Sugar maple Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠢⠤⠂⠀⠀⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠄⠀⡀⠂⠀⠘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠦⣴⠀⠀⠙⠀⢰⠗⠈⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠂⠀⠁⠚⠀⠀⠀⠨⣧⡄⠀⢣⡈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠂⠈⡀⠀⠀⠀⣿⡆⢀⢉⠀⠀⠀⠁⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠉⠀⣤⠀⢸⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠞⠂⢸⠧⠄⠁⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡓⠂⠀⠀⠑⠊⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠄⠀⠰⠀⠄⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠢⣄⣀⣀⣀⣀⠀⠀⠀⠀⢸⡇⢢⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠄⣀⠀⠈⠙⠲⢄⡀⣨⠇⠀⠓⢤⡙⢆⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠙⢆⠀⠀⠀⠉⠁⠀⠀⠀⠂⠹⢄⣱⣄⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠣⡀⠀⠀⠈⠢⡀⠀⠀⠐⢄⠀⠀⠀⠀⣀⡙⣼⣆⢀⣴⡿⠃
⠀⣤⡤⠴⠚⣉⣀⣢⡄⣀⠠⠤⠤⠵⠦⢤⠤⠤⠬⠦⢤⠤⠤⠵⠤⢤⠤⠤⠤⠤⡏⢩⡯⣀
⠀⠈⠑⠲⢤⣉⡀⠀⠔⠀⠀⠀⠀⢀⠔⠁⠀⠀⡠⠊⠁⠀⠀⡠⠔⠁⣀⡀⣠⡞⢩⡏⠣⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠈⠉⠙⢦⠀⠀⠠⠒⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠊⠁⡠⠞⠁⡇⢸⡇⠀⠹⢄⠀⠳⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠲⠶⠶⢶⡄⠀⣀⡠⠤⠤⠤⠤⢄⡠⢾⠁⠀⠸⠁⢸⠑⢄⠈⠀⠑⠢⣤⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠁⠀⠀⠀⢀⡔⠁⠀⠸⠀⠀⡠⠔⠉⡀⠈⠃⠀⠀⠀⠀⠈⠂⠙⠲⡄
⠀⠀⠀⠀⠀⠀⣤⠴⠒⠚⠉⠁⠀⠀⢀⣀⠠⠤⠄⣀⠔⡋⠀⠀⢀⠇⠀⠊⠀⠀⠀⡁⢄⠀⠀⠀⡖⠚⠓⠒⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠒⠉⠁⠀⢀⡠⠊⠁⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠈⢆⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠤⠤⢤⡤⠚⠁⡇⠀⠀⠀⡇⠀⢀⣤⠀⠀⠀⢀⡠⢴⠀⠀⠀⠣⣄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⢴⠁⠀⠀⠠⠃⠀⠀⠀⣠⠞⠁⠘⡇⠀⡐⠁⠀⢸⢀⠀⠀⠀⠈⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠔⠁⡌⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡇⡰⠀⠀⠀⣸⠀⠑⡄⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢁⣤⣤⡤⠖⠋⠙⠲⢤⣀⡞⠀⠀⠀⠀⠸⡇⠀⠀⢠⠊⢸⠀⠀⠰⠀⠀⣀⣀⣀⠈⢦
⠀⠀⠀⠀⠀⠀⢠⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠁⠀⡞⢢⠀⠀⢠⠏⠁⠀⠉⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡔⡇⠀⠆⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠃⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⢷⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣴⣧⣠⠤⠖⢩⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢹⠀⠉⠙⠉⣏⠀⠀⢀⡤⠀⠀⠀⣸⣷⣀⣠⣴⢾⢿⡿⠟⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣼⠟⠆⠀⢸⠀⠀⠀⠀⢿⣀⡴⣿⠁⠀⠀⢠⡿⣿⢹⠁⠀⠀⡾⠀⠀⠀⠀⠀⠀⠹⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⣿⠀⠀⢠⣿⢧⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠈⠿⡄⠀⠀⣇⡞⠀⠀⠀⠀⠀⢸⡆⢠⣿⢻⢸⡇⠀⠀⠀⢸⡅⠀⢀⣀⠄⠊⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡄⠀⠀⣧⣾⠋⠈⠘⡇⠀⠀⢠⠞⠒⠋⠉⠀⠀⠠⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⡀⠀⠀⠈⣇⠀⠀⠀⡼⠀⠀⠀⢿⡿⠀⠀⠀⢳⣀⠔⠁⠀⠀⠀⠀⠀⠠⢖⣻⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠢⣀⠀⢹⠀⠀⡰⠁⠀⠀⠀⠘⠁⠀⠀⢀⣼⣋⢀⡀⠀⠀⠀⠀⢔⡾⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⣾⠇⠀⠀⠀⠀⠙⠺⣇⡰⠁⠀⠀⠀⡀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠘⢶⡶⠞⠋⠀⠉⠛⠋⠀⠀⠀⢠⠀⠀⠀⢿⠀⠀⠀⠀⡴⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣋⣁⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⢷⡄⠐⢤⡀⠀⠀⠀⢆⠀⠀⠳⣷⣦⢸⠀⠀⠀⣼⠁⢀⡞⣁⡤⠄⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠁⢀⠀⠀⠛⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠈⠳⢤⡀⠈⠇⠀⠀⠉⠻⣷⡇⠀⢸⡇⣰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠻⢶⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠭⠷⣼⣀⠠⣄⠀⠈⢻⡄⣾⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠔⠚⠉⠁⢀⣹⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠉⠩⠵⢿⠿⠶⢿⣦⣬⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣥⣤⠤⠄⠀⠀⠐⠒⠒⠒⠒⠛⢛⣻⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣤⣤⡴⠾⣿⣿⢿⣍⠉⠉⠉⠉⠀⠀⠉⠻⣬⣀⣀⠀⠀⠀⠈⠓⠦⠤⣀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢹⣶⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢖⣒⣂⣀⡀⠀⢀⡤⠤⢤⣤⣤⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠘⣿⣴⠀⣿⠙⠾⣏⠁⠀⠀⠀⠀⢀⣤⠤⣤⣤⣀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠹⣿⣤⠸⠀⠀⠨⠑⣦⣄⡀⠀⠸⣄⠀⠀⠀⠉⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠋⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⣀⠱⣜⢿⣮⣿⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⡼⠛⠻⢿⡿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⣫⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡴⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠈⠀⠀⠛⡄⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⢀⠀⠀⣀⠀⠘⠄⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠛⢄⠀⠀⠀⠀⠀⠀⢠⠄⠀⢀⡄⠀⠀⠀⡄⠙⡄⠀⠀⠠⠀⠀⠁⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⡝
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠰⠈⠙⠁⠀⠀⠤⠀⠀⠀⠰⠀⠀⠘⣄⡀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠎⣠⠞
⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⠀⢠⡄⠀⠀⠁⠈⠠⠀⠀⠀⠃⠀⠀⠁⠀⠀⢀⠀⡀⠄⠀⠀⠀⠀⠌⠀⠀⣀⠔⠈⠀⡰⠃
⠀⠀⠀⠀⠀⢲⡾⣷⡾⢻⠳⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡈⠀⠈⠀⠀⠀⠀⡃⠠⠐⠈⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣇⠸⡇⠆⠀⡆⠘⠳⣤⠀⠀⠀⢁⠀⠈⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠠⠤⠄⠐⠒⠒⠒⠀⠀⠂⠀⠐⠢⠉⡿⠃
⠀⠀⠀⠚⠛⢿⣶⠆⢘⡦⠇⠘⡶⠋⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠠⠂⠀⠀⡠⠀⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⢄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠁⠀⠀⠀⡌⠁⠀⠀⢐⣀⠄⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠀⠀⢸⡀⠀⠀⠀⠀⠐⢢⠇⠀⠀⠀⠀⠀⠠⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⡀⠀⠀⠐⠤⣀⠀⠀⠄⠀⠀⠘⢃⠀⠀⠀⠒⠀⡌⠀⠠⠀⠀⠀⠀⣰⡴⠎⠀⠀⠐⠂⠐⠀⠁⠐⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⠡⡢⠀⠈⠱⠄⠀⠀⠀⠤⠾⡀⠀⠀⠀⠴⠁⠀⠀⠄⠀⡰⠞⠁⠀⠀⣀⣀⠀⠄⠀⢀⡠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣩⣿⣿⠏⠻⣀⣰⡄⠂⠀⠈⠛⢦⡀⠀⠀⡇⠀⠈⠰⠇⡀⠀⡀⠤⠛⠉⠈⠀⠀⠀⠀⠀⣀⠴⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣯⠛⡻⣏⣿⠀⠀⣄⠘⣷⢂⠑⢄⠀⠀⠙⢦⠀⢰⠀⢠⡇⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⣼⠃⢸⣇⣿⣿⠀⠀⠠⢠⠙⢾⡄⠀⠑⠠⠄⠈⠱⢌⣠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⣼⡇⠀⡟⣸⠃⢸⠀⠀⠀⠦⢤⡬⣌⠁⠀⠀⠀⠁⠀⣸⠿⠟⠀⠉⠀⠉⠀⠈⠉⠉⠀⢉⡀⢀⣠⠤⠦⠗
⠀⠀⠀⠀⣴⠋⡆⢰⠀⣿⠀⢸⡆⠀⠀⠐⠀⠶⠈⢅⠀⠀⠀⣠⡞⠁⠀⠀⢀⠠⢀⠀⢀⡔⠓⠃⠘⠋⠈⠀⡇
⠀⠀⠀⢰⡏⠀⣷⢸⠀⣏⡄⠘⡇⠀⠀⠀⠀⠀⠁⠈⠀⠀⡴⠋⠀⠀⠀⠀⠘⠦⠀⠐⠃⠀⠀⠀⠾⠀⡀⠀⡇⠀⠀⠀⠀⠠⠈⠰⢀⠀⡀⠀⠀⢠⣴⠆
⠀⠀⠀⣼⠁⠀⣿⢸⠀⡇⣇⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠜⠁
⠀⠀⠀⣿⠀⠀⣿⢸⠀⡇⢹⡀⢸⡇⠀⠀⠀⠀⠀⢀⣾⣧⣤⣀⡀⠀⠀⠀⢘⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠠⠴⠂⠁⢠⡎
⠀⠀⠀⣿⠀⠀⢺⢸⡄⢡⠈⡇⠘⠓⠀⠀⠀⠀⠀⣾⢻⡟⣿⣥⡉⢶⠀⠀⠸⡇⠀⠀⠀⡘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⣿⠀⠀⢻⠈⡇⢸⠀⢻⡐⠄⠃⠀⠀⢠⠟⡽⠀⠀⠃⠈⣧⠀⠀⠀⠀⠇⠀⠀⡜⠁⠀⠀⠀⠀⠂⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠁
⠀⠀⠀⣿⠀⠀⠈⢀⣟⠀⣀⠌⠳⠀⠀⠀⢠⡎⠀⢹⡆⣷⠀⠀⠹⡄⠀⠀⠀⡐⠀⡴⠁⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠛⠁
⠀⠀⠀⣿⠀⠀⠻⠟⢛⠉⠉⢰⣶⠆⠀⢀⡿⠀⠀⠀⢇⠈⠀⠀⠀⢷⡀⠀⠀⢁⣘⠁⠄⠒⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡐⠉⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⢸⣆⠀⠀⠀⠀⠛⠤⠿⣿⠉⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠷⠾⠃⠀⠀⠀⠘⠓⡀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠈⠉⠉⠙⠋⠁⠀⠀⠤⢀⣀⡀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⡀⠀⠀⠠⠆⢤⣄⠀⠀⠀⠀⠠⠶⠴⠒⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣤⠶⠶⢦⣤⡀⠀⠁⠂⠀⠀⠀⠈⠢⡄⠀⠀⠀⡆⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣧⣀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢠⣦⣀⡀⠀⠉⣒⣄⣀⠀⠀⠀⠀⠁⠌⢀⠀⣀⣰⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠁⠀⣼⡄⠉⠻⢷⡄⠀⠀⠀⠀⠀⣇⠀⢠⡏⠉⠙⠓⠋⠉⠉⠉⠻⡦⠀⠀⠀⣀⠼⠉⠉⠩⣯⠉⠙⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⢀⡼⠃⠘⢂⠀⠀⠙⢄⠀⠀⠀⠀⢻⠀⠞⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠟⠀⠸⠃⢀⣠⣴⠟⠈⠻⣦⣤⣀⡉⠂
⠀⠀⠀⠀⠀⣠⠖⠀⠉⠛⠀⠀⠀⠀⠀⠋⠐⠶⢬⣥⣄⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢠⡇⠔⢋⡙⠋⠀⠀⠀⠀⠀⢁⠈⠉⠉⠳⣄
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⡄⠀⠀⠙⣧⠀⠀⠀⡎⠀⠀⠀⢠⠀⠀⠀⠀⢰⠞⠁⢀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠱
⠀⠀⢠⡟⠀⠀⠀⠀⠄⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⡄
⠀⠀⡜⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⠀⡀⠀⠀⠴⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣷
⠀⠀⢇⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠙⠀⢀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⢱⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠠⡇⠀⠂⠀⠀⠀⠈⠃⠔⠀⠠⡔⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⢠⠀⠀⠀⠀⠀⠐⡀⠀⢠⠔⠁⠀⢈⠜⠏⠀⢀
⠀⠀⠀⠀⠀⠐⠢⡀⠁⠀⠈⠀⡀⠈⠠⠀⠀⠐⠄⠸⢀⠄⠈⠀⠘⠀⡀⠿⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡁⠈⠃⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⡡⢁⠊⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡁⠀⠀⠀⠈⢀⣂⠔⠁⠀⠓⠁⠀⠀⣀⠀⠀⡐⠢⢤⡤⠄
⠀⠀⠀⠀⠀⠰⠄⣀⣀⣀⠀⠈⠀⠱⡄⠀⠀⠂⠘⠁⠀⠀⠀⠀⢀⣀⠀⠁⢀⠠⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠐⠢⠀⡱⣐⠀⠄⠿⢀⠔⢀⡤⠴⠉⠀⠂⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡠⠳⢌⢆⠐⠎⣠⠔⣋⣀⣤⡄⡀⠠⠦⣄⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢱⣶⡾⠃⠉⠁⠀⠂⠀⡀⢀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢂⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡗⢺⢣⠏⣠⡀⣀⢠⣠⢏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠀⠀⠈⠈⠀⢡⠏⠉⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⢆⢀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣷⣶⠘⢛⣵⡄⠀⠀⠀⠀⠀⠀⠐⣍⢀⠈⠒⠀⡎⡰
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣮⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠄⢀⣀⣨⣿⠿⡿⠚⠏⠱⡤⠀⠀⠀⠀⠀⠐⠚⠁⠷⣄⢼⡗⡓⢤⠆
⠀⠀⠀⠀⠀⣼⣿⢿⣿⣼⣏⣿⣿⣻⠟⢻⡆⠀⠀⠀⠀⠖⠒⣏⢻⣿⣓⠀⠀⡤⣤⣶⣿⠆⠀⠀⠀⠉⢷⣀⣐⣱⢿⣿⠏⠒
⠀⠀⠀⠀⢀⣿⣿⣿⢿⣿⣿⣿⣿⣽⣷⣄⡀⠀⠀⠀⠀⠀⠞⠛⢃⣨⣷⡶⠉⠁⣉⠛⢿⣆⠀⠀⠀⠀⠀⠀⢸⡶⠬⠆⠀⠁
⠀⠀⠀⠀⢸⣿⣟⠻⣷⡹⣟⡿⣿⡻⣻⣿⣶⡄⠀⠀⠶⢒⣤⡤⣤⠋⣉⣲⣲⠞⠟⣲⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⡸⣿⣿⣿⣽⣷⣿⡟⣿⣿⣿⣿⣻⣟⠀⠀⢰⡟⢿⠿⣉⠉⣿⣿⡿⢧⣄⢀⡈⣻⡇⠀⠀⠀⠀⠀⠀⢀⣏⠢⣠⢫⡜⠀⠅
⠀⠀⠀⠀⣱⣿⠿⣿⡝⡘⣿⣾⣿⣿⣿⣿⣿⡤⠀⠀⠀⢱⣾⣶⡛⣿⣿⡋⣁⡀⣻⣟⣻⣿⠃⠀⠀⠀⡀⠀⠀⠀⢯⣤⣠⠏⠐⠕⠀⠄
⠀⠀⠀⠀⢿⡿⠾⣀⡍⡿⣿⣿⢫⡥⠶⠿⣾⠇⠀⠀⠙⢉⣵⣾⣿⢋⡈⢩⣟⣿⠉⠋⢁⣤⡇⠀⢀⣸⡏⠰⠪⠀⠛⠿⢿⡀⢤⡄
⠀⠀⠀⠀⠀⠙⠓⠀⠉⠙⢿⣯⡼⠃⠁⠀⠉⠀⠀⠀⠈⠻⡯⣁⠿⠟⢿⢻⡹⠇⣴⣿⠟⠛⠁⠀⠘⢯⢱⣤⡠⠆⠀⡜⣤⣿⡏⣧⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢣⢀⣎⠤⢿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠈⠋⠉⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠂⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣁⡤⠀⠀⠀⣀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢀⣌⠉⠓⠒⣾⣿⣇⣀⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⢟⡧⣤⣟⣾⠳⡿⠸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠂⠈⠀⠉⠻⠙⠛⢻⣿⣷⣶⣴⣀⠒⠁⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⣶⣲⣄⣀⡠⠂⠀⠀⠛⢚⡵⠝⠉⣿⠛⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣽⠛⠀⠹⠒⣄⡀⢸⣏⠉⠘⣄⣿⡇⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠟⠏⠀⢀⣤⣀⠀⠀⠘⠻⣼⢹⢦⠄⠂⠀⠘⠚⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⣠⣶⠚⠿⠿⢄⡢⠴⠓⠉⠉⠣⣄⣀⡠⣄⣴⠓⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⡁⠋⠉⠃⠀⠀⠀⢿⣾⣿⣿⠶⠄⠙⠣⠤⢃⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣏⣀⣀⣀⣠⣠⣤⠒⢻⡚⢋⣿⣇⢀⣀⡐⠿⠉⠃⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡿⢻⢿⡁⠀⠀⠈⠉⢛⣻⡟⣿⡻⣳⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⢫⠾⡷⠷⣤⣴⣶⠢⠼⠟⠳⣯⣶⡞⡉⡉⢻⣇⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢙⢦⣞⠀⠀⠂⢀⠠⣿⡙⢧⡄⢀⣀⡉⣟⢿⣿⣷⣄⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠽⠿⣿⢇⡄⠠⣽⡷⢛⡟⣿⡿⣿⣿⡍⠽⢚⢟⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠙⢼⠃⠏⠀⠀⠀⠈⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⢈⣱⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⡀⠄⢷⠄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣽⣋⠟⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣿⣿⣨⣡⣶⡆⠀⠀⠀⠀⠀⠀⠱⡄⣄⠈⢀⡎⡜
⠀⠀⠀⠀⠀⣰⣿⣿⡟⣿⢿⣾⣿⣿⣧⠀⠀⠀⠀⠀⢈⣀⣴⣶⣾⠛⠛⠉⠁⢚⣆⡀⠀⠀⠠⢤⡉⠁⣈⢣⣼⣏⢉⠘⠁
⠀⠀⠀⠀⢰⣿⣫⣳⣷⣿⣿⣾⣟⣅⠹⠂⠀⠀⠀⠀⢁⣽⡢⠛⣤⢀⡠⠗⠿⣿⣷⠁⠀⠀⠀⠈⠳⠒⡖⡛⡟⠛⠅
⠀⠀⠀⠀⣼⣟⣿⣯⡿⣿⣿⣿⣿⢿⣷⡂⠀⠀⢀⡀⣌⠀⠀⠲⠿⢏⣀⣠⣶⢀⣙⣷⠀⠀⠀⠀⠀⠐⠋⠁⠁⠀⠀⠀⢀
⠀⠀⠀⠀⣿⣿⣷⣽⣧⣻⣿⣟⣬⡞⣉⠽⡇⠀⠀⢀⣼⣽⠟⠃⢶⣾⣾⡁⠀⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⢴⢀⠀⠔⡺⠉⡄
⠀⠀⠀⠀⣷⣿⣿⡿⠋⣿⣧⡿⣪⣾⣿⣦⡁⠀⠀⠙⣠⣌⡵⣶⣾⡗⠋⠈⢛⡶⣷⣾⠃⠀⠀⠀⠀⠀⠀⣻⣂⠋⡞⢡⠀⢀⡀
⠀⠀⠀⠀⣿⣯⣌⠙⢺⣾⣿⠟⣋⣭⣿⣿⠇⠀⠀⠒⢛⣭⣿⠿⠉⠓⣿⣷⠛⠟⢋⣹⠄⠀⠀⣾⠂⡴⠀⠺⢿⣿⡀⢀⠀⠈
⠀⠀⠀⠀⠉⠒⠂⠙⠛⢻⣿⣰⠇⠒⠂⠋⠀⠀⠀⠐⢿⣛⡹⠿⢿⢺⣻⠇⣠⣶⠻⠟⠀⠀⠻⡉⣆⡀⡤⠀⡰⣤⣳⡞⣃⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⠀⣘⡁⢿⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠈⠁⠉⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣝⣫⣍⣹⣝⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⡀⡀⠀⠀⠐⢼⡆⠀⡶⡄⠀⢀⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠇⠘⠃⢸⣦⣼⠂⠘⢻⣯⡄⠘⠂⣸⡇⣰⣿⣃⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠄⠀⠀⠀⠐⠀⡙⣿⣿⣿⡄⠀⣽⣇⠝⠓⣿⣿⣿⣿⣿⣿⣦⠟⠁
⠀⠀⠀⠀⠀⣠⣄⡀⠀⠤⢀⣀⠀⠀⠀⠀⠀⣁⡿⢻⠯⣁⣰⢿⠓⠰⣿⣻⣿⣿⣿⣿⣿⣷⡿⣂⣀⣀⡰
⠀⠀⠀⠀⠐⣿⣿⠟⠶⠜⢿⠃⠀⡀⠀⠀⣀⣶⡊⠀⠀⠤⠘⠋⠀⠩⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣹⣾⣶⣦⡄
⠀⠀⠀⡄⢀⢸⣿⣶⠀⣦⣠⣾⣿⣿⣆⠔⠻⠻⠟⢀⡀⣠⣶⡀⠀⠀⠀⢠⣴⣿⣿⠿⠿⠻⣿⣿⣿⣿⣟⣟⡃
⠀⠀⠈⢗⡊⠛⢻⡏⢙⡓⣿⣿⣿⠻⠓⠀⠀⠒⠀⢀⠘⠁⠀⠁⠠⣠⡀⣠⣼⣟⣙⠶⠛⠓⣏⡰⡾⢷⢿⣿⣦
⠀⠀⠀⢘⣷⣿⣿⣿⠿⠉⠀⠀⠁⠂⢤⠠⣮⣿⣷⣦⡌⠈⣢⠀⠀⣩⣯⣿⣽⣿⣿⣿⣟⣩⡀⣰⣶⣾⣷⣿⡛
⠀⠀⠀⠀⠤⠖⢉⡙⠂⠀⠀⡀⢀⣶⣀⢀⣉⠫⣍⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⣿⣏⡉⣥⣼⣿⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠍⢀⠘⣴⢴⣿⣾⡟⠻⢋⣉⣰⣾⣿⣿⣿⣿⣿⣿⢿⣿⠟⢿⡿⠾⠛⣙⣽⣿⣿⡾⣿⣿⣿⣿⠁
⠀⠀⠘⢛⢻⣿⣇⣰⡤⠖⠛⠋⠀⠠⣠⣿⡿⠟⠛⠻⡿⠿⡿⢋⠘⢦⣭⡾⠶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⣅⢄⢀⡈⢣⠀⠰⣶⡂⠹⠁⠉⠁⠀⢀⣘⣤⣄⣶⡷⣄⡐⡻⣖⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⣯⡅⣈⠁⠀⠀⡉⠀⠀⣤⢀⠣⢼⣿⣿⣿⣿⣷⣶⣶⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⣠⢾⣿⠟⠁⠷⠠⣾⣾⣦⣏⣸⣿⣾⡏⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠏
⠀⠀⠀⠀⠁⠘⢁⣴⣆⠙⢻⣿⣿⣿⣿⡿⢿⡟⠹⠇⠈⢿⣿⡏⣼⠛⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⠻⡃
⠀⠀⠀⠀⠀⢰⣾⢿⠟⠱⣾⣿⣿⠟⠿⠀⠈⠁⣀⡀⠐⢸⣿⡇⠀⠀⠁⠀⠁⠀⠋⠀⠉⢿⡏⠁
⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠈⢸⠋⠀⠀⠀⠀⠈⠉⠀⠈⢸⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢸⣿⣇⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⡶⣦⣽⣆⣳⣤⣿⡞⣸⣿⣯⣥⣗⣶⣶⣘⣮⣷⣦⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣁⣙⣉⣛⣙⣙⣋⣋⢻⣿⣿⣿⣿⣯⣛⣻⡛⣛⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⡿⣿⣿⣅⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠉⠉⠉⠁⠙⠉⠩⠿⠋⣢⠙⠿⣿⣭⣧⠭⡭⠭⠭⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣀⣐⣀⡀⠀⠀⢂⠀⠁⠐⠚⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠀⠉⠈⠉⠛⠛⠻⠹⠏⠽⠛⠀⠀⠀⣀⠈⣕⡸⠀⢦⣠⣦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠆⠀⠰⢿⡴⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡤⠀⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⠛⠀⠀⠀⠀⢀⣀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⡄⠀⠀⠈⠙⠋⠈⠁⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⡇⡆⠀⠀⠀⠀⠀⡄⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢭⠧⣈⣀⣨⠤⠥⠤⢟⣀⣠⣤⠄⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠩⠋⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣀⣤⣄⣀⣤⣤⣄⣠⡀⣳⡶⠞⠛⠲⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣉⣏⢀⣀⢀⣉⡈⠭⣿⣿⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⢀⡞⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⠞⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡠⠂⠁⣀⡤⠔⠲⠖⠶⠢⡤⣄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠀⠀⠊⠀⡴⢛⣧⡶⠞⢃⠐⠉⠃⠄⡈⠓⣄⠀⠀⠀⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⠈⠀⢠⡞⠁⢪⡟⠀⠐⣵⠶⡄⢀⠄⠁⡀⠘⢷⡄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⠀⢠⡟⢀⡴⢃⠀⠀⣰⠃⠀⠉⣠⡄⠀⠀⢂⠈⣶⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⣴⢠⡄⣀⢀⣾⡗⠋⠀⢀⠀⢈⠷⣈⣀⣤⣔⣸⡇⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⣿⣿⡇⠀⠉⠙⠷⠀⠀⠋⠀⠘⠛⠉⠀⣸⡟⣭⢿⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠈⠀⡿⠉⣿⠀⠀⣤⠀⠀⠰⡄⠀⠀⡄⠀⠀⣼⠃⣥⡾⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠠⠀⠀⠀⢿⠠⣾⠃⠀⠀⠀⠀⢀⡄⠀⠈⠁⠀⣺⡿⠊⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⣀⠋⠛⢻⠄⠀⠀⣸⡇⠀⠀⠀⠻⣿⠁⢠⣻⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠧⠀⠰⣧⣴⡴⠶⢿⣿⠶⠶⠲⠞⡋⢀⣀⣾⠟⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠸⣄⠐⠈⠠⠀⠤⠘⠿⠀⠀⠂⠀⠀⣿⢡⡟⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠀⠀⠀⢻⠤⢚⠤⠴⠶⠶⠶⠒⠒⠛⠋⠠⠟⡿⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠰⡀⠈⢧⣤⠐⠶⠢⡄⠀⠐⠄⡠⠘⢡⣼⠃⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⠀⠀⠁⢀⠈⠛⠲⠷⠦⢿⣼⠧⠴⠷⠾⠞⠁⠀⠀⢀⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠳⣦⣄⢀⡀⠀⠀⠀⢀⠀⡀⠀⣠⠄⢀⣾⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣀⣀⣤⡤⠀⡤⠄⠀⠀⠤⠀⢠⣤⣤⣀⣉⡛⠛⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢏⣛⠛⠛⠻⠷⢤⣠⣤⣄⣀⣠⣮⣵⡿⠿⠟⣋⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠉



⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣆⠙⢦⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣆⠀⠙⠶⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡿⠀⠀⠀⠘⡆⠀⠀⠀⠸⠧⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢀⡀⠀⠀⠀⠸⡄⠀⡇⠀⠀⢸⡇⠀⠀⠀⣰⠻⢦⡴⠞⢡⠏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠉⠳⣄⡀⠀⢹⡄⡇⠀⠀⠀⢷⠀⢀⡴⠃⠀⠀⠀⢀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠙⢦⡀⢻⡇⠀⠀⠀⠈⠛⠋⠁⠀⢸⡀⠀⡼⠁⠀⠘⠓⠒⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠙⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠃⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠶⠦⣄⣴⢦⣄⠀⢸⡆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⠂⠀⠀⢸⣷⠃⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⢯⡉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⠏⠀⠀⠀⡼⢃⣠⠴⠒⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢷⣠⠏⠀⠀⢀⣼⠗⠋⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⠙⠲⠤⣀⡀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⢧⡀⠘⣏⠀⠀⠀⡾⠁⠀⠀⠀⠀⠸⣧⣀⣠⠤⠴⠖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢤⣽⣦⡀⠀⠀⠀⠀⠀⠙⢦⣽⡀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠳⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠛⠒⠦⣤⣀⡀⠀⠀⠙⣇⡼⠁⠀⠀⢀⣠⣴⣶⣋⡤⠤⠴⠒⠒⠚⠋⣩⡽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⣿⣧⡴⠖⠛⠋⠉⠉⠀⠀⠀⠀⣀⣀⡀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⡴⣻⠟⣿⣝⠳⢦⣄⠀⠀⠀⢠⠞⠉⠁⠀⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠋⠉⠉⠙⠒⢦⡀⠀⠀⠀⠀⠉⢉⡿⠋⢠⠏⢠⠻⣏⠳⣄⠈⠙⠦⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⡴⠋⠀⠀⡞⠀⢸⠀⣿⡀⠘⣦⡞⠒⠲⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⢀⡴⠋⢀⡀⠀⢰⡇⠀⢸⠀⢸⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⢀⡴⠋⠀⣰⠛⠷⢦⠀⢠⠞⠉⠁⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠔⠋⠀⠀⡼⠁⠀⠀⠈⣧⡞⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⠴⠒⠒⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⣿⣿⣿⣿⣿⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⠿⣿⣿⣿⣾⣿⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢻⣿⣷⣶⣴⣿⣷⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣿⣷⣴⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣏⣀⣀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⡉⣹⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⣿⠿⠋⠀⢸⠀⠈⠻⣿⣿⣿⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠉⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠎⠘⡗⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡇⠀⣀⠘⡇⠚⠶⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⢀⣷⠋⡀⢸⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⢸⠀⠀⠀⢢⠈⡇⠉⡍⠙⡄⠀⣀⠴⢤⣤⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣖⠚⢁⠉⠒⠒⠁⠀⠐⠢⠘⢸⡐⠋⠉⠂⡝⠍⣠⠖⠋⠁⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢯⡥⠿⡶⣭⣀⠂⠀⢠⠧⠀⠂⡆⠀⠀⠐⢻⡷⠟⠛⠩⠓⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⡚⠛⢐⠒⠉⠳⢮⣚⠳⢦⡇⢀⣠⠖⠁⠂⣠⣮⣥⠀⣢⠼⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠷⠒⢄⠀⠀⠈⠓⢼⣞⣿⢅⣤⣖⣤⣴⡞⠣⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣔⡁⠤⠄⠒⠐⠂⠛⠐⣾⡿⠿⠏⠉⡉⠉⠙⠛⠒⢿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⢤⡠⠶⠪⢄⣠⣁⣼⡷⡀⠀⠀⣈⣀⣀⣇⡴⠐⠒⠚⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠋⢸⠇⠱⣤⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠃⢸⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡇⠃⢸⣰⢙⡦⠖⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡌⠉⠑⢄⠈⠃⠊⠀⢈⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⢸⣉⠢⠀⠀⠁⣏⡠⠊⠄⡇⡇⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡑⠒⠢⣤⠏⢣⡀⢹⠇⠀⠑⠢⠀⠀⢀⡔⢸⠃⣠⢞⠙⠦⠔⠶⢒⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣻⡀⡇⠀⠀⠀⠙⠞⠀⠀⠄⠀⢀⡶⠋⠀⠈⠛⠁⠃⠀⠀⠠⣴⠏⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣃⢑⠙⢧⡀⠀⢰⠀⠰⡀⠀⡀⠈⢙⣇⠠⡁⠀⠀⢠⠀⣀⡀⠳⢂⣻⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠌⠉⠙⢙⣲⣬⠀⠀⡇⠀⡈⠢⣼⡟⣠⠁⠀⡀⠐⠄⡁⠉⡀⠀⠬⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⣤⣀⣉⠈⢀⣠⠽⢦⡇⠀⡇⠀⢀⣷⠃⠀⢠⣤⠚⠠⠀⠠⠤⡤⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⡄⠄⠀⣀⠤⡽⢶⡇⠀⢸⡷⠀⢂⡴⠁⠀⠀⣀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣤⣑⡀⠀⢈⠻⢷⣤⣼⠟⣠⢟⣿⡿⠚⠋⠉⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⢀⣀⠠⢬⠶⠚⣲⠶⢿⣿⣿⡷⢿⣅⣀⠄⠂⢀⡐⣛⣓⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢷⣒⣟⡉⠀⢐⣁⠀⢐⣁⡴⢻⠿⢦⡈⠑⢦⡀⠉⠙⠯⣉⣩⠽⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠁⠀⣾⠀⠀⠙⠒⠒⠽⣦⣾⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣻⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡟⠛⠛⣿⠟⣟⣂⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⣷⣤⣤⣴⣀⣿⠋⠉⠛⣴⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⣦⣤⠤⠦⣴⣿⡘⣄⣀⣼⣁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⣿⣿⣓⣒⣞⣿⡷⣨⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣯⣿⣶⣻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢉⣠⣽⣿⣿⣿⣿⣿⣿⣶⣀⡈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⣾⣿⣿⣿⡿⠛⠛⠉⠉⠉⠉⠙⠛⠿⣿⣿⡻⣦⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣾⣿⣿⡿⠋⠀⠠⠂⠀⠀⠉⠉⠒⠦⣄⠈⢻⡄⠙⣧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⡿⠁⢀⠂⠀⠀⢀⠘⠧⡄⠀⠀⠈⢣⠀⢹⠀⢿⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⡇⠀⡇⠀⢰⡄⠲⠂⣴⠳⠆⣴⠀⠘⠃⠈⡇⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⡇⠀⠰⢿⣲⣄⣿⣔⣢⠟⠀⠀⡄⠀⡇⢸⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⡇⠀⣇⠀⠠⠾⠑⠺⠟⠿⡼⠒⠀⢠⡇⢀⡇⣼⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣸⠀⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣽⣇⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁⣰⠇⢰⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣛⣛⡛⠒⠒⠒⠒⠛⠛⢻⣛⣛⣋⠠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣉⡁⣀⠀⠀⠀⢠⣀⣀⣈⡹⠿⢟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣟⣿⣶⡖⣶⣶⣶⡶⢶⣶⣶⣶⠒⣶⣾⣛⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣷⢿⣶⣥⣿⡀⠤⣷⢾⠠⠄⣼⣴⣀⡟⣾⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠯⢿⣽⣿⣛⣋⣘⣿⣛⣁⠽⠯⠴⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢁⠀⠀⠀⠀⡈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⡀⢠⠀⠘⡀⠀⠀⢠⠁⠀⡀⢀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠁⠀⠀⠱⡀⢀⠆⠀⠀⠈⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡀⠀⠀⠀⠙⠃⠀⠀⠀⢀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠄⡀⡀⠀⠀⡌⠑⣄⠀⠀⠀⠀⠀⢸⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡇⠀⠀⠀⠀⠀⡠⠊⢁⠀⠀⢀⢀⠄⠄⠦
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⢄⡉⠑⠘⠀⠀⡀⠑⢄⡀⠀⠀⢸⠀⠀⠀⠑⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⢀⡤⠊⢀⠀⠈⠓⠃⢁⡠⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠉⠢⣀⠀⠀⠰⠀⠀⠈⠐⠂⠊⠀⠀⠀⠀⠘⡄⠀⠀⡠⠃⠀⠀⠀⠀⠑⠐⠂⠁⠀⠀⠂⠀⠀⡠⠔⠉⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⠓⢄⠀⡆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⢦⡔⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢐⠀⡠⠊⠁⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠃⠀⠀⠀⠀⠈⠱⡅⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠐⠠⢀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢡⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡌⠀⠀⡔⠁⠀⠀⠀⠀⢀⡀⠔⠂⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⠉⠐⠂⠤⠄⣀⣱⡄⠘⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠃⢠⣎⣀⠠⠤⠐⠂⠉⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⢦⡔⠁⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⠆⠀⠉⠀⠒⠒⠒⠀⠠⠤⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠄⠀⠒⠒⠒⠈⠁⠀⠰⠅⢀
⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢀⡀
⠀⠀⠀⠀⠻⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠛
⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠉⠒⠒⠂⠹⢤⡤⠤⠄⠀⠀⢀⣀⣀⣀⣀⣀⣑⣤⣤⣊⣀⣀⣀⣀⣀⡀⠀⠀⠠⠤⢤⡴⠃⠒⠒⠂⠉⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢉⡉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠋⡟⢢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⡴⠋⣀⠔⠁⠀⠀⡇⠀⠉⠢⣀⠑⢤⡀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠔⡡⠔⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⠢⢍⢢⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡤⢀⣤⣠⣠⣶⣶⣶⣶⡶⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣡⣶⣶⢿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠘⢋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⢛⣭⣥⣤⣤⣄⣀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣍⣿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣦⣼⢿⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡿⠗⠋⠁⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣋⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣾⣿⠷⠰⢿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⢿⣧⢿⣷⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠷⠞⠋⠉⠀⠀⣚⡿⣿⣿⣿⣿⠈⠙⣿⣇⢸⡿⠁⠋⣥⣴⡿⣷⣿⣿⣃⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣷⠀⣀⡠⠐⠂⢎⣤⣿⣿⣿⣶⣽⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣻⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣤⣄⣠⣤⣤⣴⣲⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠁⠀⠀⠀⠀⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⠤⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠐
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠒⠐⢆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠁⢤⡀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢡⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠘⡲
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠠⠃⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⢤⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⢸⣇⡤⠂⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⣈⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣞⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠤⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⢸⡇⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢸⡇⠀⢀⡜⠁⠀⢀⣀⠤⠄⠲⠀⠀⠀⠀⠀⠎
⠀⠰⠶⠦⠉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠴⢤⣀⣙⣦⣇⣴⣯⠴⠒⠋⠉⠀⠀⠀⠀⠀⠐⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠹⣿⠉⡀⠀⠀⠀⠀⢀⠐⠀⠐⠢⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠤⠀⠒⠂⡄⠀⠀⠀⡠⠔⠊⠀⠀⣿⠀⠀⠁⠒⠤⢀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⡠⠔⠈⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠈⠢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠃⠉⢩⣀⡄⠀⣸⡶⠒⠻⠋⠀⠈⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢷⠀⢀⠀⠀⠁⡇⣰⢫⠁⠀⡄⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠀⠀⠀⢰⡏⠀⡀⠀⠁⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡇⠀⠀⢠⠀⠀⠀⠈⠀⠀⠋⠀⠀⠀⢘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠁⠉⠁⠀⠀⡀⠁⠀⡀⢀⠀⠀⠀⠀⠠⠶⠅⠂⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠁⠢⣀⠀⠙⢧⢰⡔⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠱⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣘⣛⣛⣶⣿⠤⠤⠄⠠⣄⠀⠐⠲⠀⠀⠀⠀⡈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢷⠑⠤⡄⠀⠈⠙⣒⡀⠀⢠⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠘⢧⡀⠀⢲⣤⣘⣤⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠞⠁⠀⠀⠀⠀⠀⠈⠱⠋⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⢾⡿⣿⣿⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⣦
⠀⠀⠀⣾⣿⣟⢈⠀⠀⠀⠀⠀⢀⡓⠒⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣿⣿⡇⠈⡇⠀⠀⠀⠀⠀⣷⡥⡁⠀⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⡾⣿⣘⡇⠘⠈⡇⠀⠀⠻⣄⣠⠋
⠀⠀⠀⡿⣿⣧⠞⢁⠀⠀⠀⠀⢀⡆⠤⠤⠀⠒⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣿⣷⢼⠀⠀⠀⡇⠀⠀⠀⢱⡋
⠀⠀⠀⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠠⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣾⡲⠀⠀⡟⠛⠀⠀⠸⠃
⠀⠀⠀⣿⣿⣿⡆⣠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠁⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠱⠷⢱⠸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢳⠛⢆⡀⣀⠀⠀⠓⠂⠰⡇⠀⢈⢇⠀⠂⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡀⢦⠀⠀⠀⠀⠀⠀⠘⠁⢢⡌⠀⠘⠀⠋⠀⠀⠀⠀⠀⡄⠀⡰⠀⢴⠄⠀⡃⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⡶⠇⠠⠇⠀⠀⠀⠐
⠀⠀⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣑⠈⠱⡀⠀⠀⠠⠀⠀⢀⢀⠊⠀⠀⠣⠀⠀⠀⠄⢀⡤⠀⠀⠀⠀⠀⠘⠿⠩⠥⠀⠀⠀⠓⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣀⠘⠢⡀⠀⠀⠀⠸⠀⠀⢀⠔⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠄⠀⠤⠐⠁⠀⠀⠀⠈⠃⢄⡀⠀⠀⣠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⠀⠉⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢉⣲⡾⠅⠀⠀⠀⠠⡀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠀⠀⠀⢤⣴⣹⢿⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠂⠀⠒⠤⠀⠀⡀⠙⢃⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⡇⠀⠀⢠⣙⡿⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠖⠀⠀⠰⠃⠀⠀⡇⠀⠀⠁⠀⠀⢀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣦⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⡈⠀⠀⢈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧
⠀⠀⠀⢿⡷⠀⠀⠀⢰⡇⠉⠄⠀⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⣠⣤⣶⣶⢶⣦⣤⣷⣶⣷⠟⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢇⠀⠀⠀⢁⠀⡿⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⡇⠀⠀⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠁⠀⠀⠰⠀⠀⠜⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠄⠐⠡⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠠⠄⠀⠀⠠⠄⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣾⣓⠲⠶⢤⣌⠁⠀⠀⠀⠀⣀⣠⠤⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠒⠤⠀⢀⠀⠀⠤⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣯⣍⣛⣓⠶⠤⠍⠓⠺⠋⠡⠤⠄⢀⡅
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢆⠀⢹⣶⠭⣭⡙⠒⠤⠤⠤⠄⠒⠒⠋⢙⠀⡃
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢄⡙⠓⠲⠤⠤⢙⣷⡶⠄⠰⠞⠛⣉⠔⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⣀⡀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⠤⠀⠀⠤⠀⠀⠐⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢠⣾⣿⣿⣦⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣴⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⡏⢀⣴⣿⣷⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛⠉⢻⠋⠙⠛⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠒⡀⠀⠄⠊⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⢀⠀⠨⠠⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⢀
⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⡀⠁⡀⠠⠀⠀⡌⠀⠀⡀⠀⢀⠀⠂⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠂⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠈⠀⡀⠠⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠄⠀⠠⠘⠃⠀⠀⠈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⣰⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠐⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠉⠀⠰⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣄⠀⠂⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⡀⠠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠄⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢄⠁⠀⠀⢀⣤⠀⠂⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠑⠀⠀⠀⠁⠀⢀⠀⣘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠁⠄⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠑⠠⡀⠀⠀⠀⠀⢰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢀⠀⠎⠑⢲⠀⠀⠈⠑⠤⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠠⠀⠀⠀⠄⠀⠉⠉⠉⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡠⠀⠀⢉⠀⠚⠃⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠐⠀⠈⠀⡂⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠂⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⡷⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠀⠀⢸⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣀⠤⠓⠲⠶⠖⠚⠤⣀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢺⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣧⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⠀⠀⣼⠀⠀⠀⠀⢸⡋⠀⢙⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣽⣤⣤⡀⠀⠒⠃⠀⠘⠋⠙⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⣸⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡬⡇⠀⢤⠀⠀⠀⡤⠖⠚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠋⣟⠙⠃⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢾⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣋⣀⣀⣀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⣉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢉⣵⣋⣉⣀⣀⣀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠃⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠘
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡠⠒⠐⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠊⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⡗⠊⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠠⠤⠷⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠾⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⡇⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠔⠁
⠀⠀⠀⠀⢀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⡇⠀⣠⠞⠀⢀⣀⠤⠔⠂⠉⠃⠀⠀⠀⠀⠐⠁
⠀⠈⠛⠃⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠶⢤⣬⣷⣧⣴⠷⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⣿⠡⠄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠂⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⠒⠂⠀⠠⠀⠀⠀⢀⠄⠂⠁⠀⠀⣿⠀⠀⠀⠁⠒⠀⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠄⠂⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣧⠀⠀⠐⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠁⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⣷⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣿⣶⠀⢀⣤⠀⠀⠀⡄⠀⠀⠀⢤⡀⠀⠀⠀⠲⣯⡀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⣿⡀⠈⢻⡆⠀⠀⠁⠀⢀⡠⡀⠉⣔⠃⣀⣠⣿⣿⡖⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣄⣤⣦⣤⣷⣴⣿⡇⠶⠄⠀⠀⣼⠀⠡⠶⣿⠀⠉⠀⠟⢉⢠⣄⣜⣥⠀⠂⠀⠀⠀⠈⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠟⢋⣿⣿⢟⣿⣿⣧⠀⠐⠀⠸⣭⠀⣤⣶⣏⠀⠀⠀⠠⠀⠸⠏⠘⠟⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠄⠻⠿⣿⠛⠉⠢⡀⠀⠁⢬⣿⣿⣿⠀⣤⣠⣦⠀⢀⡄⠀⠀⠀⣠⣴⣧⣤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣦⣰⣄⣠⣤⠤⣼⣦⣔⣘⣿⣿⣿⣷⠈⢻⡇⠀⠿⢃⠀⣰⠾⠛⠻⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⡸⠿⢾⡍⢹⣿⣿⣤⣿⣿⣿⣿⣿⣟⣿⠁⢼⠉⡼⢿⠁⠍⢉⠀⡱⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⣶⣀⡀⠀⠉⣻⡻⣧⣌⠛⠘⢿⠟⣿⠛⣿⠙⠛⠛⠉⢻⡃⢀⠖⣿⣈⣿⣅⡈⢀⡵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⡿⣿⣿⣿⣤⡀⠈⠉⠀⣹⣭⢆⡀⠐⠇⢀⠘⢓⣿⠘⠂⡈⠀⠀⡀⢻⡇⠀⠀⠀⠲⠂⡸⠗⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠃⣱⡉⠉⣛⣃⣤⢀⠀⠈⠀⠀⠀⠀⠈⠀⠻⠛⠧⢀⣄⠠⠀⠀⠀⢀⣦⢰⣦⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠑⠈⠂⠟⠋⠀⠀⠉⠋⠁⢶⡀⠀⠀⢀⡈⠁⣲⣶⣦⣴⣶⣤⠟⢂⣀⡆⡺⠻⠃⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣀⣤⣾⣿⣿⠟⠉⠉⠙⣡⣴⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⡼⠋⠉⠁⠙⠋⠀⠀⢀⣤⣾⣟⠻⠇⡹⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠋⠀⠀⠀⠀⣴⣿⡿⣷⠛⠁⡼⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠁⠐⠁⣿⠁⠄⠀⠸⠇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⡤⢠⠀⠀⠀⡀⠀⠋⠀⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠐⠃⠛⠉⠡⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⡀⠤⠤⠄⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠄⠀⠤⠔⠋⠄⠀⠀⠀⠀⢀⠀⠀⠉⢁⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠈
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠐⡀⠀⡀⠄⠠⢤⡔⠁⠀⠔⠈⠙⠀⠐⠀⠀⡀⠀⠀⢀⡌⠀⠀⠀⠠⠀⢀
⠤⠤⠄⠀⢀⠊⠀⠀⠘⡀⠄⠀⢴⡎⠀⠀⡀⠀⢡⠰⠅⠁⣘⠀⠀⢀⡀⠘⠀⠀⠠⠂⠀⠀⠀⠈
⠀⠀⠀⢠⠀⢀⠀⢠⡎⠀⠀⠀⠀⢧⠔⠁⠠⠀⢼⢠⠄⠋⠤⠀⠒⠄⠈⠐⢤⠀⠈⠆⠀⠀⠀⠀⡀
⠀⠂⠀⣼⠊⢀⠀⣀⠑⠉⠗⠀⠀⠘⣗⡂⠀⠀⢸⠪⠞⣨⡇⠈⠐⡶⡀⠀⠀⠑⠔⠄⠀⠀⠁
⠀⡄⠘⠋⠀⢸⠀⠉⢀⠀⡇⠀⠀⠀⠼⠇⠈⠉⢁⢨⠀⠉⠁⠀⠿⠇⡇⠀⠀⠀⡼⠁
⠀⠀⠑⠂⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⡇⢀⠸⢾⡄⢟⢒⠆⠙⡼⠁⠀⢀⠜⡎⠀⠁⠀⠀⠂⠊⠉⡑
⠀⠀⠀⠀⠀⠘⡤⠤⠄⠀⣀⣀⣀⣀⠢⠊⠟⢠⠀⣀⠙⢍⢃⣶⣎⠀⠤⢶⠍⢉⣀⣉⠠⢄⠀⡈⠀⠀⡀
⠂⠒⠀⠀⠀⠀⣀⡀⠀⠂⠠⠤⠀⠀⠱⢈⡀⢈⡗⠓⠀⠠⠄⠀⠀⠀⠀⠀⠁⠃⢀⠀⠀⢀⠀⠁⠀⠀⠤
⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⢂⠝⠒⠊⠎⠄⠀⠀⠀⠑⡦⡀⠀⡀⢀⠓⠀⢠⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠠⠤⢀⠔⠓⠐⠊⠌⠄⠀⠀⠀⠀⠀⡇⠤⠥⠒⢃⠤⠀⠼⠣⠂⠀⠀⠤
⣤⡄⠤⠀⠔⠀⢠⡔⠂⣄⠀⣀⣀⡀⠜⠢⢄⠀⡜⡀⠀⠀⠂⠉⠀⠀⣃⠀⠀⠀⢈⡐⠂⡀⠀⣤⠤⣤⠤
⠀⠀⠀⠀⠄⠀⢀⡛⠀⠊⠂⡁⠈⠀⢀⠠⠀⠙⠢⠄⡀⠀⠈⠒⠊⢠⠇⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠂
⠑⠂⠀⡀⠀⠁⠂⠘⠔⡤⠴⢄⡠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠰⠂⠠⠤⠄⠀⠡⠚⠉⠀⠀⠀⠀⠒⠀⠂⠠
⠀⢀⡀⠀⠈⠐⠀⠀⠈⠲⠒⢉⢀⣀⡀⠀⠀⠀⠈⠈⠁⣀⡀⠃⠀⠈⡀⠀⠃⠠⠀⠀⠀⠠⠤⠠
⠀⠀⠀⠀⠀⡠⠒⠐⠀⠊⠉⠊⠁⠉⡀⠀⠀⣀⣀⠁⠀⠀⠀⠞⠐⠂⠙⡕⡀⢀⡀⠠⠄⠀⡀⡀⠀⠀⠁
⠠⠐⠤⠂⠊⠁⠐⠀⠀⠃⠒⠂⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⠺⠀⠂⡄⢓⠀⠀⠀⠀⠀⠂⠀⠄⢉⣄⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣂⡀⠀⠀⢆⠸⠀⠠⠀⠙⠀⠀⠀⠀⠀⠠
⣤⣤⣤⣬⣬⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣤⣤⣤⣤⣤⣶⣤⣤⣤⣴⣴⣶⣦⣬
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣰⣿⣿⣿⣿⣆⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⡆
⠀⠀⠀⠘⣷⣶⣤⣤⣴⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣦⣤⣤⣶⣾⠁
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣯⣟⠿⢿⣿⣿⡇⢸⣿⣿⣿⠿⣻⣽⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣌⡙⠃⠘⢋⣡⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠁⠀⠀⢸⡇⠀⠀⠈⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠐⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠤⢪⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠑⠢⠤⠐⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⠋⠢⠠⠃⠀⠀⡀⠀⠀⠀⣬⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⢄⣀⣀⠆⠙⠁⠀⠀⠀⡁⠀⠀⠀⡆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣄⢀⡰⠃⠀⠀⠀⠀⡆⠀⠀⠤⠀⠀⠀⠺⠀⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⡧⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⠠⠤⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠈⠢⡉⠐⠒⠤⢀⣀⢀⣀⣀⣀⣠⠇⢀⣄⠀⠀⠀⡖⠀⠀⠀⠀⠀⠄⠀⣧⡆⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣀⡠⠤
⠀⠀⠀⠀⠈⠢⡀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠛⠀⠀⠀⠀⠀⢰⡞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠅⠈⠉⠁⠀⠀⠀⠋⠉⠉⠉⣁⠜
⠀⠀⠀⠀⠀⠀⠑⡄⠐⠈⠠⠀⠈⠀⠀⠀⠀⠀⠈⠲⢤⣟⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠰⠆⠀⠑⠢⡀⠐⣤⠀⠀⠀⠀⣿⠀⠀⠀⠠⢀⡼⠁⠉⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⡀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠒⠫⢀⣀⠀⠀⠀⠀⠈⠳⣆⣀⠀⠀⠀⣿⠀⠠⠄⢠⠞⠀⠈⠀⠀⠀⠀⣤⠀⠀⠀⠐⣀⠀⠄⠂⡁⠀⠀⠀⠈⣴⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣉⠉⠙⢦⡀⠀⢻⡀⠀⣴⠏⠀⠀⠊⠀⠀⠀⠀⣀⣠⡥⠚⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠞⠀⠀⠀⠉⠀⠀⠀⠹⣦⣸⣇⡾⡃⠀⠀⢀⣀⣤⠴⠶⣉⠉⠀⠀⠀⠀⠈⠀⠀⢀⡠⠤⠔⠒⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠤⠤⠤⠷⠤⠤⠤⠤⢈⣻⣿⣥⣷⡖⠛⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⢀⢠⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠣⡈⠉⠙⠛⠓⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠉⢳⠐⠀⠀⢀⠀⢀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠘⣤⠀⠀⠔⠂⢄⡀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠸⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠆⢸⠀⠀⠀⠑⠄⠞⠀⠉⠲⠴⠊⠁⠀⠀⠀⠈⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⣿⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⡀⢾⢀⣞⢧⣀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠤⡤⢾⠀⠁⢸⣾⠊⡾⠋⢁⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣄⠀⠀⠑⢄⠀⣏⡉⠀⢘⠠⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣘⠦⣀⠀⠀⠈⣿⣀⡴⠋⠄⣧⢻⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡌⠳⠤⢤⡀⢰⡏⢦⡀⠈⢿⡦⠀⠑⠢⣀⠨⠉⠀⠀⣤⢥⡟⠀⢠⣾⠟⢧⣀⡤⢤⣤⢔⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⣶⠀⢠⠉⠉⠀⠄⠻⣄⣸⠀⠢⠀⠀⠈⠈⢆⣠⡾⠁⢈⢧⡴⠋⡎⠈⠀⠀⠀⠀⣴⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢗⡿⣦⣾⠀⠀⠀⠠⠀⠈⠁⠃⠀⠈⠒⢔⡆⣾⡁⠀⡀⠀⠰⠀⢰⠃⠀⠀⢀⣈⠿⣛⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡄⣈⡉⠛⢆⡀⠀⠀⡇⠀⠸⡄⠀⠠⡀⠀⠉⣿⣔⠞⡀⠁⠁⠀⡸⠀⣀⣀⡘⠛⣉⣭⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠉⠛⠋⠙⢶⣄⡇⠀⠀⡇⠀⢀⠈⢢⣐⣿⠗⣦⠁⠀⢀⠀⠰⡄⠉⠈⠉⠀⠀⢨⡽⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣋⡢⠈⠙⠒⠉⠉⠈⣑⣦⣴⡇⠀⣼⠀⠐⠈⣻⣼⠋⠀⠀⣻⢠⢞⠐⠉⢀⣈⣉⣀⣂⣴⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣝⣓⢘⡒⠒⠒⠛⢉⠁⠙⣷⡄⣺⠄⠀⠀⣿⣧⠊⡄⢀⡿⠃⠀⠀⠀⢉⡉⢩⣭⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣍⢒⢐⠲⡖⠛⢛⣻⣿⠀⠀⢠⣿⣍⠰⣡⣾⣡⡂⣀⢡⣶⣤⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣮⣬⣁⠁⠀⢄⠹⠾⢷⣵⢲⡿⢃⣶⠟⣞⣿⠟⠉⠋⠁⢘⡷⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠥⣀⠀⣀⣨⣵⡦⠴⠦⣴⣦⣿⣿⣿⣿⣥⣿⣏⠀⢀⡤⠂⠀⡠⠾⠻⡿⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣯⣤⣴⡶⠚⠋⠁⠴⠉⠀⢈⠝⠁⣠⢾⣿⣉⡟⠓⢦⣉⡉⠙⠒⠲⣞⠛⠚⠛⣛⣿⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠶⣥⣤⠵⠶⣦⣤⣥⠶⠛⠁⣾⠃⠉⠳⣌⢀⣈⠳⣄⠀⣠⡬⠽⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠈⠙⠺⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠶⣤⣀⠀⡇⠀⠀⠘⣧⡀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⠛⠃⠀⡆⠀⠈⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠛⢦⣄⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡈⠙⠛⠷⠞⠋⢣⠠⣦⣤⠴⠶⠃⠀⠀⠀⠀⢆⠀⠀⠀⢹⣦⡴⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠈⢢⡀⠀⠀⠀⠈⢧⠀⠙⠢⣀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠀⠀⠀⠙⢆⠀⠀⠀⠈⢷⣄⠀⠈⠳⡄⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢞⣋⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠷⣦⣄⣸⡆⠀⠀⠀⠀⢹⠀⠀⠀⢸⡇⠀⠀⠀⣤⠀⠀⠀⣴⣦⣀⡀⢀⣀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⡆⠀⠀⠘⣧⡀⠀⣠⠏⠳⢤⣴⠋⠈⠉⠉⠉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢠⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠦⠤⢄⣠⣤⡴⠟⠀⠀⠀⠀⠀⠈⠑⣄⢁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢠⠀⠀⢀⣠⠖⠉⠀⠀⢾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡥⠖⠊⠉⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠐⢶⣶⠶⠚⠛⠛⠉⠀⠀⢀⡀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠤⣀⣀⡉⠢⢄⢠⠇⡤⠂⠉⠀⠀⠐⠒⠦⠄⠀⠀⢀⡴⠟⠁
⠀⠀⠀⣀⣀⣀⣤⡴⠋⠀⠀⠀⠀⠀⢀⣀⣀⣈⣤⠤⠀⠂⠁⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠒⢚⠿⠳⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠈⢳⣤⣀
⠚⠛⠻⠿⠿⠧⠤⠤⣄⡀⠀⠀⠉⠉⠉⠁⠀⣠⠎⠀⠀⣠⠴⠛⠉⠉⠙⢿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⣯⠙⠻⣿⡶⣭⡉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⣼⣿⠀⠐⠊⠉⠹⠣⠀⠀⠀⠀⠀⠘⣇⠀⠈⠙⢦⡙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⢻⡇⢀⡾⠁⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢀⠇⠀⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢻⡄⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡧⠖⠉⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠠⣴⣿⡉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠹⡄⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢳⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡠⠁⠀⠀⠀⣦⡀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣀⣀⠀⠈⠁⠀⠀⠀⠀⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠖⠛⠉⢹⡇⠀⠀⢠⡾⣦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡀⠀⠀⢠⠖⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⠉⠳⡤⠇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣠⠴⠒⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠓⢆⠀⠀⠀⠀⣇⡀
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠙⡆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢃⡴⠃
⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠉⢦
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣄⠀⠠⠀⠀⠀⣸⠂
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⡤⠊⠉⠉⠁
⠀⠀⠀⢣⡀⠀⠀⠀⠀⣊⢤⣀⠀⠤⠠⠀⠀⣠⠞⠳⣄⡀⠐⠁⠀⠀⠀⣀⡠⠞⠦⠤⠴⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠈⠙⡒⠒⠚⠋⠁⠀⠀⠀⠉⠉⠙⠉⠉⠉⠁⠀⠀⠀⢰⠀⢠⡀⠀⠈⠃
⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⡆⠀⠀⠃⠀⠀⢶⠀⠀⠀⡇⠀⠀⠀⠀⢦⠀⠀⣦⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡄⠀⠀⠀⡆⠀⣤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠀⢀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠘⠃⠀⠿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠘⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢀⠀⠰⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠉⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠦⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠑⠒⠒⠤⠂⠋⠀⠀⡀⠄⢀⠌⢈⠈⠀⠀⠀⠀⠐⠘⡀
⠀⠀⡠⠂⠐⠂⠀⡀⡀⡀⠠⠀⡀⣀⣠⠤⣤⣧⢦⣦⡤⢤⣴⠊⠉⠙⠎⠁⠈⠏⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⢀⣐⣀⡀⢀⣈⣈⠰⠐⠃⠁⢀⠔⠊⠀⡐⡄⠀⠈⢐⠢⢌⡁⢐⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡀
⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⡀⠄⡠⠉⠒⠤⡀⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠂⡈⠢⡈⠀⠀⠠⣨⣰⣄⠀⠀⠀⠀⠀⠂⢄
⠀⠀⢀⣀⣀⡀⠀⡀⢀⠊⠀⣀⠀⣠⠀⠤⠄⣄⢆⡐⡀⠄⠐⠒⠀⠀⠒⠂⠼⣄⠓⠁⠀⠀⠀⠐⠀⠠⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠐⠒⠉⠀⠀⠂⠁⠀⠀⠀⣽⡄⠈⠁⠀⠀⠀⠂⠀⠂⠄⠄⠌⠈⠄⠄⠄⠐⠀⠀⠡⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⠀⣀⠀⡀⠀⣠⠀⠀⢀⠀⠀⢀⠀⠀⡀⠐⢂⠒⠒⡒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⠀⡀⢸⡇⠀⠠⠃⣠⠅⠠⠆⠀⢠⠚⠀⢐⠛⠀⠺⠂⠰⠿⡖⠸⢃⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠁⠮⠀⢈⡀⠀⡘⠀⠀⠀⡆⠼⠁⠀⡄⠀⢨⡄⢠⡞⠀⢰⠆⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡠⠀⠀⢰⣇⠈⠁⠀⠀⠉⠀⠀⠀⠸⠀⡄⠈⠀⠀⡤⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⢸⠀⠢⠰⠃⠀⡰⠀⡼⠀⠖⠀⠰⠀⠈⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠮⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠂⠂⠐⠁⠀⠂⠀⠄⠀⠂⠀⠀⠐⠁⠂⠐⠐⠐⠠⠂⠀⠔⠀⠠⠨⠀⠄⠐⠁⠈⠐⠐⠑⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⢿⣇⠀⠀⠀⢀⣯⡉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠄⠀⡏⠉⠉⠉⠉⠉⡇⠀⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⢠⠞⠁⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢻⠀⢸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⡄⠸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢡⠀⡇⠀⠀⢿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡷⠖⠛⠋⠛⠛⠶⣄⡀
⠀⣼⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⢰⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢤⡀⠀⠀⠀⢻
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢳⢀⡠⠶⠒⠒⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢢⠀⠀⠈
⡇⠀⠀⠀⠄⠀⠀⠠⡴⠒⠚⠛⠓⠺⠇⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇
⣧⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠃
⢹⠀⠀⠀⠐⠀⠀⠀⠀⠱⢄⣀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠏
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⣀⠴⠋⠀⠀⠀⣸
⠀⢹⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣠⠄⠀⡤⠤⠤⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⡴⠃
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠓⠋⠉⠉⠉⠉⠀⢧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡟⠀⠉⠛⠲⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠃
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢰⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣬⣿⣿⠀⢾⡄⠀⠂⠀⠀⠐⢄⡤⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣤⣬⣆⣼⡧⠄⠀⢀⡏⡡⢾⡆⠉⢹⠉⢀⣘⡃⠀⠄⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠩⠟⣿⣿⣷⠀⠂⠸⠄⢴⣾⡀⠀⢀⠀⠚⠈⠋⠀⢀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⡈⡉⠁⣀⣡⣀⠘⣶⣿⡧⠲⡟⠀⡼⠀⢀⡴⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠷⣤⢀⣶⣄⣽⣿⣿⠹⣧⠀⠄⠐⠀⡐⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⣤⠀⠈⠿⠳⣤⠈⠛⣹⠙⢋⣉⠀⠸⠀⠐⢷⠜⠲⠂⡒⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠛⢒⣀⡀⠙⠃⠀⠀⠀⠰⠿⠄⡀⠀⠀⠈⢠⣤⣄⠐⠂
⠀⠀⠀⠀⠀⠀⠠⠤⠉⠁⠛⠁⠈⠉⠉⠶⠀⠀⣠⣀⣲⣶⣴⠶⢞⣀⣤⡘⠛⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⠾⠟⠛⠁⣀⡤⣶⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⡀⢠⣾⣿⠟⢠⠞⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠉⠀⠁⠽⠐⠀⡈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠓⠆⠇⠂⠀⠀⠀⠀⠀⠃


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

⠀⠀⠀⠀⠀⠀⠀⢠⠤⠖⠒⠒⠛⠉⠉⢧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠓⠀⠉⢍⡉⠉⠉⡩⠙⡆
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠸⢀⣠⠚⠙⡅
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣅⠆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠉⠂⡤⠒⠘⠋⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠂⠀⠀⠇⠀⠀⠑⠂⠤⢄⣀
⠀⠀⠀⠀⠀⢀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠢⠄⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠣⡀
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠲⡘⠁⠈⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠹⡄
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠠⠠⢤⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⡀
⢸⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠤⠀⠄⠠⣀⢄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣇
⡇⠀⠀⠀⠀⠈⠡⠆⠀⠀⠀⠂⠀⡈⣁⠞⠨⣀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⡲⣈⠁⠬⠗⠋⠂⠓⠂⠐⠀⠚⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⠀⠀⠈⡀⡀⢀⠄⡠⢄⠔⠒⠄⡠⢀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠘⠀⠀⣼
⠀⠀⠀⠀⠀⠨⢀⠘⠀⢠⠀⠀⠀⡃⠶⡅⠉⢈⠂⣈⡠⠂⠀⠀⠀⠀⠀⠀⠀⡃
⠈⣆⠀⠀⠀⢐⡉⠠⠂⠅⠌⠀⠄⠍⠒⠋⠂⠊⠒⠀⠀⠀⠀⠀⠀⠀⠆⠀⣸
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⠃
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⠀⠉⠀⠀⠀⠀⡰⠁⠀⣏
⠀⠀⠀⠀⠈⠒⣤⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠁⠀⠁⠀⢀⠔⣀⡤⠔⠉⠉⠉⠉⠙⢢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠒⠒⠶⢦⠤⠀⠤⠤⠤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢤⣀⠀⠀⣀⣀⠤⠤⠤⠤⠤⣀⣀⡀⣀⣀⠤
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⡿⠛⣺⣷⣆⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⣾⣿⣿⣿⠏⠀⠼⣽⣿⣿⣧⡀⠁⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣃⠀⢀⣘⣻⣿⣿⣿⣧⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⠃⣀⣀⣀⣀⣉⣻⣿⣿⣿⡄⠀⠀⠈⠹⡄
⠀⠀⠀⠀⢀⣤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⢸⠉⠃⠉⠙⠈⠁⠻⠻⠿⠍⠹⢽⠿⠻⣿⠙⠿⣿⣿⣹⣿⡿⠿⣿⡿⡿⠿⣿⠁
⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⠀⠸⠠⠀⠀⢸⠀⠀⣿⠀⠀⠀⠈⢸⠁⠀⠀⠀⠁⢰⠀⢻⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢀⡤⠄⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠁⠀⠀⠀⠀⠃⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⠂
⠀⠀⠀⠀⠀⠈⡍⠐⠠⠀⢄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠂⠔⠈⠀⠘
⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡄⠀⠀⠈⠲⠀⠀⠀⠀⠀⠘⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⡤
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠉⠢⢀⡠⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠂⠁⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠒⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠐⠂⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⡗⠊⠀⠀⠀⠀⠀⠜⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠃⠄⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠚⠙⣤⠀⠀⠀⡇⠀⠀⠀⡴⠛⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠐⠋
⠀⠀⠀⠀⠀⠀⡀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡇⠀⢀⡞⠁⠀⢀⣠⠤⠤⠀⠀⠀⠀⡐⠁
⠀⠲⠶⠄⠉⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠤⠤⠦⣤⣙⣦⣇⣴⡯⠴⠚⠉⠁⠀⠀⠀⠀⡔⠒⠐
⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠝⣿⠡⢀⠀⠀⠀⠀⡆⠀⠐⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⠆⠀⠀⡠⠐⠉⠀⠀⣿⠀⠀⠈⠐⠂⠄⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠄⠒⠁⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡄⠂⠐⠢⡀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠁⠀⠼⡀⠀⠀⠀⠈⢣⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣁⡘⢹⣆⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠃⠘⢆⡈⠉⠓⠢⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣛⠗⠣⠀⠠⠂⠀⢁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣄⠀⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊⠉⠚⠦⠦⢄⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⡆⠀⠀⣀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⣤⠀⠀⠀⠀⠀⠰⡆⠈⠐⠓⠀⠀⠉⠉⠁⡜⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠁⠀⠀⡔⠀⠀⠀⠀⠀⠀⣰
⠀⣀⠤⠐⠐⠦⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠠⠬⠃⠀⠀⠀⠀⡴⠁
⡴⠁⠀⠀⢐⠂⢸⠀⢀⣠⠴⣊⣡⡄⠴⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢼⡀⢀⡠⢄⠀⢠⠃⠀⠀⠀⠀⢀⡜⠁
⡇⠀⠀⠀⠀⠀⠉⠉⢁⣠⣤⠞⠁⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⡾
⠘⢦⣀⡀⣀⣀⠤⠖⣩⠟⢁⡔⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠁
⠀⠀⡼⠋⠀⠀⢀⡼⠁⠀⢾⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠤⠤⠤⠒⠋⠉⠋
⠀⢸⠁⠀⠀⡀⠈⢱⡀⠀⠀⠉⠉
⠀⠘⣄⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⣤⣀⢸⠀⠀⠹⣆⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠉⠙⠀⢲⠀⠈⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠙⠳⠦⣤⠴⢣⢀⣀⣀⣠⠇⠀⠀⠀⡀⠀⠀⢸⣀⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠢⡀⠀⠀⠈⢦⠉⠃⢄⠀⠀⠀⠀⠐⡀⠀⠀⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠟⠀⠀⠘⠂⠀⠀⠈⠳⣄⠀⠑⣄⠀⠀⠀⠠⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡿⠀⠀⠀⠀⢁⠀⠀⢿⠀⠀⢀⠧⡀⢀⡟⠶⠤⠤⢶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⠖⠊⠀⠈⠉⠀⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⢲⡤⠊⠀⠀⠀⠀⠀⠀⢀⠔⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⠂⠤⠴⠚⠃⠀⠀⠀⠀⠉⢤⡄⠀⠀⠀⠀⢸⠀⠀⠀⢠⠂⣀⠤⠚⠁⠀⠘⠧⣤⡄
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠠⣀⠀⠘⢀⡠⠄⠚⠉⣀⡀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⢀⣀⣠⡿⠀⠀⠀⠀⠀⠈⣀⣠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠒⠂⠑⣷⠯⣤⣤⣀⣀⡀⠀⠀⠀⠺⣅⣀
⠒⠛⠻⠿⠯⠤⠤⡀⠀⠈⠉⠉⠉⢉⠌⠀⢀⡤⠚⠋⠉⢻⣧⠀⠀⠀⠀⡠⠀⠀⠀⠹⡏⠛⢿⡯⣍⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣤⣄⠀⢀⡰⠋⠀⠀⠀⠀⣸⡿⠀⠈⠀⠈⠡⠀⠀⠀⠀⢹⡀⠀⠙⢦⡙⢦⡄
⠀⠀⠀⠀⠀⠀⣠⣀⠔⠊⠁⠀⢹⣧⠏⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⢀⠃⠀⠂⠀⠀⠀⢸⠇⠀⠀⠀⢳⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠛⣧⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢣⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣆⢀⠔⠋⠀⠀⠀⠀⠀⠀⠸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣠⢤⡄⠀⠀⢀⡀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣷⠀⢠⡟⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⢀⡤⠒⠉⠉⠻⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠘⡄⠀⠑⢦⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣨⠕⠢⣄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡜⠁⠀⠀⠈⠛⠀⠀⡤⠤⢤⣀⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⢾⠁⠀⢀⠇⠀⠉⠓⠢⣼⠤⠔⠒⠒⠒⠺⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠠⢎⣁⣸⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡰⠁
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠀⣲⠄⢒⡼⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢸⠁⠙⠫⠧⠴⢏⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠈⢆⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣉⠲⡖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⢴⠕⠁⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⡠⠴⠒⠳⣿⣷⠒⠲⣶⣶⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣀⡠⠟⠀⠀⠀⡿⠿⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⡇⠀⠀⠀⠀⠀⢆⠀⠀⠧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⡠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣎⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡄⣻⣖⢞⡢⡀
⠀⠀⠀⠀⠀⠀⡰⣿⣨⣼⣿⡷⠒⠂⠀⠀⠀⠀⠀⠀⠏⠇⠿⠾⣶⣶⢾⣰⡲⠀⠀⠀⠀⣀⣿⠿⡿⠀⠀⢀⠀⠀⣗⠀⢀⡀⠹⣴⡛⢿⣿⡟⣢⡀
⠀⠀⠀⠀⢀⣼⣁⡁⠈⠋⠹⣿⡶⣦⡄⡀⠀⠀⠀⠀⠰⢯⣀⢀⣘⣁⣀⣀⡀⠀⠀⠀⠸⣤⣿⣿⣷⡀⠀⢸⠛⠛⠟⠿⣿⠇⠀⠘⢷⡟⠋⣽⡿⠇
⠀⠀⠀⠀⢀⡿⢿⠋⠓⢠⣰⡎⠱⠿⣄⠀⠀⠀⠀⠀⠛⠋⢙⣿⠙⠉⢻⡟⠁⠀⠀⠀⠀⣨⣿⣿⣿⣇⠀⠀⠙⠒⠒⠚⠋⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⣿⣥⡜⠿⢤⣤⡛⠛⣅⣠⣠⠢⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠉⠉⠉⠻⣷⡄⠀⠀⢀⣀⢤⣄⣤⣴⣶⣶⣆
⠀⠀⠀⢰⣟⣁⣀⣀⠬⡿⣿⡉⣉⠿⠛⢦⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣟⡤⢀⢹⡇⠀⠀⢻⣸⠿⡟⢛⣟⠿⢯⣏⣦
⠀⠀⠀⠀⡿⢿⣿⣄⣀⣉⣿⣿⣛⡶⣶⡀⠀⠀⠀⠀⣞⣻⣿⣿⣭⣉⣳⣶⡄⠀⠀⢸⡷⣆⠙⠋⣁⣄⣾⡇⠀⠀⠀⠿⣿⠋⠽⣿⣶⣾⣿⡍⣱⡄
⠀⠀⠀⠈⣷⣤⣄⠀⣿⣧⣠⣬⣿⢿⣦⡌⠁⠀⠀⢀⣿⣿⣿⣿⠭⣽⡾⣊⠅⠀⠀⠨⣿⢿⣖⢒⣲⣿⣿⠅⠀⠀⠀⠀⠈⠛⠻⢤⣀⣿⡛⣫⡟
⠀⠀⠀⠀⠀⠈⠛⠓⠙⢺⠛⠉⠉⠒⠛⠀⠀⠀⠀⠸⣿⣿⣛⣿⣷⣿⣿⢟⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣯⣽⡷⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣶⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⣺⣿⣿⣶⣤⣬⣼⣟⡿⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣋⠙⠫⠻⡯⣿⣿⠟⠡⡄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣻⣿⣿⣿⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣽⣍⣻⣷⢤⣾⣿⣿⣵⣤⠄
⠀⠀⠀⠀⠀⠀⠙⢏⢦⣠⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠙⢛⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠽⠟⠋⠁
⠀⠀⠀⠀⢀⠀⠴⡌⢧⣁⣼⠏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡄⣰⢿⠟⠋⠨⠳⠈⣿⣠⠀⠀⢠⡀⡀⢠⢤⢴⠀⠀⠀⠀⠀⠀⡠⠚⣮⣼⠿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠤⠲⣼⢹⣿⣤⠢⡀⠒⢤⢾⣴⠃⠀⠀⣞⠁⢑⣫⠀⡤⠂⠀⠀⠀⠀⠠⠛⣻⠄⠀⠰⢤⣿⣿⣿⣙⠀⠀⠀⢀⡀⣄⣢⣼⣏⢡⡗⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠠⢵⣄⠂⠀⠀⠀⠀⢶⡞⣾⣼⣃⣀⣉⣵⠆⠀⠀⠀⠸⣄⠙⠛⠶⠾⢿⣏⣴⣿⡿⠀⠀⠀⣩⣵⣿⣿⣿⣿⠛⣦⡛⣠⡀
⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠒⠙⠟⡉⠓⠒⠂⠀⠀⠀⠑⢀⠈⠻⣷⣶⣶⣾⣿⣿⠏⡀⠀⠀⠀⣰⣿⠻⣿⢛⣿⣶⣾⡱⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣾⣿⣿⣿⣿⣦⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣾⣿⣿⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⣿⣿⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠉⠀⢹⠁⠈⠉⠉⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⢃⠀⠀⡘⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢢⡄
⠀⠀⠀⠄⣀⠀⠀⠀⠰⢢⠀⠀⠀⠀⠀⠄⠈⢂⠀⠀⠀⠀⠀⠀⡐⠁⢠⠀⠀⠀⠀⠀⡔⠆⠀⠀⠀⡀⠠
⠀⠀⠀⢃⠀⢄⠁⠐⠁⠀⠀⠢⢀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠜⠀⠀⠈⠀⠀⡀⠔⠉⠀⠈⠂⢈⡠⠀⡘
⠀⠀⠀⠈⢄⠀⠈⠢⡀⠀⠁⠀⠀⠉⠈⠀⠀⠀⠀⠱⡀⠀⠎⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢀⠔⠁⠀⡰⠁
⠀⠀⠀⠀⠈⡀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠘⠃⠀⠀⠀⠌⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢀⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡌⠀⠀⢠⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⢂⠀⠀⠉⠐⠂⠤⠀⠱⡀⠁⠀⠀⠀⢂⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⠎⠀⠤⠐⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠣⠀⠀⠔⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠐⠃⠀⠀⠀⢀⡜⢀⠀⠀⠀⠀⠤⠀⣀⠂
⠀⠀⡀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⣀
⠃⢁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡈
⠀⠀⠉⠢⢄⠀⠈⠁⠀⢚⠶⠂⠀⠠⠀⠀⠀⠀⠀⢈⡴⢦⡁⠀⠀⠀⠀⠀⠀⠀⠐⠶⡓⠀⠉⠁⠀⡠⠐⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡴⢦⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⢲⠀⠀⢀⠔⢁⠔⠋⠀⠀⠙⠢⡈⠢⡀⠀⠀⡖⠒⠒⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⢐⠥⠂⠁⠀⠀⠀⠀⠀⠀⠈⠐⠨⡐⡄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢉⡁⠤⠤⠶⠒⠦⠤⢌⠁⠀⢀⠀⠀⠀⣀⠠⠤⠐⠒⢒⣒⢂⣠⣤⣀⡀
⠀⠀⠀⠀⠀⣀⠤⠐⠒⠬⡀⠔⠁⠠⠒⢒⣋⠉⣁⡒⠂⠀⠀⠄⠀⠀⢀⣌⠠⠐⠈⠉⠀⠀⠀⠀⠀⣉⡹⠒⠚⡀
⠀⠀⠀⣀⠰⠁⠀⠀⠀⠀⠀⠁⠈⠑⠌⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠸⡅⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠈⡄⢕⠢⡀
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⢀⠔⠂⠒⢄⠈⢆⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡇⠈⢆⠈⢆
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠁⠈⢄⠈⠀⡇⠘⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⡄⠀⢣
⠀⠀⠀⠀⠙⠢⠤⠖⠀⠢⠤⠤⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠱⢄⠀⠠⡞⠀⠀⠀⠒⠒⠂⠤⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⢍⡀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠁⠰⠈⠢⣀⠀⠀⠀⠀⢀⠄⠉⠢⡀⠀⠀⡄⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠼⢀⢆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠝⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠑⡆⠀⢀⠎⠀⠀⠀⠘⢄⢰⣀⠀⢀⣀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠨⣀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢢⠆⠺⠀⠀⡇⠀⠀⠀⢀⡠⠤⠁⡠⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠃⠀⠀⠈⠀⠀⠀⠀⠀⠘⠉⠁⠈⠁⠀⠀⡐⠁⠀⠀⠀⢀⠄⠐⠐⡢⠄⠀⠒⠒⡄
⠀⠀⠀⠀⠀⡠⠔⠒⠒⠤⡈⢉⠕⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⢠⢬⠀⠀⠀⠀⠀⠸⠡⠴⠀⡏⠤⠄⠨⠁⠁
⠀⠀⠀⠀⠰⠁⡠⠒⠂⡄⠘⡜⠀⠒⠂⠁⠀⠘⢀⣄⡠⠀⠠⢄⠀⠀⠣⣓⠱⠁⠀⠀⠀⠀⢀⡸⠀⠀⠀⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠰⡀⠦⡠⠀⡸⢀⠃⠀⠀⢀⠆⠀⠜⡃⡎⢠⠂⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⠔⠊
⠀⠀⠀⠀⠒⠵⣤⠠⠴⠕⠋⠀⣀⠤⠊⠀⠀⢂⡀⠘⠄⣓⣤⡖⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠺⣂⣤⣄⠀⠀⠬⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⢿⣿⣯⣬⣍⣹⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠾⠹⠹⠴⣶⣶⡶⣟⣴⡢⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣾⠵⣋⠀⠀⠀⠀⠀⠀⠀⢀⠞⢲⣭⡽⠿⢶⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠾⣅⡀⣀⡛⣀⣀⡀⠀⠀⠀⠀⠀⠀⢼⣟⢿⠿⣿⣷⣮⣽⡷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠛⢷⡇⠄⠐⢒⠤⡾⣿⣾⡃⣣
⠀⠀⠀⠀⠀⠀⠐⠞⠛⢳⡏⠛⠛⢻⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣛⣻⡯⣁⡎⠀⠀⠀⠀⠀⠀⠸⣆⠘⠷⠶⣴⣾⣶⡿⢉⣼⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠏⢙⡛⢻⣏⣹⣆⡀⠀⠀⠀⠀⢀⠀⠙⢷⡤⢤⢄⣀⣸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣷⣟⣻⣯⡾⢻⣝⡆⠀⠀⠀⠀⠑⠢⢀⠘⠻⠿⠿⠿⠿⠟⡉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣯⣿⣿⣽⣿⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠠⢇⡉⢚⣿⣰⠂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠉⠛⠙⣛⡉⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢫⢖⣩⣶⣿⣿⣿⣿⣧⣞⡛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⣧⠞⡹⢖⠇⠀⠀⠀⠘⣿⢻⣧⢤⡀
⠀⠀⠀⠀⠸⣿⣔⢿⣋⣀⣽⣿⣯⣽⣏⣿⡛⠄⠀⠀⠀⠀⡰⣿⡤⡾⡂⢄⠀⠀⠀⠀⠀⠹⣖⢣⡼⣠⡶⠃⡠⠔⠀⠀⠀⠀⣸⣿⣿⣧⡴⠃
⠀⠀⠀⠀⠀⠉⠛⢶⣿⣿⣿⣥⣹⣿⣘⠟⠧⠀⠀⠀⠀⢻⣴⢋⡿⢾⣿⣾⡗⠢⣄⠀⠀⠐⠒⠻⣿⣥⣦⣤⣈⣩⡤⠀⠀⣀⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣵⢈⣿⢷⢺⣟⣽⠇⠀⠀⠀⠈⠹⠁⡙⠒⠶⠉⠀⠀⣴⣿⠛⠉⠉⢙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣀⢠⣄⡠⣤⣠⣴⣤⣤⡀⠈⠻⣇⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⠁⠀⣴⣷⡄⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢿⢉⣷⣿⠿⢿⣿⣿⡿⡧⢣⠀⠀⠈⠉⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⡀⠀⠀⠀⣿⡄⡀⠛⠛⠃⡠⣼⡇
⠀⠀⠀⠀⣴⣤⣤⣾⣦⣤⣴⡆⠀⠸⣟⣥⡿⠤⢾⣶⣉⢙⣗⠶⢇⠀⠀⠀⠀⠸⢷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣥⣇⠀⠀⣿⣷⣿⡭⠤⣴⣿⣾⠁
⠀⠀⠀⠀⠹⡉⠉⠉⠉⢉⣿⠃⠀⠀⠉⢿⣄⣈⡹⠿⠿⣿⣿⣇⣀⣽⠀⠀⠀⠤⣄⢟⠉⠙⠹⠿⣫⠽⣿⣿⠟⠃⠀⠀⢹⣿⣿⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠓⢦⣬⣟⠛⢫⣾⠃⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⡴⠞⠿⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⣇⣠⣾⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⢶⣖⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠿⠿⠿⣿⣿⠭⠅⠀⣈⣉⣤⣤⣴⣶⣦⣄⡀⣿⣿⠟⠋
⠀⠀⠀⠀⠈⠁⠒⠒⠂⠀⠠⠄⠀⢼⡗⣧⣤⣤⣤⣤⣤⣶⣴⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⢰⣶⣴⣾⣿⣦⣤⣴⣦⡀⠀⠀⢨⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢻⣿⣿⡿⠂
⠀⢸⣿⡟⢸⣿⣿⣿⣿⠏⠀⠀⠀⠸⠇⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⠃
⠀⢸⣟⡇⠈⠈⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⠿⢿⣿⣿⣯⣿⣿⣶⣄⠀⢸⠃
⠀⣸⡏⣗⣖⠒⡒⠒⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠛⣿⣿⣧
⠀⢻⣃⣿⡏⡆⣷⡆⣷⠀⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠀⣿⣿⣿⡀
⠀⣦⣿⡿⠃⠃⡿⠇⣿⣄⣾⢣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⣿⣿⡆⠈⣻⣿⠇
⠀⢟⣿⡏⣴⡆⣀⡀⣿⣿⣿⣾⣧⡦⠀⣀⠀⠀⠀⠀⠀⠠⠙⠀⠀⣼⣿⣿⣿⣷⣿⣷
⠀⢹⣿⡇⠘⠁⠁⢀⣿⣿⣿⠯⢿⣿⣿⡟⠗⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠸⣿⣷⣤⣶⣟⣉⣀⣴⡞⣦⡾⠋⡽⡀⠘⡀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣽⣿⣿⡇⠹⠃
⠀⠀⢹⣿⣿⣿⣿⡀⢸⠏⢻⣼⠃⠀⣁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢹⣿
⠀⠀⢹⣿⡿⠋⠀⠳⣼⠀⠀⠹⣦⣶⡿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇
⠀⠐⠉⠁⣀⣠⠤⠂⠁⠀⠀⠀⠈⢿⣴⣛⡤⠁⠀⠀⠀⠀⠀⠠⠀⠙⢿⡄⢺⡗
⠀⠀⠾⠿⣷⣶⡀⢲⠰⡀⠀⠀⠀⠀⢻⣿⣦⠂⠀⠀⠠⠀⠀⡀⠀⡀⢠⣴⠏
⠀⠀⠀⠀⠐⣿⣷⡀⢳⡹⡄⢀⡤⠞⠃⠈⠌⢁⠀⢠⠆⠀⠔⠤⡀⣁⣿⡟⠂
⠀⠀⠀⠀⠈⢙⣿⣿⣤⣿⠿⠉⢁⠐⠀⠲⠀⠨⠎⠁⠀⠀⢄⣰⣾⣿⣿⡇⢀
⠀⠀⠀⠀⡠⣬⣥⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⣾⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⡷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣿⣏⣾⣿⣿⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣽⣿⡿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⡇⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣟⣿⣷⣤⣀⣀⣀⣀⣀⡀⠠⢤⣤⣼⡿⠿⢿⠿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⣤⣬⣽⣧⣝⢿⣯⣩⣭⣭⣷⣶⣶⢶⣶⣶⡦⠶⣶⣾⠋⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⣡⣴⣿⣿⣿⣻⣿⣿⣎⢻⣿⣯⣿⣵⣯⣵⣯⣥⣾⣥⣶⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⣿⢿⣿⠋⠉⠉⠉⠉⠉⠹⣇⢻⡍⠉⠉⠀⠀⠀⢹⣿⣿⣿⣿⡿⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⣼⠏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢰⡏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣷⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⢻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡆⠀⠀⠈⢿⣿⣿⣿⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡀⠀⠀⣿⣿⣿⠏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⡇⠀⢸⣿⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣷⠀⠈⣿⣿⣿⡈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⡆⠀⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣁⣀⣀⣀⣀⣤⣀⣠⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣹⡇⠀⣿⣿⣿⣿⣿⣿⡿⣿
⢀⣤⣤⡶⠾⠿⠟⠛⠛⢛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⡇⢿⡶⢾⣿⣿⣿⣿⣿⣷⣿
⢿⣯⣀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⣶⣾⣿⠘⣿⣀⣀⣀⣩⣿⣿⣼⣿
⠀⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⡄⠃⣿⡿⠟⣿⣿⣿⣿⣿⣿
⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣷⣶⣾⣿⣿⣿⣟⣛⢁⣿⣿⣿⣿⣿⣿
⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣙⣛⣛⣿⣿⣿⣿⣿⠛⣸⣿⣿⣿⣿⣿⣿
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡈⣩⣽⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⢿⣿⣿⣿⠟⠒⡆⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⣾⣿⣿⣿⡛⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣬⣭⣽⣿⣿⣧⡖⠂⣸⣿⡟⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⣾⣶⣿⣿⣿⣷⣶⡯⢀⣿⣿⣿⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣿⡏⣼⣿⣿⣿⣿⣻⣿⣿⣧⢿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⡿⢠⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣭⣭⣿⣿⣿⣿⣿⠆⣼⡏⠀⣿⡿⣧⣻⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣒⣲⣿⣿⣿⣿⡏⢰⣿⠁⠀⣹⣷⡈⢿⣿⣿⡜⣿
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣭⣹⣿⣿⣿⠟⠀⣾⡏⠀⢰⣿⣿⠿⣼⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣽⣿⣿⣿⣶⡆⣸⣿⠁⠀⠘⢿⣿⣦⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣀⠀⠀⢉⣩⣭⣭⣿⣿⣛⣛⣳⣤⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣛⣛⣛⣛⣉⣙⣛⣛⣛⣛⣛⣛⣩⣭⣭⣭⣭⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉
⠀⠈⠁⠉⠈⠃⠀⠀⠁⠀⠀⠀⠘⠀⠁⠀⠈⠀⠈⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⠤⠒⠒⠂⠐⠒⠒⠤⢁⠂⠄⠀⠀⠀⠀⠆⠢⠠⠤⠆⠤⠄⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⢀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠊⡠⠊⣀⠔⢊⡩⠥⠤⠭⣉⠐⠠⠈⠢⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢔⠡⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠢⠈⠄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⠠⠀⠔⠀⠊⠀⠀⡅⠀⠀⠀⠀⠀⠈⠓⢢⡀⠀⠀⢰⡀⠀⠀⠀⠈⠂⠁⠘⠀⠂⠀⠀⠀⣜⣝⢍⠑⠠⠤⢄⡀⠀⠀⢀
⠀⠀⠀⠈⠈⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⢆⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣄⠀⠀⠀⢿⡀⠁⠑⢄⢀⠀⠹⠀⠀⠙
⠀⠀⠀⡀⠀⠀⣀⠤⠔⠚⠒⢒⡒⠠⠤⠀⠀⠀⠈⠑⠢⠔⠁⠀⠀⠀⠀⠀⡤⠐⠁⠀⠀⠀⠀⠀⠁⠂⠀⠈⢳⡄⠀⣸⠀⠀⡰
⠀⠀⠀⠂⡠⠺⠑⢢⠈⢀⣰⠀⠈⠳⠆⠀⠈⠢⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠦⠀⠤⠤⢤⡀⠀⣀⠀⠀⠀⠀⣠⡇⢔⠋⠀⢺⡀
⠀⠀⢀⡾⠁⠀⠀⡘⠤⠂⠈⠓⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⢺⢩⣹⠈⠀⠀⠀⠑⢄
⠀⠀⡼⠀⠀⠀⠀⠁⢀⣀⣀⠀⡠⠄⠀⢄⢠⠔⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠂⠂⠒⠁⡠⠊⠀⡇⠚⠇⠐⠀⠀⢄⠐⠈⠣⡀
⠀⠀⠗⠈⠀⠁⢢⡞⠁⠀⢨⢹⠃⠀⠀⠀⠿⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠶⣶⣶⣤⣄⠀⠀⡠⠊⠀⠀⢸⢁⢱⠀⠀⠀⠀⢀⠀⠀⠀⠈⠢⡀
⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⡆⡄⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠻⢧⣄⣀⣀⡼⠄⢇⠀⠘⢂⡼⠘⣤⠀⠀⢀⡀⠈⢢⡀⠀⠀⣠⠜⡄
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢳⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠑⠔⠃⡇⠀⠉⠀⣆⠀⠀⠀⠀⠙⠆⢀⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⡆⠀⠀⠄⠠⠄⠂⠈⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⠠⠤⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⢀⡀⠀⠀⠀⠀⢰⡉⡕⠒⠈⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠅⠀⠂⠀⡇⠁⠈⠁⠀⠅
⠀⠀⠀⢰⠄⠀⠀⡀⠀⠀⠀⠀⠀⠧⣑⡡⠇⠀⠀⢈⠂⠀⠙⠳⢤⣄⣀⣠⡤⠤⠒⠒⠂⠀⠀⠀⠀⠘⢀⡀⠄⠀⠈⠒⠂⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠭⠉⠀⠊⠁