Donuts Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⢚⡏⠉⢉⣉⠉⢉⡍⠉⠛⠲⠦⣄⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠒⠂⣀⣠⣤⠤⠤⣤⡀⠀⠀⠀⠀⠒⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡉⠀⠐⠃⠀⡴⠛⣉⡤⠴⠶⠶⣶⠏⠘⠂⠀⢠⠄⠀⣀⣰⣧
⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⣰⠃⠐⠃⠤⠀⠀⠀⠙⠻⠷⠶⠖⠚⠉⠁⢠⠀⠀⠀⠀⠀⡞⠉⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⢶⠀⠀⠀⠀⠤⠄⠀⠀⠀⢀⣠⣄⣀⣀⡼⡃⠀⠀⢸⡇⠀⠀⠀⠑⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠖⠒⣦⠀⢀⡀⠀⢀⣠⡤⣄⡀⠀⠀⣰⠋⠐⠁⠒⠂⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠳⣬⣠⣴⠋⠀⠀⠒⠭⠿⠯⠕⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡿⣠⡶⠛⣦⢰⡾⠛⢷⡰⡇⠀⢸⡆⢺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠶⠛⠁⢿⣄⣀⡼⠻⡇⠀⢸⡇⢿⣀⣼⣇⠘⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣶⠶⠚⠋⠉⠉⠛⠲⢶⣤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⡁⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⡈⠙⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠋⠉⠉⠉⠁⠀⣀⣠⣤⠴⠖⠒⢦⠀⠀⠀⠀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⣀⣀⡤⠴⠋⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢳⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⣠⠞⠋⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢿⢷⡀
⠀⠀⠀⠀⡴⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠸⣇⣠⡴⠋⠁⠀⠀⠀⣰⠞⢲⡄⠀⠀⢸⡄⠹⡄
⠀⠀⠀⡼⠁⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⡄⠀⠸⡇⠀⠹⡆
⠀⠀⣼⠁⠀⣸⠁⠀⠀⠀⠀⢸⡋⠀⠀⢀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢹⡄⠀⢻⡄⠀⢹⡄
⠀⢰⠇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣴⡿⠿⠛⠓⠦⠤⠴⠚⠛⠯⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡿⠀⠀⠙⠲⣄⢷
⠀⡟⢀⡞⠁⢀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢻⡆
⢸⣷⠋⠀⠀⠘⢇⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻
⣼⠁⠀⠀⠀⠀⠘⢧⠀⠘⣆⠀⠀⠀⠀⠀⢰⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⠀⠀⠀⢀⡴⠚⠁⢨⡇⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀⢘⡇⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⠖⠋⠀⣠⠞⠉⠀⠀⠀⠀⢰
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠻⣄⡴⠋⠁⠀⠀⠀⠀⠀⣰⢿
⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢸
⢸⡇⢳⡀⠀⠀⠀⠀⠀⢀⡞⠉⢹⠄⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠇⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣼⠁⠀⣿
⠀⡇⠀⠹⡄⠀⠀⠀⢠⠟⠀⣰⠏⠀⠀⠀⠀⣏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠂⣿⠀⢀⡇
⠀⢻⠀⠀⢻⠀⠀⣠⠏⠀⣰⠃⠀⠀⠀⠀⠀⠉⠳⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⠏⠀⢹⡀⢸⠃
⠀⠸⡇⠀⢸⠀⠀⠘⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⣴⠖⢦⡀⠀⠀⠀⠀⣼⠁⢠⡟⠀⠀⠈⣧⡟
⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣓⢶⣤⡴⠖⠓⠶⢤⣶⠚⢉⡼⠁⠀⠀⠻⢄⠀⠉⠢⣄⠀⠀⠙⠶⠛⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⢻⡀⠀⢀⡤⠤⠶⠶⠶⠶⠶⣤⠀⠀⠀⠀⠀⢀⣤⠞⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣷⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⢀⣠⠴⣾⠋
⠀⠀⠀⠀⠀⢧⠀⠸⢄⣤⣤⣤⣤⡤⠤⠞⠀⠀⠀⢀⡴⠋⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⣠⠶⢦⣄⡀⠀⠀⠀⠀⠸⣇⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣉⠉⠉⠛⠲⠦⣄⠀⠀⠀⠀⠀⠹⢤⣀⠈⠙⠓⠦⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠈⠙⠲⣤⣀⣸⠇⠀⢀⡴⠖⠒⠒⠶⢤⣤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣌⣙⣦⣄⡀⠀⠀⠀⠀⠉⠁⣠⠞⠉⣀⣀⣤⠴⠞⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣓⣶⣶⣶⣶⣞⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠒⠒⠒⠒⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⣀⠤⠄⠒⠒⠂⠤⢀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠉⠀⠀⡠⠤⢀⡀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡔⢁⡠⢤⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠤⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡜⠀⠃⠒⠁⠀⠀⠀⠀⠀⡠⢲⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠙⠄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠓⠁⠀⠀⠀⠸⡸⠀⠀⠀⣖⠈⠕⠀⠸⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠜⢀⡀⠀⠀⠀⢎⠕⠃⢀⠤⠐⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢱
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠃⠀⡄⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠉⠁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡰⡩⠃⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⣔⣂⠔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠁⠀⠀⢀⡀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢰⡫⠊⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⡔⢄⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢡⠀⠈⠪⠂⠀⠀⠀⠎⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣘⠀⠀⢀⠔⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠑⢄⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⣒⣒⡆⠀⠀⠀⢀⠔⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠉⠒⠤⣀⠀⠀⠀⠀⢔⡩⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⣀⠤⢤⠀⠀⢀⡠⠊⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠈⠢⢄⣀⠀⠀⣑⣈⠡⠔⠂⠁⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠤⠤⠤⠤⠤⠤⠀⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠛⠉⠉⠉⠉⠙⠛⠒⠲⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⢀⡤⠖⠛⠛⠒⠦⣄⣀⣀⣤⡤⠤⠤⢤⣌⡙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⣀⣀⣠⠴⠋⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠙⢦⡀⠙⠲⣄
⠀⠀⠀⠀⠀⡴⠋⢠⠞⠉⠉⠀⠀⠀⠐⠛⠛⠉⠀⠸⠀⠀⡆⠀⠈⠉⠉⠁⡤⠀⠀⠀⢧⠀⠀⠈⠳⡄
⠀⠀⠀⢠⠞⠀⢀⡏⠀⠀⠀⡴⠃⠀⠀⢀⡤⠖⢀⠀⠀⠐⠇⠀⠰⣄⠀⠘⠁⠀⠀⠀⠈⠳⣄⡀⠀⠙⢦
⠀⠀⣰⠋⠀⠀⢸⠀⠀⠀⠈⠁⠰⡄⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠈⠃⠀⠀⠐⠋⠁⢀⠀⠀⠉⠳⣄⠈⢧
⠀⢰⠃⠀⠀⢀⡏⠀⠀⠦⣀⠀⠀⠹⠀⠀⢸⠀⠀⠐⠶⠶⠆⠀⠈⢳⡀⠀⠀⡄⠀⠀⠈⠙⠓⠀⠀⢸⡇⠈⢧
⢀⡏⠀⠀⣠⠏⠀⠀⢀⠀⠈⢀⠀⠀⠀⠀⠘⢀⣀⣤⠤⢤⣄⡀⠀⠀⠀⠀⠀⡇⠀⠙⢆⠀⠀⠀⠀⢸⠃⠀⠸
⣸⠀⢀⡞⠁⠀⠀⠀⣼⠀⠀⠈⠉⠉⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⠀⠀⠀⠈⠀⢀⡞⠀⢸
⡟⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠉⠓⠀⢰⠀⠈⠀⠀⠘⣆
⡇⠀⠀⡷⠀⠀⢠⣀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⡆
⣇⠀⢠⠇⠀⠀⠀⠈⠁⠀⠀⢠⣄⣀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⠁⠈⠳⡄⠀⠀⣠⠖⠀⠀⠀⡇
⢻⠀⢸⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡈⠀⠈⠳⣄⡀⠀⠀⠀⢀⣠⠔⠁⠀⠀⢠⠄⠀⠀⢤⣄⣁⠀⠀⠀⣰⠃⢀
⠘⣇⠈⢧⠀⠀⠀⠀⠉⠃⠀⠀⠀⣇⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⣀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠉⠀⣠⠞⠁⠀⡼
⠀⠹⡄⠈⠓⢤⡀⠀⠀⠀⢠⠆⠀⠀⠀⠐⠒⠲⠦⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠏⠀⠀⠀⣰⠃
⠀⠀⠹⡄⠀⠀⠈⢣⡀⠐⠋⠀⠀⠰⣄⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⠀⠀⠈⠁⠀⠀⡏⠀⠀⠀⡴⠃
⠀⠀⠀⠙⢦⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⣤⠀⠀⠈⠉⠀⠀⠸⠀⠀⠀⠀⠀⣸⠃⠀⢀⠞⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠉⠓⠒⠲⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠁⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠈⠙⠲⠶⠶⠒⠋⠁⠀⠀⢀⣠⡤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠻⠆⠀⠀⣀⡀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣠⡴⠞⠛⠛⠙⠛⠛⠲⢦⣄⠀⠀⠀⢤⠶⠂⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⢧⣴⠞⠋⠉⠙⠛⢶⣄⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠘⣧
⠀⠀⠀⠀⣸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⠳⠶⢤⣤⣤⣤⠿⠶⠋⠁⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⣿⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣿⠀⠹⣆⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠚⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢿⠀⠀⠈⠳⠶⠛⠉⠀⢹⠀⠀⠀⣀⡀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡾⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣽⠁
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠸⣦⡼⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠹⡆⠀⠀⢀⣴⠞⠛⠛⠛⠛⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣧⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠞⠋⠁

⠀⠰⠀⠀⠀⡀⠀⢀⠂⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⡠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡲⠤⡄⣀⣤⠤⠶⠖⠚⢁⡤⠖⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉
⠀⠀⠀⡠⠂⠀⣠⠎⠀⠀⠀⠀⢸⠇⠘⠁⠀⠐⠀⠀⢄⠀⠐⠂⢤⡀⠈⠀⠂⠀⠄⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢈
⢀⠤⠚⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⡆⠆⠀⠀⢀⡀⠰⠀⠀⠐⠒⠊⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈
⣡⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠢⠄⠀⠀⠀⠈⠂⠀⠈⢁⠰⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠔⢈⡠⠖⠊⠉⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠑⠲⢶⣖
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠐⠠⠄⢀⠀⠀⠀⠀⠁⢀⣠⡔⠀⠀⠀⠀⠀⠀⠀⢁⠔⢁⡤⠤⠒⠊⢉⡠⠔⠒⠉⠁⣀⡀
⣠⠔⣊⠅⠀⣰⠖⠊⢿⡶⣦⡀⠀⠀⠀⠀⠀⠑⠢⠤⣀⣀⠉⠀⠁⣀⣤⠝⠋⠀⠀⠀⠀⠀⠀⢰⣶⠕⠋⢀⣤⣤⣤⠶⠭⣤⠴⠚⢀⣩⠭⠽⠆
⢠⠊⣀⠤⠊⢁⣠⠔⢋⡴⠋⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡤⠊⠁⣀⣀⠀⠤⠲⢯⡶⠊⠀⢀⣀⣀⣁⠀⠀⠀⠀⠀⣠
⡶⠋⣁⠤⠖⠉⣀⠔⠋⠀⣠⠞⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣪⠔⠊⠁⣀⠬⠇⠀⠤⡜⠤⠒⢉⣉⠥⠴⡟⠀⠀⠀⠀⣰⠃
⠈⠉⠀⡀⢔⠮⣤⣤⠔⠊⢁⠔⠁⢀⡀⠀⠀⠀⠀⢀⡄⠺⠋⠁⠠⠀⠀⠂⠑⠀⡀⠀⠀⠀⠀⢹⡑⢤⣠⠎⠀⠀⡠⠂⠁⣀⠴⠚⠉⣀⣠⡾⠅⠀⠀⠀⢠⠃⢀
⠐⠂⠁⢀⠂⠀⣰⠗⣳⠚⠁⣠⠔⣹⠃⠀⠀⠀⣠⠋⡔⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠂⠀⠀⠀⠀⠱⣄⠻⣤⡖⣁⠀⣰⢊⣡⠔⠊⢉⠁⢀⠎⠀⠀⠀⠀⣼⠀⣮
⣀⠤⠔⠋⡧⠉⢁⣴⠷⠒⠉⣡⠞⠁⠀⠀⠀⢠⠃⠸⠀⠀⠀⠘⠀⢠⣄⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠈⠑⠦⣄⣀⡈⠉⠉⠑⣒⣈⠥⠚⠁⠀⠀⠀⠀⠀⢻⠸⣇
⠀⢀⠠⠊⠀⣠⠟⠁⢀⡠⠊⠁⣠⡞⠁⠀⠀⢸⠀⠀⠀⠀⠀⣀⠀⠆⠀⢱⠀⠚⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘
⣏⣁⠤⠔⠊⠁⣀⠔⠉⢀⡠⠚⠁⠀⠀⠀⠀⢸⠀⢸⠀⠀⠲⠉⠀⢀⠃⠀⡇⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⢴⣶⡚⠭⠔⠒⠉⡀⠄⠀⠀⠀⠀⠀⠀⠀⢇⠈⣇⠀⠀⠀⢠⡀⠑⠞⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⡠⠐⠒⠈⡉⠁
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢢⡈⠀⠀⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠠⠞⠀⠀⠀⠀⠡⠄⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠞⠀⠠⠀⠀⠀⠃⡀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣭⣒⢦⣄⣨⠄⠀⠀⠀⠀⠀⡞⠀⡠⠀⠀⢀⠀⠈⠡⠄⢤⠀⠀⠤⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠃⠰⠀⠀⡀⠈⠀⡌⠀⡀⠀⠁⠔⠀⠀⠀⠀⡠⠊⠀⠐⠀⠋
⠒⠒⢠⡀⢀⡄⠀⢠⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⡠⠀⠖⠀⢧⠄⠀⣀⠀⠈⠀⠀⠀⢠⠀⠃⠐⠀⠀⡄⡤
⠀⠁⠜⢁⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⢀⠤⠊⠉⢀⣀⠠⠤⢒⣲⣦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡇⠀⠀⠒⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⣠⠀⠂⠀⠀⠀⠘⠢
⠆⠀⠀⠈⠀⠀⠀⢀⠞⣴⠁⠀⠀⠀⣠⢐⡡⠔⠒⠉⠁⢀⡴⠚⠉⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠂⠁
⠉⠀⠀⠀⣀⡤⠖⢋⡜⠁⠀⠀⠀⣿⠗⠁⡠⠴⠶⠶⠞⠃⢲⡖⠉⡀⠤⠶⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⢄
⠶⠤⠒⠊⢁⣠⠔⠉⠀⠀⠀⠀⠀⠀⠔⠉⢀⠠⠤⢄⠒⠉⠙⡾⠋⢀⣀⡤⠤⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠉⠀⠒
⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠖⠉⠀⡠⠔⠋⠀⢀⠌⠒⠉⣀⡤⠖⠚⣻⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⢤⡎⠀⢀⠀⠈⢀⣠⠖⠋⣁⡠⠴⠞⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠁⠀⠐⢦
⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠓⠿⠡⣀⣀⣯⣤⣒⣉⡀⠔⣠⠎⠀⠀⠀⠀⠠⠀⠴⠀⠠⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠈⣧
⢤⠀⠀⠀⢀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⣀⣀⣀⣡⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡤⠒⠉⢐⠇⠀⠄⠀⠀⢰⠈⡄
⠀⠀⠀⠀⠀⠈⠁⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣬⣀⡀⠁⠈⡀⠀⠀⠀⠀⡈⢀⠇⠀⠀⠀⠀⠀⠀⠄⠐
⠈⡁⠀⠈⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⣀⡀⠀⠈⠥⠀⠀⢀⠜⠀⡜⠀⠀⠀⠀⠀⠀⢦
⡀⠀⠸⠀⠐⠂⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠦⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠔⠁⢠⠞⠀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣲⠶⠟⢲⡶⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⡡⠏⠘⣻⣷⠄⢀⡘⣁⠴⠏⣟⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣉⠏⠉⠁⢴⠂⢰⣾⣶⢫⢾⡭⠁⠳⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢀⡴⣚⡗⣾⠃⠀⠀⢀⠤⠒⠒⣦⣝⣉⠷⠤⠿⡅⠀⠀⠀⢸⣇⣀⣀⡤⣤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣠⠞⠟⣀⣽⠂⠀⠀⡠⠚⠁⠀⠀⣠⡟⡚⣽⠀⠀⠈⠁⠀⠀⠀⢨⠩⠬⠛⠛⠓⠛⠁⢾⣷⠛⠹⠛⣦⡀
⠀⠀⠀⣰⠃⠙⢺⡤⠄⠠⠤⢎⣀⣀⣀⠴⢯⡬⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⡐⠋⢀⣭⣟⣁⣄⠴⠋⢙⣦⡀
⠀⠀⢠⠃⣀⣰⣿⢋⣀⣠⠀⠈⣩⠄⠀⠴⠆⠀⠀⠀⠀⠀⢀⠔⠂⢲⠀⠀⢸⠋⠉⠁⠀⠀⢱⣌⠿⢟⠹⢾⡝⠏⣏⣵⡛⡄
⠀⠀⢸⠛⠛⢋⡀⠼⣁⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠊⠁⠀⠀⢸⠀⡴⠯⠀⢤⡴⠴⡶⣛⢞⡶⠘⠶⣼⠒⠀⠁⠀⠀⡇
⠀⠀⠈⣆⡀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⡠⠚⠚⠋⠀⠤⠤⠙⠃⠘⠋⠉⠁⠀⠀⠚⠁⠀⠀⠀⣸⠃
⠀⠀⠀⠱⡌⠑⠢⠤⠤⠐⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡝
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠈⠉⠉⠑⠒⠀⠠⠒⠒⠒⠠⠤⠀⠀⠀⠒⠒⢢⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠄⠒⠂⠉⠁⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠔⠚⠔⠊⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠀⠀⠈⠀⠖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣝⡪⡁⠀⠀⠀⠀⠀⠀⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⠭⢥⡶⡰⣡⡾⠃⠀⠀⠀⠀⠉⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠘⢯⣅⣲⡄⠀⠀⠉⡖⢦
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡶⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢳⡿⠈⠢⡀
⠀⠀⠀⠀⠀⢠⠊⠀⠀⡀⢔⣶⠀⠀⠀⠀⠀⠀⠀⠳⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡘⠄
⠀⠀⠀⠀⡰⠁⡜⠀⣮⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣵⣾⠂⠀⠀⠀⢠⣹⡇⠈⢆
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠃⠀⠀⠀⠀⠙⠛⠀⠀⠈⡄
⠀⠀⢠⠄⣒⡆⠀⠀⠀⢀⣣⡟⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⣴⣤⣀⣠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⡀⠀⢱
⠀⠀⡧⠚⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⠇⠀⡁
⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠛⢯⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠀⠀⠀⠀⠀⠀⢀⠀⠃
⠀⢰⢁⠀⡀⠀⠀⢠⣷⠿⣶⣬⡿⠷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⢤⣤⣀⣀⡀⠀⠀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣶⣺⡇⠀⠀⠀⠀⢀⣴⡏⢀⠆
⠀⠀⢠⠀⣤⣦⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠀⣠⣬⣯⢥⡎
⠀⠸⡜⢇⠀⠺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⢀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣫⠞⣡⣾⡇
⠀⠀⠈⣾⣶⣦⡈⢿⣿⣷⣤⡀⠯⣅⣚⡆⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⢿⠶⠶⠶⠀⠀⠀⠀⠀⠸⠾⠁⠀⠀⠀⠀⠀⠀⣤⣄⡴⣾⡿⠋⠀⣴⣿⣿⣿
⠀⠀⠀⢃⠈⢻⣿⣆⠪⠿⡍⠉⠳⢶⠁⠀⠀⠀⠀⠧⠏⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⡿⢷⡾⠿⠁⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠘⣄⠀⠀⠸⢷⣶⣦⡀⠀⠐⠾⣷⣎⡈⠖⣴⣿⣿⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢤⣶⣶⣶⣿⣿⣾⡶⠎⠽⠏⠁⣀⣀⣠⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠈⢢⡀⠀⠀⠙⠿⣿⣦⣀⣀⣈⣀⣀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣶⣿⠿⠛⠿⠿⠟⠛⢋⣪⣥⣄⠁⠐⠈⠁⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠈⠛⠛⠿⠿⢿⣿⣿⣷⣄⡀⠈⠁⠙⠉⠉⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣆⡀⣀⣠⣾⢿⡿⣿⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⡀⠀⠀⠀⠘⠋⠞⠉⢉⣀⣤⣤⢦⣶⣦⣶⣿⣾⣷⣶⣿⣿⣻⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⠤⠤⠠⠶⠤⠾⠿⠶⠿⠿⠿⠦⠝⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠚⠛⠋⠉⠉⠉⠉⠙⠛⠓⠒⠒⠶⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢠⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢎⠓⢤⡀⠀⠀⠈⠉⠓⠒⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⢀⡴⢋⡟⠀⠀⠀⠀⠀⠀⠙⠲⢃⡤⠖⠛⠒⠦⣄⣀⣀⡤⠊⠉⠛⠛⠋⠉⠙⢷⠀⠀⡖⠦⣄⠀⠀⠀⠈⠳⣄
⠀⢠⡟⠀⡏⠀⢀⠴⢛⠆⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠘⣇⠀⠈⠢⣈⢳⠀⠀⠀⠀⠈⣧
⢠⡟⠀⠀⣹⠰⣡⢖⡏⠀⠀⠀⠀⡏⠀⠀⣀⣠⠴⠶⠚⠛⠛⠛⠓⠶⢦⣄⡀⠬⡑⢦⠘⠦⣀⠀⠈⠉⠀⠀⠀⠀⠀⢹⡄
⣾⠁⠀⢰⠃⠀⠀⠉⠀⠀⠀⠀⠀⡇⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⢦⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿
⣿⠀⠀⠘⢄⣀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⣠⠆⠀⠀⠀⠀⠀⣰⠒⡄⡼⠁⢸
⢿⡀⣧⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠚⠁⡴⢚⠂⠀⠀⢰⣃⠞⠈⣇⡠⢸
⠘⣧⠸⡆⠀⣠⠎⠀⢀⣀⠴⠂⠐⡄⠀⠀⠉⠛⠒⠦⠤⠤⠤⠤⠤⠶⠒⠋⠉⠀⠀⠀⣾⣡⠂⠀⠀⠀⠀⢀⡤⠖⢱⠃⣾
⠀⠹⣆⠹⣄⡇⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠋⠀⣰⠃⣼⠃
⠀⠀⠘⢧⡘⢮⡲⠞⠁⠀⠀⠀⠀⠳⢄⡀⠀⣴⣫⠴⠊⠀⠀⠀⠀⢖⣊⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣴⢃⡼⠃
⠀⠀⠀⠀⠙⠦⣍⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⠴⠚⠉⠙⠒⠤⠤⠞⣡⢞⡡⠛
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠲⠤⠴⠊⠙⣆⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢒⣫⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠋⠀⠀⠀⣀⣠⡤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣿⡇⠀⠀⠀⠒⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢹⠁⠀⠀⠠⠀⠀⠀⠀⠄⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⣀⠴⠒⢠⡀⣤⡄⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⣠⢾⣴⣤⣤⡝⣡⣿⡇⠀⢠⣷⠀⠀⠀⠀⠀⣀⠈⣷⡄⠀⠒
⠀⠀⠀⣴⢧⡞⠀⡀⠀⠀⠀⢴⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣴⠁⠀⠀⠀⠀⠀⠀⠈⠢⡘⢿⣶⣶⣄⠀⢀
⠀⠀⢸⣟⠛⠀⠰⡀⠀⠀⢀⠄⠉⠛⠛⠟⠻⠛⠛⣫⡿⠛⠛⢻⣿⣶⣀⢀⡀⠀⢠⡉⣼⠀⠙⠿⠟
⠀⠀⠸⣿⣷⣶⠀⠁⠉⠉⠀⠀⠀⢠⠄⠀⠀⠀⠊⠀⠀⠀⠐⠁⠁⢹⣿⣧⡈⠂⡀⢻⣿⡇⠀⠀⠁
⠀⠀⢀⢉⡻⣿⣷⣄⣀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⢤⣭⣾⡏⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢦⡈⠛⠹⡿⢿⣿⣶⣶⣦⣠⣄⣀⡠⠴⠴⠦⠶⠖⠒⠛⠉⠉⢐⣿⢻⣦⣿⡇⠙⣆
⠀⠀⠀⠀⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⢿⠿⠛⠀⠀⠈⠦⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠦⠤⠤⠤⢤⣤⣤⠤⠤⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠒⠀⠤⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠈⠈⠁⠀⠀⡀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⡄⠀⠈⠁⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠒⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢆⠀⡀⠀⠀⢠⠀⠀⠀⢀⠠⠄⠒⠂⠈⠉⠁⠐⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠠⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠙⠒⠤⠤⢄⣀⣀⣤⡀⠀⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⢢⣴⣷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢸
⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⢣⠁⢡⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⢁⣀⣀⣠⠞
⠀⠀⠀⠀⠈⡎⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠐⢽⣿
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠀⠀⠐⠁⠀⠀⠀⢵⡇
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠢⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠔⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀
⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⣀⠀⠀⠀⠀⠀⢀⣁⠄⠀⠀⠀⠚⢃⠀⠀⠀⠀⠀⠈⣧
⠀⢸⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⢸⡄
⠀⠘⢧⠴⠋⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠸⡇⢀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⠀⠀⢀⡾
⠀⠀⠀⢻⡄⠠⠀⠈⠣⣄⡠⠴⠚⠉⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⢀⠞⠱⣄⠀⠀⢀⡴⠃⠀⠀⠈⠙⢻⡏
⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⣠⠎⠀⠀⠈⠓⠒⠉⠀⠒⠀⢀⠀⢠⡟
⠀⠀⠀⠀⠀⠈⠙⢶⣄⡈⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢈⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠦⠤⣤⣬⣤⣤⡤⠴⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⠴⠶⠦⠤⠤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⡠⢄⠀⠀⠀⠀⠘⠧⢭⣉⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⠀⠀⠀⠀⠀⠑⢦⣙⡆⠀⣀⣤⣀⡀⠀⠀⠀⠀⢀⠤⣤⣀⣤⠴⠶⢤⡀⠀⠀⣀⡀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⡼⠁⠀⢀⣀⠀⠀⠀⠀⠈⡰⠚⠁⠀⠀⠉⠓⠶⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢣⡙⠳⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢀⡾⠁⠘⡇⢀⠔⢋⡴⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠒⠤⣀⠈⢧⠀⠀⠙⠢⠼⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠃⠀⢀⠟⠘⠚⠽⠂⠀⠀⠀⠀⡇⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠶⣌⡑⢌⠳⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⢠⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠃⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡞⢸⡇
⠀⠀⠀⢸⡇⢀⡀⠈⠂⠤⣀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠔⠁⣀⠀⠀⠀⠀⡜⢁⠇⡞⠀⠀⣷
⠀⠀⠀⠀⣷⠀⣇⠀⠀⠀⣸⠃⠀⠀⠀⢀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠁⣠⠎⠉⠀⠀⠀⠸⠱⠋⠀⡵⡐⢠⡇
⠀⠀⠀⠀⠸⣇⠸⡄⠀⡔⠁⠀⡠⠀⠊⠁⠀⡀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠧⠔⠀⠀⠀⠀⠀⣠⠖⠉⣰⠃⣾⠁
⠀⠀⠀⠀⠀⠙⣦⠹⣆⢇⠀⢀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡤⠖⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣰⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣌⠫⡙⠋⠀⠀⠀⠀⠀⠘⠲⣄⠀⠸⠥⠖⠉⠀⠀⠀⠀⠐⠭⠭⠝⠂⠀⠀⢀⡀⢀⠀⠀⠀⢀⡇⢀⡼⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠒⠒⣋⡴⢋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⠴⠊⠁⠹⡄⠀⡞⠁⠀⠀⠀⠀⠀⠀⢀⣉⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⣀⣀⣠⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠚⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀
⠀⠀⠀⡠⢠⠟⠀⣼⠃⡠⠑⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⣿⣽⡻⢷⣯⣇⢤⡀⠀⠀⡄⠉⠀⠀⠄⠀⠩⠉
⠀⠀⢸⣡⠋⠀⠈⠁⠘⡱⣠⢸⠀⠀⠂⠁⢀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣭⣻⠟⠁⠈⣛⢷⣽⡄⢸⠁⣀⢠⠀⠈⠙⡆⠈⠘⡆
⠀⠀⢸⠃⢀⡞⣠⢀⡔⣰⡷⠘⠀⢀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⢸⣍⡻⢿⣄⣀⣐⢿⣷⣿⠇⢸⡄⠀⠈⢤⣀⣴⠇⠀⠀⠃
⠀⠀⠈⠣⣜⣸⢃⡞⣸⣿⠁⠀⠀⠈⠢⣀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠻⣿⣶⣭⣛⢻⡷⡊⠁⠀⠀⠻⠰⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉

⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⡴⠛⠁⠀⠀⠀⠙⠷⡄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⠞⠁⠀⠀⠀⠈⠳⣄⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠈⡄⢸⣿⣿⣾⠿⠛⢻⣿⣿⣿⡄⢠⠏⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠘⡄
⠀⠀⡿⠀⠀⠀⢀⣀⡴⠀⠀⠘⡇⢸⡇⣿⢻⡄⠀⢸⡇⠿⣹⡇⠀⠀⠂⠀⢇⠀⡸⠀⠀⠀⡄⢐⠀⠀⠀⠀⡀⠜⠀⠀⢠⠇
⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⢿⡆⠁⠀⠀⠉⠀⠙⠀⠀⢳⣄⠀⠀⠄⠀⠀⢀⡞⠀⠘⢄⡀
⠀⠀⠀⠀⠙⠳⠦⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠙⠛⠦⠄⠀⠐⠁⠀⠀⠀⠀⠑⠢⠤⠤⠤⠂
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⣀⢀⣀⢀⠀⠤⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠴⠀⢈⣄⠀⢀⡄⠀⢡⡀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢰⡆⠀⠀⢀⠀⠀⠈⠓⠀⠀⠀⠀⢀⣄⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⠠⠀⡠⠊⢀⠀⠀⠈⠀⠀⢀⢈⠉⠋⠉⠛⠋⠉⠀⠀⠀⠀⠀⠠⠜⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠇⠀⠀⠁⡼⡀⠀⠀⠀⠀⡀⠀⠄⠀⠀⡤⠔⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠶⠀⠀⣤⡄⠀⠘⠃⠀⠀⠀⡀⠊⠀⣼⠇⢡⢀⡀⢰⢘⠥⠀⠠⠒⠉⡠⠐⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠓⠀⠀⠀⠀⣀⡠⠔⠉⢀⡤⠛⠓⠒⠤⠤⠬⠥⠤⠤⠒⠒⠉⠁⠀⠀⠠⠤⠀⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠅⠐⠒⠢⠄⠀⠂⠈⠀⡀⠠⠂⠫⢅⡀⠉⠐⢄⠀⢀⠤⠀⢀⣀⠀⠀⠀⠊⠁⢀⠀⠈⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠑⠂⠠⠄⠀⠀⠀⠀⠤⠭⠀⠀⠀⠈⢀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠃⠠⠄⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠖⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠄⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠄⣊⠠⠐⠁⠀⠀⠀⠈⠁⠄⢉⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠖⠐⠒⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠒⠒⠐⠃
⠀⠀⠀⠎⡘⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠤⣄⠀⠀⠀⠀⠀⠀⠈⠀⣣⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⢠⠌⠀⠀⠀⠀⠀⢀⢤⠆⠃⠀⠀⠀⠀⠀⠐⢆⡄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢸⠄⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠀⠀⠀⠠⠤⠤⠀⢀⡀
⠀⠀⠈⠈⠄⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠁⠢⢄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠄⠠⠤⠲⠃⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠄⠀⠠⠤⠤⠘⠁⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠞⠀⠀⠀⢈
⠀⠀⠀⠀⠈⠢⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠊⠀⠀⠀⠀⠀⢦⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⣀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠌⡐⠢⠀⠀⠀⠀⠀⢀⠤⠠⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠀⠐⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠌⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣠⠰⠹⢿⣿⣿⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⢀⡴⠲⣶⣶⢶⣄⡀⢀⣿⡶⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⣠⢤⡀⠂⠈⠹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⢏⡈⡔⢡⣁⠊⠑⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠄⣸⣥⣤⣤⣤⣭⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣷⣾⣿⣿⡿⢃⠀⠁⢹⠛⡁⢁⣤⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣠⡾⠁⢈⡼⢣⡈⠀⠁⠈⣌⠁⠀⠀⢿⣿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢢⢄⡄⠀⠀⢸⠁⠉⡀⠉⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⡠⠈⠹⠧⠖⠋⠀⢀⠑⠀⠀⡔⠙⠀⠀⣤⠈⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠸⣿⣿⣿⡏⢡⢇⡃⠃⠀⠀⠈⠀⠘⣧⠀⣀⣠⠤⠚⠁⠀⠀⠀⠠⣎⡀⢀⣀⠠⠤⠔⡚⢿⢃⡤⠊⠀⢀⠃⠀⠰⠀⡉
⠀⠀⠀⢄⡶⡾⣆⠀⠀⠹⣿⡟⡅⣵⡎⠙⢓⢠⠄⠀⠀⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡸⠀⠀⠀⠀⡇
⠀⠀⠀⠾⣿⢾⣧⠀⠀⠀⠙⢷⣴⡹⡇⠂⠈⠁⠀⠀⠀⣿⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢰⠁
⠀⠀⠀⠰⣿⣷⠁⠀⠀⠀⠀⠀⣿⣇⠈⣺⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠁⠀⢸⡆⠇⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⡌
⠀⠀⢀⣄⠘⣻⡅⠀⠀⠀⢀⣉⠁⠹⢆⣿⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡑⢌⣣⠸⢸⠀⠀⢰⠀⠐⠃⠀⠀⢀⡠⠖⣹⣷⡄⠀⠀⠐⣉
⠀⠀⠀⠏⠳⠹⣗⠀⠀⠈⠙⠛⠋⠀⡜⠛⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⡄⣏⠦⡘⠀⠀⠸⣄⢸⣤⡠⠖⠁⢀⣼⣿⣿⣷⠀⠀⠀⠈⠐
⠀⢠⣶⡆⠀⠀⢋⣄⠀⠀⠀⠀⢰⣾⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣠⠀⠠⢸⠄⠃⠀⠀⢠⣿⣿⣯⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⢠⠂⠠
⠀⠀⠻⠇⠀⠶⡀⠉⠀⢀⡠⠴⢏⡈⠙⠳⢷⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⢀⡧⠔⢻⡄⠀⠘⢃⣿⠻⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⢸⠁⠀⣿⠙⠓⣿⠌⠉⣲⣤⣀⣀⣀⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡧⠶⠀⠸⣶⣾⣿⣷⡀⠀⣸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⣸⡀⢼⡷⠟⠀⣈⢻⢫⣮⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢻⣿⣿⣿⣷⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢠⠟⣡⣤⠀⢰⣯⢓⠾⡀⠡⠊⢀⣀⣀⠀⠀⠀⢀⡴⠴⠦⠼⢄⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⡄⢀⡎⠀⠀⠀⡎⢸⠯⠜⡲⠆⠞⠁⠀⣀⠤⣊⠖⠲⣭⠻⢆⠀⠈⣞⣙⣋⠱⠂⠀⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣠⢿⠀⡜⠀⠀⠀⣸⢁⣤⣦⠞⠀⣴⣶⣶⣿⣶⣶⣶⣾⣷⣿⣶⣾⣶⣶⣿⣷⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣰⣷⡾⣷⠁⠀⠀⠀⠧⣛⣃⣍⠀⠀⠈⠉⠹⠋⠉⠉⣉⣉⣭⣭⠭⢭⣿⡉⠉⠉⠉⠉⢩⣿⣿⠉⠉⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠉⢉⣿⣸⣄⣀⣀⣀⣀⣀⢠⡭⣍⡁⠚⠻⢞⣁⢾⡏⢩⣟⠷⠀⢠⣞⠛⣿⡀⠀⠄⠀⢸⡇⡀⠀⠀⠀⣠⠊⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡠⢀⢽⢏⡀⣤⠀⢀⣐⡄⠀⠀⢹⣯⠆⢤⣴⣾⣿⡇⠀⠀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⢾⡎⣧⡻⠃⠀⠺⠙⠁⠀⣾⠎⢹⣯⣱⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣦⣸⡆⢹⢁⣶⡿⠂⢠⣶⡇⠀⣴⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣇⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣷⣾⣿⣷⣇⡈⢉⣤⠤⠽⡿⠒⠋⠙⣇⠁⠀⠉⢻⣿⣿⣿⣿⣿⣏⠙⣷⢀⠤⠀⠰⠄⠂⢀⣩⣽⡮⠁⠈⠈⠁⠚
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⡰⠉⢦⠀⠀⠹⣆⠀⠀⣾⠉⢿⣿⣿⣿⣿⣦⢹⡄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⠛⠉⠀⡆⠀⢠⡅⠀⠀⠳⡀⠀⠹⣦⣀⣿⠀⠀⠙⣿⣿⣿⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⣇⣀⣀⡈⢻⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⣁⠀⠘⣆⠀⠀⠀⠙⣿⣿⢿⣿⣿⣶⣤⣤⣀⢀⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡞⠀⠀⠀⢸⣿⠻⢿⣿⣶⣄⣀⠀⠈⣧⠀⣼⠀⠉⠛⣻⣿⣿⡿⠋⠈⠋⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠓⠚⠁⠀⠀⠀⠀⠃⠀⠀⠈⠙⠛⠿⠿⠗⠛⠚⠋⠠⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠚⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⣶⣿⣶⣯⣭⣿⣧⣿⣿⡿⣿⣿⡧⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⠟⠹⠿⠟⢻⡟⢻⣿⡶⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡷⡌⣿⣿⡆⠀⠀⠀⢈⠉⠉⠈⢳⡦⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⠀⠀⢺⣿⣿⣿⠀⣸⣇⡇⠀⠀⠀⠀⠀⣶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⠛⢀⣿⠿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠀⢤⣾⣿⣻⢋⣿⣿⣶⣤⣀⡀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢰⣿⡽⣱⣿⣼⣿⡇⠙⠋⠉⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠙⢶⣤⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⠀⢀⣠⣤⣴⣶⠿⣿⡿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠘⡟⢜⢿⣿⣿⣷⡻⣧⠄⠀⠀⣾⣧⣭⣿⣿⣿⣿⡟⣼⣿⢟⣿⣿⣿⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⣰⡿⢸⠘⠿⣿⣿⢿⣟⠛⢦⣠⠏⠀⢺⣿⣿⣿⠟⣱⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣍⠀⠀⠀⢠⣿⢣⣯⣴⡇⠨⣿⣿⡿⠃⠀⠘⠂⢀⠀⢹⡿⢻⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢀⣠⣾⣿⣿⣿⣿⣿⠀⠚⠁⠀⠀⠀⠀⠁⠘⡀⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠘⢿⣇⣀⣩⣿⠟⠉⢻⣿⣿⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢿⣿⣇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢣⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣭⡤⠀⠀⠀⠰⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠶⠿⡥⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⠳⣄⠀⠀⠀⠀⠀⣠⠞⠑⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠖⠉⠙⠦⣀⠀⠀⠀⢸⠁⠀⠈⠓⠦⣄⡀⢰⠃⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⠲⠤⣬⡦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡰⠓⢶⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣠⠶⠚⡇
⠀⠀⠀⠀⠀⠇⠀⠀⠘⠦⣀⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠇
⠀⠀⠀⠀⠀⢢⠀⣀⠀⠀⠈⠁⠀⡜⠉⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢹⡹⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡿
⠀⣴⣤⣶⢀⠀⠈⢇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⡀⣶⣤⣦
⣻⣽⠞⠻⢯⠇⠀⠘⢎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠃⠀⠸⡽⠟⠳⣿
⠙⢯⡀⠀⠸⢤⡀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⠃⠀⢀⡤⠃⠀⢀⡽
⠀⠀⠈⠳⡀⠀⠙⠦⣀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠉⠉⢉⠏⠀⠀⠀⠀⠀⢀⣠⣯⠞⠀⣀⠴⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠙⢦⠀⠀⠈⠳⢄⡀⠙⠻⣦⣄⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠀⠀⣠⣴⠿⠋⢀⡠⠞⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠉⠳⢤⡀⠉⠛⠷⢦⣤⣤⣀⣀⣀⣀⣤⣤⡴⠾⠛⠋⢁⡤⠞⠉⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠉⠳⡶⣄⠀⠀⢘⡇⠀⠀⢸⡃⠀⠀⣠⢶⠞⠉⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⡰⠃⠀⠙⠒⠋⠱⢤⡤⠞⠙⠒⠋⠀⠈⢆⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠉⣇⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣍⠀⠀⠀⣿⡈⠀⠀⡀⠀⠀⠀⠀⠀⡀⠆⠀⠔⠈⠀⡇⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡏⠐⢤⣴⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠘⣦⠀⠀⢀⠃⠠⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠋⠉⠁⠀⠈⠙⢻⣿⣿⠆⠀⠰⠂⠈⠀⠄⡀⠀⠁⠐⠠⠊⠀⠔⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⡀⠀⠀⠀⢹⠀⠘⣿⡷⠀⠀⠀⠀⠄⠀⠀⠁⠄⠀⠀⠀⠙⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠠⠁⠀⠀⠀⡆⠀⠀⠡⠀⠀⠀⠁⠂⠀⡔⠀⠀⠀⠀⠀⠀⠀⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢜⠀⠀⠀⣰⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠏⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⣼⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠖⠀⠈⠒⠇⠀⠀⠀⢠⣤⣤⣀⣀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢉⠙⠉⠀⠈⠁⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⢀⠆⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⠙⠓⠒⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⣀⡤⠴⠒⠖⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⣤⣀⡀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣴⠒⢦⡔⠛⣷⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⡴⠋⠀⠀⠀⠀⣀⢴⡄⠀⠀⠀⠀⠀⠙⠶⣤⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠳⣄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⠟⠁⠀⠀⠀⢠⣞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠇⠀⠀⠀⠈⢳⣄⠈⢷⡀
⠀⠀⠀⠀⠀⣴⠏⠀⣰⠏⠀⢀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⢾⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣷
⠀⠀⠀⠀⢰⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠐⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⠀⠸⣧
⠀⠀⠀⠀⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡇⠀⢹⡆
⠀⠀⠀⢰⡟⠀⢰⡇⠀⠀⠀⠀⠀⢠⡴⢤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⣾⠙⠶⠚⢳⠀⠀⠀⠈⣷⠀⠈⣧
⠀⠀⠀⢸⡇⠀⢸⠃⠀⢀⡀⠀⠀⢸⡄⠘⠋⣻⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⣄⢀⣴⠏⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣾⠇⠀⠻⠟⠀⠀⠀⠻⠶⠞⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣶⠀⣿⠀⠀⢹
⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⢾⣿⠀⣿⠀⠀⣾
⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠟⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀⢀⣴⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠔⢀⡿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣿⡄⠀⢾⡽⠋⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣠⡴⠛⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡇
⠀⠀⠀⠀⢷⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣼
⠀⠀⠀⠀⠘⢧⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢷⣄⠈⠻⣆⡀⠀⠘⠟⠀⠀⠀⣠⣤⡴⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣤⠖⢄⣀⡀⠀⠀⠙⠚⠀⢠⠏⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠻⣦⡀⠀⠀⠀⠸⣧⣀⡁⣼⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⡽⠀⠀⠀⠀⢠⠏⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⠯⣽⣓⣶⣤⣄⠀⠀⠀⠀⠈⠳⠶⠚⠁⠀⠀⢀⡴⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⢶⣄⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠶⠀⠀⠀⠀⢀⣠⡴⠋⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠈⠻⢦⣄⡀⠀⠀⠻⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠉⠛⠳⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠉⠁⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠎⠳⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⠦⡴⣣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⣾⣉⠓⠉⣁⣿⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⡁⠀⠀⠀⢻⣏⠙⢯⣉⡿⠀⠀⠀⢈⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢰⠋⠉⠙⠒⠒⢻⡌⠳⢄⣀⡟⠒⠒⠋⠉⠙⡆⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡤⠤⠞⠀⠀⠀⠀⠀⠈⡟⠦⠀⣸⠃⠀⠀⠀⠀⠀⠳⠤⢤⡀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠲⠶⣤⠀⠀⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠀⠀⠀⠀⡤⠶⠖⠃⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣦⡀⠀⠀⠀⢸⡀⠀⣀⣤⣤⡀⠀⠀⠀⠀⢀⣤⣤⣀⠀⢀⡇⠀⠀⠀⢀⡴⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢻⠀⠀⠙⠶⢤⣀⡀⠉⠉⠁⠀⠀⠙⢦⣀⣀⡴⠋⠀⠀⠈⠉⠉⢀⣀⣤⠖⠋⠀⠀⡗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣦⣤⡤⣄⠀⠈⠉⠛⠒⠶⠦⠤⣤⣤⣤⣤⣤⡤⠤⠴⠶⠒⠛⠉⠁⠀⣠⢤⣤⣴⡇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⡄⠀⠀⠘⣧⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⣼⠃⠀⠀⢠⡇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⢷⡀⠀⠀⠘⠷⠴⠋⠀⢻⡀⠀⠀⣴⠟⠻⣆⠀⠀⢀⡟⠀⠙⢦⠾⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠃⠀⠀⠘⠳⠶⠞⠁⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣄⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⣠⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠚⠋⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⣤⠴⠲⣄⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠲⠶⠶⠶⠦⠤⠶⠶⠶⠖⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⣠⠶⠶⣤⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠹⣆⠀⢠⡞⠉⠙⣦⠀⠀⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⠀⣴⠋⠉⢳⡄⠀⣰⠏⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠹⣄⠀⠀⠀⣰⠏⠀⠀⠹⣆⠀⠀⠀⣠⠏⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠚⠁⠀⠀⠀⠀⠈⠓⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠶⠖⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢴⣒⣚⡛⠛⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⣉⣀⠴⠋⠀⠀⠈⠓⠚⠉⠉⠻⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠉⡼⠁⠀⠀⠀⣷⠀⠈⠃⠀⠳⠀⠀⠀⠙⠦⣌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠴⠚⠁⠐⠆⠀⠀⠀⠀⠀⠴⠂⠀⠰⠋⠀⢰⠂⠈⡇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠀⢀⣀⠄⠀⡄⠀⢰⣤⣤⠤⣤⣀⠀⠠⢤⠈⠀⠀⢧⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⠈⠀⠀⠸⠁⢠⠏⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠆⠈⠳⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⠀⠀⠐⠲⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠈⡙⠂⢀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⡀⢲⡀⠀⠀⠲⡄⠸⣄⠀⠀⠀⠀⢀⡼⠁⠘⠁⡀⢸⡀⢰⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡇⠀⠀⣸⠁⠀⠀⡀⠈⠳⠦⠤⠴⠚⠁⡄⠀⠘⢁⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⠲⡄⠋⠀⠀⠀⠳⠀⠴⠁⠀⠒⠂⠀⠉⠀⠀⠀⠑⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⡀⠈⠙⠀⠀⠀⣄⠀⠀⢄⠀⠀⠠⠃⠀⠤⢤⣮⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣓⠒⠦⣀⠀⠈⢃⣀⡈⠃⠀⠀⣠⢴⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠬⢽⣯⣭⣤⡭⠷⠶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠁⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠴⢚⡿⠀⠀⠀⢀⣶⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⢳⡄⠀⠀⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠺⡏⠙⠹⠓⠗⠛⠉⡷⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠇⠀⠀⢀⣠⡴
⠀⣀⡀⠀⠀⠀⠀⠈⢳⡝⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡄⠀⣧⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣾⠤⠶⣾⢕⡠⠶⠚
⢀⣬⡿⣷⣶⡖⠶⠒⠉⠀⠀⠙⡆⠀⠀⠀⠀⢀⡾⠀⡾⠀⠀⢸⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠠⡿⠟⡒⠒
⠀⢬⣭⣻⣯⠶⣠⡤⠦⢤⡀⠀⣷⠀⠀⠀⠀⣼⠃⢸⠇⠀⠀⠈⡷⠶⠶⢶⡞⠀⠀⠀⢹⠀⠀⢻⡄⠀⠀⠀⠀⠀⣸⠃⠀⡴⠛⠉⠉⠉⠉⠙⠛
⠀⠀⠀⠾⠖⠋⠁⠀⠀⠀⣧⠀⢸⡄⠀⠀⢰⡏⠀⢾⠀⠀⠀⠀⢷⠀⠀⣸⠁⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⠀⠀⢠⡏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣇⠀⠀⣿⢄⡀⠘⣆⠀⠀⠀⢸⡄⣰⠃⠀⠀⠀⢀⣿⠀⠀⠀⠸⡆⠀⠀⠀⡞⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⠀⢰⠇⠀⠉⣱⠘⢧⣤⠤⢬⣧⣏⣀⣀⡀⢀⡾⠙⣧⣤⠴⠞⣧⠀⠀⣸⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣇⡏⠀⠀⣰⠏⠀⣎⣵⣤⡴⠷⠾⢤⣀⡿⡾⠁⠀⠘⣇⠀⠀⠸⡆⢠⠏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡿⠀⠀⢠⡏⠀⠀⠀⢈⣆⣀⣀⣀⠀⠈⣹⠇⠀⠀⠀⠘⣆⠀⠀⠙⠞⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠀⠀⣠⡴⠋⠁⠀⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⡞⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢦⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡾⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⡁⠲⣬⡀⠀⡂⠀⡔⠊⢉⠒⢄⡈⢙⡴⠊⣉⠉⢢⠀⣾⠉⡄⠀⢸⡇⢡⡠⠤⠀⠰⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⢳⠈⠀⠀⠁⠸⠀⠰⠉⢱⠘⡇⠀⢠⠎⠀⠇⠀⡆⢸⠀⡇⠀⠸⡇⢸⠃⠆⠀⢴⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⢆⠀⠇⠀⠀⠀⢠⠀⠁⠀⠸⢀⡇⠀⠋⠀⠀⢸⠀⡇⠸⠀⢃⠀⡸⠃⢸⠀⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠓⠚⠀⣦⠀⠘⣄⠈⠒⢁⠜⢃⠈⠀⠀⠀⡌⢠⠀⠀⢆⠀⢉⣠⡄⢸⠀⠸⡀⠨⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠁⠀⠀⠈⠑⠂⠁⠀⠈⠛⠀⠀⠀⠙⠃⠀⠀⠀⠁⠈⠀⠑⠃⠀⠀⠉⠢⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⣉⠤⢐⠀⠀⠀⠀⠒⠀⠤⠀⣀⠈⣉⡒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⡤⠖⠉⠠⢊⡔⠁⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠑⠢⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡺⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠈⠡⠈⠦⣱⠀⠠⠀⠀⠆⠑⢄⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠔⠁⠀⡔⢹⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠠⡑⢄⡀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠐⠁⠀⠀⠘⠖⠁⠀⠀⢆⡄⣠⢖⠀⠀⣀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠙⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠂⢴⡪⠍⠛⠀⠀⠀⠀⠀⠀⠐⡡⠊⠀⡘⡘⠀⠀⡠⢪⠂⠈⠡⢕⠀⠀⠀⠀⢀⢊⠀⠀⠀⢠⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄⢀⠀⠀⠀⢠⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⡥⠅⠠⠈⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠊⠀⠀⠀⠈⢆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡏⡄⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⡠⠊⡠⠄⠒⠒⠒⠒⠱⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢂⠈⠃
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠠⡀⠀⠀⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡑⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠁⡤⢐⠆⠀⠀⠀⠠⢋⠔⠀⠰⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⡆⠀⠧⠔⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠈⠀⠀⢀⠠⢐⠂⠀⣤⠀⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠰⠀⠀⠀⠀⠳⠈⠀⢀⣀⢏⡄⠀⢠
⠀⠀⠀⠀⠀⠀⢰⠀⠣⡀⡲⡀⠀⠀⠆⡀⠈⠖⠀⠀⠣⢌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⠂⠀⠄⡀⠀⠀⠀⠠⠉⠌⠀⢁⠀⣼
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⡑⠨⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠢⠙⢂⡄⢀⣀⣀⠀⠠⠔⢋⡠⠂⠰⡁⠊⠀⠀⠀⠀⠓⠈⠀⠀⠘⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⡜⡘⠀⠀⠀⠠⢞⠉⠉⠉⠉⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢃⠀⠀⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠐⠄⠀⠶⠀⠀⠀⠀⠀⠀⠀⢀⠔⠆⠀⠀⠔⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡠⢀⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠦⠘⠀⠀⡌⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠱⢄⡀⠀⠀⠀⠀⢀⡀⠀⠈⠐⠊⠉⠀⠺⠤⠋⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣀⣴⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠑⡄⠀⠀⠐⣄⡀⠀⠀⠀⠀⠠⠐⢄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡠⠂⣉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡐⠂⣀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⠕⠀⠀⠄⠂⠀⠀⠀⢀⣠⡡⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣉⠐⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠠⠐⢈⠩⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠲⠦⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⢀⣀⣀⡀⠤⠤⠤⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠓⠈⠉⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠤⠄⠐⠒⠒⠒⠀⠠⠴⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠤⠤⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠓⠢⢄⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⣀⣠⡤⡇⠀⠐⢆⠀⠀⠐⢢⠎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⡀⠀⠀⠀⠐⠀⢀⠀⠀⠀⢺⣤⣄⣀
⠀⢀⣤⠖⠛⠉⠀⠀⠐⠄⠀⠀⠁⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠄⠀⠉⠀⠀⠀⠁⠀⠀⠀⠟⢆⢠⠀⠀⠔⠀⠈⠀⠁⢠⠀⠀⠉⠛⠲⣤⡀
⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⢾⠀⢄⡠⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠋⠠⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢻
⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠢⠀⠠⠠⠎⠀⠀⢀⠀⢀⠈⠀⠈⠀⠁⠀⠀⡰⠣⠤⠤⠤⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠈⠛⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⢶⣤⣤⣤⣤⣀⣀⣀⣉⡒⠢⠤⠤⠤⠤⠤⠤⠤⠀⠒⠒⠊⠉⠁⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣴⡶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⣩⠝⠉⠀⠀⠀⠀⠉⠛⢭⡙⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣉⣤⠤⠔⠊⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⢭⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢠⠖⠚⢉⣁⡽⠀⠀⢰⠋⢳⠀⠀⠀⠀⢀⡠⠖⡄⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⠀⠀⠀⠀⢸⠀⣾⠀⠀⢀⠔⠋⣠⠖⠁⠀⠀⠀⠀⢸⢧⡀
⠀⠀⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣀⠇⠀⠀⠘⠒⠋⠀⠀⠀⢸⡉⢣⠀⠸⡆⠱⡀
⠀⠀⠀⣰⠁⢰⠁⠀⠀⠀⣏⣉⣉⣉⣁⡵⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢣⠀⢣⡀⢱⡀
⠀⠀⢀⠇⡰⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠉⠑⠒⠉⠉⠛⢆⡀⠀⠀⠀⠀⠀⠀⠑⠜⠁⠀⠈⠢⣇
⠀⠀⢸⠞⠁⠀⣇⠙⣄⠀⠀⠀⠀⢀⡴⡶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡑⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⡄
⠀⠀⡏⠀⠀⠀⠈⢦⠘⢆⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⢀⡠⠚⢁⠼⠀⠀⠀⡇
⠀⠀⣇⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢏⡠⠞⠁⠀⠀⠀⣼⡇
⠀⠀⢹⢆⠀⠀⠀⠀⠀⡠⢄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃
⠀⠀⢸⠈⢧⠀⠀⢀⡜⢁⡜⠀⠀⢸⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠞⠀⠀⠀⠀⢠⠋⣳⢸⠀⢸
⠀⠀⠈⡆⠈⡇⠀⡞⢀⠞⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠀⠀⠀⢀⠏⢠⠃⠘⡄⡎
⠀⠀⠀⢹⠀⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢄⣀⡤⠤⣀⡠⠔⡿⠀⠐⣏⠙⠦⡀⠀⠸⠤⠏⠀⠀⢹⠁
⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠉⠉⣀⣀⠀⠀⠑⢦⡈⣣⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⢣⠀⣞⢉⣉⣉⣉⡱⠀⠀⠀⡠⠊⢁⠇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠉⠁⠀⡠⠖⣫⠋
⠀⠀⠀⠀⠀⠈⢣⡈⠉⠁⠀⠀⠀⠀⢠⡋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⡜⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⡒⠢⠤⢤⣀⠉⠁⠀⠀⢰⡉⠲⢤⣀⠀⠈⠣⠞⠀⠀⠀⠀⠀⢰⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠙⠢⣄⠀⠀⠉⠓⠤⣈⡵⠀⣠⠴⠒⠦⢤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠽⠦⢤⣀⣀⣀⣠⡾⠥⠤⠒⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠛⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠻⡿⠰⢀⠐⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⣤⣤⣀⣾⠋⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢷⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⣀⣀⣀⣀⣀⣠⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣰⣾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣎⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢡⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠄⠀⠀⠀⠀⠈⠣⠍⠌⠄⠋⠉⢠⠀⢌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡺⠁⠈⠂⠀⠨⡹⠀⠀⠀⢀⠄⢄⠀⠀⠈⠒⠂⠀⠈⢫⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣊⠉⠁⠀⢀⠤⡀⠀⢀⣀⠀⠀⠀⠀⠑⠀⠀⠀⠤⠒⠀⠀⠀⠀⠁⢄⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠈⠤⠃⣀⠀⠀⠑⠁⠀⠡⠼⠀⠀⠀⠀⠀⡔⠒⡀⠑⠚⠀⠀⠀⠀⠀⢀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡄⡄⠀⢸⠀⠑⡰⠀⠀⠀⠀⠀⠀⢀⡤⠒⠢⡁⠊⠀⠀⠀⠔⢠⠀⠀⠀⠣⠔⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠑⠁⠀⠀⠁⠉⠀⠀⠀⡠⠤⠤⢠⡊⠠⠠⠄⢘⠠⢀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠔⠁⠀⠀⠀⠀⠀⠈⠢⡈⠢⠀⠀⠀⢀⠔⠊⡂⠀⢠⡒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⢂⠀⠀⢘⣙⠀⠀⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠑⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠁⠁⠀⠀⠀⢀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⠀⠀⢠⠒⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⢀⠤⡀⠀⠀⠀⢇⠰⠀⠒⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⡠⠀⠀⠈⠒⠁⠀⠀⠱⡠⠃⢐
⠀⠀⠀⠀⠀⠀⠀⠰⢠⠀⠈⠒⠁⠀⠀⣀⠀⠀⠀⠀⢃⣈⠐⠤⢀⣀⣀⣀⠠⢊⠸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠣⡀⠀⠀⠀⠘⠴⠁⠀⠀⠀⡄⢄⠈⠆⣀⠄⠂⢐⠀⠊⠀⠀⠀⢆⡁⢸⠀⠀⠀⣎⢱⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡆⠀⠀⡎⢢⠀⠀⠀⡔⠱⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢔⢰⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣀⠀⠀⠀⠈⠈⠁⠀⠰⣁⡑⠀⠐⡅⠠⠕⠀⠀⠀⢠⠂⠉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣈⣚⠠⠀⢤⠀⠀⠀⡀⠀⠀⠀⡀⠀⢈⡉⠀⠀⠀⡰⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡇⠀⠈⠚⠀⡠⠊⠀⠀⠀⠈⠁⢀⡡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠛⠒⠀⠀⠀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⣤⡤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠉⠉⠀⠀⢀⠀⠀⠀⠉⠉⠑⠒⢤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠠⠶⠂⠀⠀⠉⠀⠀⠀⠀⠠⣄⠀⠀⠀⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⢴⠗⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⣛⠃⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠶⠂⠀⢀⠀⠀⠀⠀⠀⠸⠀⢠⣐⠚⠂⠀⠀⠀⠀⠛⠀⣀⣀⠈⢣
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⢢⢶⠀⠐⢦⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠰⣦⠀⠀⠀⡄⣰⣾⡿⠟⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇
⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⠈⠀⠀⠀⠀⠀⣶⡿⠋⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠇⢿
⠀⠀⠀⠃⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠄⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⡆⠀⢠⡄⠙⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠱⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢶⣿⣄⡀⠀⠀⠀⠀⣀⡼⣿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠠⢤⡄⠀⠀⠉⢻⣿⣷⣶⣞⣛⣭⣾⠿⣤⡀⠀⠀⢤⢀⣀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⠿⠏⠉⠁⠀⠐⠚⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣷⡀⢀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣤⣄⡀⠘⣠⠄⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠠⣍⠀⠘⢃⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠙⠀⠀⠁⠀⠀⠀⣠⠆⠀⠰⢜⡆⠀⠀⠀⠀⠀⡺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠾⠦⢩⠉⠀⡠⢶⡦⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠆⠀⣀⣀⡴⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡄⣿⡀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣬⡻⠟⠋⠁⡱⠒⡑⠊⣁⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡠⠚⣡⣾⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠰⢯⣟⡣⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⣠⡅⣰⠟⠋⠀⢀⣤⠀⠈⣹⠶⡀⠀⠀⠀⠀⢈⡎⠱⡄⠉⡿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢡⡴⠀⠀⠋⢀⠀⠀⢄⢰⠜⢆⠀⠀⠀⢀⣷⢠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡘⠇⠀⠀⠀⠙⠁⠀⣤⣉⠆⠈⣇⠀⢀⣾⣷⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⡄⡰⢊⡁⠀⣀⡠⠤⠀⣿⣠⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠁⠁⠸⣶⣶⣶⣾⠏⢀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡐⢄⠈⠛⠛⢉⢄⣾⣿⣿⣿⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣦⣥⡒⢂⣵⣿⣿⣿⣿⣿⢵⣾⢫⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⡇⠈⠑⠼⡏⠙⠉⠙⢟⠛⠛⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠁⢃⡀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠛⠿⠿⣿⣿⣿⣶⠶⢤⣤⣀⠀⠀⠀⠒⠒⠰⠀⠓⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⠇⠀⠈⠸⣩⢻⢦⡀⠀⣠⡼⢤⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣼⡀⢀⢃⢇⠀⠄⢋⢞⠃⢀⠀⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⢩⠇⡸⠌⠈⡄⣴⠟⡌⣄⣴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡏⠈⠊⡤⢇⣄⣠⠟⢁⣤⡾⡿⡱⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢰⢰⠀⢡⣠⣟⡥⢶⣏⠁⠁⠁⠃⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⡆⠆⢾⣠⡾⠛⠁⠀⠀⠙⣶⡰⡆⠀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⡞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⣥⣼⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠁⢀⠄⠀⢀⡔⠀⠀⠀⠀⣐⠁⠴⠦⠤⢀⣀⡀⢱⠀⠀⠀⠃⣠⠂⠐⠸⠁⠀⠀⠀⡌⢪⠀⠀⠐
⠀⠀⢰⡄⠀⠀⠀⡿⠃⠀⡀⠀⠀⠉⠀⡀⠂⠠⠄⡈⠳⣸⣟⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⡼⠇⢀⣷⡀⠀⠀⠀⠘
⠀⠀⠈⢇⠀⡀⢀⢸⠀⠈⠁⠀⠀⡤⠘⠀⡐⠒⠀⠈⠀⠀⠀⠀⠀⠁⠉⠶⣠⠀⠀⢰⣤⠁⠀⠾⠋⠋⠰⡀
⠀⠀⠀⠈⢂⠙⡦⠊⡠⠀⠀⠀⠈⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠈⠙⠀⠀⠄⠀⠀⢀⡇⠆⢐
⠀⠀⠀⢀⣨⠟⠀⠀⠀⠀⠀⠐⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠐⠛⠁
⠀⠀⠠⠊⢁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠳⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠈⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣦⣤⣤⡀⠀⠀⠀⠀⠘⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠁⠀⠉
⠀⠀⠠⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠹⢯⣉⣛⠉⠙⠂⠀⠀⠠⠄⠐⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠄
⠀⠐⠀⠀⠀⣠⠞⢀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⢰⡍⠀⣎⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⢀⡴⠀⠀⠀⠀⠈⠣⡀⠀⠀⠙⡆⠈⠑
⠀⠀⠀⠀⠀⠃⠀⠈⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠽⢷⡶⠀⠈
⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣠⡤⠀⠀⡀⢐⠄⢀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠻⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡦⠀⠉⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⣾⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡀⠉
⠀⠂⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵
⠀⠀⠀⠀⠀⠙⡟⣄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠛⠶⢤⣄⣠⣤⡴⠞⠛⠿⣿⠁⠀⠀⠂⠠⠀⠀⠀⠀⠁⠑⠀⠀⠈⠁
⠀⠀⠀⢠⡺⠀⠁⠘⢳⢦⢤⣄⣀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠵⠀⠀⠀⠀⠸⠀⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠁⠈⢝⠀⠀⠀⢀⢠⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢮⣀
⠀⣀⠤⠀⢺⣀⠠⠨⠾⠺⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓
⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠘⠀⠀⠀⢀⠬⠀⠀⠀⠀⠐⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡵⢡⠀⠀⢸⠲⢤⠀⠀⢠⣦⡀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠇⠀⠀⠸⠁⠀⠀⢸⢀⣀⠀⠀⢀⠈⢀⠀⠀⠾⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠇⠀⠸⠆⣀⡇⠀⢘⠀⠩⡁⠀⠘⢠⣼⠀⠀⢠⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⢰⡄⠈⠇⠀⠘⠑⠶⠆⠀⢰⣀⢸⠀⠀⠈⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡈⠀⠀⠀⠙⡇⠀⢐⠆⣤⡅⠀⢀⠈⢹⡀⠀⠸⠰⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⡀⢰⡇⠈⢹⡔⢻⠆⣄⣥⠊⢹⠀⠀⣿⠖⣿⠑⠲⣯⣡⣸⢤⣼⣆⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠾⣷⣆⣴⣷⣿⡇⠐⢾⡿⢿⡄⠈⢿⠿⠿⠓⠶⡿⠿⢿⠦⣌⣿⣿⣿⢄⣈⣿⣶⣾⢟⣳⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⣋⢭⠤⡀⠛⢠⣼⠀⠈⡁⠳⢾⠀⠀⠦⠤⠀⠀⢸⡀⢈⡇⠀⢀⡀⢙⣃⠉⠙⡿⣄⠈⢳⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢷⣿⣇⠉⠈⡄⢠⡀⠀⡉⢠⠐⠧⢦⣼⠀⠀⠀⠀⠀⠀⠐⣠⠙⣃⠀⠈⢫⠈⢻⡻⠶⢷⣤⣍⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠛⠲⢧⣄⣠⣵⣆⠙⡄⠲⣀⠸⣼⠳⡀⠀⣀⠀⢄⠰⡀⠂⣈⢶⣄⡛⢶⣬⣿⣦⡼⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠉⠛⠛⠓⠈⢷⣼⣿⣿⣦⢹⣦⣬⡷⣮⡽⠿⠆⠸⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠗⠀⡏⢸⡀⢠⣶⠀⠀⠀⠀⣤⡄⠀⠀⠀⣠⣤⡀⠀⢀⣄⠀⠀⠀⠀⣾⣿⣧⠀⢀⣀⠀⠀⣷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠁⠀⠑⠜⠉⠀⡀⠀⣰⠋⠸⠀⠀⢸⠏⡩⡇⠀⢸⠏⠀⠀⠀⠀⣿⠟⠃⠀⢹⣯⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠋⠀⠀⠄⠀⢻⠖⠈⠁⣤⡜⢠⠀⢠⡄⠀⣷⠛⠀⢤⠞⠈⠃⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠲⠾⡇⠀⣯⠘⠀⠀⠀⢀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠜⣾⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡄⣀⠀⠀⠊⣁⣼⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⡿⠇⠀⡀⣤⣾⢿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡦⠀⡐⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠐⢁⡐⠀⠐⠀⠐⠈⠉⠋⠉⠉⠁⠂



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⣭⣷⣶⣿⣛⣟⡻⣿⣷⣾⣭⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣾⣿⣿⣿⣿⢿⣿⣿⣧⡘⢿⣿⡏⠹⣷⣾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠻⠿⠿⣿⣯⣴⣿⣿⣿⣿⣿⣶⣮⣍⣀⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠿⠿⠧⠀⠀⠀⠀⠤⠬⠭⡙⢿⣿⣇⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⡿⢁⣤⣤⡀⢶⡀⠀⠀⢀⣤⣀⡀⠀⢿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢁⣹⣿⣿⡇⠘⠋⠀⠀⠀⠁⠀⠀⠉⠀⠈⠉⠀⢸⣿⣿⣄⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⢿⠀⠀⠀⠀⠀⢾⣇⠰⠄⢀⠀⠀⠀⠀⣾⣿⣿⣿⢾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⡇⠀⠀⢀⣤⠤⠀⠶⠦⣌⢳⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠻⢿⠿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⡾⠋⠀⠀⣸⣿⣿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣴⣞⠀⠀⣠⣿⣿⣿⣆⠀⠀⠈⣉⣉⡋⠍⠀⠀⠀⢠⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⠾⠟⠈⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣷⣤⣴⣤⣤⣤⣿⣿⣿⡟⠻⣿⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠃⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⢈⢷⣹⣿⣿⡏⠘⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠙⢿⣿⣿⣿⠟⠛⠁⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢀⣦⡸⡞⣇⢻⣿⣦⡀⠑⠺⢻⣆⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⢸⣿⢿⠟⠀⠀⣀⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣾⣿⣿⣿⣹⡜⣿⣿⣿⣷⣦⣄⡙⠳⡄⠀⠀⢀⣼⠟⠁⢀⣠⣶⣿⡿⠀⠀⠀⣼⣿⣵⠏⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣧⢻⡏⢻⣿⣿⢿⣿⣿⣷⣌⠢⣠⣞⣡⣶⣾⣿⠛⡉⡁⠀⠀⣇⣼⣿⣿⡏⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠃⠈⠋⠛⠁⠂⢻⠛⣿⣷⣽⣏⠋⠉⠁⠀⠈⠀⡐⠀⣆⣿⣿⣿⡾⠀⣤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠈⠀⠀⠐⠀⠈⠃⠈⠃⠘⠛⠀⠀⠀⠀⠀⠘⠁⠀⠛⠛⠛⠛⠁⠘⠙⠋⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠓⡄⠀⠀⠀⢀⠀⠈⢱⡀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡠⠃⠀⠀⠀⠈⠂⠰⠛⠀⠀⠀⠀⠐⢄⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⣬
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡡⣿⣁
⠀⠀⠀⠀⠀⣀⠴⠂⠇⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠠⠤⠀⠸⠁⢀⣱⡿⠙⠛⠛⠦⣀
⠀⠀⢀⡤⠎⠁⠀⠀⠀⠲⠟⠳⣶⢦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡇
⠀⠀⢸⡆⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⡄⠀⢸⡇
⠀⠀⠸⡄⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡇
⠀⠀⠀⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡊
⠀⠀⠀⢸⠗⠀⠠⢀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⡇
⠀⠀⠀⢸⡌⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⢻⡇
⠀⠀⠀⠈⢆⡀⠀⠀⠇⠀⠀⠀⠁⠁⠀⠀⠀⠑⠄⣀⠤⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢡⡏⠆⠂
⠁⠀⠀⠀⠀⠲⠗⣃⠃⢢⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡴⠖⠋
⠀⠀⠀⠐⠀⠀⠀⠈⠓⠢⢀⣉⠙⠓⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠑⠒⠄⠀⢠⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠤⠶⠶⠖⠒⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠂⢀⣀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⢉⠽⠋⠁⠀⠀⠀⠈⠙⠯⣉⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠮⠥⠤⠔⠚⠁⣀⣀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠒⠦⠤⠬⠷⢦⣀
⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⡖⠋⢉⣠⠤⠃⠀⠀⡏⢹⠀⠀⠀⠀⢀⡴⠒⡆⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⡴⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢠⠞⢁⡴⠊⠁⢀⣀⠀⠀⢸⢢⡀
⠀⠀⠀⢀⡜⢠⠃⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠦⠞⠀⠀⠈⠉⠁⠀⠀⠀⠸⡀⢣⠀⢸⡀⢳⡀
⠀⠀⠀⡜⠀⡼⠀⠀⠀⠸⠤⠤⠤⠤⠴⠁⠀⢀⣤⣤⣀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠱⡀⢣⠀⠣⣀⢣
⠀⠀⢰⢁⠞⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠏⠁⠀⠀⠉⠀⠀⠈⠳⢄⣀⣀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠻⡆
⠀⠀⡼⠃⠀⠈⢆⠘⣆⠀⠀⠀⠀⡔⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⡇⠀⠀⠀⠀⣠⠴⢄⠀⠀⢹
⠀⠀⡇⠀⠀⠀⠈⢧⣈⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡤⠊⣁⠔⠃⠀⠀⣸
⠀⠀⣧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠓⠚⠁⠀⠀⠀⡰⢻
⠀⠀⢫⢣⡀⠀⠀⠀⡰⠋⡆⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠀⠀⠀⠀⢀⡤⡀⡼⠁⡜
⠀⠀⢸⠀⢱⠀⠀⡴⠁⡜⠁⠀⠀⠣⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠁⠀⠀⠀⠀⡞⢀⠇⢧⢀⡇
⠀⠀⠀⡇⠈⡇⠈⠧⠞⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⡴⢤⡀⠀⠀⡘⢀⡞⠀⠘⣾
⠀⠀⠀⠸⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠗⠋⠉⠓⠻⠥⠊⠀⠀⠑⢄⡉⠢⡀⠈⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠹⡆⠀⡤⠤⠤⠶⠶⡄⠀⠀⠀⣠⠖⢢⠀⠀⠀⠀⠀⠀⡖⢳⠀⠀⠀⠙⠲⠋⠀⢀⡠⢴⠏
⠀⠀⠀⠀⠀⠹⡈⠓⠒⠒⠒⠚⠁⠀⣠⠚⢁⠔⠁⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡴⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠒⢤⣤⣄⣀⣀⠀⠙⠚⠁⠀⢀⠤⢤⣀⠀⠀⠀⣇⡸⠀⠀⠀⠀⠀⢰⣁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣈⠉⠓⠤⡀⠀⠈⠓⠦⣌⠙⢢⠀⠀⣀⣀⣀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠬⣳⣤⣀⠀⠀⠉⢁⣴⣋⣀⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣿⡫⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠀⠀⢸⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡏⠀⠀⠀⠀⠀⡿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣀⠀⢰⠛⢦⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠶⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠇⢀⡴⠛⠁
⠀⠀⠀⠀⠀⡏⠉⠳⣾⠀⢸⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡴⠶⠦⣄⡀⠀⠀⠸⠶⠋
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣀⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠈⣇
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⡴⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡴⠋⠀⠀⢹
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⢰⣄⣀⡸⠁⠈⠒⠀⠚⠁⠈⠑⠦⠴⠈⠳⢄⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢀⡴⠒⠒⠦⡀⠀⠀⠀⠀⠘⡆⢀⡤⠚⠛⢤⡘⡇⠀⠀⠀⠀⠸⠧⠶⠶⠒⠛⠋⠉
⡏⠀⠀⠦⠼⠂⠀⠀⠀⠢⡄⠀⠐⣦⣤⠜⠀⠀⡎⠀⣠⣤⡀⠹⠀⠀⠀⠀⠀⢹⡏⠀⣶⣶⠀⢷⡇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢁⠀⠀⠀⠀⢧⠀⠙⠿⠃⢠⠇⠀⠀⠀⠀⠈⣧⡀⠙⠋⢀⡿⡇
⢻⡀⠀⢀⠀⠀⢠⠞⠉⠀⠈⠦⠤⠎⠀⠀⠀⠀⠈⠳⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⣧⠉⠒⠒⠉⠀⢹⠀⠀⠀⠀⠠⣶⠒⠒⠲⠶⠤⢤
⠈⣧⠀⠀⠁⠀⡇⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣸
⠀⠈⢧⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠇
⠀⠀⠀⠙⢦⣀⠀⠙⠓⢲⡆⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏
⠀⠀⠀⠀⠀⠉⠛⢦⡄⢸⠇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⣯⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣄⣀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢀⣤⠤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢑⡞⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣴⠋⠀⢰⠋⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡾⢄⠀⠀⠀⢠⠞⠁
⠀⠀⢰⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠜⠀⠀⢠⠏
⠀⠀⠀⢷⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠘⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢠⡞⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠑⢄⡀⠀⢀⡴⣏⠀⠀⠈⠙⠳⢤⣄⣀⣠⡴⠟
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⣢⠞⠀⠘⡆
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣾⣁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⢀⣠⠞⠁⠀⠈⠙⠶⣄⣸⡄

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⠛⠛⠛⠉⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠘⠦⣤⣉⣉⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣀⢴⡏⠀⠀⠀⠀⠀⠈⠢⣈⠑⣆⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⣠⠞⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⡤⠞⠋⠉⠉⠓⠦⣤⣀⣀⡤⠎⠀⠀⠉⠉⠉⠀⠀⠀⠹⡆⠀⠘⣏⠛⢦⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣼⠋⠀⡏⠀⠀⣠⠖⢋⡆⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⠀⠀⠈⠣⣄⠈⣧⠀⠀⠀⠀⠀⠘⣧
⠀⣼⠇⠀⠀⢹⠀⡞⣁⡴⡋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⢶⣤⣄⣀⠀⠨⣙⠲⣄⠈⠳⣄⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢹⡆
⢸⡏⠀⠀⢀⡞⠀⠉⠁⠚⠁⠀⠀⠀⠀⠀⡇⠀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣌⠳⣌⢳⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠏⠸
⣿⠀⢀⠀⠈⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠃⡽⢠⠏
⢻⡄⠸⡆⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⢠⡖⢉⠇⠀⠀⠀⢰⣃⡼⠁⠘⡆⡰⢀
⠘⣷⠀⢷⡀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠒⠂⡄⠀⠀⠈⠙⠓⠶⠦⣤⣤⣀⣀⣀⣤⣤⠤⠶⠚⠋⠉⠀⠀⠀⢠⡏⣠⠊⠀⠀⠀⠀⠀⠀⣀⡤⠞⢱⠃⣸
⠀⠸⣧⠘⢷⡀⡞⠀⠀⠀⡞⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠃⢠⡟
⠀⠀⠘⢧⡈⢳⡹⣄⠀⣰⠇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡤⠖⢋⡽⠃⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠋⢠⡟⠁
⠀⠀⠀⠈⠻⣆⠙⢮⡉⠁⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠻⠴⠚⠁⠀⠀⠀⠀⠀⠘⠳⠦⠤⠌⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣸⠇⢀⡾⠃⣴⠏
⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠉⠉⠒⠶⠞⢋⡴⢛⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠦⣤⣤⠞⠉⠹⡄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⢚⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡼⠁⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⠤⠴⠶⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠛⠻⢶⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠟⠉⠀⡀⠀⠀⠀⠀⠙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠈⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⢄⣀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣾⣷⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣛⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠔⣫⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣵⣾⣷⡄⠘⣿⣿⡟⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣛⣉⣡⣤⣿⣇⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢸⣛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠿⠿⣧⡀⠀⠀⠀⣰⣿⣶⣀⣴⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣋⣥⣶⣶⣶⣿⣿⣿⣿⣷⣶⣾⠿⣿⢫⣾⣿⠏⣴⣿⣶⠶
⠀⠀⠀⠀⠀⠀⢀⣴⣤⣝⠻⣿⣿⣿⡿⠿⠛⣛⣛⣛⣉⣉⣭⣴⣿⣷⣿⣿⠏⣼⣿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣷⣬⠻⣯⣽⣿⣿⣿⣿⣿⣿⣿⠟⢛⣛⣛⣩⣥⡾⣿⣿⣿⡿⢛⣉
⠀⠀⠀⠀⣰⣿⣶⣬⡙⢿⣿⣿⣷⣜⣿⣋⣉⣉⣭⣭⣭⣴⣿⣿⣿⣿⣿⣿⣷⣶⠦⣨⣴⢿⣿⣿⡆⡀
⠀⠀⢀⣈⡛⠻⢿⣿⣿⣶⣍⠻⣿⣿⣾⣿⣿⣿⣿⣿⡿⢛⣩⣭⣭⣥⣶⣦⣽⣶⣿⣿⡏⣾⣿⡿⢰⣿⡄
⠀⢠⣿⣿⣿⣷⣦⣌⡻⢿⣿⠷⣼⣯⣷⣶⣶⣶⣶⣶⣾⣿⡿⠿⣿⣛⣭⣽⣽⡿⠟⣉⣴⣿⣿⢃⣿⣿⠇
⢀⣛⣛⠛⠛⢿⣿⣿⣿⣶⣿⢰⣿⣿⣴⣾⡟⣿⣿⣷⡹⣿⣷⣌⠉⠉⠉⠛⠛⠻⢿⣿⣿⡿⢫⣾⣿⡿
⣿⠿⢛⣛⣩⡽⣩⠃⣿⣿⣿⠈⣿⣿⣧⣿⣷⢸⣿⣿⣷⡙⣿⣿⣆⠀⠀⠀⠀⠀⢀⣬⠛⠶⠿⠿⠛⠁
⣤⣾⣿⣿⢟⣼⣿⢠⣿⣿⣿⢰⣿⡏⢿⣿⣿⣆⢻⣿⣿⣷⠸⠿⠛⠀⠀⠀⠀⠓⠀⠁
⣿⣿⠟⣡⣿⣿⡟⣸⣿⣿⣫⣾⣿⣷⠸⣿⡿⠿⠀⠋⠉⠁
⠟⢡⣾⣿⡿⢏⣴⣿⣿⠇⠻⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢠⡈⠳⣄⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⠂⣠⡞⠁
⠀⠀⠀⠀⠱⣄⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡞⠉
⠀⠀⠀⠀⠀⠈⢡⠊⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⠷⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢿⣦⠀⠀⠀⠀⠀⢸⠃⡀⠀⢀⡀⢿⡄⠀⠀⠀⠀⣠⡾⠋⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠹⣷⡀⠀⠀⠠⢾⠀⠁⠂⠈⠁⣸⢧⠀⠀⣴⡾⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠈⠻⢦⡀⠀⢻⡄⠺⣯⡗⢀⡿⠃⢀⣾⠟⠀⠀⣠⠞⣠⣴⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠙⢦⡀⢻⠦⣤⡴⣿⣠⣴⡿⠋⠀⣠⣾⢫⡞⡀⠀⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⠀⠀⠈⢷⡈⢰⣦⣴⠛⠛⠁⠀⢀⣾⠛⠁⢸⠀⣉⣁⡀⠀⢙⠆⠀⢤⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠁⠈⠀⠉⠀⠀⠀⢀⡾⠁⠀⠀⠸⣆⠻⠾⢁⢠⡋⠀⠀⡂⢿⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠈⢓⡖⠉⠸⣀⠀⠀⢹⡄⠀⡼⠁
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣆⣤⣶⣋⢳⣤⡾⠉⠳⣶⠟⠀⡸⠁
⠀⠘⡕⢦⣄⣏⢳⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣻⣿⢋⠀⠀⠀⠙⢿⣿⠀⠤⠤⠄⠒⠒⣲⡾⠁⠀⣼⠃
⠀⠀⠙⣦⡈⠁⠘⣇⡀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣼⣿⡇⢠⡄⡄⢠⡦⠸⣿⣿⡆⢒⣛⣛⣻⠏⠀⢀⡾⠃
⠀⠀⠀⠈⠙⠶⣤⡈⠛⠷⣤⣄⡀⠀⠀⢿⣇⠀⠀⠀⣿⣿⡇⠈⠁⠀⠀⠀⠀⢻⣿⡏⣉⣁⣼⠏⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⠷⣦⣸⣿⠲⢤⣀⣙⢿⣿⡀⢿⣥⣽⠃⣰⣿⠟⢀⣠⡿⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠙⠿⣧⣤⣀⣀⠀⠉⠳⣄⣉⣡⢴⡏⠀⣴⣿⡋⠙⢦⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⡿⠙⢻⣿⣷⣦⣼⠉⠁⢘⣧⣾⣿⣿⣿⣦⡾⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢧⣠⣿⣿⣿⣿⡏⠛⣶⠛⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠉⠻⣿⣿⣿⣷⣾⣿⣷⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⣉⠝⠉⠀⠀⠀⠀⠈⠛⢭⡉⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠮⠥⠒⠒⠊⣁⣠⢤⡀⠀⠀⣀⡀⠀⠀⠈⠑⠒⠒⠒⠛⠶⢤⡀
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢞⣉⡠⠤⠖⠁⠀⢸⠀⡇⠀⠀⠀⣀⠴⠊⡧⠀⠀⠀⠘⣆
⠀⠀⠀⠀⣠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣞⣡⠔⠋⠀⢠⠤⡀⠀⢋⢳⡀
⠀⠀⠀⣰⠃⡸⠀⠀⠀⡤⠤⠤⠔⠲⡄⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠱⡄⠸⡀⢳⡀
⠀⠀⢠⠇⡠⠃⠀⠀⠀⠑⠒⠒⠒⠉⠀⠀⣰⠶⠖⠤⠤⠖⠶⢦⠀⠀⠀⠀⠀⠀⠘⢆⡹⠀⠑⢤⣧
⠀⠀⣼⠜⠁⢴⠓⡄⠀⠀⠀⠀⢀⣠⡤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠑⠲⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⢀⡏⠀⠀⠈⢧⠘⣆⠀⠀⠀⣎⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⡠⠞⢉⠇⠀⠀⣳
⠀⠈⡆⠀⠀⠀⠀⠓⠞⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣎⡠⠞⠁⠀⠀⣠⡇
⠀⠀⡿⡄⠀⠀⠀⠀⡠⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡀⠀⠀⠀⠀⠀⠀⡰⠁⡇
⠀⠀⢳⠘⡄⠀⠀⡼⢁⡞⠀⠀⢾⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠞⠀⠀⠀⠀⡴⢉⠆⡇⢰⠃
⠀⠀⠸⡄⢸⠀⢸⣠⠎⠀⠀⠀⠀⠉⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⣀⠀⠀⠀⣰⠁⡜⠀⢣⡼
⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣲⠤⠖⠒⠤⣖⡩⠃⠀⠳⣄⠑⢤⡀⠑⠚⠀⠀⢘⠇
⠀⠀⠀⠈⢿⠀⢀⣀⣤⡤⠤⡄⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠑⠤⠗⠀⠀⣀⣤⠎
⠀⠀⠀⠀⠈⢇⠘⠤⠴⠶⠒⠊⠀⢀⠔⢁⡴⠋⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⡰⠋⣠⠋
⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⡀⠀⠙⠖⠉⠀⢀⠤⣄⡀⠀⠀⢸⣀⠇⠀⠀⠀⠀⢠⢃⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣈⠉⠒⢤⡀⠀⠈⠲⢤⣉⠓⡄⠀⢀⣀⣀⣀⣀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠬⢷⣤⣀⠀⠈⠉⣡⣞⣁⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⢀⢠⡶⠀⢰⡎⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⢠⣶⡛⢿⣿⣟⠿⡄⠀⠀⠀⠀⠀⠠⠒⠛⠉⡉⠙⠛⠷⠄
⠀⠀⠀⡔⢡⠟⠐⠱⠏⢠⠞⡀⠙⡄⠀⠀⠀⠄⠐⠀⠀⠀⠁⠀⠄⠀⠀⢠⣟⡻⢿⣷⣮⡛⠿⣷⣝⠦⡄⠀⣴⠁⠈⠀⠀⠁⢤⣌⠁⠀⢠
⠀⠀⢰⣥⠏⠀⣀⠀⠀⠀⠞⣵⠃⡇⠀⠀⠀⢀⠠⠀⠀⠀⡀⢀⠀⠀⠀⢹⢿⣿⣶⡏⠀⠀⢐⣮⣝⢿⡇⠀⡇⠀⠆⢸⠁⠀⠀⣻⠀⠀⢸⡄
⠀⠀⠘⣏⠀⣰⣫⡶⢠⠎⣼⡳⠃⠀⠀⢆⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠘⣷⣬⡛⢷⣦⣤⣌⡻⢿⣿⠇⠀⢷⡄⠀⠀⠳⠤⠶⠇
⠀⠀⠀⠘⠶⣇⡟⢡⠏⠼⢿⠃⠀⠀⠀⠈⠳⣄⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⣙⣻⠿⡢⠀⠀⠀⠈⠣⠒⠀⠈⠀⠀⠀⣁⠄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⣤⠶⠋⠀⠀⠉⠳⣦⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣠⠖⢁⠀⠀⠈⠐⢤⡀⠀⠀⠀⡠⠐⠉⠀⠀⠀⡙⠂⢄
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣰⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⠀⠀⣼⠃⠠⠀⠀⠀⠀⠈⠀⠹⡄⠀⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⣆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠆⠀⠀⣼⠀⣿⠿⣿⣿⡏⠀⠈⣿⢛⣿⣿⡇⠸⠁⠀⠀⢰⠀⠀⢠⠀⠐⠀⢀⢀⡀⠀⠀⠈⠀⠀⢙⡄⠀⠀⢸
⠀⠀⠸⠀⠀⠀⠀⠢⠴⠞⠀⠀⠀⡹⠀⠻⠁⣿⠘⡷⠀⠀⢿⡌⠃⣿⠇⠀⡄⠀⠀⠘⠦⠠⠋⠀⠀⢀⡞⠸⡇⠀⠠⠀⠐⠒⠊⠀⠀⠀⠾
⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠘⢶⣄⠀⠐⠀⠀⠀⣠⠞⠁⠀⠙⢤⡀⠁
⠀⠀⠀⠀⠈⠙⠛⠦⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠙⠛⠲⠀⠀⠊⠁⠀⠀⠀⠀⠀⠉⠒⠒⠶⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡠⠄⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡠⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠁⢀⣞⢃⡀⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠤⣿⠗⣾⣓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠛⠋⠁⠀⣰⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢏⣼⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡀⣠⢀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⡶⣣⣇⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣿⣼⣿⣶⣤⣄⡀⢠⢻⣿⡇⡶⣥⡿⠤⣤⣆
⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣶⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣶⣿⣹⣷⠿⢤⣀⡞⣱⡆
⢾⣿⣶⣶⣶⣿⣿⣷⡸⣿⡿⠿⠿⣿⣿⣿⣷⣶⡾⢧⣢⣎⣐⢉⠛⢿⣿⣿⣿⠛⢦⣤⣋⣽⢋⠀⠇⠄
⠀⠛⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣏⠀⢸⣿⣿⣿⣿⣶⡇⢸⠛⣎⣲⣾⣡⡟⢿⡀
⠀⠀⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣾⣻⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣻⡟⣻⡏⣽⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠻⠦⠽⠥⠯⠥⠜⠁