠚⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢰⠟⠻⠋⣴
⠀⡤⣠⠒⠉⠉⠉⠓⢤⠁⠈⠉⠁⢣⡀⠈⠐⠀⡰⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠍⣩
⠀⢧⠃⠀⠀⠀⠀⠀⢘⡦⡀⠀⠀⢀⠉⠒⠒⠎⠑⠁⠀⠀⠀⢨⢧⢻⢀⡈⢰⢴⡧⠇⠑⡠⠀⠀⠀⠀⠀⠀⠀⠀⢋⡏⣿
⠀⡿⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⢠⣶⢰⠉⡎⠀⢸⠁⠀⠀⠀⢀⣀⡀⠀⢀⡘⠒⢹
⠈⡇⠂⠀⠀⠀⠀⡼⠁⡰⢳⠀⠀⡸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣁⣁⡈⠉⠘⣀⣁⠀⠈⠀⠀⠀⠀⢎⠀⠈⢲⠋⢹⠀⢸
⠀⠞⠆⣄⣠⠴⠊⠀⡰⠃⡜⢀⠰⠁⠀⠀⠡⢦⠈⣷⣤⠀⡐⣶⠁⢹⣄⡀⠉⢃⢦⡑⡄⠀⠀⣠⠀⠬⢦⡀⠀⢀⠎⡀⠼
⠀⠀⡅⢺⠓⡤⠀⠔⠁⢠⢯⠏⠀⠀⠀⠀⠀⠋⢖⠡⡌⠀⡽⠊⢰⢸⡔⢽⠀⠸⢀⠃⡇⡹⠆⢸⣀⢀⠀⢙⠶⠊⢟⡬⠂
⠀⠈⡢⠸⣄⠀⠀⠀⢠⠓⠋⠀⠀⠀⠀⠀⣄⠗⡨⢠⡇⠰⠇⠀⠼⠸⠗⠸⣀⡗⣋⠞⠸⢧⣾⣼⣾⢸⡀⠘⠄⣀⡠⢣⢷
⢸⡄⡠⠸⠈⠃⡶⠊⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣴⣏⠁⣠⣯⠎⠸⠆⠀⠀⠀⠀⢺
⠈⣿⠡⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠰⠚⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡳⠀⠠⠓⠀⠀⠀⠀⢸
⠀⣇⠂⡞⠛⠚⠶⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠙⡇⠀⡔⠀⠀⠀⠀⢰
⠰⣹⢰⡇⠀⠀⠀⠈⢳⡥⠦⣄⣠⠤⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡈⣿⠀⠘⠇⢠⢈⡆⠀⠘
⠀⠛⡉⠣⣎⣉⠭⢽⣾⠀⠀⣏⣀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣀⠈⣉⠀⢀⠠⢄⠀⢀⠤⡬⢀⠋
⠀⠈⠐⠀⡇⣏⠉⠉⠛⠓⣾⠓⠛⢷⠢⠬⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠘⠲⠃⢰⠤⣬⠂
⠀⠠⠐⠚⡛⣿⠀⠀⢀⠀⣿⠀⠀⠼⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢅⡂
⠀⠀⠀⠀⠁⡿⠀⠀⢸⠀⡏⠀⠀⠇⠀⣎⣩⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠛⠋⠭⠭⠭⠭⠭⠉⠛⠃⢈
⠀⠀⡆⠀⢠⡇⠀⠀⢈⢀⡇⠀⢸⠠⡄⠀⠀⣀⡈⠉⠛⠛⠒⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⣡
⠀⡀⢘⢾⠋⣇⠀⠀⠀⢸⠁⠀⣈⢀⠃⢰⢰⠃⠙⠉⠓⠄⠒⠑⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⢸⡁
⠀⠀⠜⠒⠢⠭⠿⢿⣿⠛⠒⣒⠉⠸⠤⠬⠥⠤⠤⠀⣀⣀⣀⣀⡧⣀⠀⣀⠀⠀⠀⠀⢜⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢣
⠠⠀⠚⢿⠥⡤⠤⡤⠶⠶⣶⢖⡟⠉⣓⠠⠼⠿⠷⠶⠶⠶⠶⢒⡠⡿⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠁⠊⠙⠈⠀⠈⠃⠃⠊⠘⠘⠲⠊⠘⠀⠀⠒⠋⠟⠙⠂⠓⠈⠀⠓⠖⠀⠀⠲⠒⠒⠒⠒⠈⠉⠉⠉⠉⠁⠒⠒⠂⠒⠋
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⠛⢿⣷⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣸⡟⠀⠀⢀⡀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⡇⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠻⣄⣈⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢦⠉⠛⢿⣷⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣰⡿⠛⠛⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠛⠁⠀⠀⠀⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢿⣄⣀⡀⠀⠀⢀⣀⣀⣀⣀⠠⠄⠀⢀⣀⣠⣤⡴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣭⣭⣭⣭⣭⣤⣤⡶⠶⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢉⣠⠾⠋⠉⠉⡙⠻⣷⣦
⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢒⣉⣤⡴⠞⠋⠁⠀⠀⠀⠀⠙⣦⠈⣿⣇
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿
⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⡿
⣸⡏⣼⠁⠀⠀⠀⠀⠀⣠⠖⢉⣠⡴⠶⠞⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⣧⣤
⣿⡇⢿⠀⠀⠀⠀⠀⣸⢃⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⠞⠋⠀⣨⢻
⢻⣷⡸⣆⠀⠀⠀⠀⠟⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠞⠛⠋⠉⠀⠀⠀⢀⠞⣸
⠈⢿⣷⣝⠦⠤⠄⠀⣀⣾⣿⣄⠀⠀⠀⠀⢀⣠⣤⣍⡉⠓⠦⣤⣀⣀⣀⣀⣀⣀⣀⠤⠔⠊⢁⣀⣤⡴⠶⠛⠉⠉⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⠴⠞⠉
⠀⠀⠉⠛⢻⣿⡟⠛⠋⠀⠙⠻⠿⠶⠶⠛⠋⠁⠉⠙⠻⠷⣶⣤⣤⣭⣭⣥⣤⣤⣴⠶⠾⠛⠋⠙⠿⠷⠶⠶⠶⠶⠛⠛⠉⠉⠉⠉⠉⠀⢀⣠⡄
⠀⠀⠀⠀⠘⣿⣿⣷⣤⠶⠻⢿⣶⠾⠿⣷⣦⡴⠿⢿⣦⣤⡴⠿⣿⣬⣉⣥⣤⣄⣀⣠⠶⢶⣶⣄⣀⣤⠶⣶⣄⣀⡴⢾⣦⣴⠟⠿⠶⠾⣻⣿⠃
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣤⠀⠀⠀⣷⠀⠀⠀⣷⠀⠉⠁⢸⡆⠈⠉⠉⣴⠈⠛⠛⠁⢰⡇⠉⠛⠋⠁⡖⠈⠙⠉⣴⠈⠉⠁⢸⠇⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢹⡆⠀⠀⢿⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⡿⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣷⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⠀⢸⠇⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢹⡆⠀⠘⣧⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⣼⠁⠀⢀⡿⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠈⣷⠀⠀⣿⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⢸⡇⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢻⡆⠀⢸⡇⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⢀⡿⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠘⣧⠀⠘⣧⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⢀⡟⠀⠀⠀⣼⠀⠀⢸⠇⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢻⡄⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⡿⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠘⣧⠀⢸⡇⠀⢹⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⠀⢸⡇⠀⢸⠇⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢻⡄⠘⣧⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⢀⡟⠀⠀⠀⣾⠀⠀⡿⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⣧⠀⣿⠀⢸⡇⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⢀⡟⠀⢸⠇⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠛⠀⠸⠇⠀⡷⠀⠀⠸⠇⠀⠘⠃⠀⠀⠀⡿⠀⠀⠺⠀⠀⠀⠸⠇⠀⠿⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠⠲⡦⠀⠀⠂⠤⠠⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠄⠀⠀⠀⠀⢦⣤⡶⠆
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠁⠀⡀⢢⡢⠀⠈⠀⢠⡀⠀⠾⠓⠆⠀⢰⠸⠁⠀⠀⡀⠀⠀⠀⢀⠰⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣅⠀⠀⠀⠀⢁⡼⠀⠁⣼⠁⠀⠀⠀⠄⢷⣄⠀⠀⣀⣴⡟⠀⠀⢠⠜⠁⠀⠀⠀⠀⠊⠀⠀⠀⡄⡘⠀⠀⠀⢀⠠⠘
⠀⢀⠠⠆⠀⠀⠀⢀⡷⡤⢠⣈⡀⠒⠖⠒⠛⠀⠀⢠⠇⢠⠀⠀⠆⠘⠢⡉⠙⠛⠛⠉⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣧⡇⠀⢀⢀
⠀⡁⠀⠀⠈⠄⢀⣤⣠⣴⣾⣿⡿⠒⠀⠀⠀⠀⠀⡾⠀⠈⠀⠀⠀⠀⠦⠀⠱⡖⡲⠲⣶⠂⡀⠀⠀⠀⠀⠀⡙⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠣⠄
⠀⠁⠤⠤⠞⠀⠸⣿⠿⠿⠛⢉⠑⠁⠀⠠⠆⢠⡄⢠⡄⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⢀⠉⠀⠲⡀⢠⡀⠀⠀⣓⡀⠀⠁⠀⠀⠀⠀⠀⠸⠀⠘⣧⠀⢻
⠀⢀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠦⡀⠀⢐⠎⠁⠀⡈⠀⠀⠀⠀⠠⠬⠐⠀⠀⢠⡀⣤⡀⠀⠀⠀⣄⡁
⠢⠈⠥⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣄⣀⠀⠃⠀⠀⠀⡀⠀⠰⠞⠒⣆⠳⡄⠀⠀⠀⡠⠄⣤⡀⠀⠀⠀⡛⠀⠀⣞⠸⡃⠕⢸
⠀⠃⠀⡼⠻⣦⠀⠀⠀⠀⢂⠲⠙⠶⠠⠁⠉⠀⡀⠀⠠⠀⠀⢂⠀⠀⠀⠈⢧⠙⠆⢠⠊⠀⠀⣿⠇⠀⣤⣤⠀⠀⠀⢰⠀⠁⠈⢨⠀⢀⠄⠀⠀⠃
⠀⠀⠰⠛⡁⠘⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠠⠄⠀⠀⠈⠓⠒⠃⠀⠀⢠⡿⠀⠀⣉⣉⡇⠀⠀⠐⠄⡣⣠⠞⠀⠘⠀⠠
⠀⠀⠀⠀⠤⠄⢧⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠂⠀⠀⠀⢤⢨⠄⢲⢚⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣤⣤⠄⠀⠄⠀⠀⠀⠀⠄⢁⣲⡀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠂⡀⠀⢸⢐⠀⡠⠴⡕⢾⡄⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋
⠀⠀⠐⠀⠀⠀⠀⠙⠓⠛⠀⠀⢂⠀⠀⠀⠀⠀⠘⠧⠀⠘⢨⠈⠳⠊⢀⣸⠃⢀⠆⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠐
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⣟⠋⠁⠀⠂⠀⢀⡿⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠰⣶⣶⣴⣶⡦
⠀⢠⡄⠘⠃⠀⠀⠰⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣽⠀⢠⡃⠀⣠⡾⠁⠀⠀⠀⢀⡀⠁⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⡆⠀⢀⡀
⠀⠈⣗⣄⠀⠀⠀⠀⢫⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠀⠀⣠⣄⠓⠒⠋⠀⠀⠁⠚⠛⠁⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠘⠒⠒⠒⠚⠀⠟⢻⣿⣿⣦
⠀⠀⢋⡈⣳⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⡎⠙⠏⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠤⠄⠀⠀⠋⠈⠉⡀
⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⢰⣲⠆⢠⠀⠐⢶⣯⠈⠛⠁⢀⣀⠄⠀⠤⠚⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⢃⠀⠀⠀⠠⠂⠁⠢⠀⠀⠀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠙⠀⠘⠉⡀⠈⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣫⡇⠀⠃⠀⠀⣠⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⢀⣀⡀⠀⣶⣖⠄⠐⠒⠂⠈⣁⠠⠼⠀⠀⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠂⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠠⠂⡀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⣠⡀⠀⠀⢀⠄⠒⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠂⠄⠀⠐⠚⠙⠈⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠘⣀⡀⠀⠀⠈⢀
⠀⠉⢁⠰⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠂⠀⣸⣷⠟⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣷⣿⠀⠀⠸⣭⣡⠴⣼⠁
⠀⠉⠀⠊⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠠⠤⣤⠄⣄⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⡏
⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠆⢰⠀⠀⢠⣋⡴⠃⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⣠⢲⢓⢀⡀⠀⠀⠴
⠈⢠⣴⣦⡀⠀⠀⠀⠀⠂⢀⡀⠒⠂⠉⢁⡀⠀⠀⠀⠈⠀⠀⢢⡄⠀⠀⠄⢀⠀⠘⡄⠀⠀⢠⠃⢰⠆⢀⠔⠲⠀⠀⠀⢹⢀⢂⠀⠃⠀⠀⠀⠀⠡
⠀⠘⣏⣼⠇⠀⠐⠠⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠘⢢⠀⠉⠀⠄⠁⠈⠀⠘⠇⠀⠀⠁⠀⣤⡶⢾⡿⠿⢿⠀⠀⠰⠒⠣⠼⠃⠠⠶⠤⣤⣤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠤⠤⠚⠁⢴⡒⢪⣹⡇⠀⠀⠀⠀⠀⠠⠜⠀⠲⢿⡟⠀⠀⠀⠘⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⢘⠖⠲⠘⠳⠚
⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⢁⠀⠂⠐⠁⣠⠦⠀⠐⠀⠀⠀⠀⣧⠀⠀⠇⢀⣟⢟⠣⠀⠀⠀⠁⢀⠀⠐⡂
⠀⠈⠈⠁⠀⠠⠂⠚⠉⠀⠀⠀⠀⠀⠀⠬⠱⠤⢀⠀⠀⡠⣦⠀⠀⠘⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⢀⣨⡤⡄⠒⠀⢀⡀
⠀⠀⠀⠀⢀⣤⠤⠀⠐⢠⠀⠀⠀⡄⠀⠀⠏⠊⣹⢇⢼⠉⢉⡇⠀⠀⠉⠁⢠⣶⣶⠀⠀⠩⣤⡤⣧⠀⠀⠠⠀⠀⠈⠑⠠⠆⡰⠔⠃⠀⠻⣿⣾⣿
⠀⠀⠀⠀⠈⢿⡀⠀⡠⠋⠀⠀⠀⠀⠈⠀⠀⠀⠍⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⢄⣁⠤⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣁⣴⣁⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⡀⠀⠠⠀⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣽⠇⠀⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢀⡀⠀⠀⠀⠦⠹⠴⠋
⠀⠀⠀⠀⢷⡶⠃⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠻⡆⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⣴⡀⠀⠀⠓⠚⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠉⠉⠤⠄⠈⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠟⡆⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⡰⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠐⠂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⢄⣶⣿⣿⣤⣰⣿⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣟⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⣿⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⢀⢀⣀⡀⢀⠀⡀⢀⠀⣀⢀⠀⠤⠄⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⣌⢱⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⡬⣱⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⡅⠄⢉⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⡅⠄⣩⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢰⡗⠞⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣸⡏⠏⠙⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⣠⣰⢂⠀⠀⠀⠀⠀⠀⣤⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣐⡳⠟⠀⠀⠙⠖⠧⠉⠈⠀⠀⠠⢁⢀⣱⢆⡨⠅⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡛⣡⠿⡐⠌⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠧⠈⠝⠋⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠶⠐⠁⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠦⠀⠀⠸⡀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⠃⠀⠲⠂⠀⠀⠤⠆⠰⠂⠀⠀⠀⠀⠀⠀⣚⣃⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡵⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠅⠈⢦⣀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀⠀⠈⠑⠲⣄⣑⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠸⠂⢀⠠⠀⢸⣿⠋⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⣁⡤⢚⣇⡔⢂⣤⠤⠴⣂⣼⠻⣄⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⣸⠀⣠⠞⠉⠀⠀⠈⣦⣀⣴⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⣰⠏⠀⣏⠀⠀⠀⠀⠀⣿⠻⡿⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⣠⠗⠀⠀⢀⣠⠴⠁⠀⢿⡁⢨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⣀⣀⣀⣀⣀⣀⠀⠠⠔⠊⢀⣩⠤⠶⠶⠚⠉⠀⠀⠀⣰⣿⣵⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠻⢄⠀⠉⠀⠀⠀⠀⣠⡤⠞⠉⠀⠀⠀⠀⣠⣴⣶⡾⡿⠿⡿⡿⢊⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠉⠳⠶⠶⠶⣾⣿⣦⣤⣤⣴⣾⣿⠟⠿⠋⠁⠊⣩⢄⣴⣼⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠲⣤⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠠⡠⠀⣀⣀⣧⣶⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⠸⡏⠘⡷⠒⢿⠶⣿⠾⢿⠿⣿⠿⣿⠿⢻⠛⢻⠁⣿⡿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡆⢿⠀⣿⠀⢸⠀⣿⠀⣾⠀⣿⠀⣿⠀⣽⠀⣿⣿⣿⣷⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠐⣸⡇⢸⡆⠸⡇⢸⢄⣻⡀⣹⠀⣿⢰⡿⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⢸⣧⠀⣷⣼⣆⣿⣄⣿⢤⣿⣺⣧⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣟⣾⣿⡐⣿⣿⣇⣿⡽⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣇⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣽⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣵⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢗⡚⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠻⠛⠛⠟⠛⠋⠉⠉⠉⠁



⣿⠿⡿⠿⡿⡟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣛⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠘⢍⡹⠃⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠧
⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣺⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢒⠢⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⠾⠥⠭⣭⣉⡆⠀⠀⠀⠀⠚⠶⠆⠀⠀⠀⠀⠓⢤⣀⣧⡇⠀⡀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢯⡉⢉⠐⠒⠒⠢⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⠁⠀⠀⣠⠤⠞⢧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠜⠉⠁⢀⠤⠼⡆
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⡏⠉⠉⢢⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠳⡤⠊⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇⠀⠀⢸⠁⠀⣰⣷⡀⠀⠸⣷⣀⣠⠼⠁⣀⡀⠀⠀⢻⣆⠀⠀⡜⠀⠀⠀⠀⠈⠲⢤⣀⣠⠏
⠀⠀⠀⢼⠉⠑⠖⠁⠈⡇⠀⠀⠀⣿⠋⠉⠉⡿⠀⢠⡿⠀⣧⠀⠀⣿⠉⠀⠀⣿⠉⠉⢳⡀⠀⢿⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠸⣽⡆
⠀⠀⠀⠈⢦⡀⠀⠀⣠⠃⠀⠀⢰⣿⠀⠀⠀⡇⢀⣿⠋⠉⠹⡄⠀⢿⡄⠀⠀⣿⠀⠀⣠⠇⠀⢈⡿⠀⠀⠀⠀⢏⠓⣹⠂⠀⠀⠈⡆
⠀⠀⣀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠉⠀⠀⠈⠁⠸⠏⠀⠀⠀⢧⠀⠈⠁⠀⠀⣿⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣴⡏⠙⠳⡄⠀⠀⢸⡇⠀⢰⣾⠙⠳⡄⠈⠉⢹⡏⠁⢀⣀⠀⠀⡀⢸⡇⠀⠙⡄⠀⠀⠀⠀⢶⡄⠀⠀⢰⠀⠀⡸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠀⣾⠃⠀⢸⣟⣀⠴⠃⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠸⣷⠀⠀⢹⠀⠀⣀⠀⠘⣷⡀⢠⠇⠀⠀⡇
⠀⠀⠤⣀⡄⠀⢸⣿⠉⠉⠲⡄⠀⣿⠀⠀⢸⡟⠳⣄⠀⠀⠀⣼⡇⠀⣼⡷⠦⢼⠇⠀⣿⠀⢀⡞⠀⣼⠟⡄⠀⠘⣧⡞⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠈⠉⠁⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⠿⠖⠋⠀⣼⠯⠤⡇⠀⠀⢹⡇⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠻⠦⠖⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠻⠀⣠⡀⠀⠀⢴⠏⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦
⠀⠀⠀⠀⠀⣠⡀⠀⣀⡁⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⡞⠳⠊⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠀⠀⠀⡇⠙⡖⠦⣄⡀⠋⠀⠀⠖⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣸⣄⣧⠤⠔⢲⠀⠀⠘⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡀⡇⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡭⠤⠔⠲⣚⣉⠽⡆⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠰⡶⠀⠀⠀⠀⢡⠀⢣⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⠒⠉⠉⠀⠀⣀⣱⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⠀⠀⡧⣤⢤⣖⣲⡭⠿⠽⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠴⠊⠀⠙⠦⣀⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢟⠏⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⢈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⢲⡖⠒⢦⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠃⠀⠘⣦⠤⢤⣀⠤⠤⠼⣄⡤⠦⠤⢄⡠⠦⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡄⠀⢰⡇⢠⠀⢻⠀⠐⠃⢈⡇⠀⠒⠀⡷⣄⠉⢁⡤⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠓⠒⠿⣧⣀⣸⡀⡴⡆⠘⡆⠀⣖⠋⣇⠀⢰⢚⢁⣸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠠⣏⢩⡏⠩⠙⣏⠉⣹⠉⠏⢻⠉⡙⡿⢉⢹⡌⢋⡹⠂
⠀⠀⠀⠀⠀⠀⠀⣇⣀⣘⣠⣏⣨⣇⣀⣸⠜⣆⣿⣰⣆⣼⣀⣡⢇⡴⣄⡿⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠤⠤⠤⣶⣿⣿⣴⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢤⠀⠀⠀⠀⠈⠉⠀⢀⣤⣤⣤⣄⠀⠛⠺⢏⣯⢻⡷⣾⣧⡀⠀⠀⠀⢀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣀⣀⣤⠴⣶⠟⠁⠀⠉⢻⠀⠀⠀⠀⠀⠉⠉⠘⠋⠀⠀⠀⠀⣠⣽⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢡⠞⣁⠀⣏⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⢀⣤⣴⣤⡀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣎⡁⣴⣾⣶⣶⣽⣿⣴⣶⣶⣄⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢯⣾⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠻⣿⡿⠿⠛⢻⠄⠀⠀⠀⠀⠀⣠⠀⠘⣿⣿⡇⠀⢀⣵⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠉⢸⣿⣿⣷⣯⣽⣯⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⣶⣿⣶⣦⠘⠻⠃⢰⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣧⣰⣿⣷⣄⡀⠀⠙⠻⠿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⢁⡄⠀⠘⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣻⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⢰⡄⣶⠀⢠⡀⢰⡖⣤⢰⡀⠀⢰⡒⠀⣄⠀⠐⡖⠂⠀⠀⢰⢏⡏⠀⠀⠀⡼⣼⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠸⠇⠿⠠⠈⠷⠸⠏⠧⠀⠛⠀⠸⠉⠀⠌⠛⠀⠧⠀⠀⢠⡛⡾⠁⣠⣴⢾⣿⡗⣿⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢠⣾⣿⣿⣿⣆⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡀⣠⠀⢠⡀⣄⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⣼⣿⣵⡿⠻⣿⡿⣷⣝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠹⠿⣿⣿⠿⢟⣼⣿⠆⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠈⠷⢸⡇⣿⢀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿⠟⠋⠀⠀⠙⠇⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣡⣤⡌⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⣴⣾⣿⣦⣿⣿⣢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣾⣿⣷⡴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣶⢁⣤⣀⣿⣿⣿⣿⣧⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣮⣿⡿⠆⢺⣿⣿⣿⣿⢿⣿⣸⣿⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡏⣾⣿⣿⣿⣿⣿⡏⡿⣿⣿⠇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣾⣶⡻⡯⠊⠀⣰⠀⠻⢿⣿⡿⠘⠿⢿⢸⢫⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⣈⣿⣿⣿⣿⣟⣡⣿⡿⠁⢀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⢀⠀⠹⡆⠀⠄⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠘⠚⠋⠈⠉⣉⣴⣾⣿⣿⣿⡟⠁⠀⠀⢠⣀⠀⢲⡀⠀⠀⠀⠀⢀⣿⣿⣇⠀⣟⡇⠀⠁⠴⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠋⠀⠀⠙⠠⠀⠀⠀⠜⠳⣂⠀⠀⣠⣾⣿⣿⣿⠀⢱⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⠟⠁⠠⣤⡀⠀⠀⠐⠀⠄⠠⠞⠁⢠⣾⣿⣿⣿⣿⡿⠀⠈⠣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠈⠉⠁⠀⠀⠀⢀⣭⠀⢆⣀⠔⢿⠆⠀⠀⢻⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠤⡄⠀⠀⠀⠆⢀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣀⠀⠉⠀⠁⠭⠘⢠⣦⠂⣤⠀⠁⣠⣤⠄⠰⠆⠰⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣤⠀⠈⢻⠟⠂⠐⠠⣶⡆⢲⡦⣥⡞⢻⠀⠀⠹⠏⠃⠀⣤⠀⠀⠘⠟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡉⠁⢐⠪⠂⠀⢰⠄⢨⣀⡅⠐⣠⠷⢠⣴⠌⣙⡷⠆⠀⠙⡍⡤⡹⠓⠀⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⢆⠎⣆⠀⠴⠀⡀⠀⠀⠐⠃⡂⠳⣸⣛⠒⠘⡆⣸⠁⣠⣾⠄⠈⢁⠀⠇⢀⠀⠙⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⢀⠀⠀⠐⠀⡿⣆⠀⠁⣀⣁⢀⠋⠛⠀⠀⠘⠏⠀⠀⠀⣀⣀⠈⠀⣰⢿⠐⠂⠀⠀⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠄⠀⡡⠑⢀⣀⣤⠇⣘⠛⠋⣿⢋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡙⣿⠛⠛⢃⠸⣤⣀⡀⠊⠄⠀⠠⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⡆⠰⣀⠡⠜⠿⢥⣀⠘⠿⠃⠘⠷⣄⠘⠃⠀⣿⣼⡇⣾⠀⠘⠃⣠⠾⠃⠸⢿⠂⣀⡬⠿⠣⠌⢅⠆⢰⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠄⠀⠈⠁⠃⠀⠀⠶⢹⡇⢰⠋⠓⡚⠛⠛⠀⠀⣯⢹⡇⣿⠀⠀⠙⠛⠓⠒⠙⡆⢸⡏⠶⠀⠠⠀⠈⠁⠀⠨⢠⠁⠀⠈
⠀⠀⠀⠀⣠⡄⠠⠈⠍⡚⠀⠦⠀⠀⠀⠈⢴⠄⣷⠏⢐⡦⠡⠄⠙⠀⠀⣿⢸⡇⣿⠀⠀⠋⠠⠌⢴⡂⠹⣾⠠⡆⠁⠀⠀⠀⠴⠀⢒⠨⠁⠄⢠⡄
⠀⠀⣤⠀⢃⡘⠂⢠⡄⠁⢰⠤⠤⡆⠀⠀⠀⠠⠉⠀⡸⠊⠁⠀⠀⠀⠀⣿⢸⡇⣿⠀⠀⠀⠀⠘⠑⣇⠀⠉⠀⠀⠀⠀⠰⠤⠠⡄⠈⢠⡤⠐⢃⡘⠄⣤
⠀⠀⠀⡙⣈⡁⡁⢠⣤⡀⠴⢵⣢⠥⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠛⠘⠃⠛⠀⠀⡄⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠬⣔⡮⠦⢀⣤⡌⢁⢈⣁⣋
⠀⠀⠀⠉⢁⠙⠇⢈⠁⠀⡀⠀⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣾⣾⣦⣾⣴⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠁⢀⡀⠈⡁⠸⠋⡈⡙
⠀⠀⠀⠈⠶⠆⣳⢉⠾⠅⠤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠿⠿⠿⠿⠿⠿⠿⠾⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠤⠨⡷⠉⣚⠠⠶⠁
⠀⠀⠀⠀⠀⠀⢉⡛⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢰⣄⡀⢀⡀⣠⣤⣠⣦⣄⣄⡀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢛⡉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢿⣭⣿⡿⣿⣿⣿⣟⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⣠⡄⢀⡀⠀⣀⣀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣿⣷⣶⣀⣿⣿⣾⣿⣿⣿⣿⣾⣧⣿⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠘⠾⠋⠟⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢠⣄⢠⠄⡄⡁⡤⡀⢠⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠘⠀⠃⠃⠃⠃⠉⠃⠛⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠙⠳⢦⣤⣀⣀⡀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠞⠛⠛⠛⠛⠛⠉⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠳⢦⣄
⠀⠀⣀⣴⢿⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠉⠻⣦
⢀⣼⠋⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⣹⣷⡄⠀⠀⠀⠀⣴⣶⣄⠀⢀⣴⣦⡀⠀⢀⣴⣦⠀⠀⣠⣶⣄⠀⠀⣴⣶⡄⠀⢀⣴⣦⡀⠀⣠⣶⣦⠀⠀⣠⣶⣄⠀⠀⣠⣿⡅
⢸⡏⠀⠻⣦⡀⣠⡾⠃⠀⠹⣶⠟⠁⠈⠻⣶⠟⠁⠈⢷⡾⠋⠀⠙⢷⡾⠃⠈⠻⣶⠟⠁⠈⢻⡾⠋⠀⠙⢷⡾⠋⠀⠙⣷⠾⠋⠈⣿
⠀⢿⡄⠀⠈⠻⡏⠀⠀⠀⠀⠸⡆⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⢸⠁⠀⠀⠀⣼⠁⠀⠀⢠⡏⠀⠀⣼⠏
⠀⠈⣿⡀⠀⠀⢹⡄⠀⠀⠀⠀⢷⠀⠀⠀⠘⡇⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⠀⢠⡇⠀⠀⠀⣼⠁⠀⣰⡏
⠀⠀⠘⣷⡀⠀⠀⢳⡀⠀⠀⠀⠸⡇⠀⠀⠀⢷⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⠀⣸⠃⠀⠀⠀⡼⠀⠀⠀⢠⡇⠀⣰⡟
⠀⠀⠀⠘⣧⠀⠀⠈⣧⠀⠀⠀⠀⢻⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⡏⠀⠀⢀⡟⠀⠀⠀⢰⠇⠀⠀⠀⡾⠀⢰⡟
⠀⠀⠀⠀⠹⣇⠀⠀⠘⣇⠀⠀⠀⠈⣇⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⢸⠃⠀⠀⠀⡾⠀⠀⠀⢰⠃⢠⡟
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠹⡄⠀⠀⠀⢹⡀⠀⠀⢿⠀⠀⡇⠀⠀⠀⢸⡇⠀⣾⠀⠀⠀⡟⠀⠀⠀⢸⠇⠀⠀⢀⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢹⡀⠀⠀⠀⣧⠀⠀⢸⡄⠀⡇⠀⠀⠀⢸⠇⢀⡇⠀⠀⢸⠃⠀⠀⠀⡟⠀⠀⠀⣸⢃⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⢷⠀⠀⠀⢸⡆⠀⠘⣇⠀⡇⠀⠀⠀⢸⠇⢸⠁⠀⠀⡟⠀⠀⠀⢸⠃⠀⠀⢠⣏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣬⣧⠀⠀⠀⢷⠀⠀⢿⠀⡇⠀⠀⠀⢸⠃⡿⠀⠀⢸⠃⠀⠀⢀⡟⢀⣠⡴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣼⣆⣀⣸⡆⡇⠀⠀⠀⢸⢠⡇⠀⠀⣟⣀⣤⣤⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡢⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡉⡅⠀⠀⠀⠀⠈⠗⠑
⠀⠀⠀⠀⠀⠀⠀⠸⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠐⠤⠀⠀⠀⠁⠀⠑⠀⠐
⠀⠀⢀⠀⢀⠀⠐⠖⠒⠂⠀⡄⠀⡀⠀⠀⠀⠀⠀⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢴
⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠊⠠⠀⣾⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠀⠖⠀⠠⠒⠓⠀⠈⠢⡀⠀⠀⠀⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣀⡴⠇⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠄
⠀⠀⠐⠀⠈⠂⢀⠀⠰⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠐⢁⡄
⢠⠠⣂⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠼⢁⠈⠀⠀⠀⢨⠀⠀⠉⠀⠀⠂
⠈⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠢⠶⣥⠀⠀⠄⢺⠛⠋⠀⠀⠐⠀⠻⢯⣚⠏⠈⣡⣖⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠕⠀⠀⠉⠉⠀⠀⠑⣬⣭⠤⡠⠈⠁⠉⢛⠓⠤⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠀⠐⠂⠀⠔⠀⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠈⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠂⢄⡄⠀⠉⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠴⠀⠄⠈⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⣉⢨⢁⣀⡀⠀⠘⠄⠀⠀⠀⠌⠀⠀⡃⡆⠀⠠⠀⠐⠀⢒
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⠀⠀⠂⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢁⠈⢔⢤⠀⠐
⠀⠀⠀⠀⠀⢁⡹⠈⠉⠁⠠⣹⠀⠀⠉⠀⠈⡀⣄⡀⠀⠀⢀⡨⢃⠇⡈⠛⠛⠀⠀⠁⠐⠊⠀⠠⡀⠆
⠀⠀⠈⠀⠀⢒⠀⣄⠀⠀⠀⠚⠀⠀⠀⠠⢚⠧⠀⠣⠤⠦⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠅⠀⠁
⠀⠀⠀⠈⠀⠀⠡⠌⠄⠂⠁⠀⠀⠀⠄⠁⢠⡤⠟⠒⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠄⠠⠠⠤⠀⢀
⠀⢀⣰⣶⣟⠲⢶⢖⠳⣘⣫⣶⠿⠿⠞⠛⢓⢹⠄⠂⡈⣡⢰⣺⣦⣷⣠⡄⠒⠚⠚⠇⡴⡂⢄⣃⣀⡀⢀
⠀⣠⡼⢖⣀⣤⣯⣥⠴⠂⣿⠃⠀⣀⠀⣄⣾⢻⠀⣀⠝⠨⠧⢸⡽⣏⠉⠳⢄⣄⣤⢤⡀⣤⣴⣛⣃⢼⣌⡙⣤
⢀⠏⡀⠈⠁⢈⢇⣘⣆⢀⡼⡆⠒⠉⢣⣀⢯⡘⡆⠀⠠⠤⠀⠈⢃⡷⠲⠆⠀⠀⠐⠊⠏⠁⠀⠉⠹⡀⠀⢈⣛⠁
⠊⢿⡾⠠⣿⣾⣹⡽⣝⢧⣀⣈⣀⠀⣉⡠⠀⠘⣇⠀⠐⢠⣯⠴⣟⢲⣄⢀⣐⣆⡀⢀⠶⠂⠈⠛⠂⠀⠃⣀⠉
⠀⢀⠇⠀⠀⡞⡩⠙⣶⡾⠟⠛⠻⡛⠻⣟⡣⢾⣿⣭⣶⣿⠋⠛⠉⣠⣟⠦⢌⠿⣻⣿⣾⠛⡯⡀⠠⠂⠀⠀⢀
⠀⢨⠔⠊⡰⣠⠇⢡⣿⠷⣶⡶⠀⠹⢷⡟⠙⠷⢼⣮⢻⣻⣧⠄⠞⢻⣯⣿⣃⣼⠇⠀⠈⠛⣧⣼⡁⠀⠀⠀⢨⢰⡀
⠰⠖⠶⠂⠤⠀⠀⠈⣩⡗⠈⠀⢴⡄⠀⡓⢊⠒⠶⠶⣾⡽⡈⠋⣄⣀⡏⣩⣷⡋⠀⢀⣀⣀⢸⣿⣖⡆⢸⣄⠱⣣⠂
⠀⠰⠀⠀⢘⠄⠀⠀⠀⠱⢤⣀⠤⡄⣰⡀⠙⢂⠀⠀⢪⡄⠇⡠⡤⠀⣤⢸⡂⠛⠃⢀⠁⢉⠾⣟⣿⠇⠀⠈⣄⠉
⠀⠃⣈⠉⠩⠓⠒⢲⡞⢁⠘⢿⣟⣻⠷⠖⢶⣿⣦⣐⣿⣧⣤⣀⢀⡼⠗⠛⠗⠢⡄⠛⠋⠜⠃⣁⣀⡀⠀⣀⡄⢀
⠀⢶⠉⡚⡶⠞⠶⡖⡽⠎⠃⠼⢸⣵⠴⠚⠛⠛⠿⢏⡙⠛⡛⠛⣻⠆⠀⠀⠀⠀⠙⢶⣵⣧⣼⡿⣭⣙⢷⣄⣀⠆⣃
⠀⠈⢻⠉⠀⠀⠃⠞⠀⠀⠀⠀⢈⢻⣾⣷⠄⠺⣿⡆⣿⡇⠉⣉⣿⠆⠂⠰⠶⠈⠐⢀⣏⣽⠻⠋⣹⡛⠿⠻⡆⠀⣹
⠀⠀⢩⠁⠀⠀⠀⠀⣀⡀⡵⠖⣶⠞⣇⠀⢀⣀⠀⢀⡋⠀⠘⠛⠣⡄⠷⠀⠀⠀⠀⠊⠉⠈⡆⣀⣭⣩⠀⠜⠀⠙⠃
⠀⠀⢨⡇⠤⢖⠨⠱⢠⠀⠀⠀⠀⠀⣨⣁⠠⣠⠀⡈⠀⠀⠀⠀⣰⣬⠀⠂⢀⠀⠀⠀⠀⠀⣙⢏⣁⠤⠀⠰
⠀⠀⣚⠦⣿⡴⣴⠂⠟⠀⠸⠁⠀⠀⣸⣭⠓⠻⢺⣾⡃⢤⢠⢤⣼⣿⣲⢶⠃⠘⠿⠗⢀⣶⠳⠾⠲⣄⠀⠒⠿⢻
⠀⠀⠀⡞⢿⣠⣤⠠⠒⠓⡆⠈⠀⣜⢟⣁⡈⠚⠓⢋⣷⠻⠇⡆⠨⡿⢿⠀⠀⠀⠀⠀⠀⣹⠈⠁⠰⠟⠛⡖⣺⣿⢧
⠀⠀⠀⢀⠈⠎⠘⢲⣥⠀⢈⢶⣺⢶⠊⠛⡛⡁⠸⡈⢻⠀⠀⠓⠼⠀⢸⡏⣡⠶⠄⠤⣸⠛⠟⢀⡄⠀⠀⢰⠿⠛⠈
⠀⠀⠀⠉⢠⡔⠓⠂⣶⠒⡡⡶⠀⠛⠀⠀⢀⡁⠀⢉⢠⠀⠀⠚⠻⢂⡞⠼⢿⡷⢶⣟⡹⢠⡀⠀⠀⠊⡠⠀⠆⠄
⠀⠀⠀⠀⠠⠱⡤⠀⠄⠀⡄⠀⠉⣥⠀⡠⢬⣁⣀⡠⠈⠀⠀⠤⠀⠈⠊⠉⠸⠉⠓⠛⠀⠀⠘⠃⠄⠀⠐⠈

⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⣻⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣟
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠠⠆⠈⢱⠌⠁⠦⠄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠞⢩⢋⡜⠀⡀⠀⠀⣀⣠⠀⣀⣠⢀⠀⠀⠀⠀⠀⢀⣼⡡⠃⢀⠃⣀⣀⣠⠇⣰⣁⠀⠀⢠⠃⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠈⠋⠸⠁⠸⠅⠧⢰⠃⠜⢰⠃⠜⠸⢆⡇⠀⠀⠀⣺⠅⢸⠇⠶⠀⠃⠀⠦⠀⠏⠸⠰⠄⠻⠀⠯⠸⠄⠷⣺⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠇⠀⠀⠾⠔⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣭⣽⣽⣯⣿⣭⣭⣯⣬⣭⣦⣭⣿⣭⣵⣾⣧⣭⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠦⢀⠲⠆⡀⠶⠂⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣽⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣯
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠐⠊⠱⡀
⠀⡆⠀⠀⠀⠀⠀⠉⠁⠒⠂⠠⠴⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠐⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠈⢢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡠⠐⠺⠁
⠀⠀⠀⢡⠀⢹⠒⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⠂⠂⠩⠀⠀⡇
⠀⠀⠀⡿⡰⡀⡇⠀⠀⠀⠀⠀⠉⠐⠀⡄⠀⠀⢢⡀⠀⢠⡀⠀⠀⠀⠀⢀⠊⠱⠀⠀⠁⠀⠀⣦⣆⡇
⠀⠀⠠⠟⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢣⡀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠘⠎⠙
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠒⠄⠀⢸⠀⣠⠐⠆⠲⠈⠦⡀⠰⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⡠⠒⠈⠉⠐⠠⡙⢠⠀⠀⠐⠂⠤⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢀⠇⠌⠀⠀⠀⠀⠀⠀⠈⠾⠁⠀⠀⠀⠀⠈⠆⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠑⠀⠀⠀⠀⡠⢘⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠁⡈⠛⠉⠉⠉⠋⡠⠅⠀⠀⠀⠀⡠⠊⠀⠀⣀⡴⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡎⠀⢠⠆⣤⣒⣫⠐⢒⣄⡀⡁⠀⠑⠊⠉⡀
⠂⠈⠁⠈⠑⢤⡀⠃⠀⠀⠘⠗⢀⠀⠀⠀⡀⠈⠁⠀⠀⠈⠑⠢⢄⠧⠘⠎⠒⠋⠀⠙⠇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⠀⡆⠰⠀⠒⠳⠓⣺⠀⠂⣀⠄⠀⠀⠀⠈⠂⠠⠏⣀⣀⠀⡖⠴⢀⢀⢠⠂⠈⣄⣄
⠀⠀⠀⠀⠀⠀⠘⢰⠀⢄⠀⠀⠀⠀⠠⠚⠁⠀⠐⠀⠀⠐⠂⠀⠂⠀⠀⠉⢛⠩⣟⠛⢍⣾⠛⠲⡔⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠘⠀⠀⠀⠀⠠⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢁⠀⠐⣇⡔⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠉⢄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢘⡀⠀⠀⠁⠂⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⡈⠢⠈⠑⠢⠄⣀⠀⠀⠀⠀⣀⠠⠀⠀⣀⠔⠀⠈⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠱⠖⠂⠤⠭⠭⠤⠄⠐⠐⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⣀⠀⠤⠐⠒⠐⠈⠉⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢠
⠤⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣴⠀⠀⠰⠁⠀⠀⠐⢀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠉⢦⡀⠀⠀⢡
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠐⠊⠁⠀⠀⠉⠃⠐⠃⠀⠀⠀⠀⠀⠀⠄

⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⢄⠀⠀⠀⠀⠀⣦⣄⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⡇⠀⠀⠀⠀⢀⣼⡃⢝⠛⠀⠀⠀⠀⣤⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡇⠀⠀⠀⠘⠁⠀⠀⠀⠀⣠⠯⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣼⠀⠀⠀⠀⠀⠀⠀⢀⠼⢇⠳⠞⠀⠀⢀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠿⠐⠶⠁⠀⠀⠀⢂⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡞⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⡉⠀⠀⠘⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠞⠻⠏⠀⠀⠀⠀⠀⠣⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣸⠣⠀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠓⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠳⢸⣶⠄⠀⠀⠈⠑⠄⢀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢄⠀⠀⠙⠁⠈⡂⠀⠀⠀⣀⣀⠈⠷⣰⠶⠃⠀⠀⠀⠀⠀⠀⠛⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠈⠢⡀⠈⠒⠒⠣⣀⡠⠀⠻⢸⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣴⡟⠫⣲⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⢀⣾⣦⡀⠀⠀⠈⠳⢸⠶⠃⠀⠀⠀⡠⠠⢄⠀⠀⠀⠀⠀⢠⡞⠣⣰⡿⠀⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⢀⣴⣿⣿⣿⣿⡦⡀⠺⠟⠑⢄⠀⠀⠀⠀⢄⠀⡠⠀⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠈⠂⣄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⣾⡟⠀⢠⣾⣿⣿⡿⠋⠀⠀⢀⣠⣴⣾⣿⣿⡶⠖
⠀⠀⠀⠀⠀⣼⠟⢀⣴⣿⣿⠟⠁⠀⣀⣤⣾⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣰⠏⣠⣾⡿⠋⣀⣤⣶⡿⠿⠛⠉⠁
⠀⠀⠀⢠⣏⣾⢟⣩⣴⠾⠛⠋⠁
⠀⠀⢀⣿⠿⠛⠋⠁


⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣟⠿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⠙⣏⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠈⠀⣠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣄⠈⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢂⡤⢈⣟⣿⡃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠰⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢁⡀⠑⠀⠲⢀⣀⡀⠀⣀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⣕⠈⠘⠃⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠈⣠⠀⠾⠂⠀⢴⠗⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠘⠃⣠⡀⠂⠀⣴⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠛⠃⣨⡀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⠙⠁⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣍⠕
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠻⠉⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠰⡿⠀⠀⠀⠈⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⢀⠀⠀⣶⣶⠄⠀⠀⠻⠿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⠋⠀⠈⠛⠀⠀⠙⠁
⠀⠀⠀⠈⠛⠛⠛⠶⠞⠳⡶⠟⠶⠖⠲⠞⠁⠀⠀⠀⠀⠔⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠄⠊⡁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠁⢀⣀⠤⠔⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⠃⢉⡠⠄⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⣿⢿⠿⠿⢿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠸⠀⠁⠈⠀⠀⠀⠀⠡⠀⠀⠀⠀⢠⠃⠀⠄
⠀⠀⠀⢠⣄⣀⠀⢪⣩⣆⢠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⡇⠰⠀⠀⠀⠐⠀⡔⠀⠁⠀⡁⠀⠆
⠀⣀⠐⢦⡀⠙⣷⣘⢳⠏⢰⢀⠏⠰⠀⠀⠀⠀⠀⡔⠡⡐⢤⠤⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⠀⠀⠈
⠀⠸⣆⠀⠙⠄⠈⣿⢼⠇⠰⣎⡴⠓⠄⢀⢔⣤⡞⠀⢀⠇⠈⡆⢠⠔⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠈⠑⢄⢸⣆⢻⣶⡆⠐⣽⠁⠀⠀⢈⠘⣿⡇⠀⢨⡆⠀⢿⢀⡟⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⢦⠻⡈⣻⢃⢣⡏⠀⠀⠀⠀⠄⠻⣷⡄⠸⣆⣀⡞⣼⢁⠇⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⡄⠀⣄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠣⣷⣿⣾⠋⠀⠀⠀⠀⠀⠀⠣⠼⡿⠿⠋⠜⡿⠑⠁⠀⠀⠀⠀⠀⠀⠈⠯⣤⠀⢳⠆⠀⢰⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⠘⠀⠀⠀⠀⠀⠀⡴⠒⠂⣴⠶⢄⡀⢳⣼⣇⣼⣿⠷⠚⠃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠑⣄⡀⠈⠷⣇⡙⢶⣍⢯⠉⣤⣤⡶⠿⢛⡋⡳
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢀⠀⠹⢦⣦⡭⣷⣶⠽⠷⠦⣤⠤⡤⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣉⣀⣀⣑⣀⣐⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⣟⡛⢻⡟⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣾⣿⡴⠂⠲⣾⣿⣼⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢿⡀⣀⠀⠀⠀⠀⠀⠀⢠⡈⣿⠁⣼⣏⢹⣟⣿⢉⣿⡄⢹⡏⣠⠀⠀⠀⠀⠀⠀⢀⡀⣸⠿⡁
⠀⠀⢻⢷⣄⢠⣤⡀⠀⠈⠀⣝⣿⠂⡀⠀⠀⢠⡀⢸⣷⢷⡉⢿⡟⢙⡋⣃⠙⣿⠏⣱⢷⣿⠀⣠⠀⠀⠀⡀⢾⣟⡅⠈⠀⠀⣠⣤⢀⣴⢿⠃
⠀⠀⢈⠢⣻⡆⢎⠻⡆⢶⣦⡀⢈⣿⡁⠀⠀⢸⡇⣸⣷⣿⡿⢶⠜⣿⣻⣿⡟⢶⠶⣿⣷⣿⡀⣿⠀⠀⠀⣹⢏⠀⣠⣶⠆⣾⢋⠆⣾⡣⢊
⠴⣛⣛⠙⠃⢙⣿⠷⣻⣔⣜⣿⠈⠁⡳⣜⡆⠀⢹⠟⣫⣥⠉⣀⣁⠻⢇⣹⢃⣁⡈⢡⣭⡛⢿⠁⠀⡞⡴⡃⠉⢸⣟⣄⣼⠷⢿⣟⠁⠛⢙⣛⡷
⠀⠀⠀⠀⣶⠟⠋⢀⣤⣿⠋⠙⣶⣄⡉⠻⡇⠀⠏⠀⠼⢋⣶⡽⠏⠠⡤⡥⠉⠿⣱⣏⠻⠄⠈⠇⠀⡿⠋⢁⣴⡞⠍⢻⣦⣄⠈⠛⢧⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠛⠉⠀⠀⠁⠳⠌⠀⠀⠀⠸⠃⠁⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠀⠈⠴⠃⠁⠀⠈⠙⠓⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⢰⠠⠁⠀⡀⠰⢀⠀⠀⢀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠨⠸⢰⠡⢊⠡⠂⠁⡇⠀⠀⠀⠸⠀⠇⠄⠁⠄⠰⠀⠠⠘⠈⠘⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠐⠦⣤⣄⠛⠳⣦⣀⠠⠔⡟⠑⠀⠀⣀⢸⣧⡆⠀⢀⡀⣀⠀⠀⣦⣿⠀⡀⠀⠐⠙⠂⠀⢀⣠⠶⠛⢃⡤⡴⠖⠀⢀⡄
⣀⣀⢀⡀⢋⠻⣦⡀⣨⣽⣷⣾⠋⠀⠶⡾⠇⠀⢧⡀⢽⣧⠍⡾⠧⢌⡭⣉⠤⠿⡎⢥⣿⠅⣠⠇⠀⡿⡶⠆⠈⢻⣶⣿⣭⠄⣠⡾⢋⠁⣀⣀⣀
⠉⠓⠶⠾⣖⡴⢻⢋⡟⢠⣴⡟⢠⣢⠎⠑⠁⢀⡞⣿⣶⣯⣴⢀⠄⣿⣤⢿⡖⣄⢰⣬⣵⣾⡟⣆⠀⠑⠉⢦⣠⠘⣷⣄⠸⣏⢻⠳⣔⡾⠶⠖⠋
⠀⠀⢠⣫⣾⢣⣥⡿⠁⠛⠉⣤⣤⠻⠆⠀⠀⢸⡇⢸⣏⣿⡟⣫⡝⠿⠟⠾⠟⣭⡛⣿⣏⣿⠀⣿⠀⠀⠀⠾⢣⣤⡌⠙⠃⠹⣧⣧⢻⣮⣣
⠀⠀⠿⠋⠁⠈⠀⠀⠀⡠⢠⡔⠯⠃⠀⠀⠀⠈⠀⢸⠏⣏⠶⣿⡿⢦⣶⣴⠾⣿⡷⢎⡏⢿⠀⠈⠀⠀⠀⠀⠫⠗⣤⠠⡀⠀⠀⠉⠀⠙⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠄⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⣦⣹⣧⣼⣿⣾⣤⣺⣡⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣷⣿⣿⣍⠉⢈⣽⣿⣶⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣿⡉⠀⠈⣹⡿⠙⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣧⣤⣤⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢰⢲⠀⠀⡠⠀⠈⠀⠀⠀⠸⣉⡝⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⢿⠁⠀⠀⠀⠆⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠰⠤⠜⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠋⠈⠀⠀⣠⠾⠭⣙⡆⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢍⣑⡲⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡠⠖⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⡉⠑⠒⠤⠭⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⢀⡞⠂⢦⣀⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢸⠀⢦⡀⠉⠙⠆⡼
⠀⠸⡀⠀⠈⠉⢓⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠗
⠀⠀⠱⣤⠤⠒⠁
⠀⠀⢺⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡎⠀⡀
⠀⠀⡅⠘⡝⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠴
⠀⠀⢱⠀⠈⠁
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠑⠊⠈⡇
⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡠⣄
⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠀⠠⠦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢑⡠⢴⠎⢹⠁⢸
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⣐⠚⣚⠓⣒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠈⠲⣼⠀⢸⠀⡘⠀⢴⡄
⠀⠀⠈⠉⠃⠀⡀⢀⡀⠀⠀⡖⠒⠤⠭⠤⠭⠤⢩⡇⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣎⠀⡟
⠀⠀⠀⠀⠀⢺⠈⢁⡇⠀⢀⢇⡠⢤⠄⣀⣀⣀⣀⣅⠀⠀⠀⠁⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⡠⢶⢶⠉⠁⠀⠀⠀⠈⠑⢧⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠑⠋⠀⠀⠈⠉⠉⠉⠐⠋⠚⠓⠛⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⣶⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣶⣿⣿⣿⠟⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⡟⠿⠟⠋⠀⠀⠀⣠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⣽⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⠶⣶⣶⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢾⡿⠋⠉⣲⣄⠀⠀⠀⣰⠃⠀⠀⣀⣴⣿⣿⣧⢀⣀⣤⣾⣿⣿⠟⠁⣾⣀⠀⠀⠀⠐⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣀⠀⠀⠀⠈⠛⠳⡄⠀⣷⣶⣾⣿⣿⣿⠟⠋⠀⠙⢿⡿⠟⠉⠀⢀⡜⢻⡿⠂⠀⣠⣄⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢽⣿⠆⠀⢰⣿⣦⠀⢻⠀⣿⡿⠛⠋⠁⠀⠀⠀⢀⣴⣿⠀⠀⠦⣶⣯⡀⠀⢀⡀⠀⢿⣿⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⢠⡄⠈⠛⠋⠀⢈⡆⢡⠀⠀⠀⠀⢀⣤⣾⣿⡿⡟⠀⣠⠀⠙⣿⡇⠀⠈⠁⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠈⠁⠀⠀⠀⠐⣿⡇⠀⠣⣤⣶⣾⣿⣿⠟⠋⣰⠁⠀⠀⠈⠀⠉⡀⠀⠀⣶⣦⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠀⠀⠐⣿⡇⠀⠀⣠⠇⠀⠀⠙⠻⠛⠉⠀⢀⡴⠃⠀⠀⢀⠃⠀⠀⠑⠀⠀⠙⠋⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⣀⣀⡀⢀⠟⠀⠀⠀⠀⠀⠀⠙⢚⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⢷⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⠀⠀⣀⠀⠀⢸⡇⠀⠀⣾⠁⣄⢀⡤⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣿⢸⡇⣸⠇⣾⠁⣾⠃⣸⢶⣿⢀⡿⠸⣇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⡇⠹⠄⢻⡀⣿⠀⠟⢸⡇⠈⠀⠀⠀⠈⣷⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠈⢧⠀⢠⡀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠀⠀⠀⠀⠀⠇⠀⠙⠀⠀⣼⠁⠀⠀⠀⠀⢰⠇⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠁⠀⠀⠹⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡞⠀⠂⠀⠀⣤⠀⠀⣴⠋⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢸⡇⠀⠀⢀⠀⢼⠅⠀⠄⠀⢸⡇⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⢸⡇⠀⠀⠂⠀⠘⣇⠀⣀⠀⣸⠃⠀⣿⠀⢠⡀⠀⠀⡀⢰⡟⠀⢀⡀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠅⠀⠈⣷⠀⢀⠀⢠⡆⠀⢁⡟⠀⣿⠀⠀⣿⠀⢸⡇⠀⡾⠁⣸⠇⢰⠏⢰⡏⢰⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡄⠈⣧⢸⡇⠀⢸⡇⠀⢻⡀⠐⣿⠀⢸⡇⢸⡇⠀⣿⠀⢿⡀⢺⡅⠻⠅⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠃⢰⡟⠈⠓⠀⠈⠧⠀⠈⠧⠀⠙⠀⢸⡇⠈⠓⢀⠹⣎⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠙⣶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠓⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁




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

⠀⠀⡸⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠌⠻⡄
⠀⢠⠁⠀⠀⠀⠀⠛⠀⠶⠒⠢⠤⠄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⡤⠤⣀⡠⠶⠶⠄⠘⠒⠂⠈⠁⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠺⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡕
⠀⠀⠈⢷⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⠹
⠀⠀⠀⠈⣡⠀⠈⠻⠒⠤⠄⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⣀⠤⠒⠊⢻⠀⠀⠸⠇
⠀⠀⠀⠀⣿⠀⡀⠀⡇⠀⠀⠀⠀⠉⠁⠐⠒⠠⠤⠂⡈⠀⠀⠂⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠢⠈⠀⠠⠀⠀⠀⢈⡀⣀⢀⡇
⠀⠀⠀⠀⢟⣤⠛⡄⡃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⠈⠶⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣠⠂⠀⠘⠀⠀⠀⠀⠀⠀⠈⢿⡛⣼⡇
⠀⠀⠀⠸⠏⠁⠀⠵⠁⠀⠀⠀⠀⠀⠔⠂⠀⠉⠂⢰⠂⠀⠀⠀⠀⠄⠑⣄⠐⠈⢧⡀⠀⠀⣠⠞⠁⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠃⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠲⢄⠀⠀⢸⠆⠀⣀⠠⣄⠤⣆⠈⣧⡀⠀⣩⠂⠉⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠱⡀⢸⡤⠞⢁⣠⡤⠄⠤⡄⣉⠚⣆⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢁⡜⢁⠔⠉⠀⠀⠀⠀⠀⠈⠳⡄⢶⡠⠚⠀⠁⠀⠉⠙⢦⡀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⡆⡸⠀⠀⠄⠀⠀⠉⠁⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢼⠁⠑⢆⠀⢳⣶⡶⠶⠶⠶⣿⠃⢠⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⣤⣀⠚⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠑⢄⡁⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⡴⠟⢫⠿⢣⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡂⠀⠀⠀⣏⠀⠀⠰⠆⠴⣐⢪⣍⠊⠁⢐⣦⣀⠀⠀⠀⠁⠘⠂⠀⠉
⠀⠐⠂⠈⠉⠐⠢⣀⠀⠰⠀⠀⠀⠀⢪⡗⢄⠀⠀⠀⠀⢀⡀⠜⠑⠀⠀⠀⠂⠓⠶⠤⡀⢰⡦⠴⡦⢣⠴⠋⠁⠈⢳⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⣠⢤⡤⢤⣨⣆⠣⣄⣤⠄⢋⠀⠀⠀⠰⢀⠀⠀⡀⠆⡀⠈⢣⡴⠀⠀⠀⡠⣀⢀⡤⠚⠀⡅⢀⠠⠤⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠈⠁⠁⡾⢂⣠⠀⠐⢋⠂⠈⠉⠀⡉⠀⠉⠉⠎⢰⠴⣤⣆⣸⢅⣈⣥⣚⣤⠐⣋⣀⠀⠾⠐⣦⠰
⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇⡲⠀⠰⣀⠀⡀⠆⠀⠀⠰⠙⠃⠀⠀⠈⠁⠀⠀⠈⠛⠀⠀⠃⠀⠀⠀⠀⠹⠁⠠⢷⣉⡩⢆⣭⡍⠙⠻⣶⠁⢀⠤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⠤⠩⠀⠀⠀⠈⠁⠀⢂⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡀⠁⠉⠈⢱⠀⠰⢷⡀⠰⠯⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣄⡀⠈⠀⠤⠀⠘⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡭⠑⠢⠤⢺⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠠⠖⢂⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⢢⡀⠈⠲⠇⢀⡀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢁⠀⠀⡇⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢠⣅⡀⠠⠀⠀⠁⠂⠢⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠀⡇⠑⢄⠈⠑⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⢀⡴⠃⠈⠉⠒⠤⣀⠀⠂⠄⠐⢀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠠⢄⣀⣉⠁⠒⠒⠒⠒⠒⠉⢉⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⣼⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠋⠉⠉⠉⠀⠨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠦⠐⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣀⡀⠤⠔⠒⠈⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀⡀⢀⡀⠀⠀⠀⡰⠀⠀⠈⠢⡀⠀⠀⢀⡀⠀⠀⠀⠰⣀⡠⠎
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⣸⡇⠈⠈⠈⠁⢄⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠁⠙⢆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠈
⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠘⠣⠦⠄⠊⠀⠀⠀⠀⠙⠲⠴⠄⠋⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶
⣿⣭⣭⣽⣭⣭⣭⣬⣍⣿⣩⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣮⣧⣼⣿⣿⣧⣽⣿⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⣂⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣣⣾⣀⣴⡅
⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⢀⠆
⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⡻⣿⣿⣿⣿⣿⡶⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢟⣽⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⡎⡻⣿⣿⣿⣶⣶⠶⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⢿⣿⣿⣿⠿⣿⣿⣷⢸⣿⣿⣿⣷⡝⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⣿⠏⠀⣸⣿⡿⣼⣿⣿⣿⣛⣋⣈⢻⡿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡷⢠⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣧⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⢀⣤⣤⢄⣀⣈⠉⠁⣰⣾⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣄
⠀⠀⢀⣠⣴⣾⣿⡟⢫⣍⣙⣿⢿⣿⣿⣷⡼⠛⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣟⣿⣍⠛⢻⣿⢿⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⢠⣾⣿⡟⠉⠀⣼⣿⣿⣿⠿⢿⣷⣾⣭⣭⣥⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣮⢻⡆⠊⠙⠀⠀⡿⠸⢹⣿⣿⡿⣿⣿⢻⣿⣿⣿
⢻⣿⣯⠁⣠⣾⣿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⠀⠀⠀⠜⠁⠤⠟⣿⣿⡇⣿⡏⣼⣿⣿⣿
⡞⢡⡟⢠⡛⢻⣿⠆⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⢹⡿⣿⢠⡿⢹⡏⠁
⠻⠞⠀⠀⢹⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠩⣿⣿⣿⣎⠻⡼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠃⠑⠝⠦⠓⠈⠷⠄
⠀⠀⠀⠀⢸⡋⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣶⡶⢦
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣷⣯⣿⣿⠿⢿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣧⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣀⠈⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡷⡏⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⡗⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⡏⢸⠹⠿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠐
⠀⠀⠀⠀⠀⠠⠌⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠀⠀⠀⠂⠀⠀⠀⠀⠰⠁⠀⠀⠂⠀⠀⠀⠀⢀⠃⠀⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠐⢦⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⡃⢀⡴⠀⠀⠀⢀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠠⠄⢐⢄⠀⠑⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠠⠄⠀⠀⢂⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠢⢀⡀⠒⠠⠊⢊⠳⠦⠕⣇⠛⠰⠀⠀⠀⠀⠄⠛⢈⠠⠴⠚⡓⠑⠄⠒⢁⡀⠔⢀⡀
⠀⠀⠀⠀⠰⠏⠙⠃⠉⠄⢠⠈⠖⠀⠀⠀⠀⠠⣞⢆⠀⡄⠀⠀⠈⠀⠐⣣⠄⠀⠀⢀⠀⠰⠂⣈⠠⠙⠴⠋⠽⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡀⠢⠑⠲⠁⠀⢀⠀⠣⡀⠂⠀⠀⠀⠀⠐⢀⠜⠠⠌⠔⠉⠖⢊⠔⣀⠠⣤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠋⠃⠈⠉⠀⠀⠐⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠢⠀⠀⠙⠃⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠘⠀⠆⠀⠐⠀⠁⠀⠀⠀⠀⠃⠀⠱⠀⠃⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⢠⣤⡤⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⢠⣐⠀⠀⠀⠀⢀⠀⠠⠀⡤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠤⠀⠀⠄
⠀⠃⠐⠀⢈⢈⠀⠈⠀⠀⠐⠄⠋⠈⢀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣞⣉⡛⠀⠘⡅⠀⠀⡀⠀⠀⠀⠐⠀⡀⠀⠀⣀⠀⢄⠀⠀⠄⠄⠀⠀⠀⢈⠀⠆
⠀⠠⠀⠀⠀⢂⠀⠀⠀⠀⡀⠠⡀⠡⢤⠄⠀⣀⠀⠉⠀⠀⠀⠀⠈⣴⠧⢈⠙⡃⠀⠈⠀⢀⠀⠀⠀⠠⠈⡄⠀⢠⠂⠁⠀⡠⠰⡄⠀⠀⣀⢀⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠈⠉⡄⠀⢀⠀⠀⠀⠀⠀⠀⠐⠮⡈⠐⢩⠀⠘⠀⠁⠀⠀⣀⠀⠀⡀⠀⡀⠀⠆⠁⣘⠃⡀⠁⡘⠀⡅⠀⠁⡄⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡀⠈⡀⠈⠀⠠⠀⠀⠀⣀⢀⡀⠀⠇⠀⠄⡀⠘⡀⠀⠠⠐⠀⠁⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠂⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠅⠐⠀⠀⣀⠀⠀⠉⢀⠀⠀⠀⠦⠠⢠⠄⠀⠀⠂⠀⠠⠈⠀⠀⠀⢁⠀⠀⡠⠀⡀
⠀⠁⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣇⠎⠀⢀⠀⠀⠠⠀⡀⠀⠀⡀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠈⣁⣀⣠⣀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠈⠄⢀⡀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢄⡠⣦⠀⠄⠢⠁⠀⠀⠤⠄⠸⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠄
⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠁⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢲⠀⢲⠀⡠⢤⡀⢀⣀⣀⠀⣀⣀⡀⢀⡀⠀⡀⠀⠀⢶⠖⢲⠀⣝⠀⣀⣀⡀⠴⣷⠄⢹⣀⡀⠀⢀⡀⣿⣠⢤⡄⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠛⢻⠀⡔⠚⣗⢸⠋⢙⡇⣿⠉⣻⠈⢧⣠⠏⠀⠀⠘⠗⠛⡄⣸⠀⣿⠉⠉⠀⡇⠀⢸⠉⢹⠴⠋⢉⡏⣰⠒⢿⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠀⠛⠀⠈⠃⠙⠋⠙⢸⡟⠋⠀⣿⠛⠁⢠⣨⠏⠀⠀⠀⠘⠓⠀⠁⠛⠁⠛⠀⠀⠀⠙⠃⠙⠀⠘⠃⠑⠋⠓⠈⠛⠉⠃⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⢰⡦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠊⠀⠀⢀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠠⠈⠀⠀⠆⠑⠀⢀⠀⠀⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠈
⠀⠀⢂⠀⠀⠤⠐⠀⠀⠀⠀⠀⠋⠰⢄⠀⠙⠀⠀⠀⠀⠂⢀⠀⠀⡀⠀⠀⠒⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⢰⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⡀⠀⠁⠐⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⠢⠑⠤⢀⣀⡀⠐⠁
⠀⠃⠀⠀⣉⢘⠁⠀⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢁⡂⠁⠀⠐⢓⡈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠆⠀⠈⠀⠠⠄⠀⠠⠀⠀⠀⠀⠈⠉⢢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⡀⡀⢀⢀⠄⡀⠈⠄⠂⠀⠀⠠⡀⢀⠀⠐
⠐⠄⠡⠀⠄⠀⠂⠀⠀⠀⠀⠀⢃⠀⠀⠃⡸⠀⠀⠀⠀⠤⠐⠒⠀⠈⢡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢦⠔⠇
⠀⠀⣤⠀⠀⠀⠀⡠⠀⠁⢀⠀⠀⡱⠂⠀⠀⠀⣀⠀⡈⠂⠀⢀⠄⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀
⠀⣀⠀⠀⠀⠀⠀⢰⠀⢀⡅⠂⡰⠃⢀⠀⢀⠹⢥⠌⠀⠀⡁⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠂⠐⢀⠀⠀⠀⠄⢠
⠈⠧⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠴⠠⠰⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠘⢍⡩⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠧
⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠒⠢⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⠾⠤⠬⣭⣉⡆⠀⠀⠀⠀⠚⠲⠆⠀⠀⠀⠀⠑⢤⣀⣧⡇⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢯⡉⢉⠐⠒⠒⠂⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⠁⠀⠀⣠⠤⠜⢧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠒⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠔⠉⠁⢀⠤⠼⡄
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⡆⠀⠀⠀⠀⠀⢸⡏⠉⠉⢢⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠳⡴⠊⠉⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇⠀⠀⢸⠀⠀⣰⡷⡀⠀⠸⣷⣀⣠⠜⠁⣀⡀⠀⠀⢹⣆⠀⠀⡜⠀⠀⠀⠀⠈⠲⠤⣀⣠⠏
⠀⠀⠀⢸⠉⠑⠖⠉⠈⡇⠀⠀⠀⣿⠋⠉⠉⡿⠀⢠⡿⠀⣧⠀⠀⣿⠉⠀⠀⣿⠉⠉⠳⡀⠀⢿⣄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⠄
⠀⠀⠀⠈⢦⡀⠀⠀⣠⠃⠀⠀⢰⣿⠀⠀⠀⡇⢀⣿⠋⠉⠹⡄⠀⢿⡄⠀⠀⣿⠀⠀⣠⠇⠀⢈⡿⠀⠀⠀⠀⢏⠓⣹⠂⠀⠀⠈⣆
⠀⠀⣀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠉⠀⠀⠀⠁⠸⠇⠀⠀⠀⢧⠀⠈⠁⠀⠀⣿⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢴⡏⠉⠳⡄⠀⠀⢸⡇⠀⢰⣾⠉⠳⡄⠈⠉⢹⡏⠀⢀⣀⠀⠀⡀⢸⡇⠀⠑⡄⠀⠀⠀⠀⢶⡄⠀⠀⢠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠀⣾⠃⠀⢸⣟⣀⡴⠁⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠨⣷⠀⠀⢹⠀⠀⣀⠀⠘⣷⡀⢠⠇⠀⠀⡇
⠀⠀⠤⣀⡄⠀⢸⣟⠉⠉⠲⡀⠀⣿⠀⠀⢸⡏⠳⣄⠀⠀⠀⣼⡇⠀⣼⠷⠦⢴⠃⠀⣿⠀⢀⡞⠀⣼⠟⡄⠀⠘⣧⡜⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠈⠉⠁⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⠻⠶⠋⠀⣼⡯⠤⣧⠀⠀⢽⡇⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠻⠦⠖⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠻⠀⣠⠀⠀⠀⣴⠟⠀⠀⠟⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠣⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦
⠀⠀⠀⠀⠀⣠⡀⠀⣀⡁⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⡞⠲⠚⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠀⠀⠀⡏⠉⡖⢦⣄⡀⠋⠀⠀⠖⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣘⣄⣧⠤⠖⢲⠀⠀⠘⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡀⡇⣨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⡥⠤⠔⠒⣚⣉⠭⡆⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠰⡶⠀⠀⠀⠀⢠⠀⢡⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⠒⠉⠉⠀⠀⢀⣱⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⡧⣤⢤⣖⣲⡭⠿⠜⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠴⠊⠀⠙⠦⣀⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢟⠏⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠶⠄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣠⣀⣴⠇⠀⠀⠀⢀⠀⣤
⠋⠐⠀⠀⠀⠀⠀⣸⣏⠀⠠⡐⠀⣴⢠⡆⠀⠀⠀⠀⠀⠀⡰⠶⠶⣿⡉⠀⠂⣀⠀⣠⡀⠟⠈⠀⠀⠀⠀⣼⠿⠛⣃
⣀⡄⠀⠀⠀⠀⠐⠉⣉⣀⡀⠀⠀⡆⠘⠀⠀⠀⠃⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⠁⡙⠀⠀⠀⠀⠀⠀⢰⣧⣴⠿⠛
⢸⡇⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⣤⣿⠿⢦⣤⣤⣀⠀⠀⠀⠀⠐⠆⣴⡇⠀⠀⠀⢠⣅⣴⠞⠃⠀⠀⠀⢿⣭⡏
⠀⠀⠀⠀⠀⠀⣾⣻⠋⠁⠀⠀⢾⠾⣾⡿⠟⠛⠛⢦⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⣿⡉⠀⠀⠀⠀⠀⠈⠁⡁
⠀⠀⠀⠀⢰⣶⣍⣍⠀⠀⠀⠀⢠⣤⣿⡇⠀⠀⠀⢸⠀⠀⢠⣀⣌⡁⠀⠀⠀⠀⠀⢨⠱⣶⣿⣿⣿⣿⣷⣦⣿⡀
⠐⠃⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠘⠛⠋⠃⠀⠀⠀⠘⠒⠚⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠊⠀⠈⠙⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠒⡘⠉⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⠁⠀⠈⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠁⡠⠔⠂⠩⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠇⠎⠀⠀⣀⠀⡉⠉⠁⡀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⢠⠂⠀⠀⠀⠀⠌⠀⠀⢸⢸⢀⠀⢠⠃⡸⠁⡸⢡⠃⢠⢃⡎⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠦⡀⡏⠀⠀⠀⠀⠈⠀⠀⠀⢸⠸⠘⠂⠘⢠⠛⠀⢀⠎⠂⠀⠘⠀⡜⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣹⠙⠆⠀⠀⠀⠀⠀⠀⢄⡈⠢⠑⠒⠒⠁⢀⡤⠋⠀⡠⠂⠀⡰⠁⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠃⢀⡜⠁⠀⣀⣠⠖⠁⠀⠀⠀⠀⠀⡖⠉⠐⠀⠘⡆⠀⠀⢀⡨⠭⡀⢀⡜⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⠁⠀⠉⠓⣄⠀⠀⠐⠀⡀⠀⠔⠀⢠⠇⢀⡔⠑⠐⠀⠁⣼⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡤⠖⠒⠉⢁⡟⢂⡞⠤⣑⡀⠂⠀⠙⠊⠀⠀⠀⠀⢀⠀⠀⠀⣰⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣀⣀⣀⣀⠀⠀⣼⠁⠀⠃⣀⠀⠀⢀⡞⢀⡞⠀⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁⠀⡸
⠀⡰⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠔⠋⠉⠀⠀⠉⠳⣴⠃⢀⠞⠀⠀⡤⠀⡜⠀⡼⠂⢸⠃⠀⠀⢀⡏⠀⡀⠀⢸⠃⢠⠇⢀⡞⠀⠀⡴⠁
⢰⠁⠀⠀⠀⠀⠀⠀⢠⠊⠀⡐⠁⠀⠀⠀⠀⠀⢀⠜⢻⠀⣼⡀⠀⢰⠃⢸⡃⠸⠁⢀⡏⢰⡃⠀⣾⠀⢼⠀⠀⡇⢠⡏⠀⡼⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁⠀⠀⠀⠀⠀⢐⣁⠄⣼⢀⡈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠈⠁⠀⠁⠀⠁⢰⠃
⠈⠳⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣠⠃⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⠀⠀⠀⠀⡤⠊⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⠀⠀⠀⢠⠊⠹⣆⠀⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⢠⠎⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣆⠀⢸⣇⠀⠀⣠⠟⠀⠀⢠⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣻⠀⠀⠉⠉⠉⠀⠀⠀⠀⢾⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠴⠋
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⣴⣆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢠⣶⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⣴⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣫⡖⣦⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⠵⣯⣼⣿⣿⢸⣧⡴⢞⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡔⢻⣶⣿⣿⡿⣟⠈⢷⠄⠙⠃⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣼⢋⣴⣉⣿⣿⠿⠋⣵⠄⠉⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣴⠟⣵⣧⣼⡿⢋⡅⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣿⠀⠀⠀⠀⢀⡾⢫⣾⣿⠟⠉⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⣠⡟⣱⣿⡿⣁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⣰⡟⣼⡿⢫⡄⠉⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⢸⣟⢱⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣧⠀⢰⡟⣼⠟⣥⡌⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⣿⠿⣿⣿⣶⣄⠀⠀⣿⣿⣋⣣⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡻⣤⣿⢱⠏⣦⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⢸⣿⣿⠀⠈⢻⣿⣿⣦⣼⣿⣿⣏⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡴⠛⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣦⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠛⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⢈⣿⣶⡄⠈⡳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣟⢛⡿⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⣷⣦⣤⣟⢷⣭⡻⢶⣦⣤⣤⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡋⣻⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠉⢻⣿⣿⣷⣬⡛⢶⣭⣛⠿⣍⣽⣿⠛⣿⠟⣿⠟⣿⣏⣹⣧⠼⣛⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⠈⠙⠻⠶⣮⣭⣽⣛⣓⣛⣛⣫⣭⣭⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⣴⡆⢠⣶⡴⠀⢀⣄⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣻⠋⣥⣮⡙⣿⠛⠊⣉⡺⣿⢋⣴⡳⣯⢾⣁⢠⡀⠀⠀⠰⡖
⠀⠀⣾⠛⠛⠛⠛⠛⣿⣏⢛⡟⢉⣼⣉⣀⠺⠉⠀⠈⠂⠑⠈⠂⣨⣤⢿⡙⡆⣄⠰⣆
⣤⢤⣿⡤⡤⠤⠤⡤⣿⣹⣻⢮⣽⣷⣪⣍⠋⢸⡅⢠⡖⣠⠒⣠⠂⢠⣴⠋⣳⢾⡇⢙⡤
⣿⠀⣿⠀⠀⠀⠀⠀⢹⣧⣴⣷⣬⢻⡩⠉⣶⣬⠿⢄⠸⢯⠩⣛⢲⣉⠁⠉⠀⠒⠋⠀⣷⡀⠀⠀⢀
⣿⠀⣿⠀⠀⠀⢀⣴⣿⣦⡙⢏⣥⣿⡶⢂⣍⡺⣯⣌⠶⢂⡀⠈⠁⠉⠁⠀⠀⠀⠒⠲⢼⡓⡆⠀⢸⠃
⣿⠀⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠛⠇⠈⠟⠻⠀⠀⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢳⡑⡇⢙⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⢉⣹⡇⢸⡄⠀⠀⠀⢠
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡻⡞⣄⠀⠾⠴⠀⢠⡻⡿⣠
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⠇⣸⢃⣀⡀⡀⢀⢀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠐⠻⠇⡘⠛⣣⡞⢰⡌⠋⠃⡸⠟
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢁⢰⡟⢰⢇⡞⣼⢱⢏⣾⡞⡸⢻⢣⡏⠀⠀⠀⠀⠀⠐⣶⢺⣧⠮⣼⣻⣟⣧⠵⣤⣿⣶
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠈⠀⠁⠀⡏⠈⢼⠁⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠑⢏⣰⣿⣄⢍⡹⣁⣼⣦⡹⠎
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⢿⣡⡤⢰⡾⣄⣤⣧⣤⣤⠄⠀⠀⠀⠀⠀⠀⣅⡙⣿⣁⣿⣹⣄⣻⠛⣰
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠙⢿⠋⢻⡏⠋⢿⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢺⠀⢸⡇⠀⠀⠁
⣧⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⢿⠶⠾⠃
⣿⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣾
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡚⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠇⠀⠀⠀⠀⠀⠀⣀⠤⣶⠂⠛⣀⠒⢤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡬⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡀⠉⠠⠀⠉⠀⠀⠋⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡔⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠛⠀⠀⠈⠀⠐⠗⠀⠀⠂⣠⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸⠑⠊⠁⠀⠀⠀⠀⣴⠄⠀⠀⢸⠀⠂⠆⠀⠀⢴⠄⠐⠀⡀⢀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠘⡜⠃⠀⠀⠄⠀⠀⠀⠈⢁⢮⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠘⠑⠒⡢⢄⡀⠀⠀⠀⠀⠀⠈⢺⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣔⠷⠀⠀⣶⠀⠀⠒⣥⢄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⠀⠀⠸⠇⠀⠈⠀⠉⢦⡀⠀⠀⠀⠀⠀⠢⡀⠀⢈⢈⠇⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⣀⡥⠖⠋⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠘⠟⠀⠀⠀⠀⠀⣀⠀⠠⣤⢧⠀⠀⠀⠀⠀⠀⠈⠀⠚⠣⠄⠀⠤⠆⠀⠀⠀⢠⠖⡸⠻⡽⡀⠀⠀⠀⠀⠀⠀⠎⡨⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⠀⠀⢠⡄⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢄⠀⠁⠀⠀⠀⠠⠀⢠⣄⠀⡸⠀⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡰⠆⠀⠀⣴⡆⠀⠈⠁⡴⠃⠀⠀⠀⠘⠄⠉⠀⠀⠀⠐⠟⡸⠀⠀⠀⠀⠧⣹⠴⠂⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣆⣀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠿⠀⠀⠀⠠⢤⡜⢳⠖
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⠟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⠄
⠀⠀⠀⠀⠀⠀⢴⢁⡦⠀⠀⠀⠀⠈⣓⡛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠣⡎⣀⡽⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⡃⡇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢀⡸⠀⠀⠀⠀⠀⠀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠿⡗
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠛⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⢀⣠⠔⠁⠀⠀⠀⣠⠲⡀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢉⣿⡿⡟⠒⣄⠀⠀⠀⠀⠑⣄⠃⠀⠀⠀⠀⠐⠠⢀⣰⡂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠻⣤⠖⠀⠀⠀⠀⠘⠲⠔⠚⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠉⠒⠒⠁
⠀⠀⠀⠀⠀⢮⠈⠆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣸⠚⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠰⠇⡸⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠷