Broken bone Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⠀⠀⡴⠋⠉⠉⠦⠀⠀⣀⠀⣠⠴⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⣤⠞⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢱⣄⠰⠶⠶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠈⠑⠂⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠹⡖⠂⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠒⠂⣠⡀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⢀⡠⠲⢏⠀⠀⠀⠀⢰⡄⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠂⢤⣄⠀⠈⠑⠦⣀⠀⠀⠀⠘⠉⠁⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⢠⡔⠒⠀⠹⣀⠀⢀⡇⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⡈⠱⡄⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⡰⠒⠈⠁⠀⢇⠀⠀⠀⠀⠈⠗⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠈⠑⢺⣆⠀⠀⠀⠀⠈⠃⠀⢲
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢨⢷⣄⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠂⠉⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⣀⠬⠗⠀⠀⢀⣷⠊⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⣠⣄⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⢓⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠔⠋⠀⠉⠤⠞⠁⠈⠐⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀
⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡹
⠀⠀⠀⢀⠱⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡠⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠐⠊⢹⠀⠀⠀⠀⠀⠀⠚⢅
⠀⢀⠔⠉⠀⠀⠀⢀⠠⠤⣀⠠⠜⠁⠀⠀⠰⠦⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⠚⠲⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⠀⠀⠀⡷
⠀⠻⡀⠀⠀⠀⠰⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠙⣄⠰⡁
⠀⣀⠼⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣅⠀⡉
⡜⠁⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⠤⢄⡀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢀⡠⠤⣀⠀⠀⠀⠀⢸⢀⡴⠁⠀⠛⢤
⢇⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⣉⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢈⠀⠀⣉⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠾⢀
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠁⠀⠀⠀⠀⡆
⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⣀⠞
⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠘⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸
⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏
⠀⠀⢠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡴⠶⢦⡀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠲⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡎⠁⠀⠀⡘⠑⢌⡁⠒⠀⠒⢉⣤⠃⠀⣦⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠂⢶⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠱⡀⠀⡄⠁⠀⠀⠀⠉⠉⠁⡰⠃⢀⠜⠘⠄⢀⠖⢉⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣠⡄⠒⢦⠀⠀⣠⠃⠓⡀⠃⣴⠁⠀⠀⠀⠀⠀⢀⡜⠁⢀⠎⠀⠀⢺⠃⢀⠞⣃⠀⠀⠀⠀⢠⣤⣀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⠁⠀⠀⢡⣀⠇⠀⠀⠀⠀⠀⣠⠊⠀⡰⠋⠀⠀⠀⠈⡖⠋⠀⠉⢣⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⠇⠀⢠⠈⢉⠟⠲⢢⣤⣤⣀⡔⠁⢀⡔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⡄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢣⡴⠃⠘⢤⠜⠀⠀⠾⠀⠀⠇⠀⡘⠀⠀⠀⠃⡸⠋⠀⣠⠚⡗⢢⡔⢢⡄⠀⠀⢸⠉⠉⣅⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠀⣶⠀⠀⡇⠀⡆⢠⠟⠀⢀⠜⠋⢐⡇⠀⢱⡌⠀⠀⠀⠸⠀⠀⢘⠀⣤
⠀⠀⠀⠀⠀⠐⠊⠳⡀⢀⡔⠉⠁⠀⠀⠀⠑⢇⠀⠀⠀⢠⡷⠁⢀⣴⠏⠀⡄⠸⠁⢀⠘⡟⠒⠲⠀⠀⢿⠛⢻⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⠲⠇⠀⣴⣏⣀⡃⠘⠃⡄⢠⠋⠀⠇⢀⠜⠀⠀⢹⠀⠀⣰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠁⠚⠓⠻⠧⠤⠜⠃⠁⠀⠀⠀⠘⠒⠂⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠓⢦⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠃⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⢸⠆⠀⠀⠀⠈⠁⠈⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠆⠀⠀⠀⠀⠀⠀⣀⡰⢧⡠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⠀⡼⠢⠤⠄⠀⠛⠁⣀⣀⠴⠇⠀⡆⠀⠀⠀⢀⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠤⠀⠘⠛⠁⠀⠀⣀⣸⡄⢰⠀⠰⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠦⢀⣀⣀⣀⣀⢀⣀⠀⠀⢻⠀⠀⠀⠀⠘⠛⢀⣀⡀⣶⣤⡦⣀⠀⠀⠠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢷⠄⠀⠛⠋⠁⢀⣠⠜⠁⡰⠛⣮⠦⠀⠀⠘⠚⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠉⠉⠙⠛⠉⠙⡋⠀⠀⠀⠀⢻⡉⠛⠉⢁⡴⠉⢀⡜⢁⡎⣠⠀⠀⠀⠰⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠙⠶⠟⠳⠐⠚⠋⠙⠋⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠠⢶⣶⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⣄⣦⣥⣴⡗⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠙⡟⠁
⠀⠑⣿⣿⣿⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣯⡏⠀⠀⠀⠀⠂⠀⠀⢄⡏⠀⠀⠀⠀⠇
⠀⠀⠙⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣨⠳⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠿⢿⠀⠀⠀⠀⠀⠀⠠⠻⢷⠀⠀⠀⠀⢠⣧
⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠂⢲⠀⠀⠀⠀⠀⠀⠀⠇⣾⠀⠀⠀⠀⢬⣥⠄
⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡏
⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣄⣼⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⡨⣿⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⠻⢄⡀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠐⠒⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠰⣤⣾⣷⡏⠀⠀⠀⠀⡠⠀⠠⠀⠀⠶⡾⠻⣶⡾⠇⠀⠀⠠⠐⠀⠀⠐⠀⠀⠀⢠⣤⡼⠻⡿⠆⠀⠀⠀⠀⡠⠞⠒⠀⠀⠀⠀⢴⡧

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠒⠀⡀⢀⠀⢀⠀⠈⠁⢠⣤⢤⣀⠄⠀⠀⠀⠄⠀⠲⠄⠀⠀⡀⠀⢠⠀⠐⠀⢘⡂⣀⡠⠀⢀
⠀⠀⠠⠵⣶⣶⣦⣾⠃⢀⣀⣈⣻⣿⡿⠛⠀⠀⠀⠀⠀⢠⣤⣾⣯⣧⣿⡎⠀⠐⠾⣿⣿⡿⠛⠀⠀⠀⠀⣀⣤⣰⠦⣹⣯⣤⣴⣾⠇⠠⣼⣦⣿⣾⣷⣿⠿
⠑⠶⢶⣾⣿⣿⠏⠀⠀⠀⢨⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⡟⠀⠀⠀⠀⠀⣿⢹⠃⠀⠀⠀⠀⠀⠙⠻⢿⢻⣿⣻⡟⠉⠀⠀⠀⠀⠙⢾⣿⣾⠇
⠀⠘⢿⡿⢻⣷⠀⠀⠀⠀⠀⠸⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⠀⠀⠀⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⡇⠀⠀⠀⠀⠀⠀⠘⠘⣹
⠀⠀⠊⠃⣼⡿⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣴⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⡷
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣦⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠰⡷⣷
⠀⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⢀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇
⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠈⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠰⣸⠛⣗⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⣿⡁⠀⠀⠀⠀⠀⠀⢸⢠⣧⡄
⠀⢀⠞⠛⣷⠛⣧⠀⠀⠀⠀⣘⣿⣻⡄⠀⠀⠀⠀⠀⠀⢱⣮⣿⠉⠑⣦⠀⠀⠀⣰⣠⠿⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣼⣿⠁⠀⠀⠀⠀⠀⠰⢾⣻⡦
⠀⢲⣦⡾⢯⣽⡟⠀⠀⠀⢠⡁⣽⠧⣿⠀⠀⠀⠀⠀⢷⡾⠟⢻⣶⣶⠿⠀⢠⣤⣿⢿⣤⣬⡧⠀⠀⠀⠀⠀⢠⣤⣴⠟⢿⣿⠟⠀⠀⠀⠀⣀⣀⡼⣿⣿⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡶⠛⠋⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡟⠀⠀⠀⠀⠀⠈⠙⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠹⠃⠰⠆⢀⣀
⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢿⠀⠀⡀⠀⠘⠋
⣴⠛⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠄⣸⡇⠀⠁⠀⡴⠒⠦⢤⣀
⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠖⠒⠒⠒⠒⠲⠾⠥⣴⠏⠀⠀⠀⠐⣅⠀⠀⠀⠀⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⡀
⠹⣄⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠉⠉⠓⢦
⠀⠈⠙⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠨⠇⠀⠛⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠓⡶⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣀⣀⡴⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠐⣶⣶⠾⠀⣀⣽⣿⠛⠀⠀⠀⠠⣴⣿⡿⠎⠀⠺⣿⡟⠁⠀⠀⣠⣴⣦⣮⣶⠾⠀⢶⣿⣾⡶⠚
⠀⠩⣿⢿⡇⠀⠀⠘⢟⡇⠀⠀⠀⠀⠀⢸⢿⠃⠀⠀⠀⢻⠀⠀⠀⠀⠈⠙⢿⣿⠃⠀⠀⠀⠈⢿⡇
⠀⠀⠋⣼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⣿⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⠂
⠀⠀⠀⢸⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴
⠀⠀⠀⢸⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡄⣇⠀⠀⠀⠀⠀⢸
⠀⠀⣸⣿⣆⠀⠀⠀⣠⡇⠀⠀⠀⠀⢀⣤⠿⡀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⢵⣿⡄⠀⠀⠀⠀⣾⡆
⠀⢠⣤⢿⡾⠀⠀⣀⣹⣿⠄⠀⠀⠠⡼⠿⣦⡼⠀⣠⡿⣇⣱⠀⠀⠀⠀⣀⡼⢿⡷⠀⠀⠀⣀⡽⣿⠄

⠀⠀⠀⡀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡤⡴⣄⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠃⠀⣑⠀⣀⠠⠀⢀⣆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢾⣶
⢀⣀⣈⣽⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢼⣷⣬⣵⣿⣾⡿⠿⠋⠀⠀⢀⠀⠀⠀⠐⢠⠖⠃⠀⠀⠀⣿
⠀⢨⣿⡿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢸⢫⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣿⣾⠃⠀⠀⠀⠀⠈⠀⠃⠀⠦⣬⠀⠀⠀⠀⠀⠻
⠀⠀⠹⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠸⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠃⠏⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣶
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⣾
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢰⡆⠁⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡂⠀⠀⠀⠀⠀⣿
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠘⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠧⣼⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠙
⠀⠀⠴⢿⡼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣵⠛⠣⣄⠀⠀⠀⠀⢀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠐⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿
⠀⢴⣤⣾⣗⣿⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠰⣶⡿⢿⣦⣴⡿⠀⠀⠀⠀⠄⠆⠀⠀⠐⠀⠀⠀⠀⢠⣄⣴⠻⣿⡿⠂⠀⠀⠀⠀⢀⣠⠖⠢⢀⠀⠀⠀⠀⢠⣿
⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⢠⡶⠆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⡿⢿⣾⠇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠛⣡⡿⠃⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠛⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡷⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢰⣶⠶⠟⠛⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⣆⠘⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡰⣄⢤⣿⠤⣤⢄⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣿⡇⠀⠀⠀⠀⠰⣟⣻⣿⣿⣭⣝⣯⠆⠀⠀⠸⣿⢿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡌⠐⠀⢀⣿⡇⠀⠀⠀⠀⡿⠽⠟⢹⣿⠭⢹⡿⣃⠀⠀⢶⠛⠆⠴⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠨⣟⣧⡀⠀⠀⠀⢯⣖⣂⡽⣿⢯⣐⣻⡵⠀⠀⢸⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠙⠛⠿⠆⠀⠀⠰⣳⠟⠉⠉⠉⠳⣟⠄⠀⠀⠘⡇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣴⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢛⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢡⡾⠋⠁⠈⠻⣿⣿⣄
⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢻⣿⡘⡇⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣧⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⢠⣿⣿⣿⡟⣩⣽⣯⡭⠉⠙⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣸⣿⣿⣿⢰⣿⠁⠀⠀⠀⠀⠀⠈⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡽
⣿⣿⣿⣿⡄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⣦⣤⣀⡀⠀⢠⣯⠞⠁⠀⠀⢀⣀⣀
⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠰⠯⠴⠛
⠀⠀⠙⠿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⣶⣿⣿⣿⣄⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣶⣦⣤⣿⡟⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⢿⣭⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⡧⠀⠀⠀⠀⠀⠐⠗⠀⠀⣤⣄⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⡟⢻⣆⠀⢤⠄⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⠀⠀⢸⣿⠻⠟⢰⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠛⠋⠀⢀⣿⡇⢸⠆⢸⠃⣠⣿⠀⢀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣾⡟⠛⢣⣴⣦⠘⣰⣿⣿⠀⠛⠃⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣹⡇⠀⣹⣇⠹⢆⣩⣄⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠉⣿⡇⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⣿⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠁⠀⠛⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⣧⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⠀⡀⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⣸⣿⡇⢿⡀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⣀⣤⣾⠏⣾⣿⣧⡘⢷⣤⡀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣄⡙⢛⣋⣴⣿⣿⣿⣿⣶⣬⣁⣀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠻⢿⣿⣿⣿⣿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣿⣿⣛⣁⣀⣀⣀⣀⣉⣉⣉⣁⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢉⠁⠠⢀⣤⢆⠹⠖⣀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠚⠉⠉⠁⢈⠁⡈⢠⠀⠈⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⢽⠆⠀⠀⢠⣶⣶⣤⣸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠁⠀⠀⠀⠀⠀⠀⢠⣠⠀⠀⣠⣤⡘⠆⠀⠀⠙⠀⢸⣿⣿⣿⠹
⠀⠀⠀⠀⠀⠈⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⢿⣿⠟⠀⢀⡰⣨⣼⡆⠉⠉⠉⢈⠆
⠀⠀⠀⠠⡇⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⠈⠃⠀⢀⠂⠈⠀⠀⠈⠀⠀⡀⡈⠁
⠀⠀⠀⠀⠈⠂⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢶⡔⡤⠀⠀⢎⡙⠃⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡤⡤⠂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢌⠀⠀⠀⠱⠂⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⠀⢤⠒⠐⢆⠁⣜⠀⢘⣀⣀⣼⠀⢀⣾⡖⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣀⣾⢦⠀⠀⣤⣬⡇⢸⡇⢠⣏⠙⠉⡄⠀⠀⠀⠀⠀⠎⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠋⠁⠻⣬⠀⠀⢉⠀⡄⠀⡏⠤⡜⠀⢐⡛⢀⠀⠀⢐⠞⠀⢂⣰⠴⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠙⠁⠀⢞⠁⣄⠀⢀⠀⡜⠠⠟⢄⠀⠂⢀⠂⢀⠂⠘⠁⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⢻⠉⢡⠀⢈⠀⡖⠐⢇⠀⠃⡽⠀⢀⠀⠀⠁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠦⡈⠀⠀⠀⠀⠨⠀⢨⠠⠔⠪⠀⠀⠁⠀⠀⠁⠀⣠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠇⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⡀⣤⢄⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠀⠀⠀⠀⠀⠀⠀⣘⡦⠔⠁⠀⠐⠈⠀⢰⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠐⣁⠀⠀⠈⠀⠀⠀⠀⠠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣠⣴⡾⠿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣁⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠶⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡄⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠋⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠐⠈⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠠⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⡵⠊⠁⠀⠀⠀⡠⠚⣱⡿⠁
⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠶⣶⣶⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⢠⠞⣡⣾⠋
⠀⠀⠀⠀⠀⠀⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⣿⣄⠁⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠤⣬⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣀⠀⢀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⠞⠁⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣈⣉⣀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡟⢹⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣖⣠⣿⣻⣿⣿⣿⣟⣖⠠⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣓⡒⠒⢒⠒⣶⠶⣶⣤⣬⣤⣤⣾⠿⠿⠾⠻⡅⠀⢀⡀⢠⣤⣤⡤⠤⠤⣤⣤⠤⣼⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣤⣾⣿⣿⣟⣋⣉⣿⣿⣏⣅⠀⠀⠀⠀⣬⡒⠛⠻⣿⡿⣿⣧⣤⣿⣶⣦⣶⢿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠁⢹⣿⣿⣿⣿⣿⣿⣍⣀⠶⠶⠛⠆⠀⠀⠘⡟⢻⢛⣫⣥⣾⣿⡿⣻⣿⣿⣿⣿⡀⢻
⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⢼⣿⣿⣿⣿⣻⡋⠉⠉⠙⠋⢿⣷⠄⠀⠀⣞⠻⢿⣿⠿⠛⣉⣴⣿⣿⣿⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⣿⣿⣝⣿⣿⣿⣷⣶⣌⠁⠀⣉⡁⠀⠀⠀⠈⠰⣈⣤⣶⣿⣿⣿⠟⣸⣿⣿⠏⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣯⣿⡋⠁⢀⣀⣀⣼⠇⠀⠀⠀⢺⢦⣬⡿⠿⠟⢉⣠⣾⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢿⣾⡿⣿⣿⣿⣿⠷⠀⠀⠀⣤⡀⠀⠀⢠⡖⠀⠂⢴⣶⣿⣿⣿⡿⠋⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣸⣿⣿⣿⣟⣋⠀⣀⠤⠂⠀⠛⠁⠀⠀⠀⢈⢑⡂⠀⠙⠛⢋⣁⣴⣿⣤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣯⡉⠛⠿⣟⣛⠿⠀⠀⠀⠀⣶⠂⠀⠀⠀⠈⣀⠁⠀⠛⠿⢿⣿⣿⠀⢉⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡿⠿⣯⣽⣉⠀⠀⣠⣴⡾⢀⡴⣠⣆⣀⠁⠐⣌⡻⠶⠤⠀⠀⢉⡠⢴⣧⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣤⣀⣀⣉⢿⡿⠇⠀⠀⡤⠈⣾⣿⣏⣙⡿⣧⠈⠀⠀⠐⠲⣾⣅⡀⠀⠈⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⡿⠿⣿⣿⡠⠀⠀⠂⠘⣡⣤⣿⣿⠿⢿⣇⣀⠀⠐⢌⠲⢤⠀⠙⢉⣠⣞⡁⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣦⣤⡴⠾⠓⠒⢂⣴⠾⢋⣹⣿⣿⣿⣺⡟⠛⢷⣄⠀⠑⠐⠒⢾⣧⣄⠙⢛⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣟⠛⠷⠶⡤⡔⠋⣁⣴⠚⠫⣿⣿⣅⣸⣧⣀⠀⠙⠷⣦⡀⢀⠠⣩⡤⢴⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⠛⠿⢐⠞⢡⡾⠋⠁⣠⣀⣿⣿⡿⢿⡇⠈⠻⣆⠀⠈⠻⣦⠀⠀⠀⢀⣉⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠈⠀⠀⠀⠈⢹⣿⣿⣷⢶⡟⠙⠀⠈⠧⠀⠀⠉⠈⠑⠄⠩⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⡟⠙⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡉⢈⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣠⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡀⠹⣿⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠀⣠⣿⣦⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠈⠿⠿⠿⠿⠿⠟⠁⠀⣹⣿⣿⡞⠀⠙⠻⠿⠿⠿⠿⠟⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⡀⢠⣴⡶⠁⢸⣿⣿⣿⣷⡄⠘⣷⣤⣀⠀⠀⠀⠠⢴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢠⣀⠀⠀⠀⠀⠀⢹⣿⣶⣌⠁⠾⠛⠀⡄⠘⠛⠁⠙⠋⠛⠀⠘⢿⠉⠑⢀⣈⣵⡟⠀⠀⠀⠀⠀⢀⡤⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣸⣧⠀⠀⠀⠀⠈⣿⡿⣯⠰⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⡶⠛⣿⣿⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠤⣤⣿⡇⠀⠀⠀⠀⠀⢹⡇⢹⣤⡿⡿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣸⡇⣰⡿⣿⠃⠀⠀⠀⠀⠀⢘⣿⣦⠤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⡃⠺⣿⣷⡄⠀⠀⠀⠀⢸⡁⠈⣿⡿⢿⣶⣶⢾⡶⢾⡶⢶⠶⣿⣾⣿⣿⡟⠁⢹⠀⠀⠀⠀⡀⠠⣾⣿⠛⢐⣿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⡁⠀⣀⣀⣀⣀⢀⣤⣼⡀⠀⠀⠸⣇⠀⢿⣷⡸⠀⢱⠀⠀⢠⠀⢰⠀⡇⢸⣽⣿⠀⠀⠾⠀⠀⠀⠀⣧⣤⡀⣈⣀⣀⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠰⣤⣈⡙⠛⠛⠉⠙⠻⣷⣄⠀⠀⠹⢦⡈⠿⡇⠈⠉⠐⠋⠙⠁⠈⠘⠁⠀⠘⢃⣤⠞⠀⠀⠀⣠⣾⠟⠋⠙⢛⡛⢋⣁⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠲⠶⢦⣤⡈⠹⡷⢤⡀⠀⠙⢦⠈⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠟⠁⠀⣀⡠⠾⠟⢁⣤⣴⠾⠶⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣙⠁⠻⠦⣀⠑⠢⠬⠧⠀⠀⠐⠀⠈⠡⠖⠉⣀⠴⠞⢁⣉⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⣀⠈⠐⢤⣀⠀⠀⠀⠀⣀⡤⠒⠉⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢶⣴⣈⠉⠲⠶⣉⣁⣦⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⣿⣷⣦⣄⣀⠉⠛⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⣠⣴⣿⡿⠛⠉⠉⠛⢿⣷⣦⣄⠈⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠤⢤⣴⠾⠯⠅⠐⢢⣬⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢿⣤⣐⠂⠨⠹⠷⣦⡤⠤⠄⢀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠉⣠⣤⡓⠶⠄⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣀⠀⠀⠠⠶⢚⣢⣄⠙⠉⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢠⣤⣌⡡⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣡⣤⡄⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⠃⠀⣀⣰⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠈⣻⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣀⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢂⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠶⣦⡀
⠀⠀⠀⠀⢀⣠⠶⠾⠧⣄⡀⠀⠀⣸⠠⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⡡⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⡏⠀⠀⢄⣀⡀⢀⣀⠀⠀⠈⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠟⠛⠳⣆
⠀⠀⠸⣷⡀⠲⠶⠮⠉⠉⠡⠔⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠐⢤⡶⡤⠤⠄⠀⠀⢹
⠀⠀⠀⠈⠛⠿⠶⠶⠶⠾⠿⠿⠷⣶⣄⢀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⢀⣀⠀⠀⢀⡀⣄⣠⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣕⠢⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⢀⡴⠋⢁⡤⢶⣤⣼⣥⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠈⠳⣄⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⣴⠞⢋⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡢⡀⠀⠀⠈⠻⣏⠁⠀⠀⣀⣠⠤⠚⢉⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡕⢄⠀⠀⠈⠳⣄⠀⠿⠙⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣹⣿⣦⣁⡀⡀⠀⠈⠻⣶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⢰⡞⢿⣿⣿⣿⣌⠢⡀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⢈⣿⣼⣿⠟⠋⠙⢷⣇⡀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⢀⡤⠚⠉⠀⠀⠀⠀⣀⣤⡾⣻⡿⠋⠁⠀⠀⠀⠀⠙⠻⣦⡰⣄⠀⠀⠙⢦⡀
⠀⠀⣰⠞⠋⠉⠁⠀⠀⠉⠃⠀⠀⠀⢀⣀⣴⣿⢖⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣦⡦⡀⠀⠙⢦⣀
⠀⠀⣯⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⣫⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡌⢳⣄⠀⠈⠙⠛⠒⠒⠒⠒⠒⠒⡒⢦⣀
⠀⠀⠹⣦⣀⠀⠀⠀⢀⠀⠀⢀⡴⢪⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄⢣⠀⠀⢦⣀⣀⠀⠀⢱⡐⠘⡀⠹⣦
⠀⠀⠀⠈⠛⠿⣶⣮⢁⠀⠀⠀⣤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠀⠀⢦⣭⣵⠖⠀⠀⠁⠀⣣⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡆⡉⠃⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠹⣷⣄⠀⠒⢒⣩⣃⣼⠟
⠀⠀⠀⠀⠀⠀⠈⢿⣜⡲⠶⠿⣫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢤⣤⠈⣿⡿⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠠⠚⠼⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⠾⠛⠁

⡸⠇⠰⠃⣾⢂⡀⢊⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠙⠎⠃⠀⠀⡁⠀⠀⣤⠀⠀⣹⣷⡤⠐⠀⡀⠀⠿⠂⠀⠈⣉⢀⢝⡳⣄⠀⠀⠀⠈⠀⠾⠃⠘⢋⣿⢻⠟
⠀⠆⡀⠐⢃⡉⠅⠛⢹⡇⠀⠤⢤⡀⠀⣲⠀⢀⡀⠙⢤⡄⠀⠀⠀⠀⠀⠀⠀⠩⠅⠐⠀⠀⠁⠠⠄⠀⠸⠋⠀⠀⠈⢁⡷⣠⠀⢠⡀⠀⢀⣦⣄⠀⡄⠻
⠀⠀⠃⠀⠋⠀⠀⠀⢀⡁⠐⠶⡀⠅⡀⠘⢰⠦⢀⣀⠀⠀⡀⢠⠀⠀⠀⣠⠴⠖⠀⠀⠀⠀⠀⠀⠰⣄⣀⡀⠀⠀⡀⠈⢠⠡⢄⣾⠩⠉⠀⠈⠙⢷⣿⣶⡁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡳⠄⠀⠀⠉⣄⠀⠐⠛⠛⢀⠈⣥⠄⠀⢀⣈⣥⣶⡿⢡⣆⢤⣦⢠⢀⣠⢿⣿⢀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢈⢩⣥⣶
⠇⠘⡓⠀⠀⠀⠀⠀⢈⡃⠣⢑⣈⠁⠀⠀⠀⢶⠶⠛⠋⠏⣩⠤⠞⠉⠉⡘⠋⠀⠀⣿⣷⣛⣴⢿⠃⢠⡅⠐⠻⣾⢶⠐⠆⠀⠀⠀⢻⡌⠀⣦⠀⢁⣺⡇
⠀⠀⠀⣀⡀⠘⠀⠀⠀⠀⠀⣠⣤⠆⠀⠀⠀⣷⣦⠴⠈⠈⠁⠀⠀⢰⣁⣨⡿⠀⠼⣿⡿⠉⠉⠀⢠⣿⠷⡀⣤⠀⠀⠀⠀⠞⠲⣥⠀⠹⢆⣿⣷⡀⠹⣷
⠀⠐⠡⠈⢡⠀⢀⠀⡀⠀⠀⣉⠋⠘⠀⠙⠀⢁⣠⣴⠣⠈⡀⠀⠀⠜⠨⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⡀⡈⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠿⣿⣷⣴⡟⠸
⠀⠈⠀⠇⠀⠃⠄⣀⠀⠄⢀⡈⠀⠀⠀⠀⠀⠻⠻⠧⠅⠈⢁⣀⣀⣩⣸⠂⢀⠴⠀⠀⠀⠀⠀⠀⡈⢳⡉⠛⠀⠻⣤⠀⣐⡰⣶⠂⠀⠀⠀⠰⠝⢿⣏⣀
⠄⠀⢀⣹⡆⠀⠈⢡⣴⠗⠀⢀⣤⣆⠀⠤⣀⣠⡤⢦⠄⠀⠙⠉⠋⢩⠃⠀⠨⣶⠂⣼⠃⠀⠀⣤⡙⣧⠉⠡⠍⠀⠒⠶⠀⢀⡀⠁⠃⡾⠐⠂⠀⢦⡙⠇
⠀⢠⣽⣿⠇⢀⣿⠀⢉⡀⠀⣠⡂⠀⠂⠐⢋⠁⢤⡴⣶⡶⠀⠀⢀⡁⠀⠠⣦⡦⢸⣏⣠⡄⢈⣿⠟⢨⡙⠿⠷⠈⠁⠀⠖⠀⠉⠀⠀⠀⠀⠀⠳⣄⠁⠀⠄
⣀⠘⠋⢠⠂⣸⠋⠀⢦⡙⢦⣛⢧⠄⠂⠀⠀⢀⠸⣧⢿⣥⡾⣠⠁⠁⡔⣦⣄⠀⠛⣍⠃⠀⡈⠁⣲⣄⠀⠀⠘⠇⡰⢂⠰⢀⠀⡴⠀⠀⢀⠻⣦⠙⠦⠄
⢉⡔⠚⢿⡇⠘⢁⠀⠀⠁⠈⠈⠓⠀⠀⠀⠀⠸⣆⠻⢤⠏⠐⠉⠻⢷⣶⣽⡟⠐⠂⢿⣋⡴⠀⠀⠋⣁⠀⠐⠠⠂⠀⠀⢀⣾⠀⠃⢠⠀⠀⠁⠘⢷⡘⣧
⣾⣷⠀⣾⠃⣴⠈⠣⠀⠀⢢⡀⠈⠃⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠈⢛⠫⢴⣄⠀⡄⠁⠀⠀⣀⠈⠝⠉⠒⠁⠀⠀⠀⣾⠏⣀⠀⠈⠀⠀⠀⠈⢦⠙⠌⠓
⠙⢿⠀⠠⠂⣿⡆⠀⠀⠀⠘⠳⣶⢦⡀⠀⠀⠀⠀⠀⣀⠠⠄⠠⡄⠂⠂⠀⠐⠂⢀⠀⠀⣠⠊⡽⠀⠀⠀⢀⠀⠄⠀⠀⡿⠀⢿⠀⠰⢀⣀⡐⢃⡹⢅⣰⣆
⠀⠀⠀⠀⢄⣿⣩⠄⠀⠀⠀⠀⢻⡌⠁⡀⠀⠀⠈⠓⣹⣿⣜⠇⢰⣦⡀⠀⠀⣀⠀⠀⢀⣤⣠⣮⠁⠀⡛⠡⠖⢊⣀⠀⢀⠹⠻⡀⠙⠉⣨⣤⠀⢥⣌⠭
⠠⠀⠀⠈⠴⠟⠁⠀⠀⠊⠐⢿⣆⣿⠀⡅⠀⠀⠀⠀⠀⠙⠛⠃⠈⠴⠦⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⡉⠙⢳⡶⠌⠋⠀⠉⠀⠘⠄⠀⠁⠀⠀⢀⣀⣈⡁⠊
⠀⠈⠀⡀⢰⣶⡀⠀⣠⡈⠂⠐⠋⠛⠄⠀⠀⠀⠀⠠⢠⣶⣶⠶⠊⠰⠶⠦⠾⠅⠀⠀⠀⠀⠀⢠⡆⠤⡀⠀⣴⠆⠀⠀⠀⣄⠀⠀⢀⠀⢀⠦⠚⣿⣟⠃
⠀⣠⠀⠿⠏⠀⠁⠀⠉⠛⠀⠀⠀⢰⠀⠀⠀⣇⣀⣴⡤⠏⠕⠀⠀⠀⠀⠀⢄⠀⡀⣀⣀⠀⠘⠘⠃⠴⠁⠘⠃⣘⠁⢀⣤⡏⠠⡀⠘⣦⠀⠐⠳⡮⠻⣷⣷
⠰⣿⣆⢠⢀⠀⠃⠸⢠⠷⡶⠄⠀⠀⠘⠁⡦⠋⢉⣩⡄⠀⠀⣤⡀⠀⡀⣹⠟⢀⣀⡉⠀⠷⣦⠀⠀⠀⢀⣤⣜⢿⡇⠸⣿⠃⠀⣾⣆⢿⡄⠀⠛⠁⠀⠘⣻
⠧⠈⠻⣶⠀⣀⠀⠀⠙⢦⣄⣈⠀⠄⠠⣦⠄⣉⢻⣿⠲⣿⠀⠘⠋⠘⠃⣤⠀⢠⣉⣉⠘⠁⠉⡐⠉⠀⠱⣿⠿⠆⠐⠐⠂⠀⡟⠉⠁⠈⢗⣀⡀⠀⠀⡀⢢
⢠⣤⡀⠀⠀⠻⢡⠄⠐⣩⠟⢋⡤⠻⠟⠀⠋⠉⠏⡻⠀⣂⠙⠁⢰⣿⢈⠥⠀⠈⠿⠋⠁⠀⠀⠁⠀⣠⠀⠄⠀⠀⠀⠀⠀⠘⢃⢀⡆⠄⠠⢛⠉⢦⣾⣿⣦
⢈⠋⠁⡀⡁⠀⢢⠴⠇⠴⠀⠀⠀⣈⣄⣀⡀⠀⠀⠀⢀⡉⢋⠘⠋⠉⠀⠀⠀⠀⢃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢁⠀⡸⠓⠀⠂⠘⠠⢘⣭⣄⣀
⠀⠀⠈⠀⠓⢈⡁⠀⠀⠀⠰⠆⡘⢿⠟⢉⡁⠀⠀⠀⠉⠐⠻⠄⢀⡤⢰⠂⣴⠠⠟⠀⠀⣸⡛⠁⠀⢀⠉⠓⢀⣀⣑⠀⢠⠌⠰⠆⠀⠀⠀⢠⠆⠀⠈⡭⣙
⡄⠺⢀⡀⠘⢉⡁⠀⠀⠀⠀⠰⠀⢀⠄⠘⢃⠼⣴⡿⠾⠃⠴⠲⡶⠴⠀⠀⣁⡀⣸⠇⢰⡿⢧⡀⣶⡌⠃⠰⣄⠙⠻⠁⣩⠆⠀⣰⡶⠀⠉⠀⠀⠀⠁⠑⠟
⠀⠲⠟⠀⠠⠟⠀⠓⠀⡤⠀⠀⣀⣴⡄⠐⢋⠀⠙⢷⣶⡄⠀⠈⣁⠀⡄⣰⠦⡖⠁⠀⡃⢀⣾⠄⢛⠛⠀⣀⣻⡧⠀⡀⠉⠘⣴⣿⠇⡿⣦⡠⡀⠙⣿⠶⠦
⠀⠶⢀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠿⡿⣱⡆⣿⣠⡄⠀⠜⠛⢧⡔⠉⠆⢰⣜⠁⠕⠀⠚⠇⠈⠋⠀⣀⣻⣄⠤⠴⡶⠀⠰⠇⢸⠋⠙⣻⠗⡈⠛⠻⠟⠓⡦⢀
⢀⣾⠿⠁⠀⠀⠀⠀⠀⠄⠀⠲⣄⠀⡿⠇⠉⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠰⡗⠀⠀⠀⠉⠍⠁⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⠄⣈⠙⢾
⡉⢡⣺⢇⠠⠀⡀⢄⠡⠄⠾⢦⠈⠑⠆⠀⠀⠀⢠⣦⠃⠀⣃⠱⣄⡀⣤⡁⠀⣤⡍⢣⡹⠄⠀⣀⠀⠀⠀⠀⠀⠁⠀⠢⠀⣠⣤⡶⠆⡉⢉⡿⠃⠀⢈⡿
⣃⣾⣛⣿⣸⣆⣙⣦⣀⣀⣈⣀⣒⣂⣀⣀⣀⣀⣀⣤⣶⣀⣹⣷⣀⣁⣙⣷⣀⣁⣀⣠⣶⣘⣛⣻⣃⣀⣀⣀⣀⣀⣤⣒⣛⣉⣁⣀⣀⣀⣨⣥⣜⣆⣡⣿⣞
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠒⠒⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢹
⠀⡇⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡇⠀⠀⣀⣤⣶⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣶⣤⣀⠀⠀⠸⡀⠀⠀⠀⢸
⢰⠁⠀⠀⠀⡼⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢳⠀⠀⠀⠘
⠸⠀⠀⠀⢠⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡇
⡇⠀⠀⠀⠘⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣶⣶⣦⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⠇
⡇⠀⠀⠀⢀⡇⠀⠈⠛⠿⢿⡿⠿⠟⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠈⠉⠛⠿⠿⠿⡿⠿⠛⠀⠀⠸⡀
⢡⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀
⠸⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠹⣗⠦⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠤⢺⠏
⠀⠀⠘⡆⠘⡽⣿⣿⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⠟⠁⠀⠻⠟⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟⠇⢰⠃
⠀⠀⠀⡏⠀⢱⠘⠿⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠋⡜⠀⢣
⠀⠀⠀⡇⠀⠈⡆⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⢠⠃⠀⢸
⠀⠀⠀⠙⢄⡀⡇⠀⠀⠈⣿⣿⣿⣇⣀⣀⣤⡤⣤⠲⡔⠒⡖⠒⣤⠲⡤⣤⣄⣀⣠⣿⣿⣿⠇⠀⠀⢸⠀⣠⠇
⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠸⣿⣿⣿⣿⣸⣸⣇⣽⣠⣧⣠⣧⣠⣿⣠⣇⣴⣸⣨⣿⣿⣿⡟⠀⠀⠀⣾⠋⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠻⠿⠿⠿⠧⠧⠧⠼⠼⣤⢇⠧⠼⠼⠦⠧⠷⠿⢿⠿⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡤⠚⠁

⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣀
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠘⣦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡋
⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣇⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠈⠳⢤⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣤⠴⠋

⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠳⡄⠀⡀
⠀⠀⢠⡴⠤⣄⡾⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠻⠋⠉⠛⣆
⠀⠀⣾⠀⠀⠀⠑⠀⠀⠀⢾⠀⠀⠀⠀⢰⠋⠁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠃⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠘⠦⣄⣤⣄⠀⠀⠀⠈⠻⢦⡀⠀⠸⣆⠀⠀⠀⠺⢤⣀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⡴⠞⠋
⢀⡖⠋⠉⠉⠓⣎⠳⣄⠀⠀⠀⠀⠙⢦⣾⠁⠀⠀⠐⠀⠀⠈⠙⣲⠞⠁⠀⠀⠀⠀⠀⣠⠔⠋⠁
⠸⡅⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠲⠤⠤⠽⢿⣶⣶⣲⣤⣄⡴⠊⠀⠀⠀⠀⠀⢀⣤⢾⣥⣀⡀⠀⠀⠀⢀
⢠⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⠤⣄⣀⡠⠊⠁⠀⠀⠈⠆⠉⠛⠶⠋⠉⠉⠳
⡏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠
⢷⡀⠀⠀⠀⣰⠋⠉⠉⠛⠛⠒⠲⣦⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠧⣄⡀⠀⠀⠻⡏⠁
⠀⠙⠲⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠞⠉⠉⠉⢛⠶⢶⡦⠤⣤⣄⠀⠀⠀⠀⠀⠈⡆⠀⠳⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠶⠊⠀⠀⠀⢀⡴⠁⠀⠀⠙⠢⡀⠻⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⡶
⠀⠀⣰⠲⡄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠰⡟⠳⣄⠁⠀⠀⠀⠙⠛⠻⡍⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⠦⠤⠴⡆⠀⠀⠀⢀⡗⠀⣾⠀⠀⠀⣤⣀⣀⣤⠇⠀⠀⠀⣾⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠖⠋⠀⠀⠙⢦⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⢀⠐⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠒⢄
⠀⣀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⠿⠟⡃⠀⢀⡀⣸⣤⣤⣀⣰⡇⠀⠀⠀⠀⣦⣠⣤⣠⡆⠀⣀⡀⡁⠀⠀⠀⠀⡀
⠘⢿⣿⣿⣿⣿⠟⠋⠀⠺⠿⠛⠇⠀⢠⠶⠁⠀⠢⣤⣤⣾⣿⣿⠝⠁⠀⠀⠤⣤⣴⣿⣿⠋⠁⠀⠄⠀⠀⠀⣠⡤⠒⠀⠀⠀⠀⢀⣠⠔
⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⢾⡀⣠⠀⠎⠀⠀⠀⠀⠱⢿⠟⣿⣇⠀⠀⠀⠀⠀⢿⡟⢻⡇⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠹⣿⣿⡏⠀⠀⠀⠀⠘⣧⣿⠀⠃⠀⠀⠀⠀⠘⡞⢠⣿⠇⠀⠀⠀⠀⠀⠐⠁⣿⡇⠀⠀⠀⠀⢱⡀⠀⢡⠁
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⢰⠀⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⠀⠀⠀⠀⢸⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠇⠀⢠
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⢸
⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢸⢿⠀⡆⠀⠀⠀⠀⠀⠰⡄⣿⠀⠀⠀⠀⠀⠀⠀⢰⣼⡆⠀⠀⠀⠀⠀⠇⠀⢸
⠀⠀⢨⣿⣿⣿⡀⠀⠀⠀⠀⢸⠰⡆⠇⠀⠀⠀⠀⠀⣿⣿⣻⣆⠀⠀⠀⠀⠀⢈⣿⣸⣇⠀⠀⠀⠀⢈⠃⠀⠀⣄
⠀⢰⣿⣿⣿⣿⡗⠀⠀⠀⡰⣾⠆⢐⠂⠄⠀⠀⠀⣎⠀⣽⠧⣿⠀⠀⠀⠀⢠⡁⣸⡿⣼⡇⠀⠀⢀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠛⠋⠉⠛⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠙⠛⠉⠛⠋⠀⠀⠀⠀⠈⠛⠋⠉⠛⠀⠀⠀⠀⠃⠐⠙⠂⠈⠀⠀⠀⠀⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠸⢱⢨⠏⠉⠀⠉⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡷⣳⡄⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠐⣫⣾⣶⣴⡍⣅⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢀⡧⣼⠁⢹⣟⡉⣿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣸⡏
⠀⠀⠀⠀⠀⠘⢘⠿⣦⣸⣅⣠⣿⡚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⡇⢴
⠀⠀⠀⠀⠀⡆⢺⢀⠇⣸⡠⡟⠈⣇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⢺⣟⡈
⠀⠀⠀⠀⢰⡇⣿⣾⣶⣾⣿⢿⡆⢯⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠏⠁
⠀⠀⠀⠀⠀⡯⣿⣿⡏⣯⠀⠀⢷⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⢿
⠀⠀⠀⠀⠈⢿⡏⢻⣇⣿⠀⠰⣾⡿⢿⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦
⠀⠀⠀⠀⢀⠈⠙⠿⠛⠿⢲⣏⠁⠀⠀⠀⠉⠺⢤⣆⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣎⡜⠀⠀⠀⠀⠀⣷⠶⠀⠀⠀⠀⠀⠀⠈⢻⣾⠒⢀⣠⣄⠀⠀⡆⠰⣵
⠀⠀⠀⠔⠻⠃⠀⠀⠀⠀⠀⠧⠐⠀⠀⠀⠀⠀⠀⠀⠨⠹⣟⠦⠉⠉⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠄

⠀⠀⠛⠂⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⠒⠒⠒⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠙⢆
⠀⠀⠀⠀⠀⢀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⢀⡞⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⢀⠳⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠸
⠀⠀⠀⢸⠀⣿⢿⡆⠰⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠒⠀⠠⣟⣼⠀⡇
⠀⠀⠀⢸⠞⣿⡞⠀⢀⣤⣶⣶⣶⣶⣶⣔⠒⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⡀⠑⠀⠻⡗⠀⡇
⠀⠀⠀⢸⢲⡿⡤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣄⣽⡄⠇
⠀⠀⠀⠈⣿⢧⠑⣿⣿⣯⣯⠍⠩⠝⠛⣙⢻⡇⠀⠀⠀⠀⠀⠀⠶⢠⣿⢟⣋⡙⠋⠻⢝⣻⣿⣿⡏⠻⠈⣷
⠀⠀⠀⠀⢿⢸⢸⣿⡯⣽⣏⠀⠄⠠⢙⢿⣿⡇⠀⢀⣀⣀⣤⣀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠙⣾⣿⣧⠀⠀⣿
⠀⠀⠀⢀⡇⣸⡼⣿⣯⡿⠻⣦⣾⣂⣦⣼⠟⠀⢠⣿⣿⣿⣿⣿⣄⢄⠻⢿⣍⣠⣶⡴⣤⣴⣿⣼⠟⠀⠀⢹⡀
⠀⠀⠀⣼⣸⠃⠀⠨⠛⠛⠛⠋⠛⠉⠁⠠⠶⠀⣿⣿⣿⣿⣻⣿⣿⡇⡕⠠⠄⠉⠉⠻⢛⡛⠛⠉⣠⣆⠀⠀⡇
⠀⠀⠀⢻⢹⡄⠀⠀⠌⠀⠀⠀⠀⣤⠄⠀⠀⣰⣿⣿⣏⣿⣟⢻⣿⣧⠈⠀⠀⠘⣿⠙⠀⠉⠳⣄⠸⡇⠀⢠⡗
⠀⠀⠀⠀⠳⣙⢻⡦⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⣧⣽⣿⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⣀⣀⣈⣀⣹⣦⡾⠃
⠀⠀⠀⠀⠀⠈⠙⣷⣿⣶⣦⡈⠻⣷⣦⡴⡗⠀⠙⠛⠛⣧⠙⠛⠛⠉⠁⠆⢠⣶⠿⣿⣽⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣿⣿⣆⣜⢿⣠⡃⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⣰⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠈⢿⣿⣿⣿⣿⣽⣡⡁⢸⠀⣤⠀⢤⠀⢆⡀⣠⣀⠀⠁⢿⠿⢿⡿⡟⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⢿⣧⠙⡛⢛⠉⢹⡏⢹⡟⠙⡟⠙⡿⠉⣿⠉⡟⢿⡏⢀⣾⢡⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⠃⠙⢷⣥⣌⣣⢸⠀⣰⢁⣸⣇⣀⣀⡀⢹⠀⣷⣿⡥⣾⠟⢸⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡇⠀⠀⠈⠈⠙⢻⡟⣿⢻⣟⢻⠿⠟⣿⠿⣿⢏⣿⠀⠀⢀⠒⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡸⠇⠀⠀⠀⠈⠓⠞⣧⠼⠔⢯⡬⠤⠢⠿⢬⠿⠌⠀⠀⠀⠨⢀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣴⣶⣶⣶⣦⣀⣀⣀⣀⣠⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⠤⠤⣄⣠⡤⠼⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⣀⣀⣠⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠐⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢇⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠚⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠖⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣋⣿⣩⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢶⡀
⠀⠀⠀⠀⠀⢀⡤⢤⣀⣼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠷⠚⠙⠳⣄
⠀⠀⠀⠀⠀⡟⠀⠀⠈⠛⠀⠀⠀⢸⡃⠀⠀⠀⠀⣴⠛⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠻⣄⡀⢀⣀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢿⠀⠀⠀⠀⢼⣀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⡤⠶⠚⠻⢯⡙⢦⡀⠀⠀⠀⠈⠛⢦⡀⡾⠋⠀⠀⠀⠀⠈⠙⠳⢤⣤⠞⠁⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠲⠿⠤⣤⣀⣀⣀⣀⡙⢿⣦⣀⣠⣄⡀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⠚⠿⠿⣏⣀⡀⠀⠀⠀⢀⠔⠊⠉⠙⢻⡓⠶⣤⣠⡴⠶⠶⢤⡀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠁⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⢹
⠀⠀⢸⡇⠀⠀⠀⠀⠀⡴⠦⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠄⠀⠐⠀⠀⣤⡤⠴⠋
⠀⠀⠀⠳⣄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⠉⠙⢯⡛⠒⣶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢯⠛⠲⣄⠀⠀⢈⡇
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠚⠁⠀⠀⢀⡴⠋⠛⢿⡛⠒⢶⠀⠀⠀⠀⠀⠀⢸⠇⠀⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠋⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠙⢦⣈⣣⣄⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣾⣹⡄
⠀⠀⠀⠀⠀⣾⣙⣆⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠸⡍⠙⢦⡀⠀⠀⠀⠀⠉⠉⢳⠉⠉⠁⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠶⠶⢻⡀⠀⠀⠀⣰⠇⠀⣿⠀⠀⠀⣴⢤⣤⡤⠞⠀⠀⠀⠰⣯⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠚⠁⠀⠀⠘⠦⣤⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣤
⠀⠀⢹⡏⠀⠀⠀⠀⢰⡆⠀⠘⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠰⣿⣿⣿⡇⠀⢸⣻⣟⡇⠀⠠⢙⣉⡄
⠀⠀⢸⡇⠀⠀⠀⠀⣼⡇⠀⢀⣾⠤⠀⠀⠀⠀⠀⠀⠶⣶⣷⣶⢶⠀⠀⠀⢸⣀⣀⣀⡀⡉⠉⠿⠇⠀⠀⠯⠽⠀⠀⠁⢸⡉⡇
⠀⠀⢸⡇⠀⠀⠀⣸⣿⠀⠀⠘⡙⡄⠀⠀⠀⠀⠀⢀⠀⣫⣿⣝⠀⡀⠀⠀⠀⠉⠁⠀⠀⠙⠀⠀⢠⡀⠀⠀⠀⢰⣆⠀⠀⠂⠁
⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡷⠻⡀⠀⠀⠀⠀⡜⠀⡁⣿⢈⠀⢃⠀⠀⠐⡆⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢻⡏
⠀⠀⢸⡇⠀⠀⢸⣿⡇⠀⠀⠰⢷⡄⠱⡄⠀⠀⢰⠀⢈⣟⣛⣻⡁⠀⡆⠀⠀⡇⠀⠀⢸⡀⠀⠀⢸⠁⠀⠰⣤⣼⡷⣦⠂
⠀⠀⢸⣗⠀⠀⠈⣿⣇⠀⠀⠀⢸⠁⠀⠱⠀⠀⠸⠀⠸⠈⠈⢀⠃⠀⠃⠀⢠⡇⠀⠀⢸⡇⠀⠀⣸⡀⠀⠀⠋⢸⡇⠙⠂
⠀⠀⣻⣟⠀⠀⠀⣻⣿⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢇⠀⠀⣸⡧⠀⠀⢻⡇⠀⠀⠀⣼⣧
⠀⢐⣾⣿⡂⠀⠀⣼⣿⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⢿⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠘⠋
⠀⣶⣿⣿⡆⠀⢀⡿⠟⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡛⠀⠀⢸⠀⠀⠀⢸⠀⠀⢤⣶⣶⣾⣯⣽⡍
⠀⠀⢻⡟⠁⠀⡾⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣳⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⢼⣄⠀⠀⣀⣤⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠐⠉⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠀⠀⠈⠀⠀⠛⠉⠉⠙⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠉⠀⠀⠀⠈⠁⠐⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢸⣷⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⠄⠉⠁⣀⣀⡈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢟⢲⣶⣿⣿⣿⣿⣷⣾⠓⢳⢶⣿⣿⣿⣿⣷⣶⠺⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⢸⣿⣿⣿⣿⣿⠿⢿⡅⡝⠸⣿⣿⣿⣿⣿⣯⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠳⠽⠝⠋⠉⠑⣢⣼⣿⣿⡜⠦⠍⠙⠉⠋⠕⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠐⠀⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⢳⡀⠀⠀⠨⡋⠫⠁⠀⠀⣴⠛⣿⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⣜⠧⠤⣄⣄⣀⢠⣤⣤⡤⢟⣼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⠗⠲⠤⢤⣠⣀⠤⠔⢓⢥⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⢁⣐⣒⣀⠂⠁⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠉⠁⠀⠀⢀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠔⠋


⠀⢀⠄

⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡁⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⣣⡌
⠀⠀⠀⠀⠀⢠⠀⠠⠐⢄⠀⠀⠀⠀⠀⠀⡐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠰⡇⢀⡈⠃⠀⠀⠐⣿⠆⠀⠀⠘⢇⡀⢺⡆⢈⠄
⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣄⠐⢀⡄⠃⣨⣀⣀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠙⠆⣁⠘⣀⡓⠂⣀⣀⣉⣀⣀⢀⢚⡀⠃⣣⠸⠏⣀⠀⣀⡀
⠀⠀⠀⠀⠀⡀⠈⠙⢁⡈⠋⠀⢨⡅⠄⠛⢁⡈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠙⣅⣈⠋⢤⠞⣋⠉⢻⠯⣉⡹⠟⠉⣉⠳⣤⡝⢁⣈⠋⠀⠋⠁
⠀⠀⠀⠀⡀⠀⠄⠐⡀⠓⠀⠀⠈⠁⠀⠀⠸⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠰⡇⠀⠀⣭⠐⠀⠀⠉⠀⠈⠀⢭⠀⠁⢄⠂⠙⠆
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⢋⡅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠈⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⢀⠀⠠⡄⢠⠖⠀⠀⠀⠀⠀⠀⠤⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣠⠄⠀⠀⣀⠀⠀⠀⢀⡀⠀⢀⢄⡒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣤⠶⠀⠀⠀⠰⣤⡄⣤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠘⣃⡀⠋⢀⣄⣐⣀⣄⠈⠀⣀⠋⠀⠰⠖
⠀⠀⠀⢠⣧⢠⡄⠠⠄⠠⠉⢠⣸⣦⡞⣤⠘⠡⢠⣤⠀⣦⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠌⠩⠉⢩⡄⠀⠭⣭⡭⠄⠠⣼⠈⠁⠁⢤⠄
⠀⠀⠀⠈⠇⠀⠀⠀⣴⡖⡷⢀⠐⣀⡀⣀⠸⡗⣶⡄⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠲⠆⠠⠀⡀⣿⡦⠀⠄⠀⠶⡒⠒⢢⡄
⠀⠀⠀⠀⢀⡠⠀⠀⠉⢡⡄⠀⠀⠹⠁⠀⠀⣤⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢄⡜⠑⠀⠀⠚⠀⠈⠀⠙⠂⠀⠀⠛⣤⠄⠡⠄⠂
⠀⠀⠀⢀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐

⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠦⢄⠀⠀⠄⠀⢀⠠⠴⡄⢀
⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⢀⠀⣽⠀⢀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢢⡖⠷⠲⢶⡖⠀⢶⣾⢻⣶⠗⠐⣶⠶⠲⠟⣦⠓⠀⠲
⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠠⠿⠀⡝⡅⠺⠇⠨⠀⢀⡀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⡖⢨⡡⣄⢠⡌⢁⠀⠋⣸⣿⡈⠃⢀⠉⣦⢀⣤⣉⠔⠆
⠀⠀⠐⠢⡐⠿⢒⣼⠂⠛⠓⡒⠚⠻⡛⠒⠂⠛⠂⢺⣕⠺⠇⠀⠒⠀⠀⠀⠀⠐⠛⡽⢛⢻⡿⣋⡟⠻⠞⠛⠻⡿⠏⠛⠨⠛⣯⡻⣿⢛⠻⠏⠛
⠀⠀⠀⠐⠂⠀⠀⠉⠀⠀⡄⠤⠂⣸⠀⠣⢀⠁⠀⠈⠈⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠁⢠⡍⢀⢉⣱⣆⣀⢳⣠⣷⣰⠇⣀⣶⢁⣁⡈⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠈⠉⠹⠨⣋⣉⠥⠘⠻⣽⠛⠠⢍⣉⡩⠈⠉⠉⠀⠘⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠆⢠⡄⠀⠀⠀⣤⠠⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀
⠀⠀⠀⠀⠀⣈⣉⣛⣳⡲⣊⡖⢳⢀⢁⣸⢓⣊⡞⣲⣛⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠚⢟⠓⣀⣚⣰⠄⡗⢤⣘⡆⡐⠛⠟⠂⣀⡀
⠀⠀⠀⣠⣶⣄⣹⣅⣀⣄⣤⠘⣩⡧⠨⣏⡁⢠⣄⣄⣀⣿⠁⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡦⢴⢶⣚⠱⠄⠄⠴⢈⣳⢶⠤⣶
⠀⠀⠀⠀⠁⠁⠼⢅⡀⡀⢀⠷⡼⠆⠇⠿⡴⣧⠀⠀⣀⠯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⣤⣴⡀⣌⡳⠶⠿⠶⢋⡄⣰⣤⣤⡄⠈
⠀⠀⠀⠀⠀⠀⠒⠾⡿⠃⠸⢙⠇⠀⠀⠘⢟⠻⠈⢻⡿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠐⠁⠀⠀⠀⠉⠀⠁⠟⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣤⣦⣄⠀⣠⣶⣦⠀⣠⣤⣄⠀⠀⣠⣤⠄⠠⠀⠢⡀⠀⡀⠒⡆⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠄⠀⢄⠀⠀⠔⠢
⠸⣿⣿⣿⣿⣿⣿⡿⠂⠿⠛⠯⠗⠘⠛⢋⡄⢈⣤⣜⣮⣿⣶⣶⡿⠀⢁⣦⣲⣨⣯⣶⡾⠇⠘⡀⠀⠀⠈⠁⣠⣄⠆⠀⠀⠀⠀⠀⢠⠤
⠀⠘⠛⣿⣿⣿⠁⠀⠀⠀⠃⠰⠄⠓⡜⠀⠀⠀⠙⠻⣿⣿⡿⠀⠀⠀⠀⠙⠻⣿⣿⡇⠀⠀⠀⠈⠒⠆⠐⣴⡏⠀⠀⠀⠁⠐⠀⢦⡍
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣷⡆⠃⠀⠀⠀⠀⠀⡏⣻⡇⠀⠀⠀⠀⠀⠀⠘⣻⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⣿⠁⡀⠀⠀⠀⠀⠀⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⠁⠃⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢰⡄⠀⠀⠀⠀⠀⡇⢺⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⣿⢸⡆⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⢰⣹⠨⡇⠀⠀⠀⠀⢠⠷⣼⣖⠀⠀⠀⠀⠀⠀⢦⣷⠂⠀⠀⠀⠀⠀⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⣽⡶⠂⠸⣷⠀⠀⠀⠜⢉⣿⣿⡉⠀⠀⠀⠀⠈⢹⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠿⠿⠉⠻⠋⠀⠀⠀⠘⢋⠅⠠⠠⠂⠀⠀⠰⠶⠟⠹⠿⠋⠀⠀⠀⠰⠶⠋⠹⠟⠁⠀⠀⠀⠄⠴⠟⠧⠄⠀⠀⠀⠀⠀⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⣠⣄⣀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⢠⣾⢰⣿⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢿⣿⣿⣯⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⠟⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⣀⣠⣄⠀⢀⡀⠀⢀⠀⠀⣄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠻⠟⣿⢈⠌⠁⡁⠉⠘⢶⣿⠻⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄⠀⠿⠎⠂⠀⠉⠀⠈⢿⠏⠀⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⣀⣀⣀⢀⣀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢩⣍⠉⢉⡥⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢡⡌⠉⢉⡤⠵⠆
⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⣠⠔⠛⠲⠣⣈⠀⠀⠀⠶⠜⠓⠦⣀⠀⠀⠀⠀⠀⠀⣀⠄⠄⠤⠤⠤⠄⣀⡀
⠀⢰⠂⠀⠝⠓⠲⠖⠲⢚⡂⠀⢙⡶⢤⣄⣠⠎⣡⠄⠛⠶⠖⢸⠉⠉⢻⠶⠶⠛⠢⣄⠰⣄⣀⣤⢶⡛⠁⢒⣓⠒⠒⠶⠞⠫⠄⠀⡄
⠀⠀⢢⣠⣤⡀⢀⡤⠖⢦⡈⠝⠋⡩⠖⣤⣍⠘⠓⠒⠒⠉⣻⣼⣛⣛⣺⣟⠙⠛⠒⠚⢋⣉⣥⡶⢍⠛⠋⢁⡴⠦⢤⣀⢀⣤⣄⡔
⢠⠚⠀⠀⠀⠙⣇⡀⠀⡠⠀⢀⣼⢁⠊⠀⣉⣱⣤⣀⠘⠋⠀⠀⠈⠉⠀⠈⠙⠂⣀⣠⣎⠉⠀⠑⡀⣧⡀⠀⢄⠀⠀⣸⠋⠀⠀⠀⠓
⠸⡀⠀⠀⠀⣠⡇⠀⠀⠁⡰⠉⢿⡌⢶⣉⡀⠀⠀⠉⠻⣤⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢈⣁⡶⢡⡿⠙⢦⠈⠁⠀⢈⣄
⠀⢱⠀⠀⣰⠋⢃⡀⠀⠸⣣⠟⣩⠻⢦⣙⠣⠬⢍⡥⢤⠄⢧⠀⢀⡀⠀⣼⠣⡤⢈⠭⡭⠔⣋⡴⠛⣍⡻⣌⣅⠀⠀⡨⠙⣆⠀⠀⡞
⠀⢸⠀⠀⠈⠀⠀⠙⡄⢿⡸⣏⡡⠒⣹⡥⠝⠒⠲⣥⠀⠀⣬⠉⠉⠉⠉⣯⠀⠀⣼⡄⠒⠫⢩⡇⠒⠌⣹⠏⡽⢀⠎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠙⠷⣌⡳⢦⡤⠒⠀⠀⠀⠀⠀⠶⠟⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠢⢤⡴⠞⣡⠾⢋⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⢀⠛⡇⢃⡼⠛⣶⣄⡀⠒⠶⠭⠙⠉⣤⣛⠀⠀⠀⠀⣗⣤⡉⠛⠭⠷⠖⠀⣠⣴⠛⢣⡘⢸⠟⡇⠀⠀⡄
⠀⠀⠀⠀⠘⠀⠀⠘⡀⣻⣌⠳⣭⠔⠊⠉⣠⡤⠶⢛⡓⣨⢟⡀⠀⠀⢀⡻⣅⣚⡛⠦⢤⣔⠉⠑⠦⣩⠞⣡⣿⠄⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⡉⢓⣌⠙⠒⠠⣤⣀⡉⡄⢚⣡⡎⠁⠀⠀⠈⢳⣌⡛⠁⣀⣀⣤⡄⠲⠚⣡⡶⢉⠟⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠹⣄⠙⣉⠠⠛⣠⢄⣈⣉⠡⠐⣽⠏⢼⡇⠀⠀⠹⡧⠟⢬⠲⠌⣉⣁⣠⡄⠛⠅⠉⠊⢠⠏⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠈⡴⢋⠳⣌⠒⢎⣠⠘⠉⢀⡠⢞⡝⡳⠎⠀⢀⡀⠀⠱⢞⢪⡳⢄⡀⠉⠳⣄⡱⠖⣠⠖⠙⢦⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠰⣌⠃⣀⠟⠂⣀⣈⣀⡠⠐⣩⠜⣡⠚⡴⠉⠉⢦⠓⢌⠳⣍⠂⢄⣈⢁⣀⠴⠛⢁⡸⢣⠎⠀⠀⠀⡇
⠀⠀⠀⠀⣸⠀⠀⠀⢀⠘⡶⢉⠰⢎⣩⡌⢉⡠⢞⡡⢚⠏⡼⠓⠒⠒⠲⢦⠙⡓⢌⡳⢄⡉⢩⣍⡠⠄⣉⢴⠋⡀⠀⠀⠀⡗
⠀⠀⠀⠀⢸⠀⠀⠀⢸⣇⠱⡎⡱⢤⣇⣀⡡⠔⠋⡡⠋⣼⢣⣀⣠⣄⣀⡌⣧⠙⢌⠙⠢⢈⣁⣹⡤⢎⢁⠎⣸⡃⠀⠀⠀⠃
⠀⢠⠀⠀⡼⠀⠀⠀⢸⠏⢡⡌⢦⣈⡡⠉⠀⣠⠞⠁⣸⠏⣿⠁⠀⠀⠀⡿⠸⣇⠈⠳⣄⠀⠉⠌⢁⡤⢋⣜⠹⡇⠀⠀⠀⢣⠀⠀⡆
⠀⠘⠀⢠⡇⠀⠀⠀⣦⢷⡘⡜⢠⡌⠓⠛⣉⠀⠀⣰⠇⠀⣹⡤⠒⠒⠦⣇⢀⠈⣆⠀⠀⢉⠛⠚⢩⡄⢣⢎⡾⣡⠀⠀⠀⢸⡄⠀⠃
⠀⡆⠀⠸⡇⠀⠀⠀⠸⢾⡷⠘⣆⠈⡉⣋⡴⢃⡰⠃⠀⠈⠙⠂⠀⠀⠀⠿⠈⠀⠘⢆⠘⢦⡙⢈⠁⣰⠂⢾⡷⠉⠀⠀⠀⢸⠇⠀⢸
⢠⠀⠀⠀⠙⡀⠀⠀⠀⠻⣔⢏⠄⢙⣉⣡⡴⠚⠃⠀⠔⠀⡾⠀⠤⠶⠒⢛⠖⢂⠀⠘⠓⢦⣌⣉⡋⠡⡺⣆⡟⠀⠀⠀⢀⠊
⡎⠀⠀⠀⠀⡘⡄⠀⠀⠀⠜⢧⡛⠾⠣⠉⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⡀⠉⠈⠧⢞⣴⠋⠀⠀⠀⢠⢂
⢹⣆⣀⣄⠀⣻⠁⠀⠀⠀⠸⣌⠻⣹⡽⣢⠎⠀⠀⠀⠀⠀⠘⠚⠋⠭⠒⠋⠀⠀⠀⠀⠀⠑⣔⢮⣋⠿⣠⠇⠀⠀⠀⠀⣟⠀⣠⡀⣠
⣤⣬⣭⣬⣽⣭⣤⣤⣤⣤⣤⣽⣧⣴⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣵⣶⣼⣯⣤⣤⣤⣤⣤⣭⣯⣥⣭⣭
⣿⣿⣿⠋⠙⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠖⣶⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣶⠶⡶⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢤⣤⢄⠀⢀⣀⠠⣶⠀⣀⡀⠀⡠⣤⠄⠀⢀⡀
⠀⠀⣋⠣⠄⠀⠉⠁⠀⡤⡟⠀⠰⢤⣾⣄⠄⡀⢛⡤⡀⠈⠉⠁⠹⢶⣛⡂⠀⠀⠀⠀⠀⡠⠆⠸⠗⠂⠚⠋⢷⣤⡭⣆⠘⣿⢃⣼⢡⣤⡟⠘⠃⠘⠚⠅⠰⠄
⠀⡶⣶⠀⠀⠀⠀⣰⡌⠀⠀⠶⢳⣿⣟⣷⡾⢷⠂⠀⢉⣦⠀⠀⠀⠀⢳⢶⠀⠀⠀⠀⠀⠷⠂⠀⢠⣠⡄⠀⠀⠤⠗⠿⠗⣡⠺⠟⢹⠤⠀⠀⣠⣤⡀⠀⠐⠟
⠀⠰⣿⡀⠰⠶⠴⠿⡷⠬⠷⢶⡼⣙⣫⢛⣵⡤⠶⠇⢴⡿⠦⠶⠆⠀⣼⡄⠀⠀⠀⠀⢰⡇⠀⠀⠸⡄⠀⠀⠚⠃⠛⠛⠳⠀⠛⠛⠛⠘⠒⠀⠀⢠⠁⠀⠀⢸⡆
⠀⠀⠈⠛⠺⠔⠀⠀⠁⠀⠀⡸⡿⠟⢾⠺⢷⢷⠀⠀⠈⠀⠀⠐⠶⠚⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠙⠘⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣽⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⣖⣛⡛⢿⣿⣿⢿⣿⣿⠛⣛⣳⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⢀⣀⡀⠲⠆⣹⣇⠰⠆⣀⣀⡀⠀⠀⠀⠀⠀⠒⣄
⢀⣠⣤⡀⠀⡴⣯⣭⣿⣿⣿⣯⣿⣯⣿⣾⣯⣿⣭⣿⣿⣿⣯⣽⠧⠀⢀⣠⣤⣀⠀⠀⠰⠇⠀⠀⠀⢀⢀⣭⠐⡶⠲⣶⣤⡝⢩⣤⣶⠚⣶⠈⣧⡠⡀⠀⠀⠀⠸
⠀⠈⠁⠈⠑⠲⠖⢻⡿⣟⣿⣿⠇⢰⡦⠰⣆⠈⣿⣿⣟⡿⣿⠓⠖⠀⠉⠀⠋⠀⠀⠀⠘⠋⢄⡀⠴⣇⠋⠘⣹⣿⣾⢤⡮⣷⣯⢰⣬⣷⣿⣌⠊⢑⣹⠦⢂⡄⠻
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠹⣤⣈⣷⣿⢸⣿⣇⣤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠘⠃⠘⠋⠈⠉⠋⣶⡏⢻⣾⠉⠉⠀⠙⢡⡟⢃⣞⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣚⠀⠀⠀⠀⠀⠀⠐⠒⠰⢆⣿⣣⠦⠐⠒⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠀⣠⡄⡛⣠⡀⠀⠀⠀⡀⠠⣀
⠀⠀⠚⡍⢄⠀⢀⡀⣠⢂⠀⣀⡈⡲⢟⢷⡊⣀⡀⢐⢀⣀⡀⠀⣠⠎⡗⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⡠⢰⠶⢖⡉⡛⢑⠲⣶⡤⣀⠀⠀⠈⢷⣄
⠀⠀⠡⢙⢯⠍⢻⠽⣿⣿⠯⡉⢋⢱⣍⡾⠙⠉⠩⢿⣿⡯⣽⠋⠭⡏⠁⠁⠀⠀⠀⠀⠀⠀⢴⡼⡆⠤⠠⠼⢇⡼⢧⣽⡋⣉⡛⣧⡻⣅⠻⠦⠄⠄⣸⣼⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠣⣼⣟⡿⣟⣿⠴⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢘⠶⡒⣖⠏⠁⠐⣌⣀⣋⣀⡠⠀⠘⢇⡶⡒⢶⠡⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠑⠉⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠙⠉⠸⠛⠁

⠀⠀⠀⠀⣀⣀⡤⢀⠀⠛⣶⣤⡀⠀⣀⠀⠀⣠⣴⡞⠃⡀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⡀⠀⢠⣠⣦⣠⠄⠀⡀⣠⣀⡀
⠀⠀⢀⡎⠉⢏⡶⠣⠿⢆⣀⠇⢹⣤⣿⣡⣾⠰⣇⡐⠻⠇⢳⡌⣍⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡾⢧⠆⠉⣍⠱⡕⠶⠷⠞⡥⢊⣉⠑⢤⢽⠆⠀⢠
⠀⠀⠸⠇⠀⠏⠨⢮⠧⣬⠿⣀⠈⣋⣿⣙⠋⣀⡸⢧⠰⢶⠦⠸⢗⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⠐⠛⠞⣀⠂⠒⣶⠜⢾⢿⠞⢤⡾⠒⢒⣜⠎⠓⠀⢸⠇
⠀⠀⠀⠀⠀⠶⡄⠈⠓⢄⡀⠛⠀⠉⠻⠉⠀⠹⢁⣌⠔⠁⠀⡼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣵⣆⢠⡄⡤⣾⠋⠒⠶⠽⠖⠊⢻⡦⡄⣤⣄⣆⣨⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣴⣴⣤⣤⣤⣴⣴⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣴⣷⣯⣥⣤⣤⣤⣤⣤⣤⣤⣬⣷⣷⣼⣯⣥⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⠁⣀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⣀⠀⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣆⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⠀⣿⣤⣴⠂⡸⠀⠂⠀⠀⠉⠛⠀⢀⣉⣿⣭⡿⠖⠋
⠀⠀⠀⠀⠀⠲⣤⣴⣿⢁⣠⡴⠒⢲⠖⠀⢄⠁⠈⠀⠀⠀⠀⢠⣤⣥⣀⠁⡘⠓⠶⣤⡀⣤⠂⠩⠽⠛
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠏⠀⠀⠋⠀⠀⢀⡀⠤⣒⠉⠀⠀⢀⣀⣭⣁⠘⠻⠆⡄⢤⡌⠀⠀⢸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⣴⡎⢃⠌⢀⠀⠹⠂⠀⠀⠈⠉⠙⠛⠿⠋⣴⡄⢀⠹⡆⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠉⠀⢠⡆⢉⣆⣥⡆⢤⠐⠂⠀⠀⠐⠒⠶⠷⢶⣤⣀⠁⠈⠀⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣡⠠⣏⢶⡻⠿⠞⢡⠌⣠⠀⠀⠀⣠⣈⠓⠲⠄⠈⠁⠸⢷⠆⣶⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠘⠣⣭⣤⣄⠀⠾⠁⠀⠀⠀⠈⠛⠻⢿⣿⣍⡛⠷⠆⣠⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣔⠲⢂⡉⠁⡖⢂⠀⠀⠀⢿⣶⣤⣀⠤⠉⠁⢤⣦⣌⠉⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠉⠓⠠⠅⠀⠉⠁⡀⠀⠐⣷⡄⠉⠙⠳⢶⣤⡀⠈⠋⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⣄⠀⠈⡁⠀⠀⠀⠀⠄⠀⠀⢴⣄⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⣁⠀⠀⠀⠂⠀⠉⠂⢠⡍⠀⠀⠈⠹⣦⡔⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⠒⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠌⠛⢀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡾⡆⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠟⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠙⢦⡀⠀⠂⣼⡗⠀⢷⠀⢀⣀⣤⣤⠠⠀⠤⠤⣴⣒⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠹⠀⠀⢃⠐⠦⣾⣏⢉⢄⣚⣟⠛⢉⣁⣉⣙⠻⢯⣭⣟⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢢⡀⠀⠀⠀⢀⣤⣄⣀⠀⣿⠟⠙⣤⠹⢿⡿⢟⣂⡾⣿⣿⢛⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣀⣀⠟⠉⠁⣋⠀⢾⠀⠀⠈⠙⢦⣙⢿⣍⣋⠑⠀⠀⠀⠘⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠘⠻⠀⠀⠀⠩⠦⢼⠃⣺⠀⠀⠀⠙⠳⣌⡛⠦⣚⣀⠿⠶⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠱⡀⠀⠀⠀⠀⢸⣭⠹⠁⠀⠀⠀⠀⠈⠛⠷⣄⣬⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⡦⣤⡀⠀⢀⡐⢣⣤⠀⢇⣤⡄⠀⠀⠀⠀⠙⢾⣽⣻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⠄⠀⢸⡏⠹⣶⠀⣌⠏⠓⠀⠀⠀⠀⢀⡈⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⣴⠟⠀⠀⠉⠀⡟⠀⠀⠘⢷⣴⣤⣬⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣷⣦⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡼⢿⣯⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣥⠙⠋⠻⢉⣶⢶⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠿⣿⣿⣿⣽⢃⣭⠠⣋⠈⣥⡾⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⣿⣿⣿⣏⡴⠖⠀⠰⠶⠴⠾⢛⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣟⣻⠏⠀⢐⠒⠲⠞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⣖⠉⠅⣶⡘⠯⠀⠚⠂⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⣶⡶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡄⠀⢀⣻⡇⣰⠦⡄⠓⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠛⠛⠒⠶⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⠇⠀⠰⠋⣹⣟⡉⠰⣼⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠙⠂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣿⣯⡄⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣅⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣴⣾⣿⣤⣶⣾⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⣼⣿⣿⣿⣯⣥⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣇⣴⢨⡹⣿⠟⢋⣭⠻⠆⡀
⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡋⣿⣁⣿⠿⠏⠰⣿⠳⡆⠁
⠀⠀⠀⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠃⠈⠛⠁⠀⠀⠀⠋⠀⠀⡀
⠀⠄⠁⠤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⠆⠀⠀⠀⠀⠀⢠⣯⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡄⢸⠆⠀⠀⠀⠀⠀⠘⣿⡋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣄⣠⢴⣥⣿⣤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣿⣿⣿⣶⣄⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡒⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⣹⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠠⢾⣿⢾⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡠⢜⣛⠀⠴⢴⣿⠿⠗⠦⣄⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⣤⣀⣠⣤⣤⣬⣉⣘⣋⠉⠘⣿⠄⠐⢊⣻⡴⠊⢁⣈⣛⣛⣦⣤⣤⣤⠤⠤⠶⢶⣶⣤⠀⡀
⠀⠀⠀⠀⠀⠨⢀⣈⡄⣠⣶⣶⣠⣴⣿⢿⡿⠿⢯⣉⡛⢶⣦⠠⡴⣿⠏⢷⡿⠛⠛⣿⣿⣿⣿⣿⣦⣠⣤⣤⡄⢼⣿⣗⡂
⠀⠀⠀⠀⠀⠀⢠⠀⢉⣿⣿⠉⡿⢸⣗⠸⣿⣿⣎⣉⠙⠋⠀⠀⣾⡆⠀⠀⠐⠊⣡⢿⣿⢃⣿⡜⣿⡇⢈⣿⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⢟⣧⣤⢸⣿⣆⠙⣿⡟⠙⠳⢦⠀⠀⢸⠇⠀⠠⠄⠛⠉⣹⢋⣾⣿⡿⣿⣿⣤⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⣿⡄⢿⣟⣧⡌⠓⠀⠀⢀⡁⠀⢸⠀⠀⠀⠤⠦⢒⣤⣾⣿⠟⣸⣿⢿⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠹⣟⣄⠙⢦⣆⠀⠀⣀⡈⠁⠀⢺⣇⠀⢀⣠⡠⠤⠤⠶⢃⣴⣿⢇⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⠙⢶⠃⠀⠁⣀⡀⣀⡄⠀⠀⢸⡿⠀⢀⡀⠀⠀⢀⠐⢋⡻⢋⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡍⢱⣀⠙⠶⠉⠁⠀⠈⡁⠀⠀⢺⣇⠀⠀⠀⠀⠈⠉⠒⠎⣡⣞⣽⡟⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠹⣾⠉⠀⠀⣀⣠⠤⠬⠂⡄⠀⣿⣟⠀⠒⢦⠤⣤⣄⣤⠚⠉⣿⠟⡸⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢶⠃⠈⠳⢄⠉⠁⠀⠀⡠⠋⢀⡀⣹⡃⠀⡀⠀⠀⠀⠈⠙⠳⠖⢁⠜⠳⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠌⠳⡞⠁⠀⣡⡤⠤⠖⠰⢂⠞⣥⢿⡇⠛⠀⠐⠂⠈⠀⢠⣠⠒⠛⠄⢠⢿⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢰⠂⡙⢲⡁⠀⠀⠀⠀⠀⡆⢰⣿⡺⣽⣆⠀⠀⢂⠀⠀⠀⠈⠻⠆⡰⠻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠻⡁⠀⢹⠂⠲⠶⠁⡸⠃⣾⢉⣻⣿⡿⠘⢦⠈⠶⣦⡤⢀⡠⠊⠛⣰⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⠃⠙⢦⠊⠀⠑⠒⠊⠁⡸⣹⡡⢸⣿⣇⡀⠈⠆⠤⠄⠒⠙⠷⠀⡰⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠱⡇⠈⠃⠀⠠⣤⠂⣰⡰⢉⡀⢼⣿⡏⠁⠀⠸⣦⣄⠀⣀⣠⠼⠇⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢇⠘⡄⢰⡦⢤⣄⢴⠟⠀⣸⠓⢛⣛⣿⠀⠐⢄⡈⠉⠁⣀⠉⠀⡼⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡂⢃⢁⡉⢤⠤⢴⡟⠀⠈⢹⣄⣈⣽⣿⠁⠀⠀⠈⠁⠀⠙⣲⠎⣠⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣜⠠⢤⡴⠋⠀⠀⢠⣌⠀⢈⣽⣿⡄⠀⠀⠀⠀⡀⠀⢙⡞⢣⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠻⠖⠋⠀⠀⠀⠀⠀⢸⠀⠸⢿⣷⠀⠀⠀⠀⠀⠀⠐⠠⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠀⠠⣶⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠀⠀⠢⢩⣀⢀⢀⠀⣀⠀⣀⡍⠖⠠⠀⠠
⠈⠁⠈⠓⢀⠀⣀⠀⢮⡼⠸⢾⠕⠀⣀⢀⡀⠛⠀⠈
⠀⠀⠈⠁⡘⢃⠈⡂⠢⠀⠀⠀⠂⣈⢁⡘⣁⠈
⠀⠀⠁⠀⠈⠀⠰⠮⡄⠀⣀⠀⡬⠴⠂⠠⠁
⠀⠀⠀⠀⡀⠀⠁⢤⣄⠃⠀⠙⣤⡄⠁⠈⠀⠀⢀
⠀⠀⠁⠀⠐⠖⠀⠘⠇⡟⠒⢻⠸⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠚⠂⠆⠀⠀⣧⠀⠀⠠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⠉⠀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⣤⠃⠀⢀⠈⠀⡀⠈⠀⠀⢄⠀⠁⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡨⠀⠀⠀⠂⠀⠀⠀⠐⠀⣀⢈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠘⠁⠀⠀⠑⠀⠀⠀⠀⠀⠃⠀⠀⠘⢪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠂⠂⠚⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡁⠀⠀⠀⢈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠉⠉⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣀⣤⣤⣤⠀⠀⣠⣶⣦⣤⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣠⣀⢹⣿⣿⡟⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠉⠁⣿⣿⡈⠉⠁⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⣿⡆⠀⠉⠉⠁⢰⡾⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣭⣭⣭⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠠⠤⣀⠀⠰⣄⠀⠀⠀⠁⠀⠀⢀⠄⠀⠀⣀⡀⠀⠄
⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡈⠐⠠⠤⠤⠄⠂⠁⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⠂⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⣻⣿⠇⠀⠀⠀⠀⡘⣿⡖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠙⠿⠿⠋⣾⣿⠻⢃⠀⠀⠀⠀⡅⠿⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⢆⠀⠐⠲⣶⣦⣤⣤⠄⠀⠐⠿⠛⠤⠄⠀⠀⠀⠠⠂⠀⢀⣤⢭⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠒⠚⢻⠀⠀⣿⣀⡠⠤⠰⠀⠆⠀⠀⠀⠀⠤⠤⣤⢤⡧⠀⠀⠈⠀⠀⢄⣀⡀⠠⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠐⠛⠛⠛⠃⠀⠀⠀⠀⢹⠿⠛⠋⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢘⡀⡀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣠⣤⠀⣶⣔⣶⠚⣟⠻⠴⣷⣶⣲⣤⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣠⣔⣰⠖⣾⣦⣸⣷⣤⡼⢷⣼⣉⣽⣿⣿⡟⢶⣭⡛⣿⡏⣹⣷⡿⠻⣧⡙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⢹⣯⢻⡖⠻⣶⣿⠣⣿⡷⣏⣤⠻⠇⠩⣏⣱⣾⣻⣿⡈⣿⢾⣻⣷⣤⠿⣧⡴⢦⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣹⡷⢫⣷⣬⢻⣯⣥⣘⠲⣾⡇⢸⣿⣤⡿⢗⣉⣷⠿⣹⣤⣙⣷⠃⣏⣤⣶⠆⣿⠟⢊⣻⣧⣹⣾⢴⣿⠿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⣿⣰⣶⣞⠋⢶⣌⠋⠠⢾⣾⣁⣷⡶⢛⢸⠋⠛⠲⣿⠿⢦⡿⠾⣧⡼⠋⢲⣈⣿⡿⢯⣿⣃⡽⣧⣿⣿⣤⣿⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢘⣁⣼⡷⠴⣷⢟⣠⡟⠃⡤⢠⣴⣏⠁⣶⡌⠃⠛⢏⡀⠈⠶⡾⠀⣹⡏⢳⡟⠷⠦⣸⣶⣶⠘⢿⠁⡉⣳⡍⢻⣯⡹⣯⡹⢆
⠀⠀⠀⠀⠀⢰⣦⡶⣥⣴⠀⢹⣹⣆⣚⠿⠊⢻⡿⠃⠐⠊⣠⣤⣴⠉⠀⢠⣷⣮⡐⠦⠤⣤⣾⣩⢓⣈⡁⢰⡄⠻⢬⠛⠷⠀⣼⣇⠻⠟⣉⠿⣉⣬⣿⡼⣷
⠀⠀⠀⠀⠀⠀⣴⠊⣿⣾⠶⠛⣨⠛⠘⠶⣯⠍⢹⠟⠙⠋⣌⣉⠻⠉⣀⣤⣬⠛⠁⣀⠀⢀⣙⡛⠘⣿⣷⠄⠀⠤⠀⠱⢶⣷⠋⣽⣋⣠⣿⡐⢿⡻⢧⣿⡏
⠀⠀⠀⢀⠀⣳⣾⠃⡾⠧⠖⠚⢤⡶⣟⣶⡄⠀⠛⡳⠛⠂⠀⢀⣰⣈⡛⠷⣍⠤⡟⠛⠛⠎⠙⢻⡖⣥⡅⢶⣶⣦⠡⡄⣴⣀⣶⡿⠙⠟⢉⠛⢿⢿⣞⢿⠇
⠀⠀⠐⢚⣿⢉⣯⡔⢣⠶⠒⢠⣄⣴⡟⣀⢲⣾⣄⣁⠀⠄⢀⡙⠙⢉⡽⣿⡰⠂⡶⠚⠀⠀⠙⢤⡜⠉⣴⣶⣬⠉⠀⢇⠘⢉⠿⠷⢾⣇⡀⠳⠈⢣⠙⠿
⠀⠀⠖⠸⣟⠛⠚⢡⡼⣦⠔⠀⣈⠀⣠⣍⠙⣋⣨⣱⣄⠘⠀⠹⠃⢿⣃⣨⡶⢶⡀⠢⠀⠀⠀⣠⣴⣦⡙⣷⠄⠀⡶⠿⢦⠞⠶⣤⢰⡿⢋⣀⠘⣄
⠀⠀⢰⠖⡏⠶⢀⣄⠳⣞⣤⣶⠾⡉⠛⠽⡿⢟⠉⢽⡛⠀⠀⠖⢀⣈⡋⠀⣶⠟⠑⠂⠈⠡⢌⣥⡉⠀⢩⣿⡄⠀⠴⠒⠀⠐⠄⢳⡾⠃⠘⡛⢿⡟⢛
⠀⠀⠀⠰⠚⢠⠧⣿⠀⣋⣉⡤⠀⠉⠉⠀⠰⠿⠛⠋⠁⡿⠞⠷⠎⠈⢉⠰⣬⡷⠾⣶⣷⡀⠘⠄⠠⣶⣆⡍⣠⠀⠣⣄⠀⠀⠀⠀⠀⠘⣿⠻⣆⢱⣎⡀
⠀⠀⠀⠀⠀⠈⠁⣼⡏⢁⠀⠀⠀⢀⣤⡶⠶⣈⡽⢒⡴⢤⠖⠂⠀⠉⠂⠰⠧⣤⣤⡰⡟⠆⠀⠀⢠⡈⢉⠀⠀⠀⠃⡀⠢⡄⠀⡴⡏⠀⢀⣀⠉⠚⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⣤⠟⠛⠃⠐⠆⠀⠀⠀⠀⠀⣰⡀⠀⠉⠁⠀⣤⠴⡓⢆⠙⠻⣷⠒⠠⢄⡘⣀⠀⢲⠚⠃⠀⡠⢿⠀⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⣻⠦⠚⠋⠀⣉⡀⣤⠀⢰⠞⠟⢀⢀⡀⠀⠀⣷⡖⠀⠈⠲⠀⣡⢀⠀⠈⠛⠻⡧⢹⠂⠀⠻⣷⠆⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⣰⠆⣴⠄⠀⢏⡑⢀⠘⢻⠛⠀⢩⡌⠓⠀⢀⡇⠀⠀⠀⠀⠀⠉⠈⢴⡿⠄⠛⠀⠸⠀⠐⢦⡴⠄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣋⠰⠃⠀⠐⢷⡿⣦⠁⠤⠀⠐⢿⣵⠁⠳⠀⡄⠀⠀⠀⠀⠀⠈⠷⡀⢧⣤⠁⠺⠖⠛⢃⡈⠹⢤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠷⣤⡄⠀⣷⢴⡆⢀⠄⢤⣄⡶⢰⣤⡾⠗⠀⠀⠀⠀⠀⠀⠀⠁⢮⡈⠃⠾⠋⠀⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⢌⣀⠘⢶⣷⠶⠶⢆⠐⢆⣀⣨⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠸⡉⢣⠠⡴⠟⠀⠀⠙⢠⣭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠗
⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠙⠂⢰⠻⠷
⠀⠀⠀⠀⠀⠀⢸⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣈⠁⢠⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣤⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⡟⠀⠀⣀⢀⢀⣄⠀⠀⠃⣀⠀⢀⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣾⣊⠻⣄⢠⣧⢀⣀⣥⢯⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⡀⠰⠆⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠂⠀⠠⠄⠀⠂⠀⠀⠁⠀⠀⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢄⡀⢀⡀⠤⠀⢋⠅⡓⠤⣀⣻⠘⢲⣠⡀⠀⠀⢀⣤⠖⢲⡟⣀⠤⣛⠌⠋⠀⠄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠠⠁⢣⠴⠈⢏⣴⣄⠀⠀⠱⠀⠀⠉⠀⠀⣰⣄⡹⠐⢠⠃⡀⡄⠁⠀⠌
⠀⠀⠀⠀⠀⠀⢰⠂⠐⣙⠄⠂⠀⡔⣸⣽⢴⣿⣶⡀⠙⠁⠘⠃⢰⣾⣿⢼⣽⡖⣠⠀⠒⢥⠓⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢀⡐⢂⢢⣿⢺⢺⠻⡅⢾⣶⣶⣶⣶⡇⢹⢻⢺⠒⣯⠔⡑⣀⠀⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠂⠂⢐⡟⢸⡆⠀⡇⠀⠉⠉⠉⠁⠀⢻⠀⢸⠀⣷⠀⠂⠐⠈⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠆

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡴⠤⣄⠒⠀⣀⣠⡴⢤⣄⣀⠀⠒⣠⠤⢦⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠐⠦⣚⣉⣀⣀⣭⣦⡴⡶⢾⣭⣻⡄⠀⠟⠀⠸⠉⢀⣼⣦⡀⠉⠃⠀⠻⠀⢠⣟⣭⡷⢶⢦⣴⣭⣁⣀⣉⣓⠤⠂
⠀⠀⠀⠲⠉⠉⠋⠐⠮⠝⠶⠤⢶⣿⠟⢰⡄⢀⠐⠄⡊⢹⠏⢑⠠⠊⡀⢠⡆⠻⣿⡶⠤⠶⣫⠵⠂⠙⠉⠉⠂
⠐⠁⠀⢀⠐⢀⣙⣺⣶⡖⠺⣦⣾⣿⠂⠀⢻⣾⣇⡶⣿⠀⠀⣿⢶⣸⣷⡟⠀⠐⣿⣷⣶⠖⢶⣶⣗⣛⡀⠀⡀⠀⠈
⠀⠀⠀⠙⠤⠀⠉⢉⠀⠉⠉⠉⣈⣹⣦⣀⠈⡅⠘⢙⠅⡀⢀⠨⡋⠃⢠⠁⣀⣴⣏⣁⠉⠉⠉⠀⡉⠉⠀⠤⠋
⠀⠃⠀⠀⠈⠀⢀⣀⣄⠤⠒⢈⡙⢢⣔⡛⢳⡈⢶⡍⠓⠽⠯⠚⢡⡶⢁⡞⢛⣢⡜⢋⡁⠒⠤⣀⣀⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣥⣼⡇⣠⣀⣀⣀⢸⣧⣬⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢿⢿⣿⣿⡿⡿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁⠉⠁⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠘⠠

⠀⢀⣤⠶⠖⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠲⣤⡀
⣰⠟⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠻⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣴⡋
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠈⠷⣄⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⣤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⢀⣠⣤⣤⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣗⣞⣦⡆⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠠⣅⢠⣔⣁⣠⣿⠀⠀⠀⠀⠈⠀⠐⠀⢀⡀⠀⠀⠛⣿⠋
⠀⠠⢤⣶⣿⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⠙⣿⡿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣲⣿⢿⡟⠋⠉⠀⠀⠐⠀⡀⠀⡌⢰⠋⠁⠀⠀⠀⣿
⠀⠀⠻⡟⢻⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⢱⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡧⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠆
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠁⣽⠁⠀⠀⠀⠀⠀⠀⣸⠳⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠹⢿⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⠗⠃⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠐⣾⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢴⡧⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⢻⡇⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿
⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢨⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠿
⠀⠀⢀⣽⣏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⢦⠿⣇⠀⠀⠀⠀⠀⠀⠘⠲⠀⠀⠀⠀⠀⠀⠀⠶⢾⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣦
⠀⠀⣌⢠⣿⢴⡇⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢠⣤⣿⢿⣄⣤⣷⠀⠀⠀⢀⡤⡄⠀⠀⠆⠀⠀⠀⠀⣀⣀⡼⣿⣿⡤⠀⠀⠀⠀⠀⢀⡴⢤⡀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠙⠋⠉⠛⠁⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁
⠀⡟⠉⠓
⠀⠙⠒⠃

⣷⠟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⠶⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⣀⡀
⠋⠀⠀⠀⠐⠂⠀⢠⠀⡀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠶⠁⠀⠀⠉⠙⠷⡀⠀⠀⠀⠀⠀⢻⠍⠉⠀⠘⠿⠿
⡄⣦⡄⠀⢤⢀⣀⠀⠀⢀⡾⢿⠆⠀⠀⠀⠀⠀⠀⠆⣧⠀⠀⠀⢦⡠⠰⠀⠀⠀⠀⠀⠀⠤
⠋⠁⠀⠀⠀⠈⠉⠀⠲⠸⢷⠄⠀⠀⠸⠂⢀⡚⠆⠀⣿⣷⣤⣀⠀⠀⠀⠀⢺⣦⡀⣤⣤⠀⢠⠄⠀⠀⠰
⠀⠠⠀⠀⠘⠀⡀⠀⠶⠆⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⡀⠀⠀⠃⠀⠀⠖⣸⣿⣦⠈⠈⠀⢀⠀⠺
⡃⠀⠀⠀⠀⣿⠟⠰⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠿⠶⠄⠐⠀⢀⠉⠁⠈⠃⠀⠀⠀⣤
⠇⠀⠰⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠓⠀⠀⠀⠀⠀⠒⠶⠀⠐⠀⠀⠘⢆⡠⠀⠰⢦⠀⠀⠉
⠷⠞⠋⠁⠁⠀⠀⠀⠀⠀⠒⠂⠀⢁⠀⠀⠀⠛⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⡀⠘⢠⣤⢀⠀⠘⠻
⣦⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢆⡐⠄⠀⠠⢆⡀⠀⠙⠇⠈⡈⠁⠀⠀⡀
⣿⣥⣤⣤⠀⡀⠀⠀⠀⢀⡀⠀⠠⠁⠀⠀⣤⡄⢠⠀⠀⠀⠙⠋⠀⠀⢠⣼⡇⠀⢀⣀⠀⠁⠠⠖
⣿⠿⣿⣋⡀⠀⠀⠉⠀⠰⠀⠇⡀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⠀⠀⢀⡀⠐⠋⠀⠀⢿⣶
⣿⡀⠈⠉⣁⠀⠀⠀⠀⠀⠀⠈⠛⠀⢈⣀⠀⠀⠀⠐⠀⠀⢈⡀⠈⠀⠀⠀⠀⠀⢳⣿⡇⠀⠂⠀⠀⠒
⡁⢀⡀⠈⢿⠀⣰⠀⠀⠀⠐⠀⠀⠀⠀⠘⠃⠀⢠⡀⠀⠀⠈⠁⠀⠀⠐⡷⠀⠀⠀⠈⠀⠈⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠂⠀⠈⠀⠐⠒⠒⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡤⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⢼⣰⠆⠀⠀⠀⠀⠀⠀⠰⣦⣀⠀⢙⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠁⢀⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠙⣿⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⣤⣷⡼⡀⢿⣿⣿⣿⣿⣿⣿⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠏⠀⠈⠛⠻⠟⠛⠛⠁⠀⣽⣿⣿⠃⠈⡛⠛⠻⠟⠓⠁⠂⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⣀⠔⣶⡗⠁⢸⣿⠿⣿⡧⠀⢻⣶⣄⡀⢀⣀⢔⡝⠂
⠀⢠⡖⠂⠒⢦⠀⠀⠀⠀⠘⣿⣷⡦⡘⠉⠀⠂⠀⠁⠀⠈⠈⠀⠀⠹⢀⣤⣤⣶⡏⠀⠀⠀⠀⣠⠖⠒⠒⢄
⠀⢸⣄⠀⢀⣾⠇⠀⠀⠀⠀⢿⡛⡇⢸⣳⠂⠂⢀⠀⠀⠀⠖⠀⠀⢲⡏⢸⣿⣿⠁⠀⠀⠀⠀⢿⣆⡀⢀⣼
⠀⣀⣽⠍⢽⣿⣄⠀⠀⠀⠀⢸⠃⢹⣾⣼⣤⣄⣬⣄⣤⣤⣀⣴⣤⣾⣷⡿⠉⡇⠀⠀⠀⠀⢀⣼⣿⠍⢽⣅⡀
⠘⠀⠙⠋⠉⠙⢃⣉⡆⠀⠀⢸⡆⠸⣿⡄⡏⢹⠉⡇⢹⠀⡇⢸⢹⣽⡯⠁⢀⡇⠀⠀⠀⣎⣉⠛⠉⠉⠋⠉⢸
⠸⣤⡈⠛⢟⠛⠛⠛⢷⣄⠀⠈⠳⣄⠹⣇⠀⠘⠢⠁⠛⠀⠃⠛⠈⠹⠃⣤⠎⠀⠀⢀⣼⠟⠛⠛⡻⠛⠉⣠⡜
⠀⠈⠉⠙⠛⠳⠾⣤⣌⠙⢷⣤⣀⠈⠳⡌⠀⢀⡀⠀⠀⠀⠀⣀⡀⢀⠞⠁⢀⣠⣶⠟⢁⣤⡼⠶⠚⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣭⡈⠓⠢⢌⡒⠴⠵⠀⠐⠒⠀⠁⠐⣉⠤⠚⠉⣨⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠓⠤⣀⡀⢀⡤⠔⠋⣁⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣦⣄⡉⠑⠶⢵⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣉⣤⣿⣿⠿⠶⣶⣤⣌⡑⠲⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣖⡪⠭⢒⣲⢽⠿⠛⠉⠀⠀⠀⠈⠙⠻⢿⢵⣒⠮⠭⣒⣦⣤⣀⣀
⢠⡶⠛⠛⠻⣁⣐⣒⠪⠈⠀⢀⡠⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢥⣀⠀⠈⠩⢒⣓⣀⡩⠛⠛⠳⣦
⢸⡇⢀⢀⣤⢉⠁⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⢉⢡⡄⢀⠀⡿
⠀⠈⠙⢯⡟⠐⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⢘⣿⠟⠉
⠀⠀⠀⠘⢿⣠⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣄⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠛⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⢸⠁⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⢀⠏⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣿
⢀⡇⠀⠀⠀⠀⠀⡼⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢹⡄⠀⠀⠀⠀⢸
⢸⠇⠀⠀⠀⠀⢸⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣷⠀⠀⠀⠀⠸
⡜⠀⠀⠀⠀⠀⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣀⣀⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠸⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⡟
⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠛⠿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠸⣇
⢹⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⢸⡆⢠⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⢰
⠀⣧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠈⢻⡳⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⢖⡿⠁
⠀⠀⠀⠹⡄⠈⢿⢻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⡞
⠀⠀⠀⠀⢹⠀⠘⡆⢻⣿⣿⠈⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⢱⡏⠀⡟
⠀⠀⠀⠀⣸⠀⠀⢹⠀⠙⠛⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠘⠛⠁⡞⠀⠀⣧
⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⠇⠀⠀⣼
⠀⠀⠀⠀⢹⡄⠀⠀⢧⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣄⣀⣤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠙⠦⣄⣸⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣤⡴⣶⢲⡞⠹⡟⠈⢻⠀⠈⣿⠀⠈⣿⠁⢻⠋⢷⠚⡶⢦⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⡏⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣇⣿⣸⣇⣠⣧⣠⣾⣤⣤⣿⣤⡤⣿⣀⣼⣄⣼⣀⣇⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣏⣿⣹⣇⣿⣨⣇⣸⣀⣯⢈⣇⢸⣀⣼⣀⣯⣨⣇⣿⣨⣏⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠈⠈⠉⠉⠉⠉⠉⠋⠉⠋⠉⠉⠉⠈⠉⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⣀⣠⠤⠴⠦⠤⢄⣀⣀⡠⠶⠛⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢠⣄⣀⡤⣧⢄⠀⢀⢨⠐⢒⠤⠄⠀⠀⠀⠀⠀⠤⢤⣶⣿⠒⢶⣖⣒⡀⠤⣤⣶⡶⢶⣤⣤⠤⠤⠤⠤
⠀⠀⠀⠀⠒⠀⠰⠦⣀⠒⠒⠒⠄⣙⠫⠞⣀⡄⡓⠟⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠾⣩⡿⢭⡛⠾⠿⣷⣞⣉⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠙⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠾⠿⠛⠛⠛⠉⠉

⠀⠀⠤⠠⠶⠦⣤⡤⣤⢤⣤⡴⠀⠀⢴⣤⡦⠴⣒⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⢠⣀⣀⣀⠀⣰⠶⣿⣿⣛⠻⠿⣿⣷⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⣉⡀⢶⣠⡾⠍⠐⣋⡕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠒⠦⠤⣖⡒⠒⠛⣉⣐⣛⣭⣭⣭⣽⣋⣑⣚⠻⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⢶⣤⣴⣶⣼⠿⠟⠋⠁

⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠤⡄⠐⢄⠐⠢⡀⣶⠒⠀⡐⠤⣲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⢀⣤⡄⣠⣆⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠆⠀⠘⣶⠓⠤⠤⠞⠄⢉⠀⡠⠂⠝⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⣶⣦⣤⣠⣾⣿⣴⢰⢿⡟⣼⣽⠿⠷⠶⠶⠤⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣍⣣⣍⣩⣿⠥⠗⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣄⣀⣀⠀⢀⣀⣀⣀⠀⣀⣠⣤⠤⣤⣤⣀
⠀⠀⠒⠛⠛⠋⠙⣯⣭⣽⣷⡶⡦⠀⠈⣉⢻⣿⣿⣯⡽⠟⠛⠛⠓⠀⠀⠀⣠⣴⠿⠻⡿⠾⣿⣿⣷⢨⣿⣧⣵⡿⢭⣔⠛⢉⣉⣶⣿⣷⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣍⣛⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⢿⣟⣸⠏⠰⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣤⣀⣄⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⡤⢤⣄
⠀⠠⠴⠶⢾⣯⣝⣉⠉⠶⣶⣿⣯⡙⢿⣷⠀⢈⣭⠿⠟⠛⠛⠒⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⣹⡏⣡⢽⣯⠀⢠⠞⣶⡆⠀⡠⡄⠀⠛
⠀⠀⠀⠀⠀⠈⠙⠻⢯⣛⠿⣿⢿⣷⣼⣿⠆⣁⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠷⢏⣁⣀⠻⠾⠟⠁⠀⠉⠁

⠀⠀⢹⣿⠟⠀⠀⠀⢾⣿⣟⠀⠀⠀⠀⠀⠀⠺⠿⠟⠀⠀⠀⣴⣄⠀⠀⠀⠈⠉⠀⠀⠀⢾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠠⣿⠿⠃⠀⠠⣾⣿⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣶⣤⣴⡄⠀⠀⠀⠈⠛⠁⠀⠀⢠⣶⣿⠆⠀⠀⠀⠀⢀⡀⠀⠀⠉⠁⠀⢶⣿
⡄⠀⠀⢠⣿⣧⣄⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⣿⣧⣀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⠀⠀⢠⣤⠀⠀⠉⢿⣧⠀⠀⠀⢠⣿⣿⣤⣀⠀⠀⠀⠀⠹
⣿⣦⠀⠈⠉⠉⠛⠻⣿⣿⠇⠀⢀⣿⣧⠀⠀⠈⠉⠙⠻⢷⣶⣶⠀⠀⠀⠀⠀⠀⢰⣷⣶⡾⠿⠿⠿⠇⠀⠀⠈⣿⣷⡄⠀⠀⠉⠉⠙⠻⣿⣿⠇
⠋⠁⠀⢀⣤⡀⠀⠀⠈⠉⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⣿⣷⡄⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⢀⣀⠀⠀⠀⠈⠋
⣤⣤⣶⡿⢿⡧⠀⠀⣸⣿⣦⣤⣀⣀⣤⡀⠀⢰⣶⣿⠆⠀⠀⠀⠀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⣠⣤⣄⠀⠀⠀⣾⣿⣧⣄⡀⠀⠀⠀⠀⢀
⠿⠉⠀⠀⠀⠀⠀⡀⠘⠋⠉⠙⠛⢿⣿⠁⠀⠀⢹⣿⠀⠀⠀⣴⣾⣟⠀⠀⢰⣶⣿⠆⠀⠀⢸⣿⠁⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠉⠛⢿⣿⡷
⠀⣠⣤⡀⠀⢴⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠙⠋⠀⠀⠀⠸⣿⡀⠀⣴⣿⣇⠀⠀⠀⢸⣿⠀⠀⠀⢠⣦⣤⡀⠀⠈⠋⠀⢰⣾⣦
⢀⣿⡿⠟⠀⠀⠈⢿⣧⡀⠀⠀⣴⣿⣧⣀⠀⠀⠙⠟⠛⠀⠀⠀⢀⣠⣿⣧⠀⠀⣿⣧⡀⠉⠙⠋⠀⠀⠠⣾⣿⡦⠀⠀⢸⣿⠋⠀⠀⢀⣀⣴⡿⠛⠛
⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⠉⠙⠻⣷⣶⣦⠀⠀⢾⣷⣾⠟⠋⠉⠋⠀⠘⠻⠛⠁⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠐⢿⣿⡏⠀⠀⣠
⠇⠀⠀⠀⢾⣷⣦⠀⠈⠁⠀⢀⣠⣤⠀⠀⠘⠟⠁⠀⠀⠈⠛⠁⠀⠀⠀⢀⣿⣷⣄⣀⠀⠀⠀⠘⠿⢿⣧⣄⠀⠀⠀⠺⢿⡿⠀⠀⠀⠀⠉⣀⡀⠀⠙
⣀⠀⠀⠀⣾⡟⠁⠀⠀⢀⠀⠙⢿⣯⠀⠀⠀⢀⣤⣀⣀⣀⣠⣶⡆⠀⠀⠈⠛⠉⠛⠻⢿⣿⡇⠀⠀⠀⠙⢿⣷⡶⠀⠀⠀⠀⢀⣤⡀⠀⢰⣿⣷⣤⣄
⣿⠃⢀⣴⣿⡁⠀⠀⢿⣿⠇⠀⠈⢿⣇⡀⠀⠈⣿⡿⠛⠛⠛⠻⠇⠀⢠⣶⣶⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢀⣠⣾⣿⡿⠀⠀⠁⠀⠉⠛
⠁⠀⠈⠛⠿⠃⠀⠀⢸⣿⠀⠀⠀⢾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡀⠀⠀⠀⣶⣦⣤⣤⣤⣾⣷⠀⠀⠸⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀
⣤⣀⠀⣀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⢸⣿⣶⠀⠀⠀⢹⣷⣤⠀⠀⠛⠋⠉⠉⠉⠙⠋⠀⠀⠀⠙⠉⠀⠀⠀⣠⣶⡄⠀⠀⣰⣿
⠙⠻⣿⣿⠃⠀⠀⠀⠘⠋⠋⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⣼⡟⠁⠀⠀⠀⠘⠟⠋⠀⠀⠀⢀⣀⣀⠀⠀⣶⣶⣤⣀⣀⣠⣤⠀⠀⠛⠻⣷⣄⠀⠈⠉
⠀⠀⠈⠁⠀⢠⣶⣤⣀⣀⣀⣤⡄⠀⢿⣿⡏⠀⠀⠀⢀⣴⣿⡁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠛⠋⠉⠛⠛⢿⡿⠀⠀⠀⠀⠈⢻⣿⡷
⢠⣦⣄⠀⠀⠘⠿⠋⠛⠛⠻⢿⠇⠀⠀⠉⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⠿⠿⢿⣶⣶⣶⡆⠀⠠⣿⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠈⠋
⣸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⣤⣭⣄⠀⠀⢸⣿⣿⠇⠀⠀⠰⣿⣿⣷⣦⣤⣤⣄
⡿⠁⠀⢠⣶⣿⠆⠀⢠⣤⣄⣠⣤⣴⣿⡆⠀⢸⣿⠀⠀⣾⣿⣶⣤⣤⣴⣶⠀⠀⠀⣀⠀⠀⠉⠁⠁⠀⢠⣾⡇⠀⠀⣤⡄⠀⠀⠀⠈⠉⠻⣿⠏⠀⣤
⠇⠀⠀⠀⠈⣿⣆⠀⠘⢿⠟⠋⠉⠉⠛⠃⠀⣸⣿⣆⠀⠉⠉⠈⠉⠉⠻⠟⠀⠀⣼⣿⣧⣀⠀⠀⠀⠰⣿⣿⠀⠀⢰⣿⣿⣶⣦⣤⣴⡄⠀⠀⠀⠀⠛
⣤⣤⡀⠀⠀⢘⣿⣦⡀⠀⠀⣀⡀⠀⠀⠀⠀⠙⠛⠋⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠈⠁⠙⠻⢿⣾⡷⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠙⠿⠃⠀⣤⣴⡄
⢻⣿⠁⠀⠀⠘⠛⠋⠀⠀⠀⣿⣿⠗⠀⠀⠀⢀⣀⣼⣿⡆⠈⠙⢿⣆⠀⠀⣴⣷⣄⡀⠀⠀⠈⠛⠁⢠⣶⣤⣤⣤⣠⣶⡆⠀⠀⢀⣀⡀⠀⠙⣿⡇
⢸⣿⠀⠀⠀⣠⣄⡀⠀⠀⢰⣿⠃⠀⠰⣿⣿⠿⠛⠉⠙⠁⠀⠀⠘⣿⣦⡀⠛⠛⠛⠿⢷⣾⡷⠀⠀⠘⠿⠋⠉⠙⠛⠿⠇⠀⠀⢻⣿⠟⠀⠀⢹⣷⡀
⣾⣿⡷⠀⠀⢹⣿⠋⠀⣶⣿⣇⠀⠀⠀⠙⠋⠀⠀⠀⢀⣴⣶⠀⠀⠿⠛⠃⠀⣀⣀⠀⠀⠛⠁⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢾⡿⠿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⢠⣴⣶⡄⠀⠘⠛⢿⣦⡀⠀⠀⠀⠀⣻⣿⠗⠀⢠⣶⣤⣶⠿⠿⠿⠃⢀⣠⣤⡀⠀⣴⣿⣧⠀⢀⣄⡀
⣿⡀⠀⠀⣾⣿⡧⠀⠀⠀⠀⣺⣿⣦⠀⠈⠹⣿⡄⠀⠀⠀⠀⠹⣿⣶⡄⠀⢀⣿⠇⠀⠀⠈⠿⠏⠀⢀⣀⠀⠀⠘⢿⣿⡀⠀⠈⠉⠁⠀⢹⣿⠟⠀⢀
⠛⢿⣦⣀⡀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⢻⣷⣀⠀⠀⠀⠀⠛⠉⠀⢰⣾⣿⡄⠀⠀⠀⠀⢀⣠⣾⣿⡧⠀⠀⠀⢹⣷⣀⠀⠀⠀⠀⣾⡏⠀⠀⠈