Oxeye daisy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⡀⠀⣰⡧⠀⠀⠀⠠⠀⠀⠠⠔⠂⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠁⠀⠁⠀⣨⣿⣧⠀⠀⠀⠀⠐⠒⠀⠀⠀⢰⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠄⡐⡆⠒⣄⣾⣬⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣴⣤⣤⣾⣴⢿⡿⢁⠀⠀⠀⠀⠀⠀⠀⢠⣴⢠⠄⣠⢀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠛⢉⠏⢹⣿⡄⠀⠀⠀⠀⠀⠀⠁⢀⡰⣿⣜⠄⣿⠳⢼⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⠀⠄⠀⠀⠠⠀⠀⠆⠀⠠⢾⣽⣽⡿⢻⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠈⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⡿⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢷⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠏⠀⢸
⠀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⣀⠤⢸⠄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠖⠀⠂⠆
⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠉⠁⢸⠀⠀⠀⠀⡄⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠸⠀⠀⠀⠘⣧⣤⣄⣮⡿⢁⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⠀⠀⠀⠏⠀⠀⠀⠀⠈⠉⢿⣿⣰⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠇⠀⡜⢄⠀⢄⠢⠀⠀⠀⠘⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠄⠀⠀⠠⠀⠀⠀⣼⠃⠀⢰⡾⢰⡃⠀⠀⠺⣷⣄⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠆⠀⠀⠀⠀⠀⠀⠀⡿⢀⡄⠀⢠⣿⠃⠀⢀⠀⠈⠿⣧⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⠀⠀⠀⡇⡌⠀⠀⡮⠀⠀⠒⠁⠀⠐⠶⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⢀⠻⢀⡏⠔⠀⢠⡇⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡍⠄⢠⢀⢰⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⡏⠸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡆⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠢⡌⠀⢱⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⡄⠀⢠⠀⠈⠀⠔⠁⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠐⠢⣀⠈⣢⠬⠒⠉⣨⠋⠉⠁⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⣨⠋⠁⠀⡠⢞⣄⠀⠀⠀⠒⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⡃⠀⣠⠒⢅⡀⠈⠑⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠁⢀⠜⢹⠁⠸⡄⠀⠑⢄⡀⡀⠁⠀⠀⠀⡠⡂⠲⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⣸⠀⠀⢹⢄⣀⠘⠑⠀⢀⠤⢨⠈⢁⠔⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢇⠀⢀⠍⣠⢤⠈⠀⠀⠀⠀⢠⠂⠄⠀⠀⠀⢤⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⡀⠁⠱⠔⠄⠀⡀⠑⠠⠀⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡀⠌⠑⢄⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠈⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠂⠦⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠀⠀⠀⠕⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠑⠄⠗⠈⠐⠠⠵⠈


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠣⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⡄
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⢀⣀⣄⠙⣾⡆⠀⢀⣰
⠀⠀⠀⠀⠀⠦⡘⣧⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣯⣿⡟⢉⡩⠝⠛⣿⣄
⠀⢄⡀⠀⠀⠀⠙⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣾⣿⡶⢺⠴⢮⠄⢣⣶⣤⠄
⠀⠈⢻⣤⡀⠀⠀⠘⢓⡀⣀⣣⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣞⣿⣾⣟⣿⣤⣔⣿⡷⠄
⠀⠀⠀⠙⣷⣶⠰⣆⣻⡿⣿⣿⣋⣡⠄⠤⠄⠀⠀⠀⠀⠊⠁⢻⣿⣿⣿⡿⠾⣏⠛⠁
⠀⠀⠀⠀⠈⣿⣲⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠿⠽⠉⠁
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡰⠃⠀⡔⠀⠀⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⢿⡄⠀⠀⠘⠁⠀⠈⡀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠠⢀⠌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣠⡟⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⠀⠀⣿⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣟⣴⣶⣬⣷⡀
⠀⠀⠀⠀⠆⡀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⣿⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠣⡀⠻⣷⣿⣿⣷⡼⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢻⣶⠌⣿⣿⠟⠋⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠻⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⢀⡀⠀⠀⠘⣷⣠⡞⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠛⢿⡆⠀⣰⣴⠏⠀⠀⠀⠠⣼⣿⠓⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⣿⠍⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⡄⠸⡇⠀⠀⠀⠀⡀⠀⡈⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⣷⣤⣿⢀⡐⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢿⣿⢸⠇⡴⠀⡀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⠀⡀⠀⣠⡝⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⢇⣿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⢰⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠸⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢦⣄⢰⡇⠈⣷⠀⢀⡄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣼⡇⢀⠙⣿⠀⡆⢸⣧⠞⠀⣸⣧⠴⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠈⢻⡄⢧⠸⣷⡇⢸⡟⡠⣰⡟⠁⠀⣰⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠬⢿⣦⣈⠢⣿⣾⣦⣿⣧⣾⣿⣷⣏⣀⣤⡾⠿⠛⠛⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⡀⠀⠒⠒⠢⠤⣌⡙⣿⣿⣷⣄⣠⣾⣿⣿⣿⣭⣵⣠⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣷⣶⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⣀⣉⢻⣟⣓⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣁⣤⣤⣴⠖⠛⣩⡽⠿⣿⣿⣿⣿⡟⢿⡝⢿⣿⡯⣉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣴⠟⠁⣠⡾⢋⣿⠃⠃⢻⡀⠻⣆⠙⢿⣎⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡴⢻⠁⣠⣾⡿⠁⠜⣿⡆⠀⠀⢷⡀⠙⡆⠘⣿⢷⣮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⢹⠃⢀⡼⢻⢿⡀⠀⢸⡟⢦⡈⠀⢿⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠴⠛⠁⣼⠈⠳⡀⡼⠁⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣯⣿⡦⡀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠁⠀⠚⠛⠻⢾⡂⣿⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⠀⢀⣶⣖⣿⣿⣿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⣫⣾⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠼⠋⠁

⠀⠀⠀⠀⠀⠀⠰⠶⠀⡀⠁⢠⡀⣠⠄⣡⣾⣿⣄⡀⠀⠀⢀⡤⠒⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠴⢶⣆⣉⣶⣆⣀⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣼⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠙⠉⠁⠴⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣹⠉⠛⠉⡉⠉⢱⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠃⣀⣶⠐⣆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠠⣤⠀⠀⠈⠀⠐⠀⠀⠉⠛⠁⠀⢀⣼⣿⣿⣷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢟⣿⣿⣿⣿⣿⣟⣻⣦⣤⠆⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡉⠛⠿⢿⠿⢿⠟⠃⠴⠦
⠀⠀⠀⠀⠀⠀⢰⣦⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠛⠃⠚⠀⠈⠀⠀⠀⠀⠀⠀⠒
⠀⠀⢰⣖⣿⣶⣌⠉⠾⠛⣧⠔⣿⣷⣦⣤⣄⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠀⠀⠀⠀⠃
⠶⠐⠾⠿⠿⣽⣟⡁⠀⠀⢀⡀⢁⠘⠛⠛⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣴⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣼⣿⣭⠁
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣆⣀⠉
⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣦⣾⡟⠿⠟⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣿⠿⠛⠃⢀⣀⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠙⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⡟⠛⠂⢴⠞⠋⠉⠁
⠀⠀⠀⠀⣴⣶⣍⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⣷⣴⡟⠷⠀⠀⡘⠃
⠀⠀⠀⣿⣿⣿⣿⣰⣦⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣰⣿⡁⠀⠀⠀⢰⡇
⠀⠀⣠⡼⣿⣿⣿⣿⣯⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⡘⠁
⠀⠀⠹⣧⡾⢿⣿⠟⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⣰⡿⠀⡇⠀⠀⠸⡇
⠀⣠⡀⠹⣿⣿⣿⡀⠀⣤⣶⠀⠀⠀⣆⠀⠀⢨⡟⠀⢐⡇⠀⠀⣾⠀⠀⢀⣀⣀⣠⣤⡄
⠻⣿⣿⡦⣹⣿⣿⣇⣺⣿⡋⠀⠀⠀⢿⠀⠀⢸⠁⠀⢸⡇⠀⢀⠁⣤⣤⣿⠿⠛⠉
⠀⠀⠻⣷⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸⣿⢤⡿⠗⠁
⠀⠀⠀⠀⠉⠻⣿⡏⠹⠀⠀⠀⠀⠀⠀⠟⢾⡇⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⡶⢿
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠊⠀⢸⡇⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠇⠀⠀⠀⠀⠀⠘⣧⡔⠀⠀⡘⣃⡾⠟⠋⠀⠀⠀⠀⢀⣀⣀⣀⢠⡄⢠⣶⣶⣶⣤⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠆⠀⠀⠀⠀⠀⣸⠀⠀⢸⡿⢋⠁⠀⠀⠀⢠⣤⣶⣿⡿⠿⠉⠀⠀⠸⣇⠰⠿⠃⠘⣦⣀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠛⢀⣼⠟⠀⢻⠀⠀⣄⣴⢆⡼⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣖⡉⠻⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⡄⠀⢸⣿⠀⠀⢸⠀⠀⡈⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⡁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢠⠇⠀⠈⣿⠀⠀⢸⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣾⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠇⠀⠀⠀⠹⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⣿⡄⠀⠀⠀⠀⠀⡁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠈⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣴⣤⣤⣤⣤⣶⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡴⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠁⠀⡄⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠶⠖⢞⣾⣧⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⢞⣡⣦⣶⡄⢨⣻⣿⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢃⣿⣿⣿⠛⢰⣿⣿⣟⠡⠀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠒⠄⠀⠀⠀⠀⠀⠀⠉⠉⣽⣿⣱⣾⢿⣛⢁⣧⣿⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⣿⣶⣿⢻⢧⠀⠀⠀⠈⠻⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⢿⠏⠘⣩⠈⠀⢳⠄⠀⠠⣶⡀
⠀⠀⠀⠀⠀⣐⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠝⠡⡃⠀⢀⠋⠀⠀⠈⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠉⣨⡓⠀⠀⠐⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠘⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢦⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⣠⣹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⠆⢳⠀⠀⠀⠃⠀⠀⠐⠉⠈⢓⠻⢿⣷⣦⣀⠀⠀⠈⢣⣧⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⣠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢿⣿⡿⣿⣤⠀⠀⠈⠛⠉⢿⠀⠀⠀⠀⠀⠀⠀⢰⠃⣼⠿⠟⠉⠩⠽⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⡹⣿⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡇⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⡄⠀⠀⠀⣷⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⢿⣷⣿⣁⠀⠀⢸⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⡆⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢷⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣶⠀⣇⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠠⣌⡠⠿⣷⣼⣿⣿⣠⣴⡤⢁⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⢹⢀⡏
⠀⠀⠀⠀⠀⢀⢈⣙⣿⣶⣿⣿⣿⣿⣯⣽⡶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣼⠁
⠀⠀⠀⠀⣀⣸⣯⣴⣮⣉⣹⣯⣭⣿⣿⣾⣿⣆⣨⣿⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡏
⠀⠀⠀⠀⠀⠨⠿⠽⠏⠻⠿⠧⢤⣷⣴⡿⡿⣿⣿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢀⢀⣀⢀⠀⢀⡀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠀⠀⠁⠀⠁⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠁⠀⠉⠁⠈⠉⠀⠀⠁⠈⠉⠈⠈⠁⠈⠈⠉⠉⠉⠉⠁

⠴⠂⠀⢀⣾⣇⡀⠈⠀⠀⠀⠀⠈⠃⠀⠋⠀⠀⠀⠀⠈⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⣿⡄
⠀⠀⠀⠻⠈⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⠿⣦
⠀⠀⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠷⣾
⠀⠀⠈⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣿⣿⡟
⠀⠀⠀⠀⢹⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠛⣿⡟⠛
⠀⠀⠀⠀⢸⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⢰⢀⣾⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⠃⠀⠀⠀⠀⢸⡇
⠀⠀⢰⣿⠀⡇⠀⠀⠀⠀⢠⣄⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢸⣿⡆⡇⠀⠀⠀⠀⢸⣿⡧⠰⣿⡿⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠈⣿⣷⡇⠀⠀⠀⠀⠀⢿⣿⡄⢾⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣇⣰⠀⣠⣾⣿⣦⠀⠀⡿⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⢀⣿⣿⣿⡏⣀⣠⡇⠀⠀⠀⠠⣾⣿⡆⠀⠀⢰⡄⠀⠀⠀⠀⠚⣶⠲
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢨⣿⣿⢷⣿⣿⠏⢨⣿⣿⣧⡀⠀⠀⣰⣿⣿⣷⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢸⣿⠏⠀⠈⠻⠋⠈⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⡆
⠀⠀⠀⠀⠋⠀⠀⠘⣿⣶⣤⡀⠀⠀⣿⢸⡟⠀⠀⠘⢿⣿⣿⣷⠀⠀⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⣿⣼⠃⠀⠀⠀⢸⣿⣿⡿⠀⠀⣹⣿⠏⠀⣀⣄⣤⣤⠀⠀⠀⠀⢻⣿⣷⠁
⠀⠀⠀⣀⠀⠀⠀⣿⣷⣿⣿⣿⣯⠀⣿⡿⢠⣦⣀⠀⣼⣡⣿⡇⠀⠀⣿⡟⠀⣴⣿⣿⠟⠁⠀⠀⣴⡇⢸⡇⣿
⠀⠀⠜⠋⣷⠀⠀⣿⣿⣿⣿⣿⣟⠐⢾⡇⢸⣿⣿⣄⣻⣿⣿⠁⠀⠀⣿⠁⣼⡿⠟⠁⠀⠀⠀⠀⣿⡟⠸⠇⠃
⠀⠀⠀⠀⠸⠀⠀⠘⢿⣿⣿⣿⣿⣧⣸⡇⠀⣻⣿⣿⣿⠃⣟⣀⣀⣸⠃⣸⠟⢁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣧⣀⣿⡙⣿⣿⠀⣿⣿⣿⡏⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⢹⡟⢿⣇⣸⣿⠀⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⣇⢸⣿⣿⣿⣄⣿⣿⣿⠛⡁⠀⠀⠀⣠⣴⣶⡄⠀⠀⠀⠁
⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡌⣿⣿⢿⣿⣿⣿⣿⣿⣿⡗⠀⣼⣿⣿⣿⠃
⠀⠀⢠⡿⠀⠀⠀⠀⢀⣤⣶⣶⣿⣶⣴⣦⣬⣷⣿⣿⣼⣿⣿⣿⡼⠋⢀⣠⠴⠋⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⢹⣿⡝⢻⣿⡿⠃⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣀⣹⣿⡿
⠀⠀⠀⢀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⢸⣿⠙⢦⣿⣷⡺⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⣿⣆⣠
⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⣴⠶⢦⠀⠀⠀⠀⢸⣿⠀⠀⠹⣿⣇⠀⠙⢷⣶⣿⣿⣿⣶⠀⠀⠀⠀⠘⣿⣿⢰⣿⣿
⡇⢤⣿⣿⣿⠠⠀⣤⣤⣤⠀⣿⠀⢸⡇⠄⠀⠈⣸⣿⠀⠀⢀⣿⣿⣷⣄⡀⢙⡟⠿⠟⠁⠀⣀⣀⠀⢰⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣴⣀⣿⣿⣿⠆⢹⡆⣸⡇⠀⠀⢀⢸⣿⠀⢰⡎⢻⣷⣿⢻⣿⣿⣿⣶⡷⠄⣶⣿⠏⠀⢸⣿⣿⣿⣿⣿
⠿⠿⣿⣿⣿⣋⣿⢻⣿⣿⣹⣿⣷⣿⢰⣄⢀⣘⣀⣅⡀⠿⠀⠜⢿⡻⢿⣿⣿⠿⢿⡋⢠⣼⣿⢶⣀⣿⣿⣿⣿⣿⠿
⣶⣶⣾⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣿⣶
⣿⣿⣟⠁⠉⡉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠴⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢀
⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠂⠸⠟⢀⡤⡖⠀⣀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠈⢷⣀⣤⣤⣟⣡⣶⠿⠛⠒⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢳⣄⣍⣪⣶⣿⣿⣿⣿⣿⣋⠩⠤⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⣤⣄⠀⠀⠀⠀⣀⣈⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⡷⣦⣤⠄⠃
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡀⠀⠀⣀⠞⠙⠇⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⡿⢿⢝⢷⣠⡤⠂
⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠀⠐⢾⠇⠀⠀⠀⠀⠐⠀⠈⣡⣿⣿⣿⡿⣿⣿⣿⣌⠂⢠⣏
⠀⠀⢠⣶⡀⠀⠀⠂⠀⢠⡀⠀⠖⠒⠀⠀⠀⠀⠀⠐⠨⣾⣿⢟⡿⠱⣹⡇⢁⠟⠀⠉⢿⡀
⠀⠀⢿⣽⡟⠂⠒⢤⠀⠄⠹⡄⠀⠀⢰⡾⣧⡄⠀⠠⠀⠈⠀⠀⣇⠀⠋⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠈⠀⠈⡄⠀⣈⠄⡴⠲⠃⠀⡀⠛⠓⠏⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠬⣤⡈⡇⡀⢀⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⠹⠸⣇⡌⠹⠀⠀⠚⠛⢿⣿⣿⣦⣄⡀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⣸⠇⣤⣴⣶⣤⡀
⠀⠀⠀⠀⢠⠠⢬⡆⠀⣿⠁⢀⣾⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠉⠉⣷⠀⠀⠀⠀⢠⣿⡼⠛⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠠⠤⣥⡀⢿⢠⡟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀⠀⢸⡆⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠠⢀⡀⢈⢳⣸⡾⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⠈⣧⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠐⢮⣿⣹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣀⢻⠀⣸⡏
⠀⠀⠀⠑⣾⣶⣶⣦⣻⣿⣦⣠⡿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢸⣆⡿
⢀⣀⣠⣴⣛⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃
⠀⠴⢿⣿⣿⣿⣯⣿⣿⢿⡿⣿⣷⣬⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣀⣀⣈⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⡟⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⡿⣿⣿⠿⣿⡿⡿⢿⢿⠿⠿⢷⣿⣿⣿⣿⣏⣿⣹⣻⣿⣿⣿⣿⣯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠁⠂⠘⠰⠀⠂⠂⠰⠐⠀⠛⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢋⡀⠀⠀⠀⢀⠀⠄⠢⠀⢀
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢁⠂⠠⠠⠀⠀⠀⠀⠀⠢⠔⠔⡒⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠅⠪⠚⠀⠀⠀⠀⠀⢀⠀⠈⠒⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠠⠀⡀⠀⠀⢀⠀⠀⠊⠀⢀⠁⠀⠀⠐⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠚⢀⠀⠀⠐⠒⠀⠀⠀⠂⠠⠀⠴⢁⡡⠀⡄⠘⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠈⢀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡐⠂⠀⠀⣢
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠉⠀⠀⠀⠀⠀⣆⣈⠠⠘
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠦⠤⠄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠉⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣅⢁
⠀⠀⠀⠀⡐⡛⠉⠠⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠜⡏⠀⠀⠀⠀⠀⠀⠈⣷⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠘⢀⢀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠶
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠰⠤⠊⠀⠀⠀⠀⠀⢀⡐⠀⠀⠈⢀⠃⠦⠁⠂⠀⠀⠚⢀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠸⠑⠀⠱
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠐
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢶⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⢢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠐


⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣷⣬⣿⣶⣵⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠀⠀⠀⠄⠀⠾⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠂⠀⣀⠰⣆⢀⠓⠂⠈⠀⠀⠠⠄⠀⠈⠀⠠⠐⠁⠀⠀⡀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⡞⠁⠀⠀⠀⡀⠀⠀⠀⠘⠀⡀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢂⣀⣤⣧⢹⢀⡀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠃⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠴⠖⠛⠉⠁⢠⡄⠀⠀⠈⠶⠏⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⣰⣷⡀⠀⠀⠀⠤⠀⠀⠀⢸⠷⠃
⠀⠀⠀⠀⠀⠀⠠⠚⠁⢠⡄⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⢀⠀⢠⡄⠀⠀⠀⠻⠏⠠⠀⠀⠀⢶⠁⠀⠸⠛⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟
⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢀⠞⠀⠀⠀⠀⠀⢀⡀⠀⠐⠂⠀⠀⠀⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣿⠟⠟⣶⣄⠀⠜⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠐
⠀⠀⠀⠰⢾⣯⣬⣾⡿⡉⢳⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢾⡀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⣴⣦⠀⢀⠀⢠⣾⣿⣿⡄
⠀⠀⠀⠀⢇⠀⣙⢿⣆⣤⣿⣷⠴⣿⡀⠀⠀⠀⠀⢀⣠⣼⣿⠦⣄⢸⡇⠀⠋⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⣿⡏⠀⠛⡑⠴⣟⠉⢻⡇
⠀⠀⠀⠀⠘⡄⠀⠏⢿⡿⠟⣿⡿⣿⣿⣶⣶⣶⣿⠿⣿⠿⠃⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢁⠶⣶⡄⣿⡄⢸⡆⡭⡄
⠀⠀⠀⠀⠀⠈⢦⡀⠈⢷⣤⣾⠷⡉⠛⠛⠛⠉⠀⠀⠀⠂⠀⣰⡖⣭⠆⠀⠈⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⠃⡿⠗⠈⠉⠁⠈⠙⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠻⡿⠛⠛⠦⡤⠀⠉⠙⠁⠀⠀⢠⠃⠇⠸⣄⠀⠠⠜⠂⠀⠀⠀⢀⠀⠉⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡴⠁⠀⠀⠛⠹⢶⡆⠀⠀⠀⠘⠚⠀⠘⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠔⠲⡆⠀⠀⠀⠁⠀⠀⠐⠀⢘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⣠⠀⠀⠀⠙⠀⠶⠀⠀⠀⠛⠀⠀⠀⠀⡶⠀⠘⡄⠀⠀⠀⠀⠂⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢉⡄⠀⠘⠋⠀⡀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠁⠀⠀⠂⠈⠁⡨⠄⠀⠀⠀⢀⠀⡄⠀⠀⠀⢰⡀⢀⣹⣦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠖⢀⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣦⣀⠀⠀⠠⠊⠀⠐⠢⠀⠁⣀⡄⠁⠀⠀⢠⠿⠿⠿⠋⠀⣼⣷⠦⠄⠀⠀⠀⢀⣡⣶⣿⢋⣝⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠻⣿⣷⣦⡇⠀⠀⠘⠟⠀⠀⠀⠈⠠⠀⢀⠂⠀⠀⣀⣤⣾⡿⠋⠀⠀⣹⡿⠛⠋⠉⠉⢈⡥⠍⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢏⠉⣶⠄⠙⠋⠁⠰⠀⠀⢀⣈⣥⣤⣄⠀⠀⢹⣶⣶⣿⡿⠟⠋⠀⣀⣴⡾⠋⠀⠀⠰⡦⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣜⣋⡒⢃⠀⠀⣴⣶⠖⠚⠛⠉⢉⠀⠙⠋⠀⠀⡸⠉⠩⢤⣤⣴⣶⣿⠟⠁⠀⠀⠏⢣⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⢦⣤⣀⣎⠀⠀⠀⠀⠈⠀⢀⡶⢘⠒⠀⠀⢀⡀⠰⠊⠀⠀⠀⠀⡉⢤⠚⣥⣤⣤⣤⠀⢠⠀⡀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠉⠁⠀⠀⢪⠀⢀⠀⠁⠀⠀⠂⠀⠔⠀⠈⠀⠀⠀⠀⠈⠀⡇⢠⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⢀⣠⠤⠀⠲⠉⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀⣠⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠈⠁⠃⠰⠞⢀⡴⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠉⢀⣀⠀⠈⠑⠂⠁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠾⠿⠾⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠰⠚⠓⢶⠀⠀⡹⡆⠀⠀⠀⠀⠀⠄⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠢⢤⣀⠶⣆⠴⠃⠀⠀⠀⡔⠃⠠⣨⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇⢺⣇⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⠋⠀⠄⢠⠆⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⢹⡃⠀⢀⠀⠀⢠⠀⠀⠀⠰⡾⡇⠀⢀⠀⠀⠐⣄⠒⠈⣀⣴⣀⠔⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢸⠁⢠⣉⣇⠀⠀⠂⠀⠀⠀⠉⠀⠀⠜⠀⠀⢳⠠⠀⡞⠉⢀⣸⡆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠣⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠞⡙⢱⡇⠬⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠇⠀⠀⠀⠀⠀⠀⠮⠘⠧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠰⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠳⠀⠄⠀⢀⡆⠐⣡⣔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⢆⠀⠀⠀⠀⠀⠡⢀⡏⠀⠀⠀⠀⠀⠀⠀⠇⠀⢨⣴⠓⠀⢳⢀⡜⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⢀⡄⣄⠀⢀⠀⠉⠉⠐⠆⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣀⣀⣤⣠⠀⠈⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠐⡆⠀⢳⢃⠼⠁⠀⠀⠀⠀⠀⠀⣠⠦⡞⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠙⠛⠉⠛⠛⢿⢶⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⢀⠞⠁⡆⠀⠀⠀⠀⣠⠇⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠐⡀⠀⠀⠸⡀⠀⠀⠀⠏⠀⢠⠀⠀⠀⠀⡐⠁⠀⠂⣰⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢧⠀⠀⠀⠁⠀⠀⢸⢀⢀⡇⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠘⡆⠀⠀⢰⠀⠀⡘⢸⣼⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠇⠀⠁⠀⠉⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⣷⣴⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣠⣄⣾⣿⣿⣿⣿⣿⣿⣷⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⣄⣼⣿⣿⣤
⣴⣤⣄⣠⣴⣤⣤⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⠂⣬⣙⣻⣾⣸⣿
⣿⣿⣿⣿⡟⠡⣾⣩⣿⣿⣶⣀⡀⢀⣀⣰⣾⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⣿⣿⣝⣻⣿⣏⡀⠛⠿⠛⠿
⣿⣿⣿⣿⣿⣾⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⢿⡋⢋⣹⣯⡍⠀⠀⠉⠉
⣿⣿⡿⠷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢟⣿⡛⠛⠛⢉⠉⠙⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣀⣀
⣿⣾⣖⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣿⣿⣿⣶⣤⣤⣀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿
⠉⠽⠿⠿⠿⣿⢯⡷⠶⠀⠠⠒⠒⠀⢠⣤⣀⣀⣒⣀⣠⣆⡝⠛⡛⠛⠛⠿⢿⣿⠿⢿⣿⣿⣷⣿⣻⣿⣿⡿⠟⢛⣛⣻⣉⣉⣀⣤⣠⣄⣾
⠀⠀⠀⠒⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⠚⠩⠽⠿⠿⣿⣧⣤⣤⣀⣠⣁⣀⠀⢠⣤⣭⡯⠉⠀⠚⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣚⣷⣿⣿⣿⣿⠣⠠⠶⠶⠞⠓⠒⠟⠓⠛⢯⣁⡈⠁⠊⠂⠀⠚⠛⠩⠍⢠⣭⡉⠁⠒⠈⢀⣀⡈⠀⠠⠀⢠⠌⠉⠉⠙⠛⠻
⠀⠠⠶⠊⠉⢉⠙⠃⠭⣭⣽⢿⡿⠷⠶⠿⣯⡀⠀⢀⠤⣤⣿⣿⣿⣤⣿⣿⣿⣶⠶⣶⡮⠥⢄⠀⠀⠀⠀⠈⠁
⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠲⠶⠶⠖⠒⠢⠿⣷⠮⣛⣿⣿⠾⠷⣶⣴⣄⣐⣖⠲⠚⠂⠀⣤⣤⣤⣌⡠⣤⠶⣦⣤⣤⣤⣤⣀⡤⢤
⠀⠀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠹⠖⠈⢭⣷⣈⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⡀⠀⣤⠭⣍⣀⣈⣉⣹⣛⣻⣟⣡⠈⠀⠹⣿⣿⣿⣿⣿⠟⠛
⣀⣀⠟⠣⠴⠰⠶⠄⢀⡀⠀⠀⠀⠠⠤⠶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠈⠻⢷⡌⠉⠉⠁⢿⡏⠋⠀⠤⡄⠀⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡐⠁
⠀⠀⠀⣀⠀⠀⢤⢈⠲⡀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡰⢊⠀⠄⠀⢀⡀
⠀⠘⠀⠈⠀⢀⡀⠀⠒⠸⣼⠀⠐⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠑⠀⢸⡼⠐⠂⠀⣀⠀⠈⠀⠘
⠐⠂⠠⠽⣄⡣⠀⠪⠰⠄⣹⡀⡐⠀⠀⡁⣠⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢠⡀⡀⠀⠐⡁⣸⡀⠴⠈⠂⠀⢃⡼⠥⠀⠒
⠴⠀⠀⢂⣈⡉⠙⠮⠥⣤⠌⢳⡁⠀⡐⢀⢅⡀⢰⢀⠅⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅⢰⠀⣀⢅⠐⡀⠀⣱⠋⢤⡤⠭⠞⠉⣉⡀⠂⠀⠰
⠀⠀⠐⠁⠈⠀⠈⢄⢂⠲⠙⢮⠷⣔⠀⠈⢀⡉⠚⣇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡟⠊⣁⠈⠀⢐⡴⢯⠞⠱⠂⢂⠌⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠫⠅⢠⣈⠁⢠⣤⡥⠮⠽⣶⢦⣍⣉⡙⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⡞⣉⣉⣤⢶⡾⠭⠦⣤⣤⠀⢉⣠⠀⠬⠃
⠀⠀⠀⠀⠐⠖⠠⠤⠬⢛⠏⢠⠁⠠⠞⠥⠠⢄⣨⠽⠛⠛⠶⠶⠶⠶⠶⠶⠶⠖⠛⠻⢭⣀⠤⠠⠝⠦⠀⢠⠈⢟⠫⠤⠤⠰⠖
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⣐⠀⠀⡇⡦⠠⡤⠞⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠦⡤⠤⡆⡇⠀⢜⡀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠆⠀⡇⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡇⠀⠦⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⡒⢄⠀⡀⡠⠊⡡⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠘⣿⠀⠀⠀⠀⡰⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣃⢾⣠⠊
⠀⠀⠀⠀⠀⢀⠀⡆⠀⣰⣴⡛⠀⠀⠀⢶⡅⠀⢠⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠟⠉⡫⣿⡇
⠀⠀⠀⠀⠀⢸⠀⡇⢰⠟⣉⠙⢶⠤⠤⠀⠙⡶⢠⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⡴⢋⢰⠈⠳⡈⢣⡀
⠀⠀⠀⠀⠀⢸⠘⡇⠛⠀⣈⠀⢸⣷⣶⡶⢶⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⢾⠀⠀⠀⠛⡶⠃
⠀⠀⠀⠀⠀⠀⠭⣀⣄⣸⡇⣀⣸⣥⠤⠤⠬⠧⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⣏⡀⠀⠀⣿⠉⠀⠁
⠀⠀⠀⠀⠀⠊⠄⢀⠤⠚⠉⡉⠀⢄⠀⠠⡀⠢⡐⠄⠑⠀⠀⠀⠀⠀⠀⠀⠒⡉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢠⢂⡖⣄
⠀⠀⠀⠀⠀⠀⠘⠂⡿⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠉⡐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⢰⢧⠺⢀⣤⠤⠤⠤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣬⣆⡤⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡼⠆⢰⠏⠈⢳⡤⠤⠤⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢙⣀⣹⣴⢯⣏⢳
⠀⠀⠀⠀⠀⠀⣀⡗⣆⠸⠀⡷⢸⡌⡗⢸⡇⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣸⣏⣿⢣⢺⣿⣿⣿⣼⢿⣯⠄
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⣀⣀⣼⣧⣧⣀⣠⣇⣀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣸⣯⠥⠼⠿⠾⠿⢿⣬⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⢀⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢰⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⢸⠀⠀⡇⠀⠀⡎⠈⡆⠀⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⢀⣠⣤⡶⠖⠿⣿⣿⡲⢄
⠀⠀⠀⠀⠀⠀⠘⠀⠘⡀⠈⠀⠀⠇⠀⢰⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠾⣽⠿⠁⠈⢱⡀
⠀⠀⡠⠠⠀⠀⠀⠆⠀⢳⠀⡆⠀⢸⢀⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣀⣀⣀⡤⠶⠐
⠀⠀⠱⡀⠐⠄⠀⠠⠀⠘⡄⡇⠀⢀⡘⠁⢠⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁
⠀⠀⠀⠙⣄⠀⠀⣀⠆⠀⠉⠀⠀⠈⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐
⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⡹⠳⡄
⠀⠀⠀⠀⠀⠈⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠣⡄⠤⠔⠀⠉⠀⠀⠀⠀⠀⣀⠄⠀⠤⠴⠤⣀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠀⢀⠜⠁⡠⠤⢤⠠⢀⠀⠑⠀⠀⠱⣄⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠊⣠⡾⠷⠶⣿⠶⠾⢿⣦⡀⠀⠀⠈⠳⡄⠀⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠈⠦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠁⠘⠀⠉⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠒⠋

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄

⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠙
⠀⠤⣗⡀⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⣾⣷⡿⠉⠀⠀⠐⢆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣽⢿⣿⠶⠒⠋⢛⣦⢐⢦⣜⢐⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣮
⠀⢻⡶⠇⢀⣠⣴⣿⣿⠇⠉⠈⠻⠉⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⠒⠛⠘⠙⠋⠙
⠀⢁⠀⢠⣼⣿⣿⣿⣭⣀⣴⣾⣟⣯⣹⣿⡦⠶⡄⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⣼⣾⣿⣿⣟⡉⣈⢁⡨⠽⣿⡿⢿⣿⣿⠗⠀⠰⠀⠠⠀⠁⠀⠀⠔⠂
⠀⢿⣿⠳⣶⣽⣿⣿⣟⣺⣿⣏⠙⠙⠻⢏⡀⢀⠀⠔⠀⣀⠄⠒⠀⠐⠦⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠁
⠀⣿⣿⣿⡶⣤⣈⣿⣷⣾⣝⣿⣶⠆⠀⠈⢹⣿⣦⣄⢡⡅⠀⠠⠆⠀⣀⡀⠀⠀⠠⠀⠂
⠀⣹⣿⣿⣿⣿⣍⣫⣿⣿⣿⢏⣿⣷⣤⣆⠚⢹⡽⢋⠐⢂⠐⠒⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠃⢀
⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣈⣠⡒⢀⣠⣞⠐⠂⠀⠃⠀⠄⢂⡄⠀⠤⠄
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣓⣿⣧⣻⣆⣒⣛⣐⣲⣄⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠀⠀⠉⠉⠛⠛⠛⠛⠃⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣡⠴⡾⠛⠁⢀⡄⠀⠀⢀⠀⠀⠀⠀⢄⡀⠀⠠⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⢊⡵⠂⠀⠀⣴⠋⢀⡴⠀⣾⠀⠀⡇⢠⡀⠹⣦⠘⢦⡹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠋⠀⠀⣠⡞⠁⢠⡾⠁⡸⠇⣰⠀⣿⠀⢷⡀⠈⢷⡀⠹⣌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢠⡾⢁⡔⢁⣼⠏⠀⠀⠈⡀⠠⠁⢠⡟⠀⠈⢠⡌⢷⠰⡌⢿⡄⠹⣞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣾⢡⡿⢁⡞⢀⡞⠁⠀⠀⢀⡼⢡⠇⢠⠿⠃⡤⠀⡼⣿⡘⡆⢿⡸⢷⠀⠻⡆⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣿⡇⠃⣾⠁⡞⢀⡼⢀⡴⠋⣰⠋⠀⠁⣨⣞⢁⠘⠀⠙⢧⠃⠈⠃⡞⡄⠀⢱⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠁⠘⣰⣾⠴⠚⠛⠛⠙⠛⠛⠛⠉⠉⠛⠛⠋⠙⠻⡰⠾⣶⢁⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⡀⢀⠂⢰⣯⠴⠷⠶⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⡹⢦⢹⣯⠀⢰⠀⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢃⢸⡄⣾⠁⢀⣠⣄⡀⠉⠙⠣⠀⠀⠀⠀⠘⠋⠁⢀⣰⣇⡀⠈⣟⠀⡜⠐⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⣿⣇⣿⠀⢻⡟⠋⣿⠷⢦⠀⠀⠀⠀⠀⢀⠴⢻⣿⣿⢻⠟⢠⡇⣰⢃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣇⠈⠳⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠵⠛⠀⣼⣿⣧⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢟⣥⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⡻⣿⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠛⠁⣿⢿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⠿⡄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⣲⣄⡀⠀⠀⠀⢠⣿⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⣿⣄⠀⠀⠀⠘⢥⣀⣀⣀⣀⡜⠁⠀⠀⠀⣠⠟⢿⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⣻⣦⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⡴⠫⣷⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠶⢛⣿⠉⠓⠦⣄⣀⣀⣀⣀⠠⠶⠞⠹⡗⢶⣾⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣛⣿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠠⣶⡸⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢣⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠜⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡈⠎⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡱⢀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡄⢿⡌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡟⢠⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣧⠀⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡜⠀⣼⢷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢿⠀⠀⠆⢹⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠀⡀⣶⣼⠁⠀⠀⠀⠀⠀⠀⠈⣇⣧⢠⢀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣾⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣴⠟⠋⠁⢠⣻⣿⠇⠙⢆⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠻⣦⣀⠀⠀⠉⠁⠀⣀⡬⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣤⣤⡤⠴⠚⠉⢦⣀⣠⣴⠶⠛⠛⠋⠉⠉⠙⠛⠳⢶⣤⣀⣠⠎⠑⠢⠤⣤⣤⣤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠴⠀⠘⠀⠑⠂⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠂⠀⠀⠐⠀⣇⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣷
⠀⠀⠀⢀⣠⠤⠖⠒⠒⠢⢤⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡄⠀⠀⠀⠀⢈⠄⠀⠀⠀⠉⠰⢀⠈⠀⣀⡨⠂⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠤⢤⣀
⠀⢀⠔⠉⠀⣀⡀⠐⠀⠀⠀⠈⠑⢆⠀⠀⠸⣇⠀⠀⠰⡔⠀⠀⠀⠤⠀⠀⠀⠁⠂⢤⠀⠰⠋⠉⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⠖⠉⠀⠀⢀⠀⠀⠀⠀⠈⠑⢄
⢠⠏⠀⠀⠈⠁⠀⠘⠓⡄⠀⠀⠀⠀⢳⡤⠔⢿⡀⠀⠀⠠⡀⠠⠀⢀⡠⣤⣤⠀⣀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⠗⠤⣴⠃⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⢧
⡎⠀⠀⠀⠀⠀⠀⠁⠀⡸⠀⠀⠀⠀⠀⡇⠀⠈⢷⡀⠀⠀⠉⢰⣿⣷⣾⠿⠭⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈
⡇⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⢳⣄⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠘⡇
⢱⡀⠀⠀⠱⣄⠀⠀⠔⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠳⡄⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣀⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⡴⠃
⠀⠀⠈⠳⢤⣀⣀⠈⠒⣂⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⡀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠛⠛⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠤⠄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠊⠀⠄⢀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁⡴⠿⠶⢾⠶⠾⢷⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⣀⠀⠛⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠠⡀⠀⠁⠈⠀⠀⠀⡠⠃⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⠉⠒⠒⠂⠚⠉⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⣀⡠⠤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡤⠀⠉⠀⠄⢀⠀⠀⠀⠀⠁⠄⠀⣰⡟⠀⠀⠴⠆⣹⠷⢶⣶⣄⡘⠷⠦⠈⠀⠺⣆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠲⣿⣄⣜⣿⠋⠒⢀⣀⠀⡀⠀⠀⠀⠙⢤⢴⢶⣿⣿⣿⣶⣿⣠⣤⣝⠶⠄⠈⣿⣿⣷⡶⠀⡀⠀⠀⡁⠢⡀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⡜⣻⠙⣼⣡⣤⣶⡉⠀⠀⠀⠀⠀⠒⡇⠘⢻⣰⣿⣿⢿⣿⣿⣿⣝⡋⠐⠀⠀⠀⠉⣿⣷⡤⠀⠠⣳⡌⡀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠐⠿⣷⣿⡏⢩⠿⢋⣩⠤⢀⣀⢄⡁⢀⣴⣿⡿⣿⠉⣼⣿⣿⣿⠛⠋⠀⠂⠈⠙⠢⠜⢿⣧⡠⠊⢉⠓⠏⠰⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠓⠹⣶⣿⣿⣾⡁⣀⡉⣀⠐⣎⠉⢹⣷⣿⣿⡟⠷⢃⣴⣿⣿⠿⠁⢶⡀⣀⣉⣀⠀⠌⠀⠀⠹⣷⣾⣥⠀⠀⠰⠆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⠑⢦⣹⣿⡛⣿⡗⠡⠈⠋⠲⡾⠛⢿⣿⣿⣿⡿⠀⣼⣿⢛⣤⣤⣾⣿⣯⣿⣽⣿⣿⣶⣆⡈⢻⣿⣿⣭⡇⠀⠈⠀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣎⠻⣹⣿⣿⡀⠀⠀⠀⠃⢈⣿⣿⣿⣿⣿⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣾⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢶⣽⣦⣿⣿⣧⠀⠀⠄⠁⢠⣿⣿⣿⣿⣿⣡⣼⣿⣭⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⢹⣻⣷⣬⡀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⣾⣿⣿⣿⣿⡟⠀⠀⢄⣠⣼⣿⣿⣏⣽⣿⣿⣿⣟⠿⣹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢃⣶⣿⣿⣿⣷⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣬⡿⢿⣿⢣⡄⠀⠀⣼⣿⣿⡿⠉⣹⣿⣿⣽⣿⣷⣾⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⡜⠿⣀⣹⣷⠐⣻⣾⣿⡟⣛⢡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣩⣥⣶⢾⠛⠛⡿⣟⠓⢼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⢿⣿⣿⠷⣊⣀⣿⢿⡻⠃⠘⢿⣿⣿⣿⣿⣿⠛⠂⢤⣄⣤⡙⠛⠿⠿⡿⠿⠿⡟⠀⠀⠃⢿⣠⢾⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢼⡿⣿⣿⣿⠟⠿⣿⣞⠀⢐⠀⢸⣿⣿⣯⣿⣿⣥⢤⡀⠙⠋⡄⠤⠀⠤⠀⣀⠀⠀⠀⠰⢄⣿⢀⣼⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⣂⠀⢛⣥⡶⠊⠁⢸⣿⣿⣿⣿⣿⣿⡂⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡀⣿⣿⣟⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⣿⣿⣿⡿⣇⣰⠞⢃⠀⠠⢳⣾⣿⣿⣿⣿⣿⡛⠿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⢠⣼⣿⣿⢋⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠛⣿⣣⠆⡡⠔⣁⠄⠾⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠋⣠⢾⣿⡡⢷⠂⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⠛⣻⠋⠀⠀⠀⣻⣧⠴⢊⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⣠⣇⣼⣳⣾⠵⢁⠘⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⢘⡷⣟⣡⠀⠀⣄⠉⠈⠶⣼⣷⣿⣿⣿⣯⣷⠀⠀⠀⠀⠀⠀⢠⣀⣴⣶⣟⣽⣿⡿⣫⠐⡁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢀⡀⠀⠐⣰⣥⡜⢀⣯⠄⠀⣶⡼⣿⣿⣿⣷⣿⣿⡀⠀⠀⠀⠠⠰⣞⠶⠜⠛⢿⣿⢟⡼⢋⠀⠀⠂⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠹⠁⠠⡆⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣞⢶⡀⢀⡀⠀⠲⠀⠀⢷⠈⠿⢣⠈⠀⠀⠆⠀⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⢀⠀⡀⠀⠀⢉⠠⢠⠄⢀⣽⣿⣿⣿⣿⣿⣿⣿⣦⣷⣸⣧⢀⣾⣿⡃⠀⠀⢰⡄⠀⠠⠀⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⢀⡵⠀⠀⠤⠤⠈⠀⡘⢲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠂⢀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⢀⠀⣤⡤⠶⠒⠀⠰⡦⠉⠀⠁⢀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠐⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⠀⠄⠒⠐⡎⠂⠀⢀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⢠⠀⠙⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠾⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⠉⠟⢿⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⢀⣤⡀⠀⠀⣀
⠀⠀⠀⠀⣀⠀⢂⠀⡄⠀⠀⠀⠐⠀⠀⢀⠀⢰⣰⣦⣵⣿⣿⣿⡿⣻⣥⣿⣿⣷⠀⠘⠡⠆⣈⣿⣿⣿⡄⠊⠀⠀⠀⠀⣼⡟⠉⠁⠀⠀⠁
⠀⠀⠀⢀⣒⣿⣶⣤⢁⢀⠀⠀⠀⣀⣀⣤⣴⣿⠿⢋⢛⣉⣿⣿⣿⣿⣿⡟⠋⢭⠤⠚⠁⠀⠈⠠⢿⣿⣀⡄⠀⢀⣦⡾⢋⠞⠀⠀⠄
⠀⠀⠀⠈⣻⣿⣿⣿⣯⣿⣷⣶⣆⣤⣯⣤⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠒⠲⠀⠀⠀⢴⣾⠿⠿⠄⣰⣾⠋⡅⠀⠀⠀⡀
⠀⠀⠀⢺⡿⠛⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⠁⠘⣻⣥⣿⣿⡿⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⣾⣷⢶⣾⣿⠏⠈⠀⠀⠀⡘⠁
⠀⠀⢀⣼⣿⣶⣿⣶⣦⣀⢀⣁⡀⢸⣿⠟⣠⣼⣣⣴⣿⣿⣿⣿⣿⡿⠒⠀⠄⠀⠀⠀⢀⡄⠀⣸⣯⣇⣛⣷⠃⠂⠴⠀⠀⠆
⠀⠀⠀⠀⠟⠛⢉⣿⣿⣿⣶⣉⣋⣠⣷⣌⣩⣾⣿⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠿⠛⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠧⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⢀⢀⣽⠛⠛⢠⡞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠿⠏⠀⠀⠀⠀⠈⠀⠀⠁⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⡏⠁⠀⠀⠀⠀⠲⣤⡀⠀⠀⠀⠀⠀⡠⠀⠈⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣆⠀⠀⠀⠠⢀⠀⠀⠀⠃⠐⠒⠆⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠀⠘⠏⠘⠀⠁⠀⠀⠀⠀⠀⠈⠒⠘⣦⡀⠀⠂⠀⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠⢄⣀⠀⠒⠀⢄
⣀⣀⣀⣀⡀⢀⡀⠤⠤⠤⠤⠄⠀⠀⠁⠒⠒⠒⠒⠒⠒⠐⠒⠒⠂⠙⠛⠲⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠤⠂⠈⠙⠉⠉
⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠈⠉⠉⠁⠉⠁⠂⠀⠁⠀⠀⠢⠄
⠀⠀⠀⣴⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠄
⠤⠶⠚⠛⠃⠑⠂⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠀⠀⠰⠶⣤⠠⠴⠚⠈⠉⠁⠀⠈⠁⠈⠉⠂⠀⠀⠀⠀⡈⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠤⠤⠒⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠙⠛⣛⡋⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⠄⠤⠒⠒⠂⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠰⣾⣿⠟⠀⣿⣿⣿⡄⠀⠀⠤⠀⠐⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠁⠠⠀⠛⠛⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⡄⠠⡀⣀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢐⠃⠇⠁⡇⠀⡇⠀⣼⠏⠀⠁⠀⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⢉⣥⡁⠀⠒⠀⢰⠻⠀⠀⠀⡐⡝⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡟⠉⠙⢡⠣⢀⠁⠀⠐⣸⠁⠀⠀⠀⡌⠀⠀⠀⠀⠠⠀⠀⠀⠰⡀⠀⠀⠆⠀⠀⢀⠄⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠁⠄⠄⣈⢐⠍⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠁⠀⠘⠀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⢧⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⠙⠋⠀⠀⢸⠀⠀⠀⠀⠔⠁⣠⠑⠄⠀⢠⠀⡇⠀⢀⠄⣠⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠓⠚⠆⠀⠀⡀⠀⢀⠌⢀⠜⠀⠑⠌⠢⠈⠀⡇⠠⢂⠔⠀⠑⢄⠈⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⣧⡤⢤⣤⣀⠀⠁⠀⠌⡠⠂⠀⠀⠀⠈⠢⡘⡀⡱⠡⠂⠀⠀⠀⠈⠢⡈⠆⢀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠨⡀⡜⠐⠁⠀⠀⠀⠀⠀⠀⢱⡜⣰⠁⠀⠀⠀⠀⠀⠀⠐⠌⡌
⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠃⠀⠀⠀⠀⠀⠀⢀⠏⡸⡉⢇⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⢸⡇⢰⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠈⠄⠀⠀⠀⠀⠔⢡⠎⠀⠈⢢⠑⠄⠀⠀⠀⠀⡐⠠
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣠⣤⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠠⠓⠐⠒⠒⠀⠤⠀⠀⡇⠀⠀⠀⠘⠊⠀⠀⠀⠀⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠍⣐⣂⣒⣛⣛⣛⣛⣛⣛⣛⣓⣒⣀⠨⡁⠢⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡘⣐⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⠸⡀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⡇⡟⡈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠑⠀⠠⠤⠤⢌⢧⣀⠀⠀⣀⢎⣔⣀⣢⡡⣀⠀⡀⣀⡼⣰⠇⠧⢀⡀⠀⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠉⠩⠐⠀⠀⠀⠀⠈⠂⠽⡟⢋⡊⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂

⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⢀⡤⠤⠦⠤⣄⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⣄
⠀⠀⠀⠀⡴⠋⢀⡠⠤⣀⠀⠙⣆⠀⠀⠀⡴⠁⡤⠒⠒⡆⠈⠳⡄⠀⠀⠀⡴⠉⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⢰⡇⣰⠁⣤⣿⣆⠙⡄⢸⠀⠀⢸⠁⠀⡇⠀⠀⠷⡢⠀⢹⠀⠀⢸⠁⣴⣒⣑⢒⣑⡲⡄⢹
⠀⠀⠀⠈⣇⠈⠢⢍⣛⡡⠜⠁⡼⠀⠀⠘⡆⠀⡇⠀⠀⢠⠃⢀⡞⠀⠀⠘⣆⠈⠲⠤⠤⠴⠊⢀⡞
⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡤⠞⠁⠀⠀⠀⠘⠦⣌⣒⣒⣁⡤⠊⠀⠀⠀⠀⠘⠢⣄⣀⣀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⠤⠶⠦⢤⡀⠀⠈⠉⠀⠀⢀⣠⠤⠶⠦⢤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢠⢖⠼⢖⢄⠉⢦⠀⠀⠀⣰⠋⠀⢠⠀⢀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠟⡄⣠⡼⠀⠘⡇⠀⠀⡇⠀⢀⠎⠀⠘⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡙⠤⣳⠃⠀⣸⠁⠀⠀⢧⠀⠸⠤⠄⠤⠜⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣉⣋⣁⣠⠞⠁⠀⠀⠀⠀⠳⢤⣀⣀⣀⡠⠞⠁

⠀⠀⠀⠀⣴⣖⢒⡆⡄⣠⣠⣄⠀⢀⣤⡀⣤⡄⣠⣤⢀⣤⡀⣤⡄⣠⣄⠀⢰⡆⣤⡄⣠⣄⢠⣤⡀
⠀⠀⠀⠀⠻⠉⠘⠇⠻⠇⠻⠿⠀⠘⠿⠛⠿⠏⠻⠸⠘⠿⠛⠿⠗⠻⠟⠀⠸⠛⠷⠇⠳⠞⠸⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⠭⠙⠋⠛⠚⠳⠶⢦⣤⣄⣀⣀⠀⠀⢙⣿⣶⡴⣚⠩⠐⠂⠈⠉⠀⠉⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡡⠊⠁⠀⠀⢀⠤⠀⠠⢄⠀⠀⠉⠉⠙⠛⠛⠃⢚⡙⢷⣿⣷⣄⠀⠀⠀⠀⢀⣀⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡰⠋⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⢿⡿⣷⣀⡴⢛⣩⣭⣿⣿⣦⣄⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⣰⢃⠎⠀⢀⠔⠂⠒⠒⢄⠑⢤⣀⣠⡴⠏⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢮⢻⣽⣿⢁⣾⣿⣿⣿⣿⣿⣿⠂⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢰⢁⠃⠀⠀⢊⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣿⠘⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠆⡈⠀⠀⠀⠈⠳⠤⣤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣦⢠⡘⣜⢧⡀⢀⡜⠉⠻⠟⣛⣛⡉⠕⠊⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⢀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣭⣽⣿⣿⣿⡖⠛⡏⠁⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠠⠃⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠠⣏⢰⣿⣿⣿⣿⣿⣿⡟⡀⠘⡀⠀⠘⢄⠀⢀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠱⢄⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⡠⠁⠀⠱⠀⠀⠈⣮⡴⠖⠒⠀⠈⠳⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠛⠭⠚⠁⠀⠀⠀⢳⣴⣾⣿⣆⠀⠀⠀⠀⠀⢹⡆⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⠄⣒⣲⡒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⢠⢎⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠰⢡⡟⠉⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣔⠪⠕⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢃⠘⠀⠀⠀⠀⠀⠀⢀⠽⠀⠀⠀⢠⡞⢉⣴⣶⣿⣿⣷⣄⠀⠀⠀⠈⢿⣿⣿⣿⣷⡄⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠓⣄⣀⠀⣀⢀⠴⡡⠃⠀⠀⠀⣿⣠⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢡⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠭⠅⠒⠁⠀⠀⠀⢀⡠⠖⠙⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠁
⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠞⠡⠄⠠⠀⣰⠴⠆⠀⣰⠋⣀⠀⠀⠐
⠀⠂⠀⢀⠀⢄⠎⠀⠒⣂⣸⠓⠀⠀⢀
⠸⠀⠀⢀⠡⠄⠀⢠⡞⡏⣏⠀⠂⠑
⡆⢀⠔⢁⡀⠀⠀⠉⠀⡁⡀⠀⠀⣠⠄⠀⡀
⡇⠈⠀⢀⠇⠀⠀⠄⡴⣻⠃⢀⣾⠁⠂⡸⠀⠀⠀⠠
⣇⡀⠀⣼⠇⠀⡏⣼⡀⠙⡇⢸⠀⠀⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⣿⠀⡾⣿⠃⢸⡇⠀⢱⣰⣧⠸⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢀⠀⠰
⢺⢸⠁⠓⠠⠈⣰⠀⣼⡿⣟⠆⠀⠀⠠⢊⡀⠀⣄⡎⠀⠀⠀⠀⡜⢢⢸⡀⠀⠀⠀⠀⠔
⠈⠀⠀⢀⡴⣿⣻⣸⠧⣧⢹⡆⠀⡜⠀⢸⣄⠀⣠⣧⡈⠀⡇⣰⠁⠀⢹⢣⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠄
⢰⡀⠰⣼⢣⣟⢸⣟⠀⣿⠀⣧⣄⠗⠀⡸⣏⢰⣇⣷⠳⣶⣧⡏⠲⣤⣟⡏⣄⡀⢠⣿⠀⠀⠀⢠⡆⢠⡇⡠⠀⠀⢠⠇⠀⠸⡆
⢸⣹⠀⣟⠸⣿⢸⡟⠀⣿⡇⢻⣿⠈⣴⡄⣿⣽⢹⣿⣇⣿⣿⢷⡀⣇⣻⣾⣾⠀⢿⣸⢆⡈⢣⣼⡇⠸⣧⢳⣠⠳⡟⢰⡀⢰⣻⡄⠰
⢿⣿⢰⣿⢸⣿⣾⣿⣇⣿⣇⢾⣿⡄⣽⣿⣿⣿⣻⣿⣏⣿⣿⡿⣿⣏⡿⣿⡿⡾⢸⣽⣏⢧⠀⢿⣿⡀⡇⠈⣏⢰⡏⢾⡇⣟⡿⣻⡀
⢸⣿⣾⣿⣸⡿⡿⣿⣿⠈⣏⢸⣿⣷⣿⣿⡟⣯⢿⢿⣿⣿⣿⣷⡌⢿⣿⣿⠅⣿⣼⢻⡌⣿⣶⢸⣿⢱⣷⠰⣿⢸⡇⣼⣿⡟⡇⢇⢱
⣜⣿⣿⣿⣿⣿⣷⣿⣿⡜⢻⡜⣿⣿⣿⢹⣷⣿⣼⣿⣿⡝⡏⣿⣧⡌⣿⣧⡤⣿⠻⣼⣿⣾⣿⢿⡟⣿⣿⣷⣿⣺⣿⢹⢸⣏⢧⣾
⣿⣏⣿⡘⣿⣾⣯⣿⡿⣶⢸⣇⣿⣽⣿⢸⣼⣿⣾⣇⣿⣧⡇⢿⣿⡿⣷⣿⣷⡟⠀⠿⣿⣿⢿⠛⣿⠸⣿⣿⣼⣿⣿⢸⣾⢻⡴⢹⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢤⠤⠀⠀⠀⠠⠤⣤⣀⣤⣤⡀⠀⠀⠄⠀⠀⠀⠤⠄⠀⢀⣀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣶⣷⣿⠶
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣟⣽⣭⣒⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡿⡍
⠀⢀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣘⣨⣿⣊⣻⣽⣍⣡⣤⡄⣠⡶⢾⣷⣀⠀⠀⠨⡯⠃⠀⠀⠀⠀⣀⡀
⠀⢈⣤⣀⣀⡈⣉⠛⢿⣿⠿⣿⣿⣿⡏⣽⡯⣻⣿⣿⡿⣛⣛⣛⣶⠮⠵⢿⣿⠋⢉⣐⣿⣿⡗⠂⠈⠉⠉⠛⠃
⠀⢠⣤⣤⣤⣉⣩⣉⣒⣶⣾⣿⠿⠿⠇⠻⠓⣻⣟⠛⠛⠛⠛⠋⠛⠂⠀⠸⠿⠿⠿⢿⣻⣭⣽⣤⣤⣤⣄⣠⡄
⠀⠘⢟⡛⠋⡉⠉⠉⠀⣤⣴⣶⠀⠀⠀⠀⠀⢹⣿⣥⣤⣴⢤⠶⠒⣶⣤⠖⢠⣤⡄⢠⣽⡿⠛⠿⠿⠟⠛⠛⠃
⠀⢠⣾⣷⣶⣷⣴⣷⣾⣌⠻⣇⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡈⣿⣿⡇⣶⠀⣿⣷⡆⢁⣾⣶⣮⣠⣤⣠⣦⡆
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠦⡤⢼⠄⠀⠀⠀⠙⠻⣿⣷⣇⡷⢹⣿⣤⣿⣭⣿⣬⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣄⣀⣀⣹⣿⣀⣤⣾⡄⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣟⣿⣻⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠛⠋⠉⠉⠉⠛⠛⠃

⣹⣦
⠈⢳⡀⠉⠲⣄⡀
⠀⢸⡇⣄⡀⠼⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⢤⣄⣀
⢀⡏⠸⠀⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⢸⠁⠀⠀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⢀⣀⣀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠉⡧⠀⠀⠀⠀⢀⡤⠤⢤⡄⠀⠀⠙
⠈⣆⠀⠀⠀⡼⠁⠀⠹⣄⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⡴⠛⠉⠉⠉⢻⡆⠀⠀⠀⠱⢤⣤⣤⠤⠞⠁⠀⠀⠀⡔⠁⠀⠀⠀⡿
⠀⠈⠳⢤⣴⠃⠀⢀⡴⠟⣦⡶⠛⠁⠀⠀⠀⠀⠀⠸⢅⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⡤⠞⠁⠀⠀⢠
⠀⠀⠀⠀⠀⢇⢠⠏⠀⠀⠈⢧⣠⠴⠶⠶⣦⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠈⢷⡀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⢠⡿⠳⡀⠀⠀⠀⠀⢳⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⡆⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠈⣇⠀⠙⣆⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢀⡴⠃⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠹⢦⣀⠈⢳⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠶⠋⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡙⣆⠀⠀⠀⠈⢧⣠⠤⠔⠒⠒⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠳⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡟⢦⡀⠀⠘⣧⡀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⢦⣀⣉⣹⣦⣼⡷⠞⠋⠁⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣄⣀⣀⣀⣠⣤⣤⣤⡴⠶⣾⠛⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠘⢷⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣿

⠀⠀⠀⠀⠔⢊⣉⣉⡑⠢⡀
⠀⠀⠀⠀⡴⠁⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⡶⢶⣤⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠠⣸⡀⡇⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠾⠄⠀⣿⣟⣛⣽⣇⣬⠟⠂
⠀⠀⠀⠀⠉⠉⠈⠑⡄⠘⡇⡇⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉
⠀⠀⠀⠸⣷⠀⠀⢀⠆⠀⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠈⠐⠢⠤
⠀⠀⠀⢸⣇⠔⠊⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀⠀⢀⣠⠴⣦⠀⢀⠌⠀⠰⠒⢆⠀⡀⠀⢸⠀⢠⠒⢢
⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠐⠈⠀⠀⠀⢸⠀⢸⠀⡇⠀⢸⠀⡌⠀⢸
⠀⠀⠀⠀⠀⣈⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢂⢸⠀⠘⠀⡇⠀⢸⢀⠃⠀⡌
⠀⠀⠠⠊⠉⠀⠉⠁⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠈⠀⠀⡇⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠒⠒⠛⠛⠓⠛⠛⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⡇⠀⣇⡇⠀⢠⡆⠀⢰
⠀⠀⠀⠂⠤⠤⠤⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠸⡇⠀⠈⠁⠀⠈⠀⠀⠘⠀⠀⠀⡠⠄⠒
⠀⠀⠀⡀⠤⠤⢄⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⢀⠔
⠀⠀⠊⠀⢀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⡠⠁
⠀⠀⡠⠦⠐⠠⠜⠠⠄⠢⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣴⠆⠀⠀⠀⠀⠀⠲⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⠀⣀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠂⠄⣀⡀⠠⠊⠀⠀⠀⠀⠀⠉⠑⠄⠀⠔⠉⠉

⠀⠀⠀⣀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣉⣀⠀⠀⠈⠳⡄⠀⠀⠠⠂⠀⠠⠀⠀⠐⢁⡀⠁⢀⠀⠀⠂
⠀⡐⠀⢀⠀⠀⠰⠀⠡⠀⠀⠀⠀⠋⠀⠀⠀⠑⡆⠀⠀⢹⠀⠀⢀⠀⠀⠀⠀⠁⠄⠈⠀⠀⠀⠀⠀⠀⠘⠀⣶⠾⠛⠛⢛⠒⠦⣄
⠰⠀⠀⠀⠢⡔⠁⠀⠀⡅⠀⠀⠀⡄⠀⠀⠀⠀⣸⠀⠀⢸⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠀⠀⠹⣄⣀⠔⠛⡆⠀⠀⣷
⠀⠑⠒⠒⠉⠈⠑⠒⠚⠀⠀⠀⠀⠐⣄⠀⢀⡴⠃⠀⢀⠜⠀⠀⠀⢰⠄⠀⠰⠀⢠⠀⠀⣠⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠙⠶⠚⠉
⠀⣏⠐⠒⠀⠀⠒⠂⢈⠇⠀⠀⠀⠀⠈⠉⠃⠒⠐⠊⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⢢⠴⠁
⠀⠀⠠⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⡙⠀⠀⠀⠠
⠀⠀⠀⠐⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠈⠑⠢⢀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠓⢦⠀⠀⠀⠀⠀⠈⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠰⠒⠀⠀⠠⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⣄⠐⡦⡌⢀⢴⠀⡀
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠤⡴⡼⠋⠁⠉⠙⢤⢠⠄
⠀⠙⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⠏⠀⠀⠀⠈⠢⡀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠙⡖⠒⢊⠒⣺⠉⠁⠀⠀⠠⠆⣹⠀⠀⠀⠀⠀⢸⡉⠤
⠀⠀⠙⠿⠿⠟⠁⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠘⢦⣀⠇⠀⠀⠀⠀⠀⠀⠀⢻⢀⠠⢐⡇⠀⠀⠀⠀⠀⠚⠰⠣⣀⠀⢀⣠⠺⠔⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠈⣇⠀⡽⠀⠀⠀⠀⠀⠀⠀⠋⠸⡞⢃⠝⠮⠀⠃
⠀⠀⠀⠈⡄⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⠃⢀⡤⠀⠀⠀⠀⠀⠘⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⢶⠿⠀⠁⠰⡀⠅⠀⠀⠀⢴⠿⠿⣿⣿⣿⠿⢗⡆⠀⠈⠀⠀⠏⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉
⠀⠀⠀⠈⡄⠀⠀⣴⠁⠀⠀⠀⠀⠈⣖⠒⠂⠒⠒⠂⡉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣄⢸⣷⣄⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠠⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⡷⢌⢄⠀⠀⠠⠂⠀⠀⠀⠠⢀⠀⢰⣿⠿⠛⠉⠉⠀⣶⠀⠈⠂⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠒⢰⠀⠀⠰⢐⠪⠜⠀⠘⠁⠀⠀⠀⠀⣼⣿⣧⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠈⠂⠩⡭⠐⠁⠀⠀⠀⠀⠀⠈⠂⠤⠠⠄⣊⣀⠀⡐⠁⠀⠀⠀⠀⠂⠀⠀⢀⣼⣿⣿⣿⡔⠀⠀⣀⣂⣴⣿⣀⣀⣀⠴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠒⠺⠿⠟⠛⠁⠀⠀⠀⠈⢙⡙⠛⢋⡋⠛⠋⣙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡶⣤⢀⣾⣷⣿⣽⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦
⠀⠀⠀⠀⠀⠚⠛⠘⠟⠻⠻⠽⠿⠿⠿⠿⠾⠿⠶⠿⠛⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠠⢀⣿⣿⣿⣿⣄⣠⣴⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣴⣿⡿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣻⣯⣿⣿⣿⢿⣿⣹⣯⣿⣛⣿⣿⣦⣁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣾⣿⣿⡉⠺⠾⠛⠛⠉⠉⠉⠉⠙⠛⠛⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠛⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⣼⢧⠀⠀⠀⢀⡒⠄⠀⠀⠀⠀⠀⠀⡔⣛⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⠀⢶⢤⠀⠀⢀⣠⢤⠘⢽⠓⠀⣀⡀⠰⣹⠏⠀⠄⠀⠀⡟⠁⠀⠰⣮⠆⠀⡀⠘⡿⠀⣿⠂
⠀⠀⠀⠀⢠⠀⢠⠘⠯⣅⠀⣡⡗⠈⢙⠄⣴⡏⠈⡟⢠⠀⢀⠠⢷⢁⣴⠆⡤⠸⣦⡉⡇⣱⣇⢸⡅⠋⢠⣸⢁⣶⣤⠚⡧⡀
⠀⠀⠀⠀⠂⠃⠟⡱⡛⠌⠻⣷⣴⡺⣏⡼⢯⢛⣾⡟⢸⣿⢃⣶⣾⢿⣴⣿⡞⣧⡷⡙⣣⠤⢷⢡⡮⢷⢫⢥⠿⡬⠱⠊⣼⢣⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠛⠈⠁⠀⠀⠃⠈⠀⠚⠈⠉⠉⠉⠘⠛⠈⠀⠋⠁⠉⠐⠙⠈⠉⠈⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡤⣤⣤⠄⢠⢤⣤⠀⣤⡤⣤⡤⣤⠀⢤⡤⢠⣤⡤⠤⢤⠠⣤⠠⣤⠄⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣌⡂⢠⡄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⣉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠀⠒⠐⠐⠂⢠⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠂⠐⠀⠀⠀⠀⠐⠺⣀⣀⡀⡀⢀⣠⠔⠃⠀⠀⠀⠀⢣⠠⠐⡆⠐⠒⠒⢂⢀⠐⡒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠀⣀⡄⠀⠀⠀⠀⠀⠀⠆⢠⣼⣧⡼⠇⠉⠁⠀⠀⠀⠆⠀⠀⢋⠦⠀⠇⠀⠀⠀⠀⠀⠠⡄⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⠄⠎⢙⣉⡀⠀⠀⠁⠀⣄⣠⠈⠀⠀⠀⠀⠀⠃⠀⠀⠴⡄⠀⢤⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡙⠉⠁⠀⠀⠀⠀⠠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⡀⠀⠁⠀⠦⢀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠄⠀⢠⠀⣂⡀⠦⠀⢀⠠⠤⡄⠀⠀⠀⠀⠀⡀⠦⠘⠛⠂⠁⣀⠀⠀⡀⢇⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⡀
⠀⠀⠀⠈⡀⠀⠂⠉⠀⠉⠀⠀⠀⠑⡀⠀⠐⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠰⠀⡃⠸⠀⠀⠀⠀⠂⡬⢁⡤⠂⠘⠓
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢱⡾⠃⠀⠀⡇⠀⠉⠀⠀⠰⠀⠀⠀⠀⠊⠀⠀⠀⡀⠌⢀⣉⡤⠂⠀⠀⠈⢚⠁⢸⡄⣀⠀⠀⠀⡤⢠
⠀⠀⠀⠀⠲⠄⠈⠀⠀⠀⠀⠀⠀⢀⠀⢠⠜⠂⠀⠀⠀⠀⠐⠀⠐⠂⠠⠊⠁⠀⠊⠁⠀⠀⠀⠀⠀⠛⠀⠈⠀⠀⢀⢀⡴⠇⠺⠢
⠀⠀⠀⠀⠀⠤⣄⠀⠁⠒⠐⠒⠀⠀⡠⠐⠠⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠈⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠘⠒⠈⠁⠂⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠰⠶⠲⠆⠐⠗⠶⠂⠲⠖⠲⠖⠶⠀⠶⠶⠰⠶⠲⠚⠲⠀⠖⠒⠆⠳⠆
⠀⠀⠀⢀⠔⠛⠃⠀⠧⠔⢠⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢢⠀⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡁⠀⠀⠀⠀⠀⠀⠈⠤⢤⡄⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠉⣥⠀⠀⡄⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠱⣀⡀⠀⠀⢠⠄⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡞
⠀⠀⠀⠙⡇⠲⢲⠒⠆⠀⠒⣠⠛⠄⠀⠀⠀⠀⠀⠀⠉⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁
⠀⠀⠀⠀⠀⠈⠋⠠⠛⠃⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠆⢆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠀⡀⠀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣈⠀⠀⢀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠂⢈⠉⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠐⢢⠘⠓
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠈⣈⠀⡜⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠒⠈⠘⠁
⠀⠀⠀⠀⠀⠠⠄⠀⢀⠂⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠉⢈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠑⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣌⠁⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠂⠀⠀⠀⠀⠀⠀⡀⠚⠢⡄⠀⠀⠴⠜⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠉⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⣀⣀⡀⠀⠀⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⠐⠀⡀⠈⠸⣧⡗⠉⠀⠆⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⠀⠀⠀⠀⠑⠂⠊⠁⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠉⠢⢄
⠀⠀⡠⠒⠉⠁⠀⠈⠉⠐⢤⡉⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠁⣠⠔⠊⡉⠀⠀⠉⠑⠢⡀
⢀⠊⠀⠀⠔⡈⠭⢅⠢⡀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⡄⠀⠀⠈⠰⠒⠀⠀⠃⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠘⠒⠀⠤⠄
⡇⠀⠀⠀⠀⠁⡐⡐⡠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡯⠀⡏⡇⠌⣭⠄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠄
⠠⡀⠀⠀⢀⠈⠀⢀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠃⠀⠃⠸⠁⠲⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠑⢄⠀⠀⠑⠒⠁⠀⠀⣠⠞⠀⠀⠀⠀⣀⡀⣀⡀⣀⠀⠀⣀⡀⢀⡀⢀⣀⠀⠀⠀⠀⠘⢦⡀⠈⠂⠤⠤⠐⠁⢀⠔⠁
⠀⠀⠀⠉⠐⠒⠀⠐⠒⠉⠀⠀⠀⠀⠀⠘⠦⡄⡧⠄⡟⣄⠀⠧⡄⠠⠄⠳⢬⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠓⠂⠃⠘⠂⠒⠊⠐⠂⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡀⡀⢀⣀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠎⠉⢂⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠒⠇⠒⠸⠒⠂⠲⠲⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠙⠆⠀⠈⠀⠀⠞⠁⠀⠀⠃⠈⠉⠉⠉⠁⠸⠀⠀⠀⡠⠂⠀⠀⠀⠢⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⢄⡀⢀⠔⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠢⠤⡀⠀⡠⠤⠂⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠈⠀⠀⢀⠔⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣶⣶⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣶⣶⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢰⣇⠀⣴⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⢠⣶⣾⣿⣿⡍⡅⠀⠀⠀⢠⡀⣼⣟⣩⣁⡀
⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⢿⣿⣿⣿⣧⣗⠀⠺⣿⣄⠀⢹⣿⣟⣋⣠⡐⢀
⠀⠀⣴⡈⢤⠄⠀⠀⠀⠀⠈⠁⠀⠉⠀⢻⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣟⣁⣀⣿⡟⢩⢹⣿⣟⣟⠩⢉⣯⡤⠆
⠀⠶⠿⣭⡤⠶⢖⠉⠉⠉⠁⠈⠃⠋⠉⠙⡛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠋⠀⠈⠙⠛⠛⠐⠊⠐⠀⠉⠀⣀
⠀⠀⠀⡔⣤⠡⢄⠀⣤⣀⡠⣤⠀⡠⠤⢠⢄⢄⠀⠀⠀⢀⣠⡄⢠⢀⠀⠀⠀⠠⣀⢀⡀⢀⡀⡀⡀⢀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⢹⡶⡌⢱⢛⠀⣿⡌⠉⣢⡽⢇⣦⡏⢀⢜⣮⣆⠀⢇⢁⠡⣉⣬⢠⣴⡧⣌⡅⣚⡤⣡⡶⠗⠠⠄⠀⠵⢹⣅⡠⡄
⠀⠀⣹⣽⣇⣷⢡⠲⣦⡆⢼⡣⡇⣻⡀⣧⠨⠞⢸⡟⠻⣤⡘⢹⣫⡍⣊⡡⢿⢳⣼⠽⢿⠾⠃⢜⡋⠦⠟⠃⢨⣏⣀
⠀⠀⢸⡇⡏⢾⢸⡟⢫⡇⢻⡟⣇⢺⣆⡟⢻⡯⢱⡏⠿⡳⢻⢾⣷⡄⣿⢠⣬⡀⢸⡷⣺⣧⡴⣦⢶⡖⡐⢺⣫⠌⠐
⠀⠀⣹⣏⡉⣺⠘⠒⢸⡇⢤⠮⣯⣼⠇⣷⢸⣋⣸⠎⠑⡟⡴⠛⢻⠂⠿⠠⠾⠉⣸⣏⠟⣻⣐⡗⣻⡿⠆⣶⠡⡆
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠚⠷⠤⠤⣭⣤⣄⣹⡅⠉⠈⣿⠀⠉⠃⣛⠄⠣⠀⢸⡇⢀⣹⣎⡟⣹⠛⠁⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠒⠒⠦⠿⣀⣀⡀⢸⡇⠀⠀⢸⡏⠈⠐⠋⡟⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠓⠒⠓⠠⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣶⠞⠂⠲⣄⡠⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⣾⡁⠀⣹⠏⡰⢻⣿⠃⠀⢀⡴⠋⢀⣀⣀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⣄⠙⣶⠁⣸⠁⡃⣿⡼⢀⣿⣶⣿⣿⡿⣿⣿⣶⣤⣽⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠛⠂⠀⢨⣧⣿⣆⣿⣿⡇⣸⣿⣿⣏⣀⣠⠤⠾⠿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣁⣀⠀⠀⠀⣈⣿⣿⢿⣿⣿⣿⡿⠿⠛⠛⢿⣟⠒⠐⠀⠈⠺⣿⣯⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠋⢈⣩⣿⣿⣿⣿⠋⠀⠀⠈⠻⠟⠀⠀⠀⠀⠈⠛⢿⣗⡂⠀⠀⠙⢿⣇⣈⣢
⠀⠀⠀⠀⠀⠀⢠⠞⢁⣤⠖⠋⣁⣠⣾⣿⣿⣿⠇⠀⠀⠀⢠⡄⢀⡀⠀⠀⠀⠀⢻⡙⢿⣿⡟⠛⠛⠢⡁⠀⢣
⠀⠀⠀⠀⠀⢠⠃⡤⠋⠀⢠⣾⣿⣿⣷⣿⠟⠉⣀⡀⠀⠀⠀⠙⡟⠀⠀⣀⣠⣄⡀⣧⠘⣿⠙⠷⣦⣄⠈⠢⡈⡃
⠀⠀⠀⠀⠀⡌⠀⠀⠈⣉⣵⣾⣿⢃⣼⢻⠑⢿⣿⠿⣞⡧⠀⠀⠀⢀⠐⣿⣿⠟⠁⠹⣆⣿⠀⠀⠀⠙⠦⡀⠈⣇
⠀⠀⠀⠀⠀⠁⠀⠔⠀⠀⣩⣿⣿⣿⡏⠀⠀⠀⠀⣦⢹⡷⠂⠀⠀⠊⠻⣯⣷⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢉⠆⢼⡆
⠀⠀⠀⠀⠀⢰⠁⠀⢠⡞⠉⠁⢻⣿⣿⡄⠀⠀⠀⢫⣟⣵⠃⠀⠀⠀⢲⡌⢿⠂⠀⣰⢻⣿⣆⠀⠀⠀⠀⠈⢂⢸⣷
⠀⠀⠀⠀⠀⣿⠊⣰⣾⠁⠀⠆⠘⡟⣧⣑⠀⠀⡶⠀⠻⣿⡟⢛⠛⣹⣿⠗⠈⢱⡄⠁⢀⠟⠙⢆⠀⠀⢦⡀⠈⢧⣻⡄
⠀⠀⠀⠀⠠⣿⡸⢱⡇⠀⠘⠀⠀⢃⠘⢿⣶⣾⣇⡀⣠⡬⠿⢿⡟⢡⣤⣤⣤⡬⣷⣾⡏⢳⡀⠀⠣⠀⠈⢷⡀⠈⢿⠛⠦⠄
⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⣸⡤⠖⣿⣿⡥⠖⠚⠫⠀⣸⣧⣸⣿⣿⣚⣳⣾⡿⠤⢌⣿⠀⠐⠂⠀⢸⣧⠀⢸⠂
⠀⠀⠀⠀⠀⠹⠀⠘⣆⢀⡀⠐⢿⠁⣀⠼⠟⣹⣦⢂⣡⠴⢛⣿⣿⡿⠳⢦⣭⣿⣿⡧⠀⠀⢸⡆⠀⢸⠀⠀⣿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⠰⡼⡏⠀⣠⣿⣿⣿⡏⡏⢀⡈⠛⠈⠀⠀⣄⢨⡏⠁⠻⣦⡀⠘⠇⢀⣞⠀⠀⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢩⣿⠞⢽⣿⡿⠈⡇⣇⡎⠻⣄⠀⢀⡜⢹⠏⠁⠀⠀⠈⢷⣼⣷⡿⠃⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⡾⣿⡇⠀⠀⢸⣄⠀⠈⠀⢀⠀⠀⡆⢸⣆⠀⠀⢸⣿⡿⠁⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⢙⠁⠀⣦⡟⠹⡆⠀⠀⡿⡇⠀⠀⠸⠻⣇⠀⢠⣿⠇⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⣿⡇⠀⠹⡄⢠⠇⢿⠀⠀⠇⠀⢸⣄⡾⣿⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⡀⢸⠀⠃⠀⠀⠹⣾⠀⢸⠀⡜⠀⠀⢸⡟⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣸⡀⠀⠀⠀⠀⠙⡀⢸⡟⠀⠀⠀⠎⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠁⠘

⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣼⣿⣅⠀⠀⠀⠰⢾⠧⠄
⠀⠀⠠⣾⣿⣏⠀⠀⢀⣴⣿⣶⣄⡀
⠀⢀⣼⣿⣿⣯⡅⠀⣼⣿⣿⣿⣮⡅
⠀⣨⣿⣿⣿⣷⣶⣿⠿⣿⣿⣿⡿⣿
⣴⣶⣿⣿⣿⣿⣷⡖⢀⣼⣿⣿⣿⣷⡄
⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣶⡄
⣿⣻⣿⣿⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⢠⣆
⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣆⢠⣿⣷⠀⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⡄⢠⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣿⣯⣷⣷⣧⣤⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠛⢛⠛⠿⠿⣿⣿⣿⣿⡯⢿⡷⣤⣤⣤⣤⣤⣶⣶⠶⠀⢁
⣤⣤⣛⣛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣶⣦⣿⣭⣽⣿⣷⣶⣷⣾⣾⣶⣶⣶⣶⣾⠋⠁
⠉⠉⠛⠿⡿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⠉⠛⠯⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴
⠀⠀⠠⣄⠀⠀⠀⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣤⣄⠀⠀⠀⠉⠁⠚⠿⢿⣿⣿⣿⣿⣛⣿⣿⠙⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠙⠆⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣉⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠉⠙⠻⣿⣻⣿⣿⣿⡏⠁
⣷⣦⡀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣴⣶⣶⣤⣙⣣⣾⣿⣷⣤⡄

⠀⠀⢀⣀⣀⣀⣀⠀⠀⢠⠀⠀⢄⠀⠀⠐⡄⠀⠀⠀⢀⡠⠤⠄⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣄
⠊⠉⡀⠀⠀⠀⠀⠈⠱⠒⠦⡀⠀⠆⢀⠀⠚⠀⠀⣀⠨⠤⠀⢀⠠⠀⠛⠁⢄⡀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠂⠀⠈⠤⠶⢤⣖⡀⠀⠉⠈⠀⠀⠲⡀⠔⠓⢤⠚⠃
⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠈⠢⠚⠀⠀⠀⠄⠀⠀⠐⡖⠂⣠⣤⠀⠀⠀⠀⠙⣤⠤⠀⠒⠂⠀⠉⠁⠀⠀⠀⡀⠐⠀⠀⠀⠉⠢⡀⠀⠀⠴⠦⡁⠀⠀⠀⠡⠶
⠀⠀⠀⠀⢌⠀⠀⠀⢁⢀⣀⠀⠀⡡⠀⣛⡀⠀⠀⠐⠃⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⢄⠀⠀⠀⠀⠀⠂⠁⠀⡠⠠⠀⠀⠄⠀⢈⠳⢄⠀⣀⡕⠄⡠⠔⢥⡀
⠀⠐⠒⠂⣀⠔⠂⠉⠈⠀⢉⠈⡙⣤⢤⠇⠙⢤⠠⠄⢀⡀⠋⠀⠐⢄⠒⠒⠀⢀⠠⠼⠀⠀⠧⠄⣀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠀⠀⠡⡀⠑⢌⠀⠐⠗
⠀⠀⡠⠀⠓⠀⠀⡤⠀⠒⠉⠀⢀⡈⣎⠀⡠⠊⠉⠉⠀⡇⠀⠒⢀⠀⠑⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠡⠁⠀⠀⠀⠧⠀⠀⠀⠐⠄⠀⠑⢄⠀⠀⣀⠄
⢀⠎⠀⡰⠉⠈⠣⣀⠀⠀⠀⣩⣄⡄⠈⣱⣷⡄⠀⢴⠏⢀⣄⣀⠀⠈⠀⠈⠆⠈⠂⢀⣤⠀⠀⠀⠀⠀⠀⠀⠝⠳⠄⠀⢤⣀⠀⠈⡀⠀⠀⠀⠄⠀⠠⡑⢎
⢃⠔⢨⠅⠠⠀⠊⠀⢁⡦⠁⡸⠂⠘⡏⠀⠀⢰⠀⣈⣶⠂⠈⡄⠀⠉⠁⠒⠬⡄⠒⠀⠀⠀⠤⠤⠤⠤⢤⠎⠰⠇⠀⠀⠀⠀⠓⠢⣄⠠⠤⠤⢈⣂⠀⠀⠄⠳⡄
⠠⠄⠚⠀⠀⠀⠀⠈⢣⡀⠀⢠⣴⡈⠉⠑⠲⡗⠻⣄⢈⣶⣍⠈⢑⠶⠀⠀⠀⠀⠒⠢⠀⠐⠒⠒⠒⠒⠚⠒⠓⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠠⠀⠈⢩⠉⠉⠁⠚
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢹⠂⠉⠛⠉⢲⠖⠋⠀⠀⠈⠁⣉⡇⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠆
⠀⢠⠄⠀⠀⠐⠠⠄⠀⠨⠤⢤⠚⠤⣈⡆⠀⣴⣦⠉⠉⣶⡎⠉⠁⣰⠲⡀⠀⢰⠋⠉⠉⠙⢲⣼⠋⠉⠉⠑⢦⢰⡖⣄⠀⢠⢤⡄⠀⠀⠀⠀⡁⠪⠥⠤⠤⠤⠄
⠀⢸⡠⠀⠀⠢⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⣏⣿⢀⣠⡏⡇⠀⢠⠏⣀⢳⠀⢸⡇⠀⠛⠀⣸⢻⠀⠈⠛⠀⣸⠃⠹⣼⢶⣫⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠖⠆
⠀⢻⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣉⢹⠛⠒⡗⡇⢠⣏⣀⣉⡀⢧⢸⢰⡖⠒⠋⠁⢸⢰⠖⠒⠋⠁⠀⠀⠘⣲⡇⠀⠀⠀⠀⠀⠀⣄
⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⢨⣿⠀⠀⣷⠇⣾⠼⠁⠀⠱⠼⠦⠶⠇⠀⠀⠀⠸⠾⠀⠀⠀⠀⠀⠀⠘⣯⠇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣀⢠⣤⡀⣠⢤⠀⠀⡴⢦⣴⢲⡀⠀⠰⠒⠆⠖⣦⠀⢀⡖⢶⢠⣤⣤⣤⣤⡀⣤⣤⣤⣀⡀⠀⠀⠀⡗
⠀⠀⡆⠀⢀⠠⠀⡀⠀⠀⠾⠀⡇⢠⠏⡴⠒⢦⣿⣜⢺⠀⠀⡏⣿⡿⣀⣇⢠⢷⡀⣆⡆⣸⡄⡸⣧⢸⢾⣰⠒⠚⠚⠃⡆⠀⣤⠀⠙⡆⠀⠀⡇
⠀⠈⣵⠚⠀⠀⠀⠈⠁⠀⢸⠀⡇⠈⠳⢯⣷⠲⣄⢸⣼⠀⠀⡇⣼⣯⣿⣸⡼⣸⠞⢃⣤⣧⣷⡇⣿⢺⢸⢈⣯⣉⣹⠀⡇⡀⢀⣠⠜⠁⠀⠀⡃
⢀⠞⢰⡀⠆⠁⠀⠀⠀⠀⢺⠀⡇⠸⡟⢧⣬⡷⣹⢳⡜⠦⠴⢃⡽⡇⣺⣏⢣⡟⣤⣾⠀⡿⡈⣼⢋⣸⢸⣹⣀⣀⣀⡀⠇⡟⢦⡑⢦⡀⠀⠀⡅⠀⠈
⠊⠀⠀⣇⠰⠀⠀⠄⠀⠀⢸⠀⡇⠀⠉⠓⠒⠛⠁⠀⠙⠓⠒⠚⠁⠻⠏⠙⠚⠀⠛⠛⠿⠇⠓⠋⠘⠛⠸⠾⠶⠚⠺⠋⠛⠃⠀⠉⠉⠁⠀⢠⠄⣀⠤⢄
⠠⡀⠀⢹⠀⢃⠘⠀⠀⠀⠘⠤⠇⡀⣀⠀⢀⢀⡀⠀⠀⡀⡄⠀⠀⣠⢠⡄⠀⠀⠀⠄⠀⠄⠒⠀⠀⠀⠤⠤⠤⠄⠤⠰⠀⠠⠖⠀⠐⠐⠒⠘⠁⠁⠂⠀⠀⠐
⠀⠈⠚⠀⢃⠈⢄⠠⠂⠀⠀⠀⠄⠠⠀⢀⠸⣀⣠⣶⡄⡅⡇⠐⠴⢁⠎⠄⡀⠀⠀⡀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠠
⢀⠖⠀⠀⠘⣄⠚⠄⠀⠀⠀⠀⠤⠠⢰⡁⡀⠈⣧⡉⠀⢱⣇⣠⢁⡆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⢠⣔⡂⠁⠀⠀⡤⠓⢌⠑⢤⡀⠀⠀⠀⠈
⠁⣀⠀⠀⠀⠸⡀⠚⠀⠀⠀⠀⠀⠠⡉⠀⠀⠠⠿⢶⠀⠉⠐⡄⠉⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡗⠉⠀⠀⠀⠀⠀⠦⢤⡼⠁⠐⠙⢆
⠙⠛⠛⠁⠀⠀⢱⠀⠀⠀⠀⣶⡀⠐⠉⢢⣰⠁⠀⠀⣣⣠⡾⢔⡊⣡⣷⡆⠀⠀⠀⠀⠀⢀⡠⠒⠒⠆⠀⠀⠀⡎⠀⠀⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠱⡈⠆
⠀⠀⠀⠠⠄⠤⠀⢧⠀⠀⠀⠽⡓⠉⠞⠙⠴⢇⢲⡖⣏⠀⠀⠀⠵⠈⠁⠐⢄⠀⠀⠀⢠⠋⢀⠎⣁⠛⡄⠀⢸⡇⠀⠀⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠐
⠀⠀⠀⠀⢀⠠⠀⠀⢣⡀⠈⠓⠿⣶⣀⠀⠀⠘⠷⠎⠁⠀⠈⢳⣤⡆⠀⠰⠦⡀⠀⠀⠘⢆⠈⠎⠾⣰⠃⠀⠘⡇⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠃⠒⠊⠁⠀⢣⡀⠀⡰⠋⠛⠄⠀⠀⢴⡰⣀⠀⡠⠊⠙⢃⠐⠀⠀⡘⠴⠆⠱⠀⠙⠒⠊⠁⠀⠀⢀⡐⣆⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡰⠁
⠉⠀⠀⠀⠀⠀⠄⠂⠀⡐⠁⢲⡀⡀⠀⠘⠒⠖⡁⢠⡌⠉⢀⡀⠀⠀⣦⠴⠚⠁⠀⠀⠀⠀⠀⠐⠒⠂⠁⠂⠁⠀⠈⠢⣀⠀⠀⠀⠀⢀⠌⠀⠀⡠⠞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠤⠘⠉⠑⠠⠤⠤⡼⢀⠄⠈⠉⠣⢈⠁⢀⠁⠀⠀⠀⠀⢀⣠⠄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠾⠐⠒⠉⢀⡀⠤⠂
⠀⠀⠀⠁⠉⠐⠈⠀⠀⠁⠀⠀⠀⠐⠒⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠘⠓⠒⠒⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣁⠀⠀⡀⣀
⣿⣿⡟⠻⠟⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠠⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠐⠄⠁⠀⠀⠂⠀⠀⠠⠀⠀⠀⠠⠖⠒⠓⠒⢄
⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠂⡀⠂⠀⠀⠐⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀⡀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⡦⠶⣂⡠⣀⣰⠦⢴⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠀⠀⡀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣗⣾⠀⠀⠀⠘⠋⠈⠀⠀⠠⠀⠁⠀⠀⠂⠀⠀⠬⣘⠒⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⠑⠂⠴⠊⠁⠈⠱⢦⠀⢄⡤⠀⢆⠁⠀⠀⠀⠀⡌⠈⠀⣀⡠⠋⠁
⠀⠀⠀⠀⠀⠅⡀⠘⠀⡀⠊⠁⢠⠀⠃⣀⣾⣒⣛⣋⠉⠉⠉⣙⢂⣋⣛⣺⢄
⠀⠀⠀⠀⠀⣀⠁⠠⠂⠀⠰⠀⠀⠐⠀⠀⠀⠀⠁⠉⠈⠉⠉⠉⠉⠈⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣈⠂⡀⠈⢠⠀⠁⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂
⠀⠀⠀⠀⢀⣐⣄⠐⠂⠤⠌⠠⠤⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⢦⣐⠂
⠀⠀⠀⠈⣞⠐⡼⠆⠐⠆⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⣂⢸⠡
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡜⠀⠀⠀⠠⠄⡐⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠸⠀⡇⠀⡀⠀⠐⣋⢺⢉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠰⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⠏⠏⠰⠆⠀⠀⠀⠄
⠀⠐⠀⠀⢀⡨⡄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠠⠌⠀⠆⠀⡂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠊⠀⠀⠀⠐⡀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠆⠃⠀⡈⠁⢢⠀⢠⡤⠀⠙⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⢸⠀⠀⡀⠀⠀⠰⠀⠀⠀⠁⠀⠠⠀⡆⠀⠐⢠⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠠⢒⡀⠀⠀⠁⠸
⠀⠀⠉⠀⠀⠀⠀⠄⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢂⠀⠘⠃⠀⠀⡀⢀⠀⠀⠀⠀⢠⢠⠀⠟⡄⠀⠀⠀⠀⠠
⠀⠈⠀⠀⠀⠀⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⠀⠀⡺⠂⠀⠀⠀⠠⠃⠈⠀⠇⠀⠀⠄⠀⠣⠜

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⡄⠀⠀⢀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⣹⡿⠟⠿⢦⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣶⣶⣿⠟⠀⠁⠀⢉⡟⠉⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡛⠂
⠀⠀⡆⢸⠀⡆⡀⠀⠀⠚⠛⠛⠛⠛⠉⠙⢻⣿⣿⠋⠀⠀⠀⠀⣞⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⣄⣠⣼⣿⣿⣧⠀⠀⠒⠒⠶⠛⠀⣿⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣹⣿⣿⣿⡀⢰⡄⡦⠀⠀⠀⠉⢠⢜⣿⣿⣿⣯⣼⣿⣿⣿⠟
⠀⣀⣤⡤⠤⠤⢐⣒⣄⡨⣤⠤⠖⢒⣣⣬⣼⡭⢽⠛⠛⣿⣶⡶⠶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧
⢉⢩⣀⣤⢴⠞⠍⠉⢠⣦⣴⡶⠟⠉⣉⣡⣴⣶⡾⠟⢋⣭⣰⣤⣄⣼⣧⣯⣹⡟⣟⠛⠛⠉⠉⠉⠁
⠛⠛⠉⣀⣤⣤⠼⠚⠛⠥⣤⣴⣶⣿⠛⠙⡋⣠⣦⣼⣿⣿⠏⠛⠋⠉⠉⠀⠀⠀⢳⡝⡄
⣶⡞⡿⠿⠷⠶⠶⠶⢿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠰⢶⣶⣦⡀⣶⡄⣤⡀⠀⠀⢀⡤⣠⡶⣠⣶⣦⠶⢦⣆⢠⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⣄⣠
⠀⠀⣛⠋⢽⠟⢫⡿⢓⠶⢶⠛⢿⡝⠿⡯⠛⣓⠀⠠⣿⡟⣽⡾⣱⣯⢣⢰⣄⠀⢠⠆⡴⣹⣞⡟⣯⢯⣷
⣤⣾⣌⢃⡀⣀⠀⣤⡀⠀⠀⢠⡄⢀⡀⢀⢘⣼⣧⣤⣠⣾⢿⢷⡿⡻⣿⢽⣼⠀⣧⣯⣷⢷⣻⡿⡿⣗⣤
⠀⢙⣿⣽⣧⣹⣷⣼⣗⡶⢶⢿⣧⣿⣇⣾⣹⣷⡋⠀⠉⠀⠟⢫⡮⠞⡵⡺⠛⣶⠛⢿⣪⡳⢽⣍⠺⠂⠈
⠀⣈⠁⠸⠃⠘⠋⠉⠘⠀⠀⠋⠉⠙⠀⠹⠆⠈⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⡜⠀⢳⡀⠉⠃
⠀⣻⣴⡆⣤⢀⡀⠀⠀⠀⠀⢀⠀⢀⠀⣦⢰⣦⣟⢰⢲⣀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⢠⣄⡔
⠀⠉⣩⣷⣿⣼⣇⣸⡇⠀⠀⣼⣇⣼⣧⣿⣮⣉⠁⠈⠙⣻⣿⢾⣶⣷⣴⡄⢄⠀⣠⢤⢶⣞⣷⣿⣿⣟⠛
⠀⠀⠀⠀⠰⠟⢡⠿⠋⡶⢖⠙⢿⡍⠻⠄⠀⠀⠀⠀⠺⠛⣡⣿⢗⣿⢾⣿⠚⠋⠓⣿⡷⣿⣞⢿⣬⠓⠓
⢰⠓⡄⡠⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢠⣄⡰⢻⠄⠀⠀⠉⠀⠛⠁⠛⠉⠀⠀⠀⠈⠛⠈⠛⠀⠉
⠀⠛⢯⣧⡷⡟⡆⡴⢄⠀⠀⡴⣆⣰⢹⢷⣾⡿⠋⠀⠀⠐⢖⡄⠀⣶⡄⡴⡄⠀⢀⣦⢀⣶⠀⢠⣶⠂
⠀⢮⠽⠋⣓⣿⡧⣵⣾⠀⠀⣷⡯⢿⣿⡊⠻⢯⡧⠰⣿⢿⣾⡿⣲⣿⢧⣳⣷⠀⣼⣜⣸⣿⣶⠻⡷⡿⢿
⠀⠀⠀⢰⠥⠛⣴⣻⠏⡽⢯⠹⣟⣎⠻⠼⡀⠀⠀⠀⠀⠺⠊⠾⠟⡵⣊⠝⢛⡶⡛⠻⣕⢦⡳⠷⠙⠿
⠺⣷⣦⣿⣆⣤⠉⠀⠈⠀⠈⠀⠀⢁⣤⣸⣷⣴⣾⠇⠀⠀⠀⠀⠀⠈⠁⢠⠋⠀⠘⣆⠀⠁
⢠⣺⣿⣿⣻⣽⣷⣦⡀⠀⠀⢀⣶⣾⣯⣿⣿⣿⣳⡄⡶⡀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡶
⠈⣉⣭⢤⣽⣿⣉⣿⡇⠀⠀⢾⣿⣸⣿⣧⡤⣍⡉⠀⠳⣿⣿⡔⡶⣜⠿⣢⣤⠛⣧⣴⡿⣣⢴⢆⣾⣿⠞
⠀⠙⠛⠛⠉⣤⣾⡿⡹⠓⠺⣝⢿⣶⣄⠉⠛⠛⠋⠀⠀⠈⢛⣿⡬⠾⣷⡚⢏⣷⣹⠓⣶⠷⢥⣾⡟⠁
⢀⣀⣐⣷⣈⣯⢁⡀⠀⠀⠀⠀⢀⣈⣽⣠⣿⣀⣀⡀⠈⠓⠿⠚⠁⣴⡷⠃⠘⠁⠓⠀⢯⣧⠀⠑⠾⠞⠃
⢉⣿⠟⠛⢻⡿⣿⣧⡄⠀⠀⣠⣼⣿⢿⠟⠛⠻⣿⢁⢤⣿⣷⣼⣷⣾⣦⢶⡄⠀⢠⣶⣰⣶⣾⣿⣼⣿⡤
⠀⠉⠀⠀⠀⠙⠿⢿⣿⡷⢿⣿⡿⠿⠉⠀⠀⠀⠉⠈⠉⠾⠋⠾⠿⡿⢫⡿⢳⠶⢞⢿⡝⢿⡟⠵⠙⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠓⠺⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⣄
⠀⠀⠀⠀⠀⠀⡞⠛⡇⠀⣿⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⡟⠙⡇⠀⡇⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠚⠛⠓⢦⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⣿⠀⣧⡞⠓⡆⠀⠀⠀⠀⠀⠸⠁⠺⣤⡀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⡇⠀⠃⠀⠃⠀⠛⠀⣿⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡼⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⣾⠀⣀⣤⡀⠀⠀⠀⣠⣄⡀⠘⡇
⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣤⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⠤⠉⠲⠴⠚⠁⢤⣥⠴⠃
⠀⠀⠀⠀⠀⠀⠙⠒⠲⠖⠒⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠛⠉⠉⠉⠛⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⡉⠀⠀⠀⠈⠉⠁⠀⠀⠀⢉⣓⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡾⠁⠀⣠⣤⠀⠀⠀⢳⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢮⣉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⣉⡴⠋⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣇⠀⠀⢿⣿⡿⠀⠀⢸⠃⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣄⣀⣠⣤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣽⣄⠀⠀⠀⠀⠀⣠⣏⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠈⠐⠠⠀⠀⠢⠐⠈⠀⠀⠂⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠐⠀⠐⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⣀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠢⠀⠀⡀⠀⠀⠀⠀⡐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠈⣆⠂⠐⠀⠀⠐⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠁⠘⠀⠀⠀⠀⡅⠙⠂⠀⡀⠀⠀⢀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠄⠀⠄⠀⠀⠀⠀⠈⠀⠈⡇⠀⡠⠰⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⢀⡀⠀⢠⣄⠀⠀⠀⠈⠒⠤⠚⠀⠀⠀⠀⠀⣷⠄⠀⠈⠁⡀⠁⠜⠀⡀⠁⢀⣠⠔⢃⠀⣠⠀⣂⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⡇⠀⢦⠠⡉⠂⠺⠀⣈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢫⠁⠀⣱⠀⢸⡟⣉⣉⠀⢈⣐⡛⣋⣩⣯⣷⣿⣿⣟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠐⠀⠀⠀⠙⠋⠉⠁⢀⠀⠉⠉⠁⣹⠳⣶⣂⡀⠀⡐⣿⡊⢀⢀⠁⠈⠈⠉⠉⠉⢩⢩⣍⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⡉⢹⡍⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠃⠙⠘⠘⠂⠁⠀⠁⠀⠀⠀⠀⠈⠀⠉⠋⠀⠘⠀⠈⠉⠈⠁⠁⠉⠀⠉⠈⠈
⠀⠀⠀⠀⠀⠢⣰⠈⠀⠠⢍⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⢢⣢⠀⠀⠀⡀⠀⠀⢠⡴⣆⢨⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⠄⡀⠐⠅⡇⠀⠀⠙⠟⠺⠏⠀⠀⠀⠀⠊⠱⠃⠠⠠⠀⠀⠀⠀⠀⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠄⠤⢤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣤⠎⠩⢞⠀⠅⠉⠒⠠⢬⣃⡉⠉⣹⠋⠐⠤⡀
⠀⠀⠀⠀⣚⠿⠦⠁⠡⠀⠋⠓⢒⠒⠃⠐⠌⠉⡁⠀⣤⡀⠈
⠀⠀⠀⢼⡛⣠⢡⠰⡀⡔⣲⠀⠀⢀⠬⣤⠀⠀⠀⠀⠊⠀⠀⠐
⠀⠀⠀⠈⠁⠁⠉⠷⠃⠂⠠⢸⣆⣁⢠⠰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠄⣠⠖⢀⡴⠋⣠⠞⠁⣠⠞⠁⣠⠞⠀⠀⡠⠂
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢤⠀⠀⠁⠀⠀⠉⠛⠁⠀⠀⠀⠀⢀⣠⣀⠀⠀⠉⠘⠁⠚⠀⠞⠀⠴⠋⢀⡜⠁⢀⡔⠁⢀⠔⠁⠀⢀⠘⠁⠀⢀
⢀⠀⠀⠠⣀⣠⡄⣤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⢦⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠜⠀⠀⢠⠂⠀⠀⣠⠋
⠈⠐⠱⣶⠟⠁⠀⠹⠛⣶⠖⠲⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⠋
⠀⠀⠠⠿⣧⣄⣀⣾⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢣⡿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠂⠀⠉⠉⠉⠛⠃⠦⠤⢯⣄⣀⡀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⢀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠃
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣤⣶⣿⣠⣴⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠠⠀⠤⣄⠀⠠⡄⠠⡖⡄⣄⠀⠀⠀⠀⠀⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⡄
⢰⣤⣄⡈⠙⠢⠈⢆⠁⠁⡯⢢⠀⠀⠀⠀⣑⣀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⠒⠀⠉⠠⠋⠀⠀⠀⠀⡇
⢨⣀⣀⣈⣙⡆⣀⡝⠀⠊⠁⢀⣴⡀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⣀⣤⡶⠶⠶⠄⠃⠀⠀⠀⠀⡇
⢘⠉⠁⣠⡤⠶⠀⠀⠀⠀⠀⠘⠠⣤⡤⠀⠀⠀⠀⢀⡀⠀⣀⠀⢠⣮⣤⣤⡄⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠟⠛⢉⡲⠆⠀⠀⠀⠀⠀⠀⠚⣄⡀⠠⠀⠀⠀⠀⠡⠖⠃⠀⠉⠉⠉⠉⠁⠄⠀⠀⠀⠀⠐⠓⠫⣷⠄⡐⡇
⢀⢀⣴⠿⠛⡷⣀⡀⠀⠀⠀⠀⢎⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⡇
⠸⠿⠁⢀⣼⠟⠉⣷⠋⢳⣿⠓⢬⣣⡀⠈⠀⠤⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠘⢠⠀⢀⠩⠥⠀⠛⠂⠀⠿⠄⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇
⢘⡀⠐⠀⠰⠈⢠⠈⢀⠰⠆⠠⠆⠐⠄⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣀⣀⣀⣀⡀⠀⠖⠁⠀⠂⡇
⢀⠀⠦⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡈⠁⠈⠈⠐⠐⠂⠄⠌⡀⣈⠙⠋⠉⢉⠉⠙⠢⠤⠄⠀⠠⡇
⢈⠁⠄⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠠⠒⠅⠀⠀⢀⠀⠈⠁⠘⢂⣀⠤⠭⠉⠑⢒⠺⠇
⠘⢀⠐⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠷⠀⠡⠤⠀⠀⠐⠒⠺⢋⠉⠃
⠘⠀⠐⠈⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠋⠛⠋⠃
⠐⠀⠄⠈⣠⠐⢀⠠⠐⠤⠀⢀⠀⢀⡤⠀⠤⠤⠎⠀⠀⡀⠠⠀⢦⡀⠀⠒⠒⣶⣶⣖⣶⠆⠀⢿⢽⣛⣻⠷⡇
⠘⠁⡀⠓⡀⠂⠀⠤⠈⣀⡈⠥⠤⠒⠒⠘⠈⣉⣉⢭⢓⢄⡀⠀⠀⠁⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠇
⢠⠀⢀⡀⣥⣐⠦⠻⣽⠒⢙⡆⠀⠀⠀⠀⠀⡱⡀⢠⡗⠁⡊⢆⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠰⠦⢽⡍⠀⣿⡄⠀⢿⡀⠈⡇⠀⠀⠤⢀⡀⠙⠙⠓⢀⣄⡀⠅⣺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢘⠒⠒⡇⠀⡯⡇⠀⣿⡇⠀⡇⠀⠹⣤⣼⡅⠀⠀⠰⠟⡣⠈⠰⡒
⢨⡭⠭⡇⠀⡭⣇⣀⠿⢧⡴⠷⠀⠀⠁⠀⠄⠄⠀⠀⠀⡀⠀⠀⠀⠀⣂⡀⢀
⠰⠖⢒⡓⠠⣭⠉⠐⠾⣁⡨⠆⠀⡀⠀⠀⠶⠞⠀⠀⠀⠀⠂⠀⢠⡐⠠⠯⢭⣆⠆
⠘⠛⠙⠂⠐⠛⠑⠛⠐⠒⠒⠒⠂⠠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠙⠒⠈⠛⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠈⠂⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠛⠀⠀⢁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡀⠀⠀⠀⠄⠀⢀⠀⢀⡠⠄⠐
⠀⠀⠀⠀⣀⣁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⣠⡀⠀⠀⡀⠄⠀⠅⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠁⠀⠈⠀⠅⡀⠀⠀⠀⡀⠀⠶⣆⠰⠀⠲⠐⢶
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⡀⠀⠠⠂⠀⡀⠐⠀⠀⠁⠀⠀⠑⢦⡓⠙⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢠⠤⢤⠀⠀⠀⠙⠢⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠠⢀⠁⠐⠁⠀⠀⠸⠦⠼⠀⠀⠀⠀⠀⠈
⠀⠐⠁⠠⠂⠀⠓⠄⠀⢄⠀⠈⠁⠒⠀⠑⠀⠂⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠚⠂⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡠⠀⠄⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡤⢤⡼⠀⠀⠀⢲⡖⢲⡆
⠀⠈⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠂⠀⠀⠠⠄⠀⠀⣀⠀⠀⠂⠀⠀⠀⣿⣰⡆⠀⠀⠀⢸⢻⣼
⠀⢨⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠂⠦⠴⠂⠀⠀⠄⠤⠄⠤⠄⠀⠀⢐⠈⡅⠀⠀⠀⠀⠀⢻⣏⡅⠀⠀⠀⢸⢸⣷
⠀⢈⡅⡉⠁⠉⠀⠀⠀⠁⠠⠈⠩⠀⡏⢁⠀⠠⠀⠀⠀⠀⠀⣀⡤⠜⠙⠀⡇⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⢸⡟⢸⣇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠄⡐⠠⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⢒⠤⠉⢙⠀⠀⢀⠀⠀⣇⢀⠠⠀⠀⠀⠸⠑⠛⠒⠒⠀⠈⠉⠉⢉⡀
⠀⠀⡄⣀⠀⠀⠈⠀⠁⠀⢥⡀⢤⠀⡧⠄⠠⠖⠂⠀⠀⠀⠀⠈⠙⠀⠉⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⡍⠉⠉⠉⠀⠐⠂⠀⡀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⢈⠓⢧⢈⡂⡄⢠⡖⠍⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠩⣁⣨⡇⣨⡶⠈⡀⠒⠂⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡰⠐⡐
⠀⢠⡌⠉⡳⣈⣤⣾⠫⣀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⠘⠛⢙⠁
⠀⠀⡀⠈⢻⠷⠌⢶⠶⠘⣠⢅⣠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢻⣯⠏⠠⠁
⠀⠀⠉⠀⢲⠀⠀⠀⠁⢈⡋⠡⠀⠄⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣐⣠⡡⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢋⡁⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣈⣉⣩⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠛⠁⠀⠁⠈

⣉⣉⣉⣭⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣾⣿⣿⣭⣿⣭⣭⣭⣯⣭⣽⣿⣿⣦⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠻⠿⠿⠿⠿
⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠛⠋⠙⠛⠛⢛⣋⣸⠉⠉⣣⣥⣤⣈⣩⡝⢹⣄⡤⢤⠤⠀⠁⠉⠋⠛⠛⠟⠛⠋
⠀⠀⠀⣀⣠⣠⠀⠀⢀⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠐⠛⠻⢿⠐⠞⠻⠿⣿⠻⠛⠛⠒⠋⠁⠒⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠄
⣴⣶⣿⣿⣿⣯⣵⣿⣾⣧⣼⣧⣆⣠⡄⣀⣄⢰⣴⣀⣤⠀⠀⠀⠀⡀⠂⠀⢀⡀⠉⠀⠀⠈⠁⠰⢃⠀⠀⠀⠀⠀⠈⠉⠁
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣥⣶⣿⣿⣼⣿⣇⣀⢸⠀⠀⢠⡄⠀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⣤⡄
⣢⣿⠿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⢿⣿⡿⡿⣿⣿⣿⣇⠘⠆⠋⠀⠀⠉⠙⡃⡀⠀⠀⠀⠀⠀⢀⠀⣤⡀⠂⠋⠙⠀⠁⠀⢀
⣿⣿⣰⢿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠻⣿⣿⣿⡟⢈⣽⣷⣦⡄⠋⠉⢩⣴⣄⡄⢠⠀⠐⠀⠹⠏⠀⠀⠀⠀⠐⣼⡁⡈⠁⠀⠀⢀⣠⠀⢀⢀⠠
⣿⣿⡿⢠⠀⡼⣿⣿⣿⣿⡟⣿⡟⠻⡗⠛⠀⠹⠋⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠛⠛⠇⠀⠀⣦⣶⠀⠀⠀⠀⠀⠠⠗⠾⡿⠟⠸⢱⣴⠜⡿⠗⠏
⣿⣿⣷⠀⠀⣽⣿⣿⣿⣿⣿⣇⠀⠀⡀⠀⢀⠴⣆⠀⡀⠀⠀⢰⡄⠠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡀⠉
⣿⣿⣿⣷⣤⡿⢿⢿⡿⢻⡟⡿⠀⠛⢿⠳⢷⠀⠁⠀⠩⠄⢠⡈⠂⢃⢸⣧⣾⡠⢠⣠⠿⠆⠀⡀⠀⠀⠀⢁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⢙⠛⠿⠛⠃⢿⡸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣿⣖⠁⠁⠈⠛⠀⠀⠈⢀⠤⠄⠑⠀⠀⠀⢠⠀⠀⡀⢀⣠⣤⡄⢈⢙⣶⡦⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⢼⣿⣿⣶⠀⠀⠀⠀⠀⢀⡾⠥⠄
⣼⣿⣧⣌⣴⣆⠖⣶⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠴⢦⣤⣤⣤⣾⣷⣶⣦⡤⠀⡀⢠⣦⣴⣿⣷⣤⣀⠀⢀⣀⣀⠀⣀⡀⢠⣦⣤⣤
⢻⡿⠿⢿⡿⠿⠲⠿⠿⠧⠔⠀⠀⠀⠀⠿⠀⠀⠉⠉⠉⠙⠻⠿⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠉⠉⠉⠙⠋⠛⠛⡙⠉⠉⠉⠈⠉⠛⠛⠛
⡁⠐⣋⠤⠒⠈⢁⠠⠖⠂⡠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠉⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⡠⠀⠁⠀⠀⢠⠀⠘
⠴⠊⢁⡤⠒⠉⡠⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⡀⠂⠀⠈⠀⠄⠀⡠⠀⠀⡀⠐⠀⠀⠀⠀⢀⠔⠁⠀⡀⠀⠀⠂⠘⠀⡆
⡠⠖⠁⣠⠔⠀⣠⠀⠀⠐⠠⠄⢈⢁⠂⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠊⣠⠄⠈⢀⠔⠈⠀⠀⠀⠀⢀⠔⠁⠀⠀⡄⠀⠀⠆⠀⡆⠀⡇
⠀⢠⠎⠀⢠⠀⠀⠀⠹⠀⠀⠀⠉⠉⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠂⠁⠀⠂⠁⠀⠀⠀⠋⠀⠀⠀⠊⠀⠀⠀⠀⢰⠃⠀⡇
⠀⠀⠤⠈⠁⣀⠒⠒⠀⠀⠋⠉⢀⣀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠁⠄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠁
⠆⠙⠂⠀⠤⠈⠁⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠒⠀⢀⠤⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡐⠁⠀⣁⠀⠀⠀⢐⢠⢤⡄⡠⠀⠀⠀⠀⡈⠀⠀⠀⠀⣀⠄⠠⠄⠠⣀⠀⠀⠀⠑⠂⢐⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠐⠄⡐⣛⠂⠈⠂⠀⠀⠊⠀⠀⠀⠀⠀⠉⠉⢀⡀⠉⠉⠀⠀⠀⠂⠁⡼⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠑⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡤⠀⠀⠆⠈⢁⠀⠋⠀⠀⠀⠀⠰⠃⠀⠀⠀⠐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⣠⠴⠖⠠⠀⠀⠀⠂⠀⠀⠢⠴⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠄⢠⡀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔⠐⡢⣄⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠿⠀⠀⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣿⣼⡁⢔⠂⠀⠀⠀⠀⠀⠀⢄⢀⠀⢈⠁⠀⠀⠀⠀⠀⠀⡀⢠⡀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡂⢠⠟⢻⡅⡡⠐⠀⠀⠀⠀⡀⣌⠾⢲⠢⢈⠀⢀⠀⠀⠆⠀⠀⢀⠀⡇⢀⠁⠀⠀⠳⠠⠁⠼⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠂⠦⡇⠀⠁⠀⠻⡀⠀⠀⠈⠓⠊⠙⢀⠀⠘⡄⢠⠠⠄⠆⢬⡆⠑⡧⠤⠂⠀⠀⣀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⢀⡇⠀⠄⠀⡄⠀⠀⢰⠀⢠⠀⠀⠀⠀⠒⢉⡞⢃⠑⠢⠀⠁⡀⣙⡙⠉
⠀⠀⠀⠀⠀⠉⠃⢀⣀⡴⡆⡀⢠⠠⠀⠈⠼⠀⢀⠀⠸⠀⠄⠈⠀⢡⠀⠀⠘⠀⢸⠀⠀⠐⠀⠠⠂⡀⠘⡇⠀⠀⠀⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠓⢐⠾⡄⠄⠄⡘⠃⠀⠆⠀⠀⠀⠰⠄⠀⠂⠓⠀⢁⠈⠀⠀⡶⡀⠀⠀⠀⠀⢀⡀⠀⠀⡖⣤⠖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠁⣊⠀⠀⡃⢀⠀⠀⠀⠐⠀⠀⡞⠰⠉⣄⢀⠀⠃⢀⠀⢹⠁⠀⠠⠄⠀⢺⠁⠀⢨⣟⠡⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡷⣧⣿⠁⢰⠃⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⡑⠀⠀⠀⠀⢠⠚⠂⠀⢀⠀⠀⠘⡄⠀⠘⠀⠐⠁⠀⢤⠵⢶⡄
⠀⠀⠀⠀⠀⠀⠐⠢⡄⣨⠆⠐⠃⠙⡄⠀⡐⠀⠀⠀⠀⢀⠇⠀⠀⠈⡉⠓⠀⠀⠀⠸⡎⠀⠌⣰⡔⠀⠀⢰⠀⠀⠀⠀⠀⠀⢁⡹⣄⣀⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠶⢄⡅⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠁⠀⠠⢀⠀⠀⠀⢸⠀⢀⠀⡀⠀⠀⠀⠀⠈⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠀⠀⠀⠀⣂⣸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠺⠓⠙⠂⡀⠀⠠⠀⠍⠀⣠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠑⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠁⠐⠀⠄⠀⠀⠀⢡⣴⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠀⠠⠀⠀⡔⠀⠀⠀⠀⡀⢆⠀⡤⢀⠊⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠐⠀⡁⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠌⠀⠀⠀⠀⡀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠄⡀⡄⠀⡀⠀⠀⠀⠀⢀⣈⠀⠤⠠⠠⠀⠦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⡀⠀⠳⢠⣶⣶⣶⣶⣶⣶⣦⠑⠄⠔⣀⣀⣒⡂⠀⠀⢈⠐⠀⢀⠀⠀⠀⠖⡚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡠⢌⣿⣿⣿⣿⣿⣿⡿⣀⠀⣾⣿⣿⣿⣿⣿⣶⣦⡈⣱⠦⢈⠢⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠠⠀⠀⡠⠊⠀⠈⢮⣻⣿⣿⡿⠛⠁⠉⠃⢿⣿⣿⣿⣿⣿⣿⡿⣱⠳⠤⣀⠀⠈⠒⠤⢀⠈⠁⠀⠂⡐
⠀⠀⠀⢀⠔⠀⠀⠐⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⠉⠛⡀⠀⠀⠀⠀⠀⢩⣟⣻⠿⣟⣫⠞⠁⠀⠀⠈⠙⠦⣀⠀⠀⡰
⠀⠀⠀⠈⠐⠠⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠤⠐⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠀⠀⠃⠐⠠⠆
⠀⠀⠀⡠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠆
⠀⠀⠈⠁⢀⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢀⠂
⡄⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀
⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄
⠀⠀⠀⡠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠐⠂⡀⠦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⡀
⠀⠀⠀⡈⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⡠⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢
⠀⠀⠐⠁⠀⠀⠠⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⡠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⡠⠀⠄⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠤⠆⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⣀⠀⠇⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡌⠀⠀⠀⠀⠤⠀⠐⠒⠀⠀⠀⠀⠀⠒⠀⠁⠀⢀⠀⠀⠀⠠⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡐⠁⣀⠰⠃⠀⠀⠙⢀⠀⠀⠀⠡⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠡⠀⠃⠀⠀⡂⠀⠄⠀⠁⠀⠀⠁⠂⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠘⢦⠀⠀⠀⠀⡴⠃⠀⠀⣀⣤⠴⠒⠲⢤⣄⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⡔⠊⠁⠀⠀⠀⠀⠀⠈⠑⢤⣀⠘⡗⠒⠒⢺⠃⢀⠔⠋⠀⠀⢀⣤⠀⠀⠀⠈⠓⢄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠨⡍⠉⠉⠉⠉⠉⣁⠔⠉⠀⠀⡇⠀⠀⢸⠀⠳⣄⠀⠀⠀⠸⠿⠟⠀⢀⠀⢀⡴⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠘⡇⠀⠀⠑⠢⠤⣄⣀⣀⡤⠤⠚⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠢⠄⠀⠠⠊⠀⠀⠀⣰⠋⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⢄⣀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⢀⣠⠞⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠓⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⢉⠉⠙⠒⢤⡀
⠀⠀⠀⣠⠞⠉⠀⢠⢢⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠔⢉⡁⢈⡉⠢⡀⠙⢦⡀
⠀⠀⡰⠃⠀⠀⠀⢸⢘⡤⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠇⢰⠁⠀⠀⠙⠄⢰⠀⠀⢳
⠀⢰⠃⠀⠀⠀⠀⢸⠸⠇⠾⠉⠖⡄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢃⠈⠓⠦⡀⠀⠀⡜⠀⠀⠈⡇
⠀⢸⠀⠀⠀⠸⠈⠶⠀⠀⠀⠀⠀⠂⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢠⠃⢀⠴⠋⠀⡰⠁⠀⠀⢀⡇
⠀⠘⣇⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠰⡀⠈⠀⠀⡐⠁⠀⠀⠀⡼
⠀⠀⠘⢆⠀⠀⠀⢣⠀⠀⠀⠀⢀⠇⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠸⡀⠀⡰⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠑⢦⣀⡀⠉⠐⠒⠂⣁⡤⠞⠁⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⡀⢀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣉⣈⣁⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠙⢦⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢰⠁⠀⢡⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⣸⠁⠀⠀⠀⠀⡇⠀⠀⠈⡆⠀⠀⠀⠀⢹⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡏⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣧⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡠⠃⠀⠀⠀⠀⠈⢢⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⣃⠤⡀⠀⠀⢀⡤⣄⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⠉⠂⠐⠋⠉⢁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠀⡾⠀⠀⢈⢸⢠⠄⠀⣦⠀⡏⡰⠀⣄⠀⠀⠀⠇⢸⢠⠆⢠⠀⠀⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠀⠀⠈⠈⠈⠀⠀⠀⠀⠁⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠁⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡥⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⡀
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠉⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⢠⡄
⠀⠼⢻⢶⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣋⠱⠄⠀⠀⠀⠸⠃⠀⠀⠀⠀⠼⠻⠶⡄⠀⠀⠀⠀⡀
⠀⠄⠈⠈⠃⣀⣄⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠈⠡⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠀⠀⠃⢀⣄⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠄⠀⠀⠀⡀⠀⠀⠀⢼⠌⠋⠀⠀⠀⠤⠤⠆⢨⠈⠃⠀⠀⠘⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠃⠂⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠈⠀⠂⠀⠀⠀⠀⠀⠂⡀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⣤⠀⠆
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⣾⣆⡀⠀⠀⠀⠀⠠⣤⣤⣠⠄⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠰⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⣾⣆⡀
⢙⡗⠈⠀⡤⠆⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠸⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡓⠈⠀⡠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠀⠀⠀⠐⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠿⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠑⣶⡗
⠀⡆⠀⠀⠀⠉⠀⠀⠀⠀⠐⠀⢀⠀⠀⡄⠀⠇⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⢀⠀⠀⡄
⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠹⠰⠇⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠂
⡠⠀⠀⠀⠆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⡀⢠⠀⠀⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⡰⠁⢠⠀⠀⠀⠠⠀⠰⡄⠀⠀⡄⠀⠀⠀⢠⠀⡇⠀⢀⠀⠀⢰⡄⠀⠀⠀⠀⢰⠀⠘⡇⠀⠀⢠⠀⠀⠂⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠀⠰⡄

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠙⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠙⠛⠲⢤⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⠬⢀⠢⡀⠀⠙⢦⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⡞⠀⠀⠀⠀⢁⠂⠀⢑⠱⠀⠀⠈⢧⠀⠀⡞⠀⠀⢀⠔⠂⠒⠒⠙⠢⡀⠀⠈⣧⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠀⢸⠀⢸⡇⠀⣀⠤⠴⠖⣦⣴⡒⠦⣌⡀⠀⢸⠀⠀⡇⠀⠀⡜⠀⡀⠀⠀⢀⡀⢳⠀⠀⢸⡇
⠀⠀⠀⠈⣇⠀⠀⠀⢠⡀⠠⠜⠀⡸⠀⠀⠀⡾⠀⠈⣇⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⡾⠀⠀⢷⠀⠀⠈⠈⠁⠀⠀⠈⠁⠉⠀⠀⣸⠁
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠐⠈⡠⠞⠀⠀⢀⡼⠃⠀⠀⠘⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡼⠁⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠈⠓⢦⣄⣉⣁⢀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⡀⢀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⢀⣀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⡴⠫⠀⠈⠁⠀⠀⠄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⣤⣷⣶⣾⣿⣶⡦⠀⠀⠹⡆⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠻⠿⡿⠋⢹⠡⣶⠈⡏⢦⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠹⠦⢬⡷⠴⠎⠀⠈⠀⢠⡇⠀⠀⣧⠀⠀⢀⠄⠀⠀⡤⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠘⢦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀⠀⢀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀⠀⠀⢀⣀⠤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠶⠆⠀⢀⡀⡀⢀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢶⣶⣄⠡⠰⠀⠛⡈⠀⣰⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣿⡟⠀⠁⠄⠂⠛⠀⠛⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠇⠀⠃⡀⠠⠀⠀⠀⠆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡆⢰⠇⠀⣰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢃⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠇⠀⢠⠏⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠑⠀⠠⣄⠀⠀⢀⣀⡈⠤⠤⠚⠁⠀⠀⠀⠠⠀⠀⠀⠈⠃⠀⠁⠠⡆⢰⡶⢁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⡆⠀⠀⢷⠊⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢻⠀⠁⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠆⠀⠱⡀⠜⡓⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠐⠋⠀⢠⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢄⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠐⠂⠨⠶⠜⠀⠀⢀⡠⠄⡺⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠀⢢⣀⠘⠲⠅⡀⠡⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⢀⣀⠞⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⣍⠣⠠⣀⠁⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠀⠂⠘⠿⢊⠂⡀⡙⢋⠿⠋⣻⠱⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⡗⠚⢠⠀⠘⠏⠹⡄⢸⠉⠁⠲⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣀⡀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⣨⠤⣄⣀⡖⠀⠆⡉⢦⠀⣠⠸⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠈⠀⢦⡌⠀⠘⠀⠈⣄⠉⠀⠄⡴⠁⠉⡅⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠙⠐⠂⠀⠀⢀⡀⠀⠉⣠⠟⠉⠋⠐⡇⠰⠈⠺⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠤⠀⠀⠂⠀⠈⠐⢳⡄⠀⠁⣄⢠⡟⠓⠂⡄⠈⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠤⢤⣄⣎⠀⠀⠠⣷⢶⡆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠓⠀⠤⢀⡶⠀⢀⡆⠀⠈⢹⣄⣄⣀⠿⣠⣇⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠰⠀⠠⡀⠀⠈⠷⠂⠀⠉⢀⡜⠁⢀⡈⢧⣀⢘⡏
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠒⠀⢀⠀⠀⣠⠀⠐⠀⠐⣒⢄⢠⠘⢡⠛⠈⠻
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠑⢠⠁⢀⠀⠀⠀⢭⡀⣚⣄⣎⣠⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⠀⢸⡀⠀⠀⢀⠔⠊⠁⠈⠨⣏⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣄⠉⠀⠈⠓⣾⠀⣖⢀⣦⡼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠂⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠩⡬⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠈⢠⣃⠀⠈⠂
⠀⠀⠀⢀⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠨⢁⠀⡑⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠒⠉⠁⡗⠄⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠐⠉⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⡀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⢀⣤⡤⢤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠁
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠜⠀⢀⠀⣁⠶⠉⠀⠀⠀⠈⠐⢀⡀⠐⠁⠀⠀⠀⠰⠀⠔⠀⠂⠠⣄⠈⠃⢢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⠀⠁⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠳⣥⣤⠤⠤⠐⠁⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡴⠒⠾⡥⠀⠀⠐⠃⠀⠙⢢⠃⠲⠷⠂⠲⠄⠀⡀⠀⠀⠀⠀⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⠐⠒⠀⠘⠀⠀⠠⠄⠀⠤⠖⠐⠢⡀⠐⠒⠀⠧⡅⠀⡀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠁⠀⠀⡀⠢⠀⠀⠀⢀⠄⠉⠀⡀⠀⠀⠈⠂⠀⠀⠀⠀⠰⠀⠀⠀⠠⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢄⡔⠀⠀⠀⢁⠆⡁⠀⠀⠀⡨⠆⡁⠀⠀⢀⡄⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⢀⡐⠁⠀⠈⢀⡀⠊⠀⠀⠀⣤⠊⠀⠀⠄⢀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⢀⠨⡖⢄⠀⠠⠀⠀⠐⢄⠐⠁⠀⠠⠀⠀⠊⠀⠂⠀⠀⠐⠎⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠈⢁⡀⠀⠃⠀⠈⠆⡀⠀⠀⠊⠑⠀⢀⠔⠉⢂⠀⠀⠀⠋⠀⡀⠁⠂⠒⠠⠄⣀⡀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⢲⠁⠀⠀⠀⢇⠀⠀⠀⡴⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠱⠄⢠⠁⠀⠠⠠⠌⠈⠂⠈



⡿⢿⠿⠿⡿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⡄
⢠⡔⣇⡆⢠⢸⡧⠀⢰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈
⠸⣿⣿⡧⢸⣾⡷⢸⣿⡇⣀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡄⡀
⠀⠈⠉⢻⡾⠿⣿⣸⣿⡧⣿⢸⡇⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠙⠋⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠗⢿⣾⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠴⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠨⢲⠀⠀⠐⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠳⠄⢠⣴⠀⡁⢠⠈
⠀⠰⠃⢄⠂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠚⢥⣠⢌⢠⡯⠗⠠
⢨⡇⣾⣝⣀⣰⣖⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢪⡈⣴⢢⣄⣫⡾⣾⣝⠈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏