Pepperoni Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠩⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠒⠲⠦⢤⣀⣀⠀⠀⠈⠉⠤⠿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣶⡄⠀⠀⠀⠀⠈⠉⠳⢧⣴⢂⡀⠈⢩⡭⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⡴⢫⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⡇⡖⢘⣫⣭⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⠷⣾⣵⣯⠾⠃⠀⠀⣀⡴⣶⢶⡶⣤⡀⠀⠈⠻⣧⡞⢹⢰⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣡⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢞⡵⣫⢞⡵⢻⣄⣠⡴⢾⠃⣾⣸⣷⠋
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡿⢟⡥⢞⡽⣷⠀⠀⠀⠀⠀⠀⠸⣷⢋⣼⣡⣿⡖⢻⣏⣼⣷⣿⠿⠛⠉
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⢷⣫⣖⣫⣾⠟⠀⠀⠀⠀⠀⠀⠀⡼⣿⣩⣿⣾⣿⡿⠟⠋⠉
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠉⠉⠉⢁⣀⣤⣤⣤⣀⠀⠀⣸⣿⡿⠿⠛⠉
⠀⠀⠀⠀⢸⡀⠀⠀⣠⣶⢦⡀⠀⢠⣿⣧⣷⣿⣿⣿⣷⣾⣿⠏
⠀⠀⠀⠀⠈⣧⠀⢰⣧⣧⣿⡷⠀⢸⣿⡿⠟⠋⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢸⡄⠈⣿⣿⣿⠷⣤⣾⣿
⠀⠀⠀⠀⠀⢸⠇⠀⢸⣧⠀⠀⠻⠿⠟
⠀⠀⠀⠀⠀⠸⣄⢀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠓⠦⣄⣤⡤⠴⠦⣤⣤⣤⣤⣄⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣭⣷⣶⠶⢒⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⢦⣤⡀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡷⢦⣬⣷⣼⣦⣳⣤⣀⢰⣤⣦⣀⣠⡀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠷⣀⣢⣾⡿⠃⢨⠙⠻⠷⠾⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣄⠉⠙⠉⠀⠀⠈⠳⠋⠀⠀⢼⠻⠋⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡟⠂⠀⢠⣴⠾⠭⡛⣦⡀⠀⠸⣄⣴⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡸⠘⠆⠀⢻⣷⠀⣄⣠⠟⠀⠀⣧⣉⠉⣙⣿⣿⣿⣿⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡍⠁⠀⠀⡄⠀⠈⠛⠉⠀⠀⠢⠀⠙⠁⣾⣿⣿⣿⣿⠃
⠀⢠⣾⣿⣭⣝⢦⠀⠀⠀⠀⠀⠀⢀⣼⠀⣄⠀⠀⣠⣶⡶⠊⠿⣦⠀⢠⢲⠿⣷⣄⣼⡟⣵⡿⠃
⠀⠈⣿⣿⣿⣿⡧⢳⡀⠀⠀⣠⠚⠋⠉⣷⡌⢻⣄⠘⢿⣷⡶⠾⢛⣴⣮⡀⣠⣼⣿⢏⣼⡟⠁
⠀⠀⠘⢿⣿⣿⣿⣆⠙⣶⣾⣧⡱⢤⣤⣿⠇⠈⠁⠀⢸⡇⢀⠀⠘⢿⣿⣿⣿⡿⢃⡼⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣷⣌⡛⢿⣿⣿⣿⣿⡷⡷⠒⢢⣀⠛⠋⣤⣶⣦⣿⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣮⣝⠛⠿⣧⣀⣠⣴⣿⣷⠟⠛⢛⣻⠽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢶⣤⣤⣭⣭⣭⠥⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⢈⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠐⠁⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠄⠒⠲⠄⠀⠀⠀⠀⠤⠒⠈⠀⡀⠀⠀⠀⠀⠀⡀
⢐⠶⡠⠄⣀⠀⠀⠀⠀⡠⠄⠒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⠀⠀⠀⠀⡇
⠀⠑⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠛⠀⠀⠀⠀⠀⠀⢀⠀⠔⠁⢀⠁⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠡⢌⠀⢄⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠠⠊⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠁⠢⡈⠁⠐⠠⢄⠀⠀⠐⠀⠀⠀⠀⠉⢀⠤⠐⠈⠁⠀⠀⠈⠈⠁⠒⠤⡀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠐⠤⡀⠀⠄⠀⢰⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡈⠂⢄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠞⠀⡀⠎⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠂⢄⠈⠂⠨⢑⠈⠡⠔⠒⠐⠢⠈⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⢀⠄⠀⠑⠠⢀⠀⠈⠐⠠⣀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠖⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠀⡀⠀⠈⠁⠚⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⢠⠀⠑⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠄⠀⠀⠀⢸⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⠀⠀⠒⠤⠠⠆⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠚⠿⠋⠉⠉⢉⣉⡉⠛⠛⠛⠶⢶⣶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⡾⠟⠋⣉⠁⠀⠠⠒⠒⠒⠉⠀⠀⠄⠀⠀⢉⣉⣐⡰⠤⠀⠀⠈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢻⠘⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⣷⡘⡻⣝⡄⠀⠀⠀⠈⡜⡷
⠀⠀⠀⠀⠀⠀⠀⢣⡁⠀⠠⣄⣔⢒⠲⠒⠂⠄⢡⠤⠀⣼⡇⢠⠂⠋⣀⣀⠈⠳⡆⠀⠀⢹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⠈⠀⠀⠀⠀⠆⢧⠤⣁⡀⠁⠊⣇⠀⠁⠀⠈⠋⢀⠀⡇⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠈⢈⠀⠀⠀⠀⠀⠚⠰⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣀⠀⡀⠀⠀⡴⠁⠂⠈⠑⠦⠤⠤⠤⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡺⣧⠀⢦⠟⠗⠄⠀⠒⠊⠀⠀⠐⠂⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣤⠑⢀⢰⣦⡄⠀⠀⠀⢂⠀⠙⡱⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡇⢸⠷⣋⢀⠈⠀⠀⡼⠙⠋⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣼⣱⡎⠀⠐⠀⢸⣗⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠁⠀⠀⠤⣤⠀⠗⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠰⠠⠀⠃⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡄⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡀⠀⠈⠉⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠙⠛⠳⣤⣄⡀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣠⠤⣤⢄⡀⠀⠉⠙⣧⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠋⣀⡀⢀⣥⣈⠀⢀⣀⠹⡂⡀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠛⢛⠃⠸⡏⠁⠀⠀⠀⠀⠈⠳⢄⣄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠆⠀⠀⠈⠲⠖⠃⠀⠀⠀⠈⠈⠙⠒⢦⡈⢳⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠀⠁⡀⠀⠀⣀⠀⠀⡄⠀⠈⠀⠀⡀⠀⠀⢱⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣓⢒⣡⠐⡠⠤⣄⡀⠀⠸⡄⠀⠁⠀⡀⠀⠀⠀⢸⣿⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢎⠸⠷⠇⢀⠔⠁⠀⠀⢳⣄⠀⠀⠀⠀⣀⡴⠋⣿⣧⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⡄⠀⠀⠙⢛⠆⠀⠀⠀⢈⣙⣛⣛⣭⡥⠤⠾⠁⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠁⠁⠀⠈⣑⣲⣾⡵⠶⠞⠛⣛⣋⣩⡭⠤⠤⠖⠒⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣐⣒⣫⠭⠭⠖⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠓⠛⠛⠛⠒⠶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠻⣹⣇⡆⣤⡀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣈⠛⠻⠿⠷⠷⣧⡆⡶⢀⢀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⡊⡩⠃⠀⠀⠀⠀⠀⢙⠳⢿⣼⣰⣆⡇⡄⠠⢀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⠈⠉⠉⠛⠳⢧⡞⡀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣀⡤⢶⣚⣿⣛⣛⣓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢡⠆⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡼⡫⠊⠁⠀⠀⠀⠘⠍⠟⠂⠙⢦⠀⠀⠀⠀⠀⠀⠀⣿⡟⣰⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣾⠁⠀⢀⣀⡀⠀⠀⠀⣠⣤⣤⡀⢸⠇⠀⠀⠀⣠⠶⣄⠘⣧⠹⢰⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢻⣤⡞⣏⣍⣹⠆⠀⢸⣧⣦⣮⣽⠏⠀⠀⠀⠘⠧⠚⠁⠀⠈⠳⣬⡸⣧⡄⡀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠲⢤⡀⠀⠀⠉⠉⠉⢈⡟⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣅⣁⠓⢶⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢤⠀⠳⡄⠀⠀⠀⠀⣾⢀⡀⠀⢀⡎⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠉⠙⠳⣦⣰⠃⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠧⢼⡷⠀⢳⠀⠀⠀⠀⠘⠦⣬⣭⠵⠞⠃⠀⠀⠀⠀⡠⠔⣒⡋⠉⠉⠉⠉⡩⠙⠛⠳⢦⣄⠀⠀⠈⣿⢺⡄⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⠰⣫⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢞⣁⣨⠄⠀⠀⢊⠀⢀⠔⠀⠄⠙⢷⡄⠀⠈⠻⡀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠚⠞⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⢿⡄⠀⢰⡗⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣤⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣖⣹⠆⠀⠀⠀⢰⠇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡞⠁⠀⢀⡄⠀⠀⠘⣧⢠⣿⠊⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣶⣀⣸⡇⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⠀⠀⡿⢸⡇⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣈⣉⣠⣤⣖⠋⠀⢀⡴⣛⣛⣒⣶⣦⣄⠀⠀⠀⠀⠀⢻⡄⠀⢀⠴⠂⠀⠀⠀⠒⡆⠀⠀⠀⠀⣠⠄⠀⠀⢰⡇⣾⣷⡁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⢡⠞⠉⣭⢹⡄⠘⡇⠀⠀⠀⠀⢙⣹⠂⠀⠀⠀⠀⠘⣷⠜⢁⡤⠂⠀⠀⠉⠈⠁⠀⠀⠀⠘⠧⠤⠀⣴⡟⢀⡿⣿⣥
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣿⠀⠀⠻⢿⣿⡾⠃⠀⢀⡴⠛⠉⠁⠀⠀⠀⢀⢀⠀⠹⣷⣉⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠏⠀⢸⣇⣿⣷⣦⣤⣤
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡈⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⡄⠀⠀⠀⠰⠆⠀⠀⠈⠻⢷⣶⣦⣤⣤⣤⣤⣤⣴⠶⠾⠋⠁⠀⠀⠀⣾⢏⠁⠄⡏⡼⡿
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢳⡡⡀⠀⠀⠀⠀⠀⠈⠉⠋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣀⣀⣀⣤⣤⣤⡶⢶⢾⠇⠈⠈⠘⠰⢹⠹
⠀⠀⠀⢀⡞⠀⠀⢠⠴⠒⣦⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠖⢋⣠⠞⠁⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣶⣿⠿⣿⠟⡿⢛⠟⠉⠟⠁⠚⠀⠊⠈⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢀⡞⠀⠀⠀⠹⠤⠒⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⢛⣛⣩⣥⣶⣶⡿⣿⢿⢿⡟⡿⠻⠏⠹⠋⠠⠋⢀⣁⣀⣀⣤⣤⣤⡴⠶⠶⠶⠞⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠟⡿⢛⠟⠹⠋⠋⠀⣁⣀⣀⣤⣤⣴⠶⠶⠾⠛⠛⠛⠉⠉⠉
⠀⡼⠁⠀⠀⢀⣀⣠⣤⡴⣶⠞⠟⠛⠋⠙⢁⣐⣡⣬⣤⡴⠶⠶⠛⠛⠛⠋⠉⠉
⣼⡡⠴⠒⠋⢉⣁⣀⣠⣤⣤⠶⠶⠞⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⢤⣤⠶⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⠉⠙⠛⠻⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣋⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠉⣭⡉⠉⠙⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⢀⡾⠋⠀⠀⣀⣀⣀⡀⠀⠀⢷⡿⢀⡴⠞⠲⣄⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⢠⠏⣰⢖⡦⠀⢻⡄⠉⠙⢷⡀⠀⠀⠘⣇⠀⠀⠘⣧⠀⠀⠀⣀⣌⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⢠⡟⠀⠙⠋⣁⠀⠀⠻⣤⣀⣼⠃⠀⠀⠀⠈⠓⠶⠶⠋⠀⠀⠀⣯⠀⠹⡎⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⢸⠁⠀⠀⢺⣍⣷⠀⠀⠀⠀⠀⢀⡴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣿⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⣶⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⣧⠀⠀⠀⢀⡴⢦⡀⠀⠉⠛⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣷⠀⠀⠀⣿⠘⣧⠀⠀⠀⠀⠀⠀⣈⡛⠶⠋⢀⣀⡀⡘⢧⣀⡿⠀⢀⡀⠀⣠⣄⠈⣇⠀⠀⠀⠀⠀⢀⡴⠋
⢿⠀⣠⡄⠈⠓⠋⠀⠀⠀⠀⢠⡞⠉⢹⡆⠀⠸⣍⣉⣹⠆⠉⠀⠀⣿⠙⣧⠙⠾⠃⣿⠀⠀⠀⢀⣴⠏
⠸⡆⠙⠃⠀⠀⠀⠀⢠⡞⢲⡌⠳⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⡿⠀⠀⣠⠞⠁
⠀⢻⡀⢸⡋⠳⡄⠀⠀⢿⡀⣻⠀⠀⠀⣀⡀⠀⠀⣴⠲⣄⠀⠀⢀⣠⣄⡀⠀⠀⣸⠇⣠⠞⠁
⠀⠀⢳⡄⠙⠶⠃⠀⠀⣈⡙⠉⠀⠀⠈⢯⣽⠀⠀⠈⠙⠉⠀⠀⠺⠥⠴⠇⠀⣰⣯⠞⠁
⠀⠀⠀⠹⣆⠰⣿⡇⢺⡋⠙⢧⡀⠀⢀⣀⡀⠀⠀⢠⠶⣄⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠙⠶⠞⠁⠀⢯⡈⠙⣷⠀⠈⠷⠾⠁⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣿⣽⠆⠀⠉⠛⠁⠀⢀⣀⣤⡴⠞⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣷⣶⣶⣶⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⠀⠀⠀⠀⠙⠀⠀⠄⢀⠄⡂⠡⠀⠂⠈⠄⠐⢈⠀⠈⢄⣀⠀⠁⠢⡀⠀⠘⠄⠀⠀⠀⠀⠈⠀⠀⠄⢀⠄⣂⠅⠀⠒⠈⠄⠐⠌⠀⠈⠂⣀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂⠔⠁⠀⠈⠀⠀⠀⠅⠀⢀⠀⠀⠀⣀⠌⠑⠐⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠂⠌⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠈⠑⠘⡀
⠀⠀⡀⠀⠀⠀⠀⠀⢀⠰⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⢰⠀⡆⠀⠀⠠⡀⠀⠀⡀⠀⠀⠀⢸⢀⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⢄⠃⠐
⡀⠀⠀⠄⠀⠁⠀⠀⠈⢄⠢⡑⠒⠀⠀⠀⢀⠀⠦⠀⠀⠀⠀⠂⠀⡈⢠⠁⢀⡀⠀⠀⡄⠀⠁⠀⠀⠈⢆⠢⡃⠐⠈⠀⠀⢀⡀⢦⠀⠀⠀⠀⠂⠀⡀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⠄⠐⠀⠁⠂⠀⡠⠄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠈⠢⣀⠐⠀⠁⠂⠀⡠⠄⠂⢈⠔⠁
⠄⠠⠄⢀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠑⠂⠌⣑⡀⠀⣀⠤⠀⠀⠈⠀⠀⠀⡀⠀⠄⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠂⠄⣁⡀⠀⣀⠤⠀⠂⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⢂⠈⠁⠒⢂⠠⠀⠄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠠⠔⢂⠩⠁⠒⠆⠠⠄⠄⡀⠀⠀⡀
⠀⠀⠀⠔⡪⠑⠒⠈⠀⠀⠄⠀⠀⠑⠄⠀⡈⠢⡀⠉⠁⢰⠉⠉⠑⠠⣀⢀⠀⠀⠀⠀⠄⡨⠑⠒⠈⠁⠀⠀⠀⠀⠱⠄⠀⠈⠀⡀⠈⠀⢰⠉⠉⠑⠤⡀
⠀⠀⠆⠈⠀⠈⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠑⠌⠄⠀⠈⠉⠛⠉⠐⢄⠀⡱⠀⠀⠌⠈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠐⠀⠑⠈⠄⠀⠈⠉⠋⠉⠑⢄
⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠉
⠀⠀⠐⡡⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡁⢀⣀⡀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠐⢀⠄⡐
⡀⠀⠀⠈⠢⢀⠀⠑⢄⠀⠀⠀⠐⣀⠄⠂⣈⠡⠊⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⡀⠀⠀⠈⠢⢄⠀⠑⢄⠀⠀⠀⠐⡀⠔⠂⢈⠡⠊⠀⠀⠀⠀⡀⠂
⠄⠀⠀⠠⠀⠀⠈⠐⠀⠌⠀⠈⠉⠄⠂⠁⠀⠀⠀⠄⠠⠀⠈⠀⠀⠀⠂⢀⠠⠄⠁⠀⠠⠄⠀⠈⠐⠠⠈⠁⠈⠉⠄⠂⠁⠀⠀⠀⠄⢠⠀⠈⠀⠀⠀⠒⢀
⢀⠀⢀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⡀⢀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠁⠀⠀⠐⠀⢠⠀⠀⠀⠀⠀⡀⠄⠂⣁⠠⠐⢀⠠⠉⠢⠈⠁⠂⠄⡀⠀⠀⢰⡁⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⡀⠄⠊⢁⠤⠐⢈⠠⠉⠢⡈⠁⠒⠄⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠁⡰⢁⠂⠀⠀⠀⠀⠀⠀⠙⠀⠀⠑⠒⠀⠠⢌⢂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⡐⢁⠒⠁⠀⠀⠀⠁⠄⠑⠀⠀⠐⠒⠀⠠⢌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠁⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠒⡄⢀⠀⡆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⡄⢀⠀⠇
⠀⠀⠂⠀⠀⠄⠀⠀⠐⠈⡀⠖⣐⢠⠀⠀⠀⠀⡀⠀⠀⠀⠈⡁⠀⠨⠀⠆⠀⠀⠀⠂⠀⠀⠖⠀⠀⠠⠘⡀⠖⢐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡑⠀⠈⠀⡆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⢌⠂⠠⠤⢀⠀⢐⠀⠝⡀⠀⠀⠀⠀⠠⢀⠜⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠐⢌⠂⠀⠤⢀⠀⢐⠂⠌⠄⠀⠀⠄⣀⠠⢊⠜
⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠁⠢⢄⡀⠢⢄⠀⠀⢀⠤⢊⡁⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠁⠢⢄⡈⠱⢄⠀⠀⠀⠤⠊⡁⠠⠐⠁
⠁⢤⠁⠀⠀⠀⠀⠀⡀⠤⠄⣀⡀⠀⠈⠁⠒⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁⢄⠁⠀⠀⠀⠀⠀⡀⠤⠀⣀⡀⠀⠀⠁⠒⠀⠀⠒⠈
⠀⠀⠀⢀⠠⢔⡊⠡⠐⠀⡀⠀⠑⠄⠀⠐⠢⠀⠀⠦⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⣂⠡⠔⠀⠀⠀⠑⢌⠀⠐⠢⠀⠀⠢⠀⢀⠤⠤⢄
⠀⠀⡐⠡⠊⠠⠀⠀⠀⠀⠁⣀⠀⠈⠀⢀⠀⢄⠢⠀⠀⠸⠤⠠⠤⢍⠒⠐⢄⠀⠀⠠⠡⠊⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⢄⠢⠀⠀⠸⠤⡠⠤⢍⠒⠐
⠀⢠⠁⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⠀⢀⠀⠀⠀⠀⠑⠠⠊⠀⠀⠁⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⠀⢠⠀⠐⠀⠀⠑⠤
⢀⡀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠢⡐⠒⠒⢄⠀⠐⠀⠀⠀⠀⠀⠀⠠⠔⡠⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠢⡐⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⡡⠂⠀⠀⠀⠀⡀
⠂⡆⠀⠀⠈⠑⠠⢀⠑⠢⠄⠀⠄⠂⡁⠄⠒⠈⠀⠀⠀⠀⠠⠂⠀⠀⣀⠀⠀⠂⠀⠀⠀⠈⠐⠠⢀⠑⠠⠄⠀⠤⠒⡁⠄⠐⠈⠀⠀⠀⠀⠠⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠐
⠄⠒⠀⢒⠀⠑⠄⠀⠀⠀⠀⠀⠀⡀⠄⠐⢀⠀⠀⠤⠀⠠⠄⣀⠀⠀⠀⠀⢀⠄⠀⠀⢒⡀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⢀⠀⠠⠤⠀⠠⠄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⢀⠀⠂⢈⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⣀⣤⣴⣴⡟⠽⠛⢿⠀⠀⡿⢛⣻⡦⢶⣄⣀⡀⠀⠀⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠁⢀⣤⣴⣿⣿⣿⣿⢟⢠⡀⢘⠳⠀⠀⢻⠡⣴⠦⣼⣿⡟⢙⣢⣴⢤⡀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣰⣾⡽⠋⠀⢾⣿⣟⢧⣾⢯⡩⣍⡉⣷⡀⠀⡇⢠⣧⣀⣻⣀⣿⣿⡿⣿⢶⡝⠲⣦⣴⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⡀⠘⢯⡀⠙⠋⣰⠟⠋⠳⡙⣛⡓⠋⠷⣭⡁⠀⡷⣿⣿⡟⡔⢲⡀⣃⢻⡻⢰⠈⣄⡟⠁⢠⡄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡟⢻⣆⠈⠳⢶⣿⡽⠀⠾⠓⢻⣧⣻⡀⠙⠉⠁⠀⠛⠿⣿⢾⡑⢯⠷⡁⢙⢡⢃⡾⠋⢀⠐⢻⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢚⠿⠟⠱⡄⠈⠻⣤⣰⣤⣀⡛⣿⣿⢧⣐⣠⠀⠀⡀⣸⡿⡢⣴⣺⣩⣅⣘⣻⠋⢀⣴⣿⣿⣿⡷⢸⣆
⠀⠀⠀⠀⠀⠀⡴⠀⠀⢰⠟⠴⢹⣦⣼⡆⢠⠅⡄⠀⠙⢧⣴⣦⣹⠟⠻⢭⣰⡇⠀⣴⡇⣰⢨⡭⣍⣘⡬⠛⠁⣰⣿⣟⢏⣫⣴⣷⣟⠸⣧⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠁⠀⣠⡧⢰⡾⠤⢯⣔⣡⢀⠼⠶⡄⠀⡀⠙⣦⠚⢛⠀⢦⣽⠇⠀⣷⣺⣉⡈⢿⣭⠏⠁⣠⡾⢿⡷⣭⣾⣿⣿⣿⠯⠤⡌⣧⠀⠐
⠀⠀⠀⠀⢀⠀⠀⠀⡛⠀⠋⣾⠟⠻⡟⠂⢬⣨⠉⠲⠞⡁⠄⠈⠻⣯⣐⣾⣡⡄⠀⡏⠿⣟⣧⠝⠁⣠⣾⣿⣿⣾⣴⣻⢯⡟⡛⣿⣿⢷⡈⢸⠀⠀⠁
⠀⠀⠀⠀⡘⠀⠀⣻⡃⣰⡾⡓⣛⣋⣵⠎⣽⡟⢳⣏⣤⠐⢶⣥⡄⠈⠻⣥⣷⡇⠀⡷⣮⡟⠃⢠⣎⣻⣯⡿⠿⡿⢵⢹⣭⣟⣰⣿⢏⡎⡄⠈⡗
⠀⠀⠀⠠⠀⠀⠀⣿⢹⡿⡈⠺⡟⠛⠙⠀⢤⣈⣩⠁⣸⠶⡞⠋⡴⢒⣀⠈⠳⡇⠀⣷⠋⢀⣤⣿⢯⡿⢳⣦⣭⠝⠟⣭⠍⢳⣟⡿⠮⡀⢿⠆⢸⡀⠀⡂
⠀⠀⠀⠀⢤⣤⣼⠿⠬⠤⠦⠤⡴⠾⢿⠤⠴⣤⠥⠴⠦⢾⡴⠼⠤⠥⠷⠷⠄⠀⠀⠀⠴⠯⠿⠿⠿⠷⠿⠿⠶⠴⠤⠤⠤⠰⠿⠶⠿⠾⠾⠦⠼⠷⠾⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠉⠲⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣮⡻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣉⣀⣀⣤⠾⠀⠀⠀⠀⠀⡀⠈⡆⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⢋⣼⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠚⣠⠤⡉⠉⠁⡀⠀⣀⠘⠶⠶⠞⠃⠀⣹⠀⠀⢀⡟⠀⠀⠀⣀⣴⡿⣿⢧⣶⣶⣿⣿⣿⣿⣏⣛⣋⣡⣾⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⣀⠔⠉⠀⠀⢷⣄⣼⡀⠒⠁⠈⠁⠀⠠⠒⣒⣈⣉⡥⠤⠖⠋⠀⠀⣠⣾⣿⣿⠸⢿⡗⣿⣟⣽⣿⣷⣾⣿⣿⣟⣿⣭⣭⡵⠿⠟⠋
⠀⠀⣠⢚⣁⠀⠄⠤⢐⣊⣉⠩⢄⣀⣠⠶⣄⠀⡏⠉⠉⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣟⣷⣤⣤⢿⣿⣿⠿⠿⣿⡟⠉⠉⠉
⠀⠀⠘⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠈⠀⠀⢸⣀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠛⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠎⠀⢰⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣀⠀⠀⠀⠀⠈⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡰⠁⠀⣠⣄⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡜⠁⠀⠀⠻⠋⠀⠀⠀⢸⣷⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⣶⠄⠀⠀⠀⠈⠉⠀⠀⢠⣤⡀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠈⢣
⠀⠀⠀⠀⠀⢀⠞⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⡠⢧⡀
⠀⠀⠀⠀⢠⣾⣷⣄⡀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⣀⣴⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣦⣄⣀⠈⠉⠐⠒⠒⠒⠠⠤⠤⠤⠄⠒⠒⠒⠊⠉⠀⣀⣠⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠛⠛⠛⠓⠲⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⣏⣿⣴⣠⡄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣈⡙⠛⠻⠷⠿⢿⣎⣴⢀⢀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣎⣡⠟⠀⠀⠀⠀⠀⠉⡻⠾⣼⣴⣆⣇⡄⡠⣠⠀⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠀⠀⠈⠉⠙⠛⢧⡞⡀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢀⡴⢖⡻⠯⠭⣭⣛⡓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⠂⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡴⠫⠊⠁⠀⠀⠀⠁⠀⠝⠁⠈⢳⡀⠀⠀⠀⠀⠀⠀⣿⡟⡼⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⡇⠀⣀⣠⣀⠀⠀⠀⣤⡶⢦⣀⣸⠇⠀⠀⠀⡠⠒⣦⠘⢧⡙⢸⢀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠘⢷⣞⣣⣥⣬⡇⠀⠘⣧⢧⣷⠿⠋⠀⠀⠀⠘⠓⠋⠀⠀⠈⠻⢮⡘⢷⡠⡄⡀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠲⣄⠀⠀⠀⠉⠁⢀⡞⠀⠀⠐⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢥⣅⣑⠷⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠲⣄⠈⢧⠀⠀⠀⠀⢸⡁⢤⣀⣀⠄⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠉⠛⢦⡞⡀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠙⢒⡿⠃⠈⡆⠀⠀⠀⠀⠛⠶⠶⠖⠛⠁⠀⠀⠀⢀⠴⢚⡩⢅⠀⠀⠀⢀⠔⠈⠉⠛⢶⣤⡀⠀⠈⣇⣳⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠔⢫⡦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠻⣤⠴⠂⠀⠀⡡⠂⠠⠊⠐⠁⠈⢻⡆⠀⠈⢹⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠐⠈⠑⠁⢀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢿⡄⠀⡼⡋⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠰⣦⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠾⠴⠃⠀⠀⠀⢰⡇⠀⠀⢀⠴⡄⠀⠀⠀⠀⠰⣏⠀⢀⡤⠂⠀⠀⠸⡇⢸⡟⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠸⠧⠤⠞⠀⢀⡴⠋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢰⡇⣿⢎⠄⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⡤⠤⠤⣶⣿⣅⡀⠀⣾⠩⠐⠩⠽⢿⢦⡀⠀⠀⠀⠀⢸⣇⢀⡠⠊⠁⠀⠀⣀⣉⡇⠀⠀⠀⢀⠖⠀⠀⢀⣼⢁⣿⣯⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡞⠁⢸⣆⣷⣀⣽⠀⠀⠀⣀⣈⡴⠃⠀⠀⠀⠀⠀⢿⣏⣠⠖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⣠⡾⠃⢸⡏⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠘⡇⡄⠈⠛⠻⠛⠁⠀⢀⣼⣉⡀⠀⠀⠀⠀⢠⠒⠀⠈⠻⣧⣞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠁⠀⣾⡤⠿⠿⡷⣶⣾
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢿⢣⠀⠀⠀⠀⠀⠀⠸⢯⣯⣿⣷⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⠻⠿⠶⠶⠶⠶⠾⠟⠛⠉⠁⠀⠀⢀⣠⡟⡰⠰⢸⢡⢳⢻
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⡡⡀⠀⠀⠀⠀⠀⣀⠄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⡶⣶⠞⣻⠋⡝⠙⠀⠁⠀⠀⠀⠇⠋
⠀⠀⠀⣼⠁⠀⠀⡞⠉⣩⠆⠀⠀⠀⠙⠳⢦⣤⣀⣀⣈⣥⠶⠋⣀⣀⣤⣤⣴⣶⣶⣶⣿⠿⡿⠛⡿⢋⠟⠉⠋⠐⠃⠀⠁⠀⣁⣀⣀⣀⣤⣤⣤⣤⣤⡤⠾
⠀⠀⣸⠃⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣵⣶⡿⣿⣿⠟⡿⠹⠋⠋⠘⠀⠁⣘⣁⣀⣥⣤⣴⠶⠶⠶⠛⠛⠛⠋⠉⠉⠉⠉
⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⡾⠛⡿⠋⠝⠁⣊⣈⣁⣠⣤⣤⡴⠶⠾⠛⠛⠛⠉⠉⠉
⣰⠃⢀⣀⡤⠤⠖⠒⠟⠹⢋⣈⣁⣠⣤⣤⠶⠶⠾⠛⠛⠉⠉⠉
⠻⣮⣥⣤⣤⡴⠶⠶⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠶⠶⠶⠶⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠞⠋⠉⠀⢀⣀⣀⣉⡭⠁⠀⠠⣤⣀⣤⣤⢴⣤⣀⠀⠀⠀⠉⠙⠓⠚⠒⠶⢤⣀⡀
⠀⠀⠀⣠⠶⠛⠉⠉⢁⡄⠀⠴⠿⠖⠚⠉⣀⣄⣀⠀⠀⠠⢀⣀⣤⣀⢀⣠⠀⠉⠉⠓⢒⠋⠀⠐⠦⠤⣄⠀⢨⠉⠉⠛⠲⢤⡀
⠀⠠⠚⠁⠀⢠⣤⠶⠋⠀⠀⠀⠀⡀⡄⠠⣥⣼⣿⢃⣤⡄⠀⠀⠀⠉⠈⠁⢸⠀⠀⠁⠀⣐⣣⣴⣦⠲⢖⡂⠈⠳⢦⣤⡀⠀⠈⠢
⠀⠠⢤⡀⠐⠋⠀⠀⠀⠀⠭⠤⠠⠁⠸⣀⠀⠈⠋⠢⣭⣡⡤⠤⣀⣀⣀⠀⡸⠀⠀⢀⡀⠈⠛⠻⠿⠊⠛⠃⠀⡀⠀⠈⠙⠂⣠⠤
⠀⠀⢀⣽⠀⢀⡄⠐⠂⢀⣀⠀⠀⠄⠀⠈⢁⠠⠤⢀⣰⣿⣂⣤⣴⣶⡄⠀⢄⢀⠠⣁⣀⣠⠤⠖⠒⠒⢛⡷⣞⠁⢀⠀⠀⠸⣇
⡆⠀⠀⠹⡆⠈⢛⡲⣶⣶⣿⠦⠤⠤⠄⠀⠀⣉⣛⡉⠘⢿⣿⣯⣬⣙⣀⣠⢨⠇⠤⣤⣾⣄⢀⣀⠲⡄⢡⣶⠀⣀⣤⣄⠀⢸⠁
⠇⠀⠀⣰⣅⣀⠈⠻⠿⠟⢋⡀⠂⢀⠀⠀⠉⠀⠀⠉⠓⠶⠬⠍⠀⠈⡁⠀⣀⠤⠛⠶⢿⡿⠿⠟⠀⠃⠸⣿⣿⣩⡍⠉⢀⣸⡀
⠸⣦⠀⠀⠀⠈⠑⠆⠀⠀⠀⠉⠉⠉⠀⠀⣠⠀⣰⣶⡶⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠉⢉⡴⠞⠋⠉⠀⠀⣰
⠀⠻⣄⠀⠀⠀⠀⠀⠒⠒⠒⠢⣄⡀⠹⢌⠻⠿⠿⠷⠶⠃⠀⠀⣀⠋⠀⢀⣀⣀⣠⠤⠎⠉⠉⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠶⠶⠶⢦⣄⣀⣠⣀⣀⠈⠙⢋⣉⣤⣤⣤⣤⡴⠖⠛⠛⠛⠓⠒⠤⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠋⠉⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣫⠱⢄⡐⣖⣉⣤⣤⡀⠜⢦⠤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡀⢐⠓⠀⡄⢰⣿⣿⣿⣿⣿⡇⢂⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⠔⠁⠀⠀⡠⠀⢾⣿⣿⣯⣿⣿⡿⠃⠠⠄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠋⣀⠀⢰⠌⠀⠀⠀⣦⠈⠉⠉⠉⡁⠠⠠⠂⢀⡀⢠⣌⠙⢦⡀
⠀⠀⠀⠀⠀⣴⢃⠀⠀⠀⢺⣿⡿⣸⣄⡀⠀⠀⠀⢀⢀⣴⣶⣦⣄⠀⠀⠞⢊⣨⢉⣴⣶⣿⣷⣦
⠀⠀⠀⠀⢰⡁⢻⡔⢱⣿⡷⢿⣿⣿⣿⣿⡷⢀⣀⣀⠘⢿⡿⣿⣿⣿⡿⠟⠻⠟⠈⠻⣿⡿⣿⠿⣀
⠀⠀⠀⠀⠈⢿⣄⠉⣶⠀⢀⣄⠈⠉⠉⠉⠀⠷⡿⠿⢠⡤⠞⠁⠀⠀⠀⡤⢀⠀⠀⢀⣈⡠⠖⣤⣬⢣
⠀⠀⠀⠀⠀⠀⠉⠙⠻⡀⢸⠿⠷⠤⢤⣻⠀⠀⣠⠓⠶⠤⠖⠠⣄⡀⠀⠀⠀⠐⠀⠁⠀⠀⠶⢭⣥⡬⠱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠳⠔⠉⠉⠙⠋⠉⠙⠛⠓⠤⢄⣈⣱⣊⡐⠀⠀⠀⠀⢠⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠛⣤⡰⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢠⣍⡁⠉⠐⠂⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⢈⣀⣤⣦⠀⡖⢪⢉⣌⡛⢳⠚⠲⢦⡀⢑⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣤⣾⣤⣾⠿⢓⣚⣓⢃⣿⣥⣬⣿⣄⣐⡄⡟⠟⠀⢠⣶⠍⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⣐⣤⢻⠐⣾⠀⠉⢢⠋⢻⡿⢸⠋⠁⢸⣿⢻⣿⠞⠀⠀⢰⡏⠙⠗⣆⠈⢂
⠀⠀⠀⠀⠀⠀⡼⠁⣰⠿⣿⣿⣻⠿⢦⡁⢀⢿⣯⠩⡝⢶⣶⣟⡼⠟⠋⠀⣰⡈⡿⠁⠉⢸⣏⣃⠀⡄
⠀⠀⠀⠀⠀⡸⠁⣸⣿⣯⠟⢺⣱⡤⡞⡿⠿⢿⢿⣛⡷⣈⣼⡋⠂⠀⠀⠀⠈⣿⡇⠈⠈⣸⢿⣿⠄⢻
⠀⠀⠀⠀⠀⠇⢰⣿⣏⣿⠀⢀⣿⣿⡟⠀⣰⠻⣿⣌⣼⣉⠉⠀⡀⢴⣧⣤⣦⡿⠥⣴⠾⠋⢭⡿⣇⣠⡆
⠀⠀⠀⠀⢸⠀⣽⣿⣰⡟⠀⢊⣿⣿⣆⣱⣀⣀⣸⢟⠉⠀⠀⠘⠿⠛⠋⠀⠈⠉⠐⠚⠉⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠈⢈⣩⣯⣕⡭⣁⣼⣬⡭⢽⢿⣿⣴⣶⡂⢆⡴⢲⣦⢶⣶⢐⣶⠖⡒⠲⢶⢿⡛⠗
⠀⠀⠀⠀⠘⠀⢸⣧⣿⢿⡕⠩⠗⡋⡶⢛⣿⣿⣿⣽⠃⣬⡿⢿⠉⠛⠿⢳⣿⠤⣀⣸⣿⣶⠂
⠀⠀⠀⠀⠀⠄⠀⣿⡇⠀⢿⡤⠨⢷⣟⣻⡿⢿⣴⣿⡽⢏⣿⠛⣿⢇⡀⠀⠛⢻⠟⠈⢱⠟
⠀⠀⠀⠀⠀⠘⡀⠈⣿⣾⣿⣿⣷⢾⣯⠟⢱⢯⣏⣼⣧⠄⠁⠄⠚⢳⢆⠖⣾⠀⠋⣰⡏⠀⠎
⠀⠀⠀⠀⠀⠀⠐⠀⠉⢻⡿⢟⣾⢿⣇⢻⣀⠀⡙⣿⣛⣾⣃⣤⡂⢚⡎⠶⡙⣥⡞⠁⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⡀⢻⣿⣿⣟⠘⠉⢁⣴⣍⣿⣀⣥⠀⠉⠩⣤⣶⡿⠿⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠛⠺⢿⣿⣷⣿⣸⣉⣿⣤⣴⡶⠛⢉⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠰⠄⠀⡩⠵⢸⣁⣈⠀⠄⠖⠒⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡠⢂⢭⣬⣭⡐⡢⡀
⠀⣀⠝⢄⠱⠤⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠌⡂⠀⠀⢀⡀⣀⠀⠀⠻⠟⠂⠀⠀⠈⠀⠁⠁⠀⠠⡈⢊⢪⠢⡀⠀⠀⢀
⠀⠒⠉⢎⢒⡢⡑⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣷⣶⣦⡑⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⣑⠨⠲⢙⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠀⢀⣀⠐⠀⠀⠀⠀⠀⠀⠀⣸⠋⠤⠄⠉⠓⠄⠀⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⣀⠀⠀⠩⠭⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠱⡤⡀⠀⠀⠀⢠⡎⠋⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢈⠀⡄⠀⠀⢀⠜⠀⡟⠁⠀⠀⠐⢯⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢴⡇⢈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠁⠉⠁⠀⡐⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠑⢌⠑⠒⢉⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠒⠉⠀⠀⠀⠀⡀⠘⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⡢⡑⢄⠀⠀⠀⠀⠀⠲⠤⣜⠛⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣎⢢⠀⠀⠀⠈⠒⠋⠀⠡⠀⢀⡥⠶⡀⠀⠤⠀⡠⡀⠀⠀⠀⠀⠀⣀⠎⠔⠥⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠉⠀⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡰⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⡀⠰⡀⠀⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠐⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⢠⢠⠀⢃⠀⠱⢄⠀⠈⠢⠄⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠤⠀⠊⠁⠀⠀⠀⠀⠀⠐⠒⠒⠊⠁⠀⠀⠀⢠⣄
⠸⡀⢢⡀⠑⠀⠀⠉⣐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢟⠘
⠀⠑⠄⠀⢐⣒⣀⣀⣤⣍⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡎⠉⢁⠠⡀⠀⠀⠀⠀⢀⣤⡩⠿⣭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠈⠁⠈⠁⠀⡂⠀⠀⢀⠎⠊⠁⠉⠀⠀⠀⠈⠢⠑⣜⠀⠀⠀⢀⠈⠝⣏⠀⠀⠁⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⢱⠀⠂⠀⠀⠈⡌⠀⢀⠀⠀⠀⠀⢠⠀⠃⢸⡄⠀⢀⢼⠈⠓⠈⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠜⡄⠣⡀⣀⠴⠃⢀⠂⠀⠀⠠⡠⣰⠈⠦⡀⢀⡠⠊⢀⢃⣼⠁⠀⠀⠙⢄⠘⢄⣀⡠⠖⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⠀⠔⠁⠀⠀⠀⠀⠈⠉⠑⠤⠀⠀⠤⠐⠉⠚⠁⠀⠀⠀⠀⠈⠓⠤⠤⠤⠐⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠐⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⣋⠡⠤⠶⠶⠦⠀⢤⡝⠉⠋⠍⠙⠉⠛⠲⠶⠤⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠶⢊⡥⠶⠦⠖⠚⠀⠀⠀⠀⠀⠈⠉⢠⢁⡀⠠⠂⠀⠀⠈⠉⢛⢯⣁⣤⠑⣆
⠀⠀⠀⢀⡴⢋⣵⠆⠈⣁⡠⠀⠀⠀⠀⠱⠀⢀⠔⠀⢠⠀⡘⠘⠆⢀⡠⢤⠀⠀⠀⠒⠁⠉⠉⠳⡌⢳⡀
⠀⠀⢀⡞⠒⡎⠀⠀⢀⠠⠍⠒⣄⡀⢠⣒⡄⠸⣄⡠⠊⢀⠇⠀⠀⠉⠀⠔⠁⠀⠠⠄⠀⠈⢂⣀⠤⢶⠻⣄
⠀⠀⡾⠐⠈⠀⠀⡞⠉⠉⢢⠈⠀⠈⠓⠬⣀⠤⣀⠀⠀⡼⠴⠀⠰⠤⠀⠀⣀⣀⠤⠤⠖⠋⡉⠀⠀⢀⡇⢸
⠀⠀⡗⢰⠀⠀⠀⠑⠀⠀⠀⠀⠀⠂⠘⠰⠀⠑⠺⣇⣠⠡⠤⠤⠖⠐⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⢊⣀⢸
⠀⠀⣧⠘⢀⠀⠂⠀⣤⠤⠔⠒⠒⠒⠀⠀⠀⠈⠉⠉⠏⠒⠄⠀⠀⠀⠄⢠⠀⢨⣀⣀⡀⡀⠀⣠⣖⠀⠈⡟
⠀⠀⠘⣤⠋⠉⠀⠐⠪⡀⠀⢠⡂⠉⠁⢠⡀⠁⠀⡄⠀⠟⠂⢈⡒⠤⣄⡁⠀⠀⠀⠀⠈⠀⡰⠁⠀⢀⡼⠁
⠀⠀⠀⠈⠳⣴⣅⠀⠀⢝⠦⠀⠤⢍⡛⠛⠁⠀⡼⣁⣄⡀⠀⡘⠒⠀⠀⣉⣉⣓⡒⠲⢦⣄⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡉⠀⠀⠀⢀⠽⠒⢠⢖⠒⠤⢤⠄⠀⠀⠐⠲⡞⠉⠁⠀⠀⠀⡀⣨⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣸⡀⣀⣀⣈⠀⠀⠀⢀⣀⣀⣠⣤⡾⠴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠛⢻⠋⠉⠉⠛⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢉⣀⣀⣠⣤⠴⠖⠚⠻⡏⠙⠛⠲⠦⣤⣀⣀⡀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⣁⠤⠖⠛⠉⠉⠁⢀⣠⣤⣄⣀⣠⣧⢀⠀⠀⠀⠀⠈⠉⠉⠛⠳⢦⣀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡤⠊⠁⠀⠀⠀⡤⠶⢒⡯⠶⠦⣤⡈⠀⢺⠀⠑⠶⠚⠙⠶⣒⡶⠦⢤⣀⠈⠳⢤⡀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⡀⢠⠒⠒⠚⠁⢠⣯⠞⠋⠙⠲⣝⢦⠀⠀⠀⠀⠀⠀⡞⡱⠊⠉⠓⣌⠻⣄⣀⣉⠳⢤⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⡠⠋⠀⠀⣀⡼⢧⠀⠀⠀⠀⠘⡏⠠⢀⡀⠀⠈⢿⡆⠀⠀⠀⠀⠐⣇⢣⡀⠀⠀⡸⠀⣿⠀⢸⡇⠀⠙⢦⡀⠙⢷⣄
⠀⠀⠀⠀⢀⡾⠁⢀⡞⠁⠀⠀⢀⣽⣀⡀⠑⢄⠀⠀⠀⠘⢦⡀⠈⠉⢲⡞⢠⠀⠀⠀⠀⠀⠙⠶⣬⣉⣩⡤⠞⡗⢦⡀⠉⠑⢲⡄⢹⡖⠂⠙⣧⡀
⠀⠀⠀⢀⡾⠁⢠⠏⠀⠀⣠⠞⠉⠀⠈⢻⡳⡌⢢⡀⢀⣄⠀⠉⠛⠛⢋⠀⢘⠀⡴⢦⡀⠀⣀⣀⠀⠀⠀⠀⡰⠃⡼⠀⠀⠀⠀⠧⣄⠙⣆⠀⠈⢿⡄
⠀⠀⢀⡾⠁⢠⠏⠀⠀⢀⡏⠀⠀⠀⠀⠀⣧⢹⠀⠱⡞⢄⡙⠒⠒⠚⢉⡇⠸⠀⢹⡀⢱⡞⠁⠈⠹⣶⡒⢋⡠⠞⠀⢀⡠⠂⠀⠀⠀⠙⣌⢳⣄⠀⢻⡄
⠀⠀⣼⠁⢀⡏⠀⠀⢰⠋⢧⠀⠀⠀⠀⢀⠏⣼⠶⢄⠈⢢⡈⠙⠒⠋⠁⠀⠀⠀⡼⠁⡾⠳⣄⣀⣠⠏⠈⠁⠀⣀⠔⠋⠀⢀⡴⠚⠛⠓⢾⣄⠙⣆⠈⣷
⠀⢰⡇⠀⣼⠀⠀⠀⢸⠀⠈⠳⣄⣐⣂⣡⠞⠉⠓⣄⠳⠀⠙⢄⠀⠀⠀⠀⢸⠛⠥⠞⠀⣀⠤⠒⠲⢤⡀⡠⠊⣁⡤⣤⣤⡏⠀⠀⠀⠀⠈⡏⣷⠘⡇⠸
⠀⣾⠀⢰⠇⠀⢀⡤⠞⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⠄⡧⢴⣦⢧⡀⠀⠀⢸⠀⠀⠀⡜⠁⠈⢉⣽⠾⢷⣠⠞⠁⡎⠁⠘⣇⠀⡀⠀⢀⡴⢃⡟⠀⢻
⢠⡿⣤⣞⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡜⢋⡼⡇⠀⠀⠀⢹⡄⠀⢸⠀⠀⢸⡀⢤⣾⠟⠁⠀⡀⣿⠀⣏⠁⠀⠀⠈⠳⠦⠭⠵⠖⠛⢦⡀⢸
⣼⠁⠀⠉⠅⠁⠐⠒⠠⢤⣀⣀⠀⠀⠈⠑⠬⠄⠐⠋⠀⠘⠤⣀⡠⠞⠈⠄⢸⠀⢀⣠⢶⠛⢄⡀⢀⠴⢡⡟⠳⠬⠃⠀⣠⠴⠒⠒⠒⠢⢄⡀⠀⡇⢸
⣿⠀⢠⠀⡜⠀⢀⡴⠋⣉⣉⣉⠛⠮⡉⠈⠀⠐⠂⠀⠀⠀⠀⠀⠤⠤⢄⣀⣽⠶⠋⠀⣀⣙⣲⠶⠶⠒⠋⠀⠀⠀⠀⠀⠙⠦⠖⠛⠛⠲⣄⠉⢲⡁⠸⡇
⣿⠀⢸⠀⢧⠀⠀⠓⠚⠉⠀⠈⠙⠲⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡠⠊⢹⠀⠀⢄⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⠒⠲⠤⠤⢤⣤⣀⣈⡓⢿⡀⠀⡇
⢻⡄⠈⡆⢸⡇⠀⢀⡤⢖⣒⡒⠲⣤⡀⠀⠀⠀⠀⣰⠇⡷⠀⢀⢔⠁⠀⠀⠀⠀⡴⢚⣛⢢⡀⠀⠀⠀⠀⡔⢉⡷⢀⡴⢾⠛⠻⣖⢦⡀⠈⣩⠟⠁⢰⠇
⠘⣧⠀⢳⡘⢧⠀⡏⠜⠁⠀⠀⠁⠀⢻⣾⣉⠛⢋⣡⠜⡡⠂⠀⢏⠓⠤⣄⠀⠘⡀⠅⢈⠆⡍⠢⡀⠀⢸⠀⣾⠀⢸⠀⠈⡄⠀⠈⣧⢳⠀⢧⠀⢀⡞
⠀⠹⣆⠈⢧⠀⠑⢿⡀⠀⠀⠀⠀⠀⢀⡇⠀⠉⡁⠀⠈⡠⠔⠒⠚⠻⢶⡞⠀⠀⠈⣢⡤⠴⠥⣄⠈⠢⡈⢇⠹⡄⠈⢧⡀⠀⠀⢀⡞⣸⢣⠏⢀⡾⠀⢰
⠀⠀⠻⣆⠈⢧⡀⠈⠳⣄⡀⠀⢀⣠⠞⠁⠀⠂⠀⠀⡞⠀⠀⠀⠀⠀⠀⢻⡆⢠⠎⣡⡖⠉⠑⢦⠙⣆⠈⠪⡒⠉⠀⠀⠉⠓⠾⠿⠚⣱⠃⠀⣼⠁⢠⡿
⠀⠀⠀⠹⣦⠀⠱⣄⠀⢀⡟⠉⠉⠁⠀⢁⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣾⡇⠄⢨⠀⠀⠀⠀⣀⠧⠿⠶⠤⣌⠲⢀⠀⠀⠀⠀⣠⠖⠃⠀⢰⠇⢠⡿⠁
⠀⠀⠀⠀⠘⢷⣄⠈⠳⣄⢧⣀⣀⡀⠀⡌⢼⠁⠀⠀⠈⢦⣀⠂⠤⣔⡿⠋⡅⠈⠊⠁⠀⠀⡾⠡⠒⠉⠉⠐⠪⣷⡀⠰⠄⠀⢀⡇⠀⠀⣠⠋⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠸⠳⢌⡀⠙⢦⣱⡘⢄⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠇⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢸⣇⣀⡞⠛⠁⠀⢀⠜⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⠀⠙⠦⣀⠈⠙⢤⡘⠦⠔⢓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⢀⣠⠟⠀⠀⠀⠀⣠⠞⠁⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠈⠓⢦⣀⠉⠹⢯⣁⣠⡤⠶⢤⣀⠀⠀⠀⣠⠖⠛⠓⠦⢤⠴⠋⠉⠉⠀⠀⣀⡤⠖⠋⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠈⠙⠒⠦⢤⣀⣀⡀⠀⠈⠑⠛⠋⠁⠀⣀⣀⣀⣀⣠⠤⠤⠒⠚⠉⠁⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠈⠉⠉⠉⠛⢻⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠋⠉⠁
⣿⣿⣿⢿⣿⠿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣷⣾⣶⣶⣦⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠻⣅⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠈⢆⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⢋⠁⠀⢀⠧⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⡟⠁⠱⡍⢳⡀⠀⠀⠉⠉⠒⠂⠤⣄⣀⡀⠀⠀⠀⠀⢸⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠐⠀⠀⠀⣇⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣛⠉⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⠁
⠀⠀⠀⠀⠀⣰⡿⡍⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⣿
⠀⠀⠀⠀⠀⣿⠀⠹⣆⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠇⢠⣿⡏
⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧⡀⠈⠲⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⣠⠇⢀⣾⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⢦⡀⠈⠲⣄⣀⠼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⠚⠁⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠈⠙⠒⠢⣀⠀⠀⠀⣸⠛⣆⠀⣀⣀⣀⣠⠴⠋⠀⣠⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⡀⠉⠉⠉⠁⠀⠈⠁⠉⠉⣁⣠⠤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠒⠚⠋⢉⣡⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⠦⠴⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⢁⡄⡤⠔⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⠁⠒⠚⠀⠀⠀⠀⠀⣀⠤⡔⠁⠀⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠢⡀⠉⠀⠀⠀⠀⢀⠔⠂⢰⠒⠉⠀⠀⠣⡀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠌⠀⢘⠀⠀⠀⠀⢀⣇⣀⠁⠀⠉⠡⣀⡀⠀⠈⠉⠉⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠄⠀⠀⡀⠠⠒⠪⡀⠀⠀⡐⠁⠀⠀⠉⢆⠀⠀⠀⠘⠢⢄⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠉⠁⡠⠊⠀⠰⠢⠀⢡⠀⠀⢡⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠀⠂⠒⢉⠑⡄
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠜⠀⠀⣠⠎⠀⣼⠁⣈⠻⡁⠘⠀⠀⠆⠉⠒⢤⢀⡀⠀⠀⠈⠒⠤⢀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⣠⣊⡀⠀⠀⠀⡠⠒⠁⠀⢠⠤⡘⣆⠙⠆⠱⠀⢡⠀⠄⠀⠀⡆⠀⠀⢉⠖⠂⠤⣄⣀⠈⠳⠀⠀⠀⠀⠄
⠀⠀⠘⢡⠠⠌⢂⠠⠊⢀⡀⢤⠀⠀⠙⠃⠈⠓⠶⠊⠀⢂⢳⠀⠀⠀⠀⠀⠢⡜⣄⡀⢀⡇⠀⠀⢩⠃⠒⠒⡞
⠀⠀⠐⣌⢢⠔⠁⠀⠀⠚⠉⢡⠒⠒⠢⢄⠀⠀⠀⠲⡒⡀⠈⡀⠀⠸⠀⠀⠀⠇⠀⠈⡌⠑⠈⢀⠇⠀⠀⡐
⠀⠀⠀⠀⢹⠀⠀⢠⢤⡀⠀⠹⢦⡘⠓⠀⢑⢠⡀⠀⠐⠓⠀⣇⠀⠆⠀⠀⡘⠀⠀⢠⠁⠀⠀⡎⠀⠀⡰
⠀⠀⠀⠀⠃⠀⢠⠉⠒⢬⠇⠀⠀⠉⠛⠛⠋⠸⢌⡤⠀⢤⡀⠸⡀⠀⠀⢀⠃⠀⠀⠄⠀⠀⡜⠀⠀⡰⠁
⠀⠀⠀⠀⠢⠔⠁⠀⠀⠸⣀⠠⠲⢵⠀⠈⠀⠀⠘⣇⠰⢦⠘⠄⠹⠤⠄⣜⠀⠀⡘⠀⠀⡰⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢍⡢⡀⠈⠳⢤⣤⢜⡀⢣⠀⠀⠈⠉⠑⠂⠤⠧⣀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢍⡐⢄⠀⠈⠮⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢕⢄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣆⠀⠡⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡋⠔⠀⠘⡆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠊⠀⢀⡄⠀⢸⡀⠈⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕⠁⡠⠐⠈⠀⠀⠀⠀⠇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⠐⠁⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠕⠀⠀⠀⣀⠠⠄⠀⠐⠂⠉⣀⣀⡇⠀⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⣀⣀⣀⡬⠥⠤⠤⠒⠒⠒⠉⠉⠉⠉⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⢀⣀⣎⠰⡀⠀⠈⠂⠄⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡟⠉⠀⡌⠢⡈⠢⡀⠀⠄⡀⠀⠒⠠⠀⠀⠀⠀⠀⠀⢀⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⡤⠀⠀⠀⡇⠀⠀⠈⢂⠈⢢⡈⠢⠀⠈⠐⠠⡀⠀⠀⠈⠁⠀⠀⡘⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⠔⠁⠀⠀⢀⢀⠇⠀⠰⠀⠀⠑⡄⠙⢦⡀⠑⢄⠀⠀⠁⠀⢀⠀⠀⢠⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠐⠁⡀⠀⠀⠀⡄⢸⠀⠸⠀⠀⠀⢦⠈⠢⡀⠑⢄⠀⠑⠀⡀⠀⠀⠀⢠⠃⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠔⠀⠀⠐⠀⠠⠃⠀⠀⡘⠀⠀⠀⠀⠀⠘⠁⠀⠑⢄⠀⠱⣄⠀⠀⠀⠀⡰⠃⢀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠔⠁⠀⢀⠌⠀⠠⠁⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠑⠀⠈⠳⡄⣠⠞⠀⡐⣡⠋
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠔⠁⠀⠀⠀⠂⠀⢠⠁⠀⢀⠃⢠⡇⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⠞⠁⡠⢊⠜⠁
⠀⠀⠀⣠⠞⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⣨⠖⠁
⠀⠀⠈⠣⢄⡂⢄⠈⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠈⠀⢀⣀⡤⠖⠋⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠈⠑⠢⢅⡂⠠⠀⡈⠉⠉⠒⠒⠢⠤⠤⠤⠧⠤⠤⠔⠒⠒⠉⠉⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣟⣛⡛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣄⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠸⣟⣛⣻⡿⠀⠒⢠⣿⣷⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠐⢉⡿⢇⣉⠋⠀⠀⡉⢸⣿⣿⢨⡅⠀⠈⠉⠉⠉⠛⠛⠿⢷⣦⣦⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⡿⢮⣿⣿⣿⠂⠀⢸⣿⣿⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳
⠀⠀⠀⠀⠿⠿⠷⠿⠿⠿⠿⠀⠀⠘⠿⠟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⢀⣀⡀⣀⣄⡀⣀⢀⡀⠀⠀⠀⠀⣠⣴⣾⣿⣟⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⡟
⠀⠀⠀⠀⠀⠀⣼⣿⡟⣼⡇⢀⣿⣿⢰⡿⠛⢳⣿⡿⠁⠀⠀⠀⢸⣿⣛⢋⣵⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢠⣿⣽⢇⣿⣄⣼⣿⣿⢾⣷⡶⣾⢻⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣤⠤⠥⢤⡤⡤⣤⣤⠀⠀⠀⢸⠟⠉⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⢙⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠀⡟⠀⡌⠀⢱⢰⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⣤⢠⣤⣤⢤⣤⣤⣤⣤⣭⣭⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰⣶⣶⣤⣤⣶⣿⣿⣿⣿⣧⣍⠹⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣶⡀
⠀⠀⠀⠀⣿⠀⣿⢻⡽⣷⢾⡿⣿⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠀⡿⣿⣾⣿⣿⣷⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣉⣀⣀⣉⣉⣉⣉⣉⣉⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠒⠒⠂⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡠⠤⠀⢤⣤⠖⡓⢂⠛⢠⠔⠦⢤⡐⡶⣤⡠⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠈⡆⠀⣶⣷⠶⠀⠀⠐⠢⠗⠀⠈⠛⠒⠰⣄⠀⠀⠑
⠀⠀⠀⠀⢀⠊⠀⣠⠞⠁⠚⡀⠀⠀⠀⡀⢀⠟⠀⠀⠀⠀⢲⡟⠂⢠⣤⠀⠀⠀⠀⠀⠈⠓⠀⠀⠈⠂
⠀⠀⠀⡐⠁⢠⠞⣉⣨⣤⠢⡜⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠘⠷⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠡
⠀⠀⡐⠀⠀⠃⠼⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡂⠀⠀⢁
⠀⢀⠁⠀⢠⠛⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠒⢄⡀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⡀⠀⠄⡅⠀⠀⠀⡄
⠀⠄⠀⠀⡘⠀⠰⠒⠀⠀⠀⠀⣀⠀⠉⣿⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠊⠀⢾⡿⠋⠘⠀⢿⡄⠀⠀⠠
⠀⠀⠀⠀⣇⡤⠀⠀⠀⠀⠀⠀⢿⣦⣴⠚⠃⠀⠀⠀⠠⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠶⠿⢋⡄⠈⣧
⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠛⠊⠁⠀⠀⢻
⠀⠀⠀⠀⢸⡟⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⡼⠀⠀⠀⠀⣄⠀⠀⢀⢹
⠀⡄⠀⠀⠀⢷⠘⠿⡿⠋⠁⠀⠀⠐⢄⠀⠠⠀⠐⠀⢀⡀⠀⠀⢀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡀⠀⠰
⠀⠠⠀⠀⠀⠈⣀⠤⡁⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠈⠁⠀⠀⠻⠿⠟⠀⠀⠀⢀⣶⠄⢀⣀⡐⣸⡸⠀⠀⠂
⠀⠀⠄⠀⠀⠀⢈⠂⠑⢄⣀⡠⠂⢉⣁⡀⠀⠀⠐⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢀⣰⡿⡴⠉⠁⠀⡐
⠀⠀⠈⡄⠀⠀⠀⠢⠀⠀⠁⠀⠀⠿⠟⠁⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠈⣱⠞⠀⠀⠀⠠⠁
⠀⠀⠀⠈⢄⠀⠀⠀⠀⠑⢄⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠐⠊⠁⢀⢀⠾⡁⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢤⣀⠀⠠⠀⠈⢀⢠⠄⣄⡀⡀⠀⠀⠀⠀⢄⡢⠞⠁⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠉⠓⠶⣄⣀⣀⠀⠐⢆⣁⣙⡠⠤⠔⠊⠁⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠤⠀⠀⠀⠀⠀⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⠛⣛⣛⠛⠛⠉⠙⠛⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠸⣖⠀⢀⣀⣀⣀⣠⣠⣤⣄⣀⣀⠀⠀⢀⡿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠀⠈⣷⠀⠘⣏⠉⠁⠀⠴⡄⠀⢠⠖⠑⠄⠉⠙⡏⠁⣼⠭⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢀⡠⠖⠛⣄⠀⢻⠀⣀⠤⢄⡀⠀⠈⠣⠞⡁⠀⣸⠁⢠⡟⢦⣀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣠⢞⡡⠀⢀⠔⡫⠐⢄⠀⠘⣆⠈⣷⠁⠀⠀⢸⠀⡖⠢⢀⣉⣠⠇⣰⠏⠀⠀⠈⠓⢄⠀⠱⠝⢦⣄
⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠁⠀⠣⠤⠝⠘⠀⡸⣆⠸⡗⠤⠔⠋⢀⡈⠀⡧⢀⠏⣰⡷⠒⠲⡄⠰⠇⠀⠙⢄⠀⠀⠈⠳⣄
⠀⠀⠀⣼⠁⠀⠀⣠⠏⠰⠲⠀⠀⠀⢤⠢⠀⣡⠘⡆⢻⡄⠀⢀⣈⠁⠀⢑⡞⣰⠿⡀⠀⠀⡸⠀⠀⢠⠖⠢⠱⡄⠀⠀⠽⣆
⠀⠀⠀⠻⣴⣀⣴⠃⠀⠀⣠⠚⠈⠒⡌⠉⣀⠈⠀⠹⡄⢷⠀⡅⢂⠇⢀⡞⢠⠏⠀⠉⠐⠊⢠⠐⡄⠘⠴⠔⠁⠘⣄⡀⣠⡟
⢀⡴⠖⠶⣄⠀⠈⠛⠦⣄⣳⡀⠀⢀⠆⠀⠉⡠⢄⠀⢳⠈⣧⠀⠁⢀⠞⢠⠏⡠⠀⡀⠚⠇⢀⡩⠤⡈⠉⣀⡤⠖⠋⠉⢉⣀⣀
⣾⠃⠀⠀⡟⠉⠙⠲⠤⣄⣉⠛⠿⢥⣀⡀⠀⢄⣡⠃⠈⡇⠈⠳⠴⠋⢀⡟⠀⠣⠈⠂⠀⠀⣂⣩⠤⠟⢋⣁⣤⡤⠴⢶⠋⠓⠈
⣿⠀⠀⢰⢁⠄⣤⠀⠆⠸⣉⡙⢲⢤⣈⠙⠓⠶⣤⣀⣀⡟⢀⡠⠤⣄⡘⢧⣠⡤⠤⠖⠚⣉⣡⠴⢶⠟⠛⠳⡄⠀⠀⠸⡆
⣿⠀⠀⢸⠹⡄⠴⠀⢠⠒⡌⠉⠁⠀⠈⠙⠲⢤⡀⠀⠁⠀⠁⠀⠀⠀⠙⣦⠀⣠⠴⠚⣋⢉⠀⠀⠸⡀⠀⠀⡸⢀⣤⠀⡇
⣻⢰⠀⢾⠀⠀⠀⠀⣈⢉⡀⠘⠃⢰⠁⢑⠀⠀⢙⡆⢰⠀⠀⡀⡈⠡⠀⢸⠺⣄⠀⠐⢀⣄⠇⢠⡄⠈⡀⠈⠀⠀⠁⠀⡇⠀⡇
⣿⠀⠀⢸⠀⠋⠀⡞⠀⠀⠙⡄⠀⠀⢁⣩⡤⠖⠋⠀⠈⢧⡀⠀⠁⠀⣠⣏⡀⠈⠓⠦⣀⠀⠀⢀⣀⡘⠤⠃⢠⠖⠒⡄⡇
⡇⠀⠀⢸⡄⠀⠀⠑⢤⣠⣴⡥⠖⠛⣉⡥⠴⠒⠚⠋⢳⡄⠈⠉⠈⠉⣼⠉⠉⠛⠲⢦⣌⣙⠲⠧⣈⡈⡆⠐⠌⠳⠄⢡⠇
⢻⡀⢀⢀⡧⠶⠖⠚⠋⣉⣤⠖⠚⠩⠀⠀⠠⡂⢢⠀⣼⠁⣠⠖⢲⡀⢸⡄⠰⢉⠙⠄⠀⠉⢙⣶⣦⣍⡓⠲⢤⣀⣀⣾⠀⠀⣠
⠀⠙⠛⢋⣀⣀⠤⠒⠉⣡⡈⠒⣚⠁⢠⡠⠘⠀⠊⣰⠃⡰⠁⠀⠀⢹⡄⢣⠀⠉⠈⡠⡀⢰⠁⠀⠀⢳⠉⠳⢦⣄⣈⣹⠦⡤⠞
⠀⠀⣰⠋⠉⠹⡄⠀⠴⠦⡄⠈⠤⠃⣀⢀⣀⠀⣰⠏⡸⠁⠰⠡⢈⠄⢳⡈⣧⠤⣀⠉⡀⠈⠢⠄⠴⠋⠀⠀⢠⠞⠉⠏⢷
⠀⠀⠸⣶⠀⠀⠘⢆⠦⠤⠏⠀⠀⡌⠀⠀⠈⣦⠏⣰⢅⠀⢀⡉⠁⠀⠈⢧⠘⣆⢛⠄⠢⠚⠀⠀⠀⠾⠂⡰⠋⠀⠀⢠⡟
⠀⠀⠀⠙⢦⡀⠀⠈⠳⣄⠀⢰⡂⠘⠦⠤⢴⡟⣰⠃⢶⠀⣈⠁⢠⠔⠒⢺⣇⠘⡎⠐⡆⣴⠉⢲⠀⣠⠞⠁⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠙⠳⣔⢦⠈⠑⢦⡀⠀⠀⢠⠏⢠⠏⣉⠁⠨⠤⠁⢇⠀⠀⢀⠿⡄⠘⣆⠀⠘⠒⣪⠞⠁⠀⢊⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠉⠳⣴⠏⠀⡞⠀⢈⡤⠠⡀⠀⠀⡑⠒⠉⠀⢷⠀⠘⢦⠴⠋⠁⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢐⡾⠀⣸⣇⣀⠘⠄⡤⠃⠀⠈⠓⠀⢀⣀⣸⣆⠀⢻⣄⣀⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢼⠁⠀⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠁⠀⠼⣧⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⣤⣀⣀⣤⣤⡬⠭⣤⣤⣤⣤⡤⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠄⡀⠀⠀⠈⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⣾⣏⠀⠈⡄⠀⠀⠀⠀⠀⣾⠿⣄⠀⣰⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⢱⣿⠇⠀⠢⠒⠘⠀⠙⠿⠇⠿⠟⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⣀⡤⠴⠒⠒⣚⣉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠶⠤⣄⣀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢯⠉⠀⠀⠀⢠⠋⠁⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣄⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⣠⠚⠉⠙⢦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡼⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠒⠉⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⡴⠒⠒⢦⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢯⠹⡄⠸⡇⠀⠀⢸⠇⠀⠀⣰⣧⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣧⠀⠈⠓⠚⠁⠀⠀⢀⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⡀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠀⢧⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠒⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣡⠤⠤⠤⣄⡙⠻⣶⢄⡀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠞⠁⠀⠾⠀⠀⢳⠀⠈⠳⣙⢦⡀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠀⡟⢠⡄⠀⣀⠀⠆⡼⠀⠀⠀⠈⠳⣕⣄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡴⠹⡆⠹⣄⠀⠀⣉⡤⠞⠁⢀⣠⡖⠚⠓⠺⢮⣧⡀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡏⠀⢠⠇⠀⠈⠉⠉⠁⢀⠖⠋⠉⠉⣙⠦⣤⠴⣞⠉⢳⡀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣀⣀⠀⠷⠒⠉⢀⣀⣀⠀⠀⠀⣿⠈⠃⢀⠀⠉⠀⢹⠀⠈⠢⡀⢱⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡴⠋⠠⠆⠉⢢⠀⠀⢯⠀⠈⠙⢦⡀⠈⠳⢤⣈⣀⣃⠴⠃⠀⠀⠀⢹⠀⢳⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡾⠃⢸⢠⡄⢀⡄⠆⡼⠀⠀⠀⠑⠒⢒⣋⣉⣤⠤⠤⠤⠤⠶⠶⠖⠲⠶⠖⠛⠒⠶⠷⠤⠤⢾
⠀⠀⠀⠀⠀⡰⣻⠁⠀⠈⠦⣄⡤⠴⣊⣠⡤⠶⠒⢛⣉⣉⡤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⡴⣡⠃⢀⣀⣠⣤⠶⠚⢋⣩⠤⠖⠚⠉⠉
⠀⠀⠀⠀⣇⢈⣩⠽⠛⣉⡤⠖⠋⠉
⠀⠀⠀⠀⠈⠻⠤⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠒⠚⠋⠉⠉⠉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠒⢒⡒⠺⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⣀⣀⠀⢤⣖⣉⠉⠉⣉⣑⣄
⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⣉⠠⠤⣀⠐⢎⣁⡠⢲⠒⠒⠒⣻⢫⠕⠒⠺⡝⢆
⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢠⠋⡖⠉⠉⣢⢹⡀⠈⠀⠈⢆⠀⠀⢹⡬⣓⣒⣒⢥⣟
⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⣠⠖⠙⢷⠭⠍⠭⢕⡾⡀⠀⠀⠀⠈⠢⣄⠀⠉⠒⠒⠒⣩⠞⢦
⡴⠣⠤⠤⣀⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢰⠁⠀⠀⠀⠉⠀⠈⠁⠀⠘⡄⠀⣀⠤⠒⡆⠉⠁⠒⠊⠉⠀⠀⠀⢣⡀
⡇⠀⠀⠀⠀⠉⠓⢄⡀⢀⡔⡡⢊⠭⠭⡒⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠊⢀⠔⠒⠛⠀⠀⠀⣀⣀⣀⣀⠤⣀⡱⡀
⠘⢄⣀⠀⠀⠀⠀⠀⠙⠯⣀⡧⡘⢄⣀⣈⠆⡷⣄⠀⠀⠀⠀⠀⢀⡠⠮⡧⠤⣇⠀⠀⢀⡴⠊⠉⠀⢠⠋⡔⠛⠒⢮⠻⡄
⠀⠀⠀⠉⠒⠤⣄⡀⠀⠀⠈⠓⢬⣑⣒⣒⠾⢏⠑⢍⠑⠒⠒⠊⡏⢞⠉⠀⢙⠎⡇⢀⡏⠀⠀⠀⠀⠘⡓⢌⣒⠶⢚⣠⢋⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⡀⠀⠀⠈⠲⢄⡀⠀⢣⣀⣳⠀⠀⠀⠻⡒⠭⠭⢕⡺⠃⠈⣇⠀⠀⠀⠀⠀⠈⠓⠒⠀⡞⢁⠎⢠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠉⠲⢄⣀⠤⠒⠒⠒⠒⢤⠭⠭⢅⡀⠀⠀⠈⠲⢄⣀⡀⠀⣀⣀⣤⠮⠖⢁⡰⠃⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠉⠒⢤⡀⠀⠈⠙⠒⠢⣤⡈⢳⠀⠀⠀⠀⢀⣉⡉⠁⠈⠑⠒⠊⠉⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠈⠑⠦⣄⠀⠀⢱⠘⣤⠃⠀⡔⣫⠕⠒⠨⡑⣄⣀⣀⣀⡠⠔⠒⠒⠒⢤⣘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠉⠒⢼⡀⠁⠀⠀⣧⡑⠢⠤⢒⣡⡇⠀⠀⢯⣠⢖⠉⢩⠋⡵⠒⠭⡕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠈⠑⠢⢄⡈⠪⠥⠭⠕⠊⠀⠀⠀⠀⠀⢸⠀⠸⡣⣕⠢⠤⠜⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠙⠣⢄⡀⠀⠀⠀⣀⡀⡠⠊⠀⠀⠉⠒⢬⠭⠛⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⡀⠈⠙⠒⠮⣁⠙⠢⠤⠤⠤⣄⠀⠈⠢⣄⢀⡀⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣀⡀⠉⠙⠳⢌⣉⠁⠀⠀⠀⣜⡡⠤⠒⠒⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢄⣀⠉⠑⠲⠤⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⠤⣄⣉⣑⣒⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡴⣞⡯⠭⠭⠭⣍⣳⡆⡼⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡰⠟⣛⣛⣛⡻⠿⠆⣠⡻⣷⣄
⠀⠀⠀⠀⠀⡴⢫⠞⠙⣆⠀⠀⠿⢣⢏⡞⣵⣮⢱⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢫⣶⡜⣿⣿⣅⣸⠃⣴⡟⠍⣦⢹⣧
⠀⠀⠀⠀⣼⢱⠋⠿⠗⠈⢧⠿⣣⢋⡞⣶⠆⠀⠀⢱⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⢴⣇⣂⣿⣜⢇⡼⢁⣼⡋⣹⣿⣿⡧⣻⡇
⠀⠀⠀⠀⣧⣾⠤⠤⠤⡤⠬⣷⡧⠬⠭⠭⠭⢭⢭⡍⠉⠀⠀⠀⠀⠀⠀⠀⢘⡃⣛⣛⣛⣛⣛⡊⢁⣈⣉⣉⣉⣉⢉⡁⠉⠁
⠀⠀⠀⠀⢷⢹⠀⢀⡘⠟⡼⣡⣷⡀⠀⣶⠄⡼⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⢿⣿⢿⣤⠟⡼⠇⢻⣿⡋⢻⠟⣼⠇
⠀⠀⠀⠀⠈⢯⡳⡝⢋⡜⡡⡍⠁⠹⡔⢀⡼⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⠳⣤⢏⡞⡳⣶⣧⡹⡿⢟⣼⠟
⠀⠀⠀⠀⠀⠀⠙⢯⣟⠦⠽⢧⣤⠴⣻⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢢⣜⣓⣒⠿⣛⣧⡰⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣲⣿⣿⠇⠈⠈⠙⠀⠀⠂⠀⠀⠐⠁
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣿⡟⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⡿⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⠄⠒⠀⠂⡀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣿
⡋⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠒⠉⠉⠐⠄⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⣀⣀⣄⣄⢀⣤⣾⣿⡋
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⢦⠀⠊⠙⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⣿⣯⣤
⠦⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⡠⠄⠀⠀⣻⡿⠜⢻⠻
⠀⠀⠀⠀⠈⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠱⡦⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠑⠀⠀⠀⠐⠈⠻⠆⠀⠀⠀⠀⠤⢤⣾⣿⣷⠀⣿⣀⣠⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠤⠾⠿⣿⣾⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⢀⠃⠀⣀
⠀⡄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠉
⠀⠀⠼⢆⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡂⡬⠞⡉⠀⠉⢧⡀⠀⠀⠀⠐⠂⠀⠄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠎⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠷⠶⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠢⠄⠤⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣤⠀⠀⢀⣴
⠀⠀⠀⡃⠒⠂⠴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢆⣠⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⣤⣿⣶⣿⠿⠁
⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⣿⣧⡀⢠⠋⠀⠀⣠⣶⡥⠀⠀⠀⠀⠀⠀⣸⡿⣿⡁
⡀⠀⠤⠀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠒⠤⡀⠀⠸⣿⣿⣤⡆⢀⣾⣿⠋⠠⠀⠀⠀⠀⠐⢀⠂⠀⠀⠙⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⣀⣈⣠⣤⣤⣙⠛⠠⡘⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⠒⠒⠉⠭⠛⠛⢛⡿⡿⢉⣤⠚⣽⣯⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⣀⣠⡴⠖⠒⠛⠛⠛⠿⣓⠒⠒⠲⠤⢄⡀⠀⠈⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢀⣠⣶⡿⢋⣥⠴⠤⣄⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠈⠙⠲⣄⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⣠⠶⠛⠛⣿⣶⣾⣄⢛⣠⣤⠁⠀⢀⣴⣿⣄⡴⡞⢫⠻⣍⠐⠀⣤⣙⢢⣀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣠⠞⠁⣀⢰⣾⡿⡿⢿⡁⠸⡧⢀⠀⠀⣸⣿⣿⣿⣘⠂⠃⡴⠉⠀⣠⣾⣿⠁⠙⢦⡀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⣠⡟⠁⠀⣼⠁⣴⡟⠏⠍⡛⠄⣿⣤⣭⡓⠒⠁⠀⠀⠹⣿⣿⠟⢿⣎⠁⣤⠀⠈⠻⠟⣻⠷⠤⣄⠙⢆⠀⠈⢳
⠀⠀⠀⠀⢰⡿⠁⠀⡴⡏⠈⡇⠤⢘⠀⠗⠀⠘⠿⠿⣿⣶⣀⠀⠀⠉⠉⠁⠀⠀⠈⠉⣠⣴⣶⡗⣼⡑⠫⡍⠠⡕⠈⠆
⠀⠀⠀⢠⣿⠃⠀⣸⠁⣗⢀⣙⣦⣌⡠⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⡴⢶⡦⣄⠀⠐⠺⢿⠿⠟⠁⠹⣥⡇⢼⢃⠀⠀⠈
⠀⠀⠀⣼⡏⠀⢰⣇⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠃⠨⣏⡉⣇⠰⢋⡅⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠁
⠀⠀⠀⣿⠇⠀⣼⠏⠀⢉⡿⠛⢿⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⢤⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣦⣄
⠀⠀⠀⣿⠀⠀⣿⠀⣰⣋⠓⣀⠾⠁⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠉⠓⠈⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⢈⡿⢿⣿⡷
⠀⠀⠀⣿⠀⠀⢿⡄⢸⡐⢆⠉⠶⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠉⠉⠀⢰⡯⠘⠀⡅⠼⠆
⠀⠀⠀⣿⡆⠀⢸⠻⣄⠙⠳⠤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣱⢃⠴
⠀⠀⠀⢻⣇⠀⠸⡇⠘⢦⡀⠸⣿⣷⣦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠃
⠀⠀⠀⠘⣿⡀⠀⢹⡀⠀⢣⠀⠛⢋⡟⢿⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⢄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠸⣧⠀⠀⢳⡀⣾⠀⠀⢺⠛⠶⣘⠈⣁⣴⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡟⣓⢰⠀⣰⠁
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠳⣷⠀⠀⠘⢿⣃⣥⡀⠉⠙⠿⠿⣿⡿⠟⡧⣄⡀⠀⠀⠀⠀⣰⣿⣿⣆⢻⣁⢩⠄⢶⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠘⢷⣄⡀⠀⠀⠁⣄⠀⠀⠀⠀⢰⠦⠄⠀⢆⠑⠀⠀⠀⠀⣿⣿⣿⣿⠀⠈⠑⠊⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⠙⠻⣟⠓⠶⣿⣿⣷⣄⡀⠸⣖⠆⣉⠈⠶⠀⠀⠀⠠⣼⡿⠿⠁⠀⣀⡤⠔⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠈⠛⠶⣌⡛⣟⡛⠁⠀⠈⠓⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⠀⠉⠙⠛⠶⠤⠤⣶⣤⣤⣤⡤⠤⠤⠤⠴⠞⠉⠀⢀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣤⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠓⠚⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⡠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⠀⠉⠉⠙⠊⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠲⡄⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⠀⠀⠀⢠⠰⠌⡡⠃⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠅⠾⠃⠀⠀⠤⠒⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡙⠂⠀⠀⠴⠶⠶⣤⡀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢹⠀⠀⠐⠀⠀⠀⠀⠀⠠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⠞⠀⠀⠀⠈⢰⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠈⠁⠀⠀⠀⠀⠀⠸⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⡀⠀⠀⠀⠐⢒⠲⡄⠀⠀⢀⡤⣶⠄⠀⠀⠀⠀⠠⠀⠀⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠆⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⢰⣘⣊⠀⠀⠀⣖⣩⠴⠋⠀⠀⠄⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⡀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠘⠂⠀⠀⢉⡁⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢤⡐⠎⡀⠀⠀⢀⠀⠀⠀⠀⠀⣠⢏⡴⠃⠀⠀⢀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠲⢤⠀⠀⠈⠙⠉⠀⠀⢀⣀⣀⣀⣀⠀⠀⠈⠋⠀⣀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣧⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠓⠤⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡾⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣥⡀⠀⡾⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⡴⠤⠴⠞⠉⠀⠀⠁⠀⡇⠀⢀⡴⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠤⡲⡄⠀⠘⠊⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠘⢜⡣⠂⡀⠀⠀⡀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤
⠀⠀⠀⠁⠴⠾⠃⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠂⠑⠀⠀⠂⠀⠀⠀⠀⠉⠀⠒⠃⠠⠀⠌⠠⠨⠁⠌⠄⠸⠸⠀⠀⠀⠀⠨⠝⣂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢌⡠⢄⣆⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠈⠀⢠⡀⠀⢈⠰⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠔⠠⠔⠀⠀⠀⠀⡂⠈⠐⢠⡄
⠀⠀⠀⠀⠀⡐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠁⢀⠀⠘⣁⣛⠀⠀⡁⠀⠀⠀⠑⢔⡢⠊⠀⠀⢠⡒⠀⠠⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠄⠀⠀⠀⠀⠐⡔⠀⡇⢢⡔⢸⡇⢢⡂⠐⠀⠀⠀⠈⡀⠀⡄⢀⡀⠀⡃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⠁⡀
⠀⢀⡀⣀⠀⠂⠀⠀⠀⢲⡂⠂⠒⠒⠲⠀⠐⠐⠀⠃⠂⠐⠘⠂⠂⠂⠀⠤⠀⢸⠀⡇⢠⡤⠈⡀⠀⠁⠀⣲⡆⠀⠀⠀⠀⠀⠀⠸⠁⢀⡄⠘⠛
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⠿⠯⡿⢿⡷⠀⠶⡆⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⡇⠘⡏⠘⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠈⠈⠉⠉⠉⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⠀⠀⠴⠒⢦⡀⠀⠉⠉⠉⠉⠉⠋⠉⠙⠉⠁⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠃⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣄⠛⣠⠇⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠁⠈⠀⠀⠁⠈⠀⠀⠈⠴⠄⠠⠄⠡⠦⠀⠤⠀⠀⠀⠉⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠘⠀⠀⠀⣻⡍
⠀⠰⠠⠠⠆⠆⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⢴⣴⣴⠄⠀⠀⠀⠀⠴⠂⠠⠀⠲⠠⠄⠠⠀⠀⠄⠠⠀⠀⠠⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠗⠀⠁⠀⠀⠹⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠶⠶⠶⠶⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡛⠛⠛⠿⠓⠦⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⢿⠾⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⣶⣶⣿⣷⣶⣶⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠿⠿⡃⠀⠀⠀⢀⣠⣤⣀⣉⣶⣶⣶⡶⠾⠛⠋⠉⠉⠉⠉⢻⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠁⠀⠀⠀⢀⣠⣶⣤⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠻⣷⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢁⠀⠀⠀⠠⣄⠀⣀⣸⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠈⠳⠘⢻⣦
⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠁⠀⠀⠀⢠⣶⣾⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⢀⣤⠞⠛⠉⠀⠀⠀⠀⢢⣤⣉⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⣠⣾⣿⣿⣶⣶⣀⠀⠀⠈⠉⠉⠛⢻⣟⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠘⢿⣧
⣼⣿⡍⠉⠁⠀⠀⠈⠉⠛⠻⠿⣶⠶⠿⣿⣿⣦⣄⡀⠀⠀⠠⢄⡀⠀⠀⠀⡀⠈⠑⢦⡀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⡄
⠉⠻⢿⣶⣤⡀⠀⣶⣤⣦⣤⣄⡈⠑⠂⠀⠉⠙⠻⣿⣷⣄⠑⢦⡙⠲⣄⣀⠈⠂⢄⡀⠈⠲⣄⠀⠀⠈⠙⢷⣤⡈⠢⣄⠰⣄⠀⠀⠐⠘⣿⡆
⠀⠀⠀⠉⢿⣷⡀⠸⣿⣿⣿⠿⣿⣿⣾⣶⣤⣄⠀⠀⠙⠻⢿⣦⣍⣳⣤⡙⠳⣤⣤⠉⠳⣤⡈⠓⢷⣄⠀⠀⠙⢿⡦⠈⠓⠌⠑⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠈⢿⣧⠀⢻⣿⣿⣤⣿⣿⣿⣿⣙⣿⣿⣿⣷⣶⣤⣈⡉⢉⠉⠛⢷⣬⣿⣿⣿⣦⣿⣶⣤⡈⠻⣦⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠘⣿⡄⠀⢻⣿⣿⣿⣧⣄⣼⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣅⡀⠀⠈⠙⠛⠿⠿⠿⢿⣿⣿⣿⣆⠹⣄⠀⠀⠁⠀⠳⣄⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⣿⣿⣽⣿⣿⣿⢿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠈⠙⠻⠿⣿⣷⡘⣷⣤⠰⡘⢷⡑⢄⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠸⣿⣿⠿⢿⣷⣴⣿⠻⣧⣼⣿⣶⣿⣤⡿⠋⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⡀⠀⠈⠙⠻⠿⣷⣾⣦⣿⣌⠳⡄⠱⣄⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢻⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⠉⣻⣿⣿⣶⣿⣷⣾⡿⠛⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠉⠙⠻⢿⣧⡙⣆⣘⣆⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣿⣿⣿⡃⣰⣿⣿⣀⣸⣿⣿⡟⠉⣻⣿⣿⣿⣿⣷⣦⣿⣿⣦⣠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠁⠘⠿⢿⣷⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣌⠉⠙⠛⠿⢿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⠋⢙⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣤⣴⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣄⣀⠈⠉⠛⠻⠿⠿⠿⢿⣿⣿⣷⣾⣿⣿⡟⠛⢻⣿⣿⣷⣴⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣶⣤⣤⣄⣀⣀⠀⠉⠉⠛⠛⠿⣿⣶⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⡁⢰⣿⣿⡉⣹⣿⣿⣀⣼⣏⣈⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣶⣦⣤⣀⡀⠀⠈⠙⠿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣦⣤⣀⠈⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣏⣁⣽⣿⣿⣿⠋⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢷⣶⣤⣀⡀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣧⣠⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣄⣀⠀⠀⠉⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣤⣤⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢰⡏⠙⢦⣄⣀⣀⣀⣠⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡿⠙⢧⡀⠈⠉⠉⠉⣵⠞⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢠⣿⠁⠀⢸⡇⠀⠀⠀⢰⡏⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢀⣿⣃⣀⣴⠟⠀⠀⠀⠀⠈⢿⣄⣀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⣾⠷⣿⣥⣶⠶⣄⠀⠀⠀⡠⢶⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⡾⢯⣸⣿⣿⣤⣤⣿⠀⠀⠀⣇⣿⣿⣧⣤⣤⡟⢻⡄⠀⠀⠀⢀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣼⠃⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠙⢿⣿⣿⣿⡿⠁⠀⢿⡀⠀⣴⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠃⠀⠀⠀⠉⠛⠋⠀⠀⠰⠚⠆⠀⠀⠉⠛⠉⠀⢀⣤⣬⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣠⡾⠛⠉⠉⠉⠛⢷⣄⠀⠀⣄⡷⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠶⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣀⣤⡶⠟⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠉⠛⠻⠶⢦⣤⣤⣄⣼⣏⣀⣀⣀⣀⣀⣀⣤⣤⠿⠟⠛⠉⠀⠀⢀⡼⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⠛⠛⠛⠛⠛⠶⣤⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⡤⠶⠾⠋⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣄⣀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠶⠶⢦⣤⣄⣠⣤⠾⠋⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣏⠉⠉⠉⠉⠙⠻⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⠀⠀⠀⠀⠀⠈⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠡⣄⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠚⠠⠶⣿⠿⠿⣷⠦⡀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡋⢠⡀⠨⣀⠀⠀⠠⠈⠑⡄⠀⠱⡌⢂⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⢠⣼⠏⠀⠀⠀⠀⠀⢀⣵⠆⠀⠪⡖⠘⡀⠀⢘⡀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢈⠔⠁⠐⣿⡿⢀⡐⣆⣀⠀⠀⠙⠿⠃⢠⣾⡿⠞⠀⠀⠸⢀⠇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠈⠀⠀⠀⠄⠏⠀⠀⠀⢻⣿⡐⠌⠿⠟⠁⠀⣀⡤⠶⡛⠄⠀⣀⣠⣴⡷⠃⠘⠀⠀⠀⠀⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣀⡡⠐⠀⠀⠒⠒⠤⡁⠀⡄⠀⣾⠿⡟⣧⣡⣤⣤⠶⠾⠋⠉⠀⠀⠈⠛⠛⠟⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠽⣿⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠈⢆⠈⠂⠤⠐⣡⡼⣿⠛⠛⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠠⠀⠈⠹⣧⣤⣶⣿⣿⣿⣿⣷⠄⣿⠿⠆⠀⠀⠀⢀⠸⠀⠀⣠⠎⠀⠛⠛⠀⠀⠀⠙⠁⠀⢙⣆⣀⠠⠤⠴⠋⠳⠤⣀⢂⣍⣟⡆⠀⠀⠀⠀⡇
⠀⠠⠃⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠋⠴⠊⠀⡠⢶⣶⠄⠀⠀⠄⠀⢠⡏⠀⠀⠀⠀⣎⠶⠀⠀⠀⣰⠟⠉⠀⠀⠀⢀⣴⣶⣦⣌⣿⣿⣿⡿⠀⠀⠀⢀⠃
⠀⠈⢦⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠴⠋⠀⠀⠄⡤⠴⠂⠀⠀⠀⢷⡀⢤⡤⠀⠀⣀⠠⣴⣿⢃⡤⠋⠁⠙⠒⠺⢿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠸
⠀⠀⡄⢀⣠⡴⠶⠶⣦⡀⠀⢀⣠⣤⣤⣠⣤⣤⣄⠒⠒⠂⠀⠤⠄⠀⠈⠙⢷⣤⣄⣀⣀⣀⣾⣿⣼⣆⠀⠀⠠⠀⠐⠂⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⡖
⠀⠀⠙⢏⠁⠀⠀⣀⣀⡙⣖⣉⣁⣀⣀⠀⠀⠀⢻⣄⣰⠟⠛⠛⠛⠻⣷⣀⣤⣤⣤⠉⠉⢉⣁⣘⠿⠟⠁⠄⠀⠀⠀⢀⣤⡶⠶⠒⠶⣦⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠉⠡⠤⠤⠄⢀⡀⠀⠀⠀⠐⢿⡀⢠⡿⠉⠉⠉⠙⠉⠙⠶⣤⡴⠋⠀⠁⠀⠀⠀⠈⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⢀⡀⠠⠄⠀⠒⠒⠒⢒⡒⠦⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⣀⣠⠤⠀⢉⣤⣤⣶⠎⣛⣛⣉⠛⢁⣤⠐⣦⣤⣄⠐⢶⣦⣄⣀⣀⠀⡀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠛⡌⠀⠁⢈⣽⣃⣬⡁⣀⠀⠂⣙⡁⢹⡀⠉⠓⢶⣶⣠⡑⢄⠀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣦⠏⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠻⠿⠿⠋⠀⠀⣀⠀⠀⠈⠁⠀⠀⠂⠁⠀⠀⠁⠘⢦⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⣠⡴⠋⡴⠊⢡⠀⠀⠀⠀⠀⢀⣀⣀⡸⠃⠀⠀⠀⠀⠀⠀⣾⡿⠓⠀⠠⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡰⠁⠀⢀⡬⠟⠐⠚⡀⠤⣀⠳⣄⡀⣀⠔⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⣯⡄⣄⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡜⠀⠀⣠⠏⢠⠰⠞⡛⠛⠀⠉⠃⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⡋⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⡘⠀⠀⠠⠋⠈⠞⡠⠔⣂⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠢⡄⠄⠀⠉⠐⠂⠀⠐⢃⠁⠀⠀⠀⠡
⠀⠀⠰⠁⠀⢠⢁⡟⡒⠚⠡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⣄⢈⡀⢀⠀⠀⠀⣃
⠀⠀⡄⠀⠀⠆⣸⢁⡁⡇⣃⡀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣦⢀⠀⠀⠀⠄⠀⠙⠒⠀⠀⠀⠀⠀⠀⠣⣀⢀⠀⣀⡴⠋⢀⣤⣤⣶⠀⣡⠀⠸⣧⠀⠆⠀⠀⠨
⠀⢀⠁⠀⠘⠀⡟⠸⠀⠛⠉⠀⠀⠀⠀⠀⠄⣠⡤⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠈⠈⠁⠀⠀⠀⠸⠿⠟⡁⢀⡘⠄⠐⢹⡆⠸⠀⠀⠀⡀
⠀⢸⠀⠀⡄⠀⡇⣨⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣤⣰⡐⠿⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠐⠂⠒⠀⠀⠀⢀⠀⠀⠀⠀⣰⢤⣼⠏⠈⣠⠃⠈⢿⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠁⠀⡷⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠴⣧⣬⣤⢰⠋⠁⠀⢰⢸⠀⠁
⠀⠀⠀⠀⡀⠀⣷⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢘⠀⠄⠀⠀⢸⢸⠆⠀⠀⠀⡀
⠀⢰⠀⠀⠇⠀⢸⠻⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢀⣸⠅⠀⠈⠉⠀⠀⡌⡐⠀⠀⠀⣈⢸⠀⡆⠀⠀⡇
⠀⠸⠀⠀⠐⠀⠈⢿⡀⢰⣿⣶⣷⡖⠚⠁⠈⠀⠒⢤⡀⠀⠀⠀⠀⢀⠠⠀⣀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡝⠾⢀⠀⠀⠀⠃
⠀⠀⡀⠀⠀⢡⠀⠘⡇⠀⠈⢙⠋⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⠁⠀⠀⠀⠀⢱⠤⠔⠀⠀⢠⣶⣶⣶⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡘⢰⠈⡆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⢂⠀⠱⣀⢖⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠤⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⠿⠟⠁⠠⠀⠀⠀⠀⣼⡷⠂⠁⣀⡃⣠⢃⡟⡸
⠀⠀⠐⡀⠀⠀⠀⠀⠀⡋⠈⠈⢧⡀⠀⠀⢀⠴⠒⠒⠂⠀⠀⠀⠀⠀⠤⣀⠀⣰⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⠀⠀⢿⡆⡀⢀⣼⡿⢀⠞⠙⠁⠀⠀⢠⠁
⠀⠀⠀⢡⠀⠀⠀⠀⢂⠰⡘⢄⠀⠉⠶⠒⠁⠀⢠⣶⣾⡿⠀⠀⠀⠈⠀⡀⠀⠀⠀⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢱⠀⠈⠉⠛⠴⠿⣋⣱⠏⡀⠁⠀⠀⢀⠆
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠡⡈⠢⢁⣢⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⡄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣤⡿⢃⠔⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠐⢄⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠐⠚⠃⠀⠀⢀⢔⡱⢋⠔⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡀⠀⠙⢀⠀⠉⠈⠀⠀⠀⠀⠈⠂⠀⢀⠄⠀⠀⠄⡀⠀⠀⠀⠀⠐⠋⠀⠀⣀⠤⣊⠵⢋⠔⠁⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢄⠀⠙⢶⣤⣀⠒⠈⠉⠉⠀⠰⡔⠞⠉⠡⢦⡠⣄⠀⠀⢀⡀⠤⢒⣪⠴⠚⠡⠀⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠁⠢⢀⠉⠛⠯⣔⣒⡂⠤⠤⠤⠤⠴⠖⠂⠀⣸⣋⣡⠤⠖⠚⠩⠔⠂⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠀⠈⠐⠀⠄⠀⠉⠉⠉⠉⠋⠋⠉⠉⠉⠉⠠⠀⠒⠈⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠒⠒⠒⠒⠒⠀⠉⠉⠁
⣶⣾⣷⣶⣶⡾⢷⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣿⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⡿⣶⢾⠿⠷⢶⣶⣶⠶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠋⠉⠃⠀⠂⠀⠠⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣀⡀⠀⠀⣀⡀⠠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡀⠒⢄⡀⠀⡜⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⢿⡀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⠀⠄⢈⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠉⠙⠓⠀⠠⠤⠀⠐⠀⠀⠀⠉⢁⣀⣤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠐⠀⢤⡤⠀⠤⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣤⡴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡰⠟⠉⠀⠀⠀⠀⠀⢀⣀⣠⠶⠄⠀⠀⣉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢠⠜⠉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠒⠉⢁⣠⣤⠶⠞⠉
⠀⠀⠀⠀⣰⠏⠀⠀⠀⢞⣀⣤⠤⠖⠋⠁⣀⣤⠴⠶⠋⠉⠁
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠉⢉⣀⠴⠖⠋⠉⠁
⠀⠀⠰⢆⠁⡀⠀⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⠉⠐⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣃⡀⠰⠶⠠⠞⠀⠈⠙⠶⠛⠂⢀⠄⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠙⠛⠓⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢣⣌⠀⣈⡄⠀⠀⠠⠄⢀⠀⠀⠴⠈⠈⠠⠤⠘⣛⠛⠓⠶⠤⠤⢀⣀⣀⣀⠀⠀⠀⢠⠄⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠾⠃⠀⠈⠋⠡⠄⠐⡄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠒⠓⠀⠉⠉⢩⠑⠠⠄⣦⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⣈⠓⣴⠊⠀⠀⠠⣄⢀⡠⢤⠠⣄⠀⠈⠀⠈⠑⢂⡴⠦⠤⠄⠀⡹⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠠⠀⠒⢦⣄⡀⠀⣀⠉⠀⠈⠁⠀⠀⠀⠈⠀⡐⣶⠓⠂⠀⢀⡰⠤⠚⠀⠀⠀⠀⢀⣠⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⣀⡄⠀⠌⠀⠀⢘⡩⠿⠿⠆⠀⠀⠀⠐⠂⠤⠄⠂⠁⠈⠁⢚⣦⠄⠁⠂⢀⣤⡴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⢠⡬⠃⠀⠀⢠⡴⠊⠀⠀⠘⠀⠰⠶⠀⡈⠀⠀⠀⠀⢀⣀⡄⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠉⠠⠀⠂⠀⠀⡠⠂⠀⢈⠀⠀⢀⡀⠀⠀⠘⠃⠀⠐⠓⠀⡀⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠙⠒⠀⢁⣤⡴⠂⠈
⠀⠀⠀⠀⠀⡴⠃⠀⢀⡀⢀⠽⠂⠀⠀⠀⠀⠀⠈⣀⣤⠴⠖⠋⠉
⠀⠀⠀⢀⠞⢡⡄⠒⢉⡉⠲⠀⠈⣁⣤⠴⠖⠊⠉
⠀⠀⢴⠁⠀⠀⠈⢀⣀⠀⠔⠛⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠄⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⣀⣀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠒⠀⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢈⡉⠁⠘⠂⠠⠄⠀⠠⠤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡘⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠁⠒⠈⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⢿⡀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠑⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠔⠚⠉⠀⠈⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠁⠀⠀⢀⣀⣤⠔⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠒⠈⠁⠀⠐⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⢤⡤⠖⠀⢀⣤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡤⠀⠀⢀⠀⠂⠀⢉⡀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢀⡀⠀⠲⠄⠀⠀⠀⠉⣀⣤⠶⠊⠉
⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠲⣤⡄⠗⠀⠉⣀⣠⠴⠖⠋⠋
⠀⠀⠀⠜⠁⠀⠀⠀⠀⠈⢁⣀⠴⠶⠛⠋⠁
⠀⠀⠰⢄⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣀⣤⣬⣦⣀⠀⠀⠀⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⢀⡀⠀⠀⠉⠠⠈⠁⡕⠄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣼⠃⠈⠀⠀⠀⣨⡖⠀⠢⡂⠡⠀⠘⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⣻⡇⠠⣰⣤⡀⠀⠙⠋⣀⠿⠟⠃⠀⠰⡠⢃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠐⠀⠁⣀⠀⠀⠀⠀⢀⣤⣽⡓⡈⠈⣋⣀⡤⠶⠚⠋⣤⣤⣴⣾⠏⠁⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠔⠚⢛⣿⣿⣿⠆⠀⠀⠀⠀⠈⠐⡀⠢⠘⡋⠋⣻⣿⠿⠏⢉⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢨
⠀⠀⢀⠠⠀⢺⣤⣤⣶⣿⣿⣿⡄⣴⠷⠀⠀⠀⠀⠠⠀⠀⡴⠉⠳⠓⠀⠀⠒⠀⠙⢢⡀⠀⠀⠴⠪⢉⣉⢉⣹⣦⠀⠀⠀⢸
⠀⠐⠁⠀⠀⠀⠙⠻⢿⣿⠟⠉⠒⠁⡠⢶⡦⠀⠀⠀⠀⢼⠁⠀⠀⠰⠵⠀⠀⢀⡼⠋⠁⡀⠀⣠⣶⣦⣬⣿⣿⣿⠀⠀⠀⠘
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠐⠠⠒⠀⠀⠀⠘⢦⡲⠆⠀⠠⠀⢲⡿⢠⠊⠀⠈⠉⣛⠿⣿⣿⣿⠟⠋⠀⠀⠀⠃
⠀⠰⣤⠴⠛⠋⠙⠷⣀⠤⠖⠓⠒⠚⠛⣦⠀⣠⣤⣤⣤⣤⠀⠙⠳⠶⠶⠶⠟⢿⣿⡆⠀⠀⠀⠀⠀⣀⣈⣀⣀⠀⠀⠀⠐⡇
⠀⠀⠈⠂⠐⠂⠀⠀⠁⠀⠀⠀⠐⠀⠠⠘⠒⢁⡀⠀⠀⠉⠑⠛⠫⣷⠀⣰⠒⠒⠛⠖⠲⣄⣀⡠⠛⠋⠀⠀⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠍⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⢠⡤⠄⠂⢒⠂⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠘⢉⠔⠀⠀⠀⠁⠂⠠⠊⠁⠀⠀⠀⠂⢌⠁⠀⠠⣈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠤⠒⠁⠀⠀⢀⣀⣤⠤⠄⠠⣠⣄⣀⣀⣀⣄⡀⠀⠀⠀⠀⠁⠀⡡⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⣀⡀⠔⢊⣀⡠⠀⠀⣀⠉⠁⣀⠀⠉⠉⠁⠭⠀⠈⠙⠳⢂⠀⢊⢊⡆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⢻⡀⠢⠎⠀⣴⣾⣿⣿⣿⣷⣦⡉⠀⡀⡞⠙⠒⢋⠤⠀⠀⡝⠪⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠂⣾⣿⠛⠙⢿⣿⠛⠻⣿⡀⠥⠃⠘⢀⣴⣶⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣃⡄⢸⣿⣧⣀⣠⣿⣿⣶⣾⣿⡇⠀⡀⣴⠿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣿⣿⠿⣿⣏⠉⣿⡿⡃⠀⢺⣿⣶⣿⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⢿⣿⣶⣿⣿⣿⣿⠟⠀⢠⣻⣿⠉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠛⠛⠛⡫⠥⠀⠸⠀⠫⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣠⠰⠀⠀⢠⠆⢠⠀⢦⡄⢀⠉⢻⡟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣶⣤⡈⠁⡀⠀⠄⠂⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁⢀⣿⣻⠀⢤⠄⠀⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⣿⡟⠇⢀⠤⢈⡀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣿⡿⠁⠀⠀⢀⡾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⢀⠀⠠⠆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⡎⠀⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⢀⠦⠄⠀⠀⠀⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⡞⡀⠀⠐⠤⡴⡃⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⠀⠠⡀⠐⠁⠀⢤⠀⠠⠀⣰⣁⠄⠐⠒⠁⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠟⢂⠨⠀⢀⠄⠼⣧⠀⡰⠁⠐⠀⣀⣁⡤⠐⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠈⠀⠐⠀⠈⢲⠈⣈⡔⠷⠚⠚⡉⢁⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠸⢇⣀⡠⠀⠐⠉⢀⣚⡓⠀⠀⠠⠜⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠈⢁⠀⠢⠃⠀⠀⠄⢀⠠⠜⠀⠀⠐⢀⠴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠄⢠⠃⠀⠤⠘⠀⠂⠀⠀⡈⡀⠂⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⠀⠠⠀⠒⢊⠀⠃⠀⠄⠂⠒⠁⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠀⠄⠀⢠⡀⠀⠹⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠛⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡞⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠔⠚⣉⠱⠒⢂⠀⠀⠀⠒⠒⠖⣉⠉⠀⢀⠇⠀⠀⠀⠀⠀⠈
⡶⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠊⠉⠁⠀⠀⠀⠀⠄⠠⠊⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠃⠀⢸⠁
⠳⣌⠑⢄⠉⠉⠉⠀⠀⠘⠉⠀⠀⠀⠀⣀⠄⠒⠈⠅⠀⡀⢌⡣⠐⠠⡀⠀⠀⠁⠈⠠⠤⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸
⠀⠈⠳⡄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⠡⠔⠂⠀⠀⠰⠠⠕⠈⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⠢⣄⠉⠢⢄⡀⠀⠀⠂⠀⠘⢦⠄⠀⠀⠀⠀⠀⠐⡀⢀⠠⠃⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠉⠢⣄⠉⠉⠑⠢⢤⡀⠀⠀⠀⠈⠁⠐⠀⠈⠀⢀⡠⠔⠊⠉⢁⡀⡀⠠⠀⠄⠈⠉⠑⠲⣄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠈⠑⠢⣄⠀⠀⢠⠀⠀⢠⠎⢀⠀⠀⠀⠈⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠑⠦⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⡿⠀⠀⣠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠈⠑⠤⡀⠙⠭⣒⠤⢄⣈⣀⣀⣀⣁⣀⡤⠄⣒⠭⠊⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠈⠑⠒⠤⢉⡑⠒⠒⠒⠂⠐⠒⠉⠁⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⡀⠀⠀⠉⠑⠤⣀⠀⠐⠈⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠉⠑⠰⠓⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡼⠀⣀⠔⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣤⣤⣞⣂⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠉⠉⠉⠛⠲⠦⣄⡀⠀⠀⣸⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠆⠀⠀⠀⠀⠀⠀⠀⡴⠛⢷⠀⠀⢠⡇⠀⢠⡏⠀⠀⣀⡙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣤⣤⡀⠀⠀⠀⠀⠻⣤⠞⠀⠀⡾⠀⠀⣼⠀⠀⡏⠉⣷⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⡄⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⠇⠀⠀⠙⠚⠃⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡄⠀⠀⢀⠀⢀⡟⠀⠀⡟⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⠋⠀⣼⠁⠀⣸⠃⠀⠐⠲⡄⠀⠀⠳⠶⠞⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡏⠀⠀⠀⣠⠟⠀⠀⠀⠀⢀⣤⣤⠀⠀⣧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣾⣀⣀⠀⠈⠁⠀⠀⠀⠀⠀⢺⡀⣸⠇⠀⢹
⠀⠀⠀⠀⢰⡇⠀⠀⠀⣀⡀⠀⠀⠀⢠⠞⠋⠀⠀⠀⢀⣀⡀⠀⢸⣇⣀⠀⠀⠈⠉⠙⠓⠶⠦⣤⣀⣀⠀⠀⠉⠁⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⠀⠀⣟⠉⢹⠀⠀⠀⠘⢧⡀⠀⠀⢰⡏⠉⡧⠀⠀⠈⠉⠙⠓⠲⠦⣤⣀⣀⠀⠀⠈⠉⠙⠓⠶⠦⣤⣀⣸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣀⣀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢳⣀⣀⡴⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠹⣤⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣴⠛⢳⡄⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢙⡇⠀⠀⠀⠀⠹⠦⠞⠁⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣀⠤⠤⠤⠄⣤⡤⠤⠤⠒⠒⠀⠉⠉⠑⠒⢤⠀⠤⠤⠒⠚⠉⠉⠉⠓⠒⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠳⣄⣀⣀⡀⠀⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡐⠠⣄⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⢏⠏
⠀⠀⠀⠀⠀⠀⠀⡧⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠈⠑⢦⠀⠀⠀⠀⡤⠒⠒⠒⢤⡎⡞
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠄⠐⠘⡄⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠁⢈⡇⠀⠀⢸⠀⠀⢀⠁⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣠⠞⠀⠀⠀⠘⢄⠀⠀⡸⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠉⠀⢀⠔⠂⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣆⠀⠀⠀⠀⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⠦⣀⠀⢀⡠⠃⠀⠀⠀⢀⠤⠒⠒⠦⡀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⢹⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠂⣀⠞⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡠⠚⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⡌⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡄⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⠤⣀⡠⠞⠀⠀⡠⠴⠶⢤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡞⠀⠁⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠱⣄⠀⢰⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠉⠹⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⠢⣀⠀⠀⠐⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢂⣉⣀⣀⣀⠉⠢⡀⠙⡄⠀⠹⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠁⠀⠣⠤⠤⠤⠤⠗⠀⠈⠒⠬⣦⠤⢄⡀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⣪⠓⠒⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣀⡀⠀⠑⢄⡑⡄⠀⠀⠠⠛⢢
⠀⠀⠀⠀⣀⠤⠔⠊⢁⡀⠀⠈⠢⠒⠊⠁⠀⠮⣀⡀⡀⢀⡱⠀⠘⠀⠀⠀⠉⠙⠆⠈⠪⣑⠲⣮⡁⢸
⠀⠀⡰⠊⢀⠀⠰⢉⣉⣉⡹⠂⠀⠀⠀⠐⠒⠀⠀⠀⠉⠁⠀⣀⠀⠈⠁⠒⠒⣊⣁⣀⣤⡚⠃⠤⠔⠋
⠀⠀⠄⣠⠤⠤⣤⣄⠤⠤⠤⠶⠖⠰⠤⠶⡀⡴⠶⠦⠮⠭⠁⠐⠓⠤⠤⠚⠋⠉⠉⠉






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

⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡾⡆⠀⡄⢀⠀⠀⠴⠒⠋⠉⠉⠉⠀⠒⠒⠀⠤⠀⠀⠀⣐⣒⣒⣚⣿⡷⠀⠠
⠀⠀⠀⢸⠠⡏⠀⡆⡎⡇⢹⠃⣰⣇⢾⡰⡀⢀⠂⠀⠀⠀⠀⢀⡬⢒⠃⡔⠀⠀⠈⣉⣩⡭⢭⣗⢮⠁⡀
⠀⠀⠀⠈⠁⠳⠜⠛⠀⡡⠈⠉⠈⠋⠀⠀⠀⠀⠀⠀⡰⠃⠄⠀⠀⠸⠪⣖⡳⠆⠻⡉⠉⠉⠁
⠀⠀⠀⢀⡴⣢⠅⠀⠘⠻⣷⡄⡠⠀⠀⠀⠐⠒⠀⢒⡣⠎⠀⠀⠀⠀⠀⠀⢊⡀⠰⠒⡲⢒⣊⠉⠁
⠀⠀⠀⠉⠊⢔⡩⠄⠐⡂⠀⠰⠁⠀⠀⠀⢀⣠⢴⢾⠳⢴⣈⡀⠉⠁⠀⠀⡀⠀⠀⠀⠛⣉⠶⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠖⡍⠀⠀⠀⠤⠔⠊⠉⠀⠄⠁⠘⠀⠈⠉⠀⠉⢙⠀⢈⠀⢀⣤⠄⡈⠀⠀⠀⠰⠁⠇
⠀⠀⠀⠀⣴⡂⠀⠐⢀⠀⡀⠔⠀⠀⠀⢰⠀⠀⠀⠀⠁⠘⠀⡀⠀⠀⠀⠀⠀⠈⠀⠔⠠⢀
⠀⠀⠀⠈⠉⡠⠃⡴⢋⠎⠃⠀⠰⠃⠀⢸⠀⠰⠀⠀⠀⡠⠂⢁⠖⣼⡂⠢⣠⣠⡄⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠜⠁⠃⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣠⣲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⢧⠆⠄⢠⠃⢠⠆⠼⢠⠄⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⢄⢠⣿⣧⠉⠙⠗⠀⠀⠀⠀⠀⠀⣀⠀⣠⡐⢰⠇⠟⠎⡠⠃⡴⠃⠀⢀⡎⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡿⡴⠀⠁⠀⠸⠀⠀⠈⢠⠞⠁⠀⠀⡜⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠙⠻⠿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⡜⠀⠈⠂⠀⠀⠀⠛⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣤⡀⣴⡄⢠⣦⣤⣦⣤⠀⣴⣤⣴⣤⠄⠀⣴⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣿⠃⣿⡇⠀⠉⢉⡿⠃⠀⠉⢉⣽⠋⠀⢰⣿⣨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠛⠉⠀⠀⣿⡇⠀⣰⡟⠁⠀⠀⣠⡿⠃⠀⠀⣼⡟⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠿⡇⠸⠿⠶⠶⢶⠰⠿⠷⠶⠶⠆⠿⠁⠀⠘⠿⠆⠀⠀⣴⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣄⡉⠻⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠺⠟⠛⣋⣉⣩⣭⣭⣥⣭⣭⣭⣍⣉⣛⠛⠿⠓⠀⣠⣾⣿⣿⣿⣿⣶⣄⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⢋⣉⣤⣶⣄⠙⢿⣿⣿⣟⣻⣿⣿⣯⣄⣠⣿⠟⠁⠀⣠⣾⣿⣉⣻⣿⣿⣿⢿⣿⣿⣦⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⣠⣶⣿⡛⠉⠉⢛⣷⣤⡙⢿⣿⣿⣋⣛⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣇⡀⢀⣸⣿⣿⣷⡄⠘⣿⣿⣦
⠀⠀⠀⠀⠀⣠⣾⣿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣟⠛⣛⣿⣦⡉⠿⣿⡿⠋⠁⠀⠀⠶⠿⠿⠿⠿⠿⠿⠛⠟⠛⠟⠛⠛⠛⠛⠛⠛⠀⠘⠛⠛
⠀⠀⠀⠀⣀⣛⣛⠁⣈⣛⣋⣛⣛⣛⣋⣉⣙⣉⣛⣉⣛⣛⣉⡂⢈⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀
⠀⠀⠀⢠⣿⣿⡏⢠⣿⠋⠉⠉⠉⢻⣿⣿⣿⠿⣿⣿⣿⠟⣣⣴⣿⣷⣬⡛⢿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⠀⣻⣿⣿
⠀⠀⠀⢸⣿⣿⣇⠸⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣾⠟⣡⣾⣿⡿⠿⠿⣿⣿⣦⡙⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⡆
⠀⠀⠀⠸⣿⣿⣿⡀⢻⣿⣿⣿⣏⣀⣹⣿⡿⢋⣵⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣌⠻⣿⣿⣿⣟⣛⣿⣿⣿⠏⢠⣿⣿⣿⠁
⠀⠀⠀⠀⢻⣿⣿⣷⣄⠹⢿⣿⣿⣿⡿⢋⣴⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⠿⢿⣷⣌⠻⣿⣿⣿⣿⡿⠋⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣄⠙⠟⣡⣾⣿⣿⣿⣿⣄⡀⠀⠀⣀⣼⣿⣿⣿⣿⣀⡀⣀⣠⣿⣷⣦⡙⠿⠋⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢋⣡⣦⣈⡙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢉⣡⣤⣘⠿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣿⣿⣿⣿⣿⣷⣶⣤⣄⣉⣉⣉⠙⠛⠛⠛⠛⢉⣉⣉⣉⣤⣴⣶⣾⣿⣿⣿⣿⡷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠒⠈⠉⠉⠁⠐⠒⠒⠀⠀⠐⠢⠄⠀⠀⠤⠤⣀⡀
⠀⠀⣀⠤⠐⠒⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡷
⡰⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⣒⠚⠛⠉⠉⠉⠉⠉⠉⢉⡉⠓⠒⠒⠒⠒⠒⠒⠠⠀⠀⠀⡰⠁
⢇⠐⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⠿⠛⠛⠓⠀⠀⠀⠀⠀⠚⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠈⠳⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⡠⠄⠒⠂⠀⠀⠁⠀⠀⠀⠀⠀⠐⢀⡜
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣀⠀⠀⠚⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣿⢛⣷⠀⠀⠀⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡖⡇⠀⢂⠀⠈⠉⠁⠀⠘⢄⡈⠉⠁⢀⠄⠀⠀⠀⠀⢠⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣷⠹⡀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠄⢠⠏⠀⠀⡌⠀⠀⡐⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⣦⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠎⠀⠀⠀⡴⠀⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠀⢻⣿⣷⣶⣤⣥⣼⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠴⡁
⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠙⠿⡉⠉⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠤⣄⠠⠄⠂⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡔⠁⢀⠀⢢⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠧⣄⣀⣀⣀⠤⠐⠀⠀⠀⠀⠀⣀⡀⠔
⠀⠀⠀⠀⢀⡞⠀⡠⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈
⠀⠀⠀⠀⣼⠀⡜⠀⠀⠀⠀⠀⠱⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠔⠈⠁⠁⠐⠁⠂⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⣼⣷⡄
⠀⡔⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠹⡄⠀⠀⠀⠀⣰⠁⢻⣿
⠀⡄⠀⢰⠋⠀⠑⠠⠀⠀⠀⠀⢸⣿⡇⠀⠙⢄⡂⠀⣰⠃⠀⢸⣿⡇
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠉⠉⠁⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣼⣷⣤⣄⠀⠀⠀⠀⣀⣤⣾⣯⣤⣤⣤⣤⣄⡀
⣀⣀⡀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣀⣀⣀⣀⡀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⠛⠛⢻⠋⠉⠉⠛⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⢉⣀⣀⣤⣤⠴⠖⠚⠻⡉⠙⠛⠲⠦⣤⣀⣀⡀⠉⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⣁⡤⠖⠋⠉⠉⠁⢀⣠⡤⣄⣀⣠⣧⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢦⣀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡴⠚⠁⠀⠀⠀⡤⠶⢒⡭⠶⠦⣤⡈⠁⢻⠀⠑⠶⠚⠙⠲⣒⡶⠦⠤⣀⠈⠳⢦⡀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠄⡰⠖⠒⠚⠀⢰⣯⠞⠉⠙⠲⣝⢆⠀⠀⠀⠀⠀⠀⡞⡱⠊⠉⠓⣌⠱⣄⣀⣉⠳⢤⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⣴⠋⠀⡰⠋⠀⠀⢠⠼⢧⡀⠀⠀⠀⠘⡟⢠⢀⡀⠀⠈⢿⠄⠀⠀⠀⠀⠘⣇⢣⡀⠀⠀⡼⠀⣿⠀⠸⡇⠀⠙⢦⡀⠙⢷⣄
⠀⠀⠀⠀⢀⡾⠁⢀⡞⠁⠀⠀⣀⣥⣀⡀⠑⣄⠀⠀⠀⠙⢦⡀⠈⠉⢲⡞⢨⠀⠀⠀⠀⠀⠙⠶⣬⣉⣭⡤⠞⡟⢦⡀⠉⠙⢲⡄⢹⡖⠀⠙⢧⡀
⠀⠀⠀⢠⡞⠁⢠⠏⠀⠀⣠⠞⠉⠀⠈⠻⡳⡌⢢⡀⢀⣄⡀⠉⠙⠛⢉⠀⢸⠀⡴⢦⡀⢀⣀⣀⠀⠀⠀⠀⡰⠃⡼⠀⠀⠀⠀⠧⣄⡙⣆⠀⠈⢻⡄
⠀⠀⢀⡾⠀⢠⠏⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⢹⠀⠑⣝⢤⡙⠓⠒⠚⢉⡇⠈⠀⢹⡀⢹⡎⠀⠈⠙⣦⡒⢉⡠⠞⠀⢀⡠⠂⠀⠀⠀⠙⣎⠳⡄⠀⢻⡄
⠀⠀⣼⠁⢀⡏⠀⠀⢰⠋⢧⠀⠀⠀⠀⢀⠇⣼⠲⢤⡈⢢⡈⠉⠛⠉⠁⠀⠀⠀⡼⠁⡜⠱⢄⣀⣠⠏⠈⠁⠀⣀⠔⠉⠀⢀⡴⠚⠛⠓⢿⣄⠙⣆⠈⢿⡀
⠀⢰⡇⠀⡼⠀⠀⠀⢸⡄⠈⠳⣄⣀⣀⣡⠞⠉⠑⢆⢱⡀⠙⢄⠀⠀⠀⠀⢘⠛⠤⠊⠀⣀⠴⠒⠲⢤⣀⠠⠊⣀⠤⣤⣤⡏⠀⠀⠀⠀⠈⡏⣷⠘⣇⠸⣇
⠀⣾⠀⢰⠇⠀⣀⡤⠚⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠂⡧⠖⡶⢷⡀⠀⠀⢸⠀⠀⠀⡜⠁⠈⢈⣽⠾⢷⣠⠞⠁⡊⠀⠘⣇⠠⡀⠀⣀⡴⢣⡟⠀⢿⠀⣿
⢠⡿⢤⣞⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⢀⡜⢋⡼⡃⠀⠀⠀⢹⡄⠀⢸⠀⠀⢸⡠⣴⡾⠛⠁⠀⡆⣿⠀⢏⠁⠀⠀⠈⠓⠶⠶⠶⠞⠛⢦⡀⢸⠀⢹
⣾⠁⠀⠀⢏⠁⠒⠒⠢⢤⣤⣀⣀⣀⠈⠓⠀⠡⠒⠉⠀⠘⠦⢀⠤⠊⠈⠄⢼⠀⢀⡠⢾⠛⠄⣀⣀⠔⢡⡏⠳⠤⠃⠀⣠⠴⠒⠒⠒⠲⢤⡀⠀⡧⢸⡀⢸
⣿⠀⢀⠀⡜⠀⢀⡴⠋⣉⣉⣉⡙⠢⡌⠉⠉⠁⠐⠂⠀⠀⠀⠀⠠⠤⢤⣤⣽⠖⠋⠀⣀⣙⣒⣶⡶⠚⠉⠀⠀⠀⠀⠀⠙⠦⠖⠚⠛⠲⣄⠈⢲⡇⠸⡇⢸
⣿⠀⢸⠀⢧⠀⠀⠑⠋⠁⠀⠀⠉⠲⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠤⠊⢹⠀⠀⢄⠀⠀⠀⠀⠀⠉⠉⠉⢉⠉⠒⠒⠒⠶⠤⠤⢤⣀⣈⡓⢫⡀⠀⡇⢸
⢻⡄⠘⡇⢸⠇⠀⢀⡴⢒⡛⣓⠲⢤⡀⠀⡀⠀⠀⣰⠃⡷⠀⣀⢔⠁⠀⠀⠈⠀⡴⡚⣛⢢⣄⠀⠀⠀⠀⡔⢉⡗⢀⡴⢿⠛⠛⣖⢦⡀⠀⣬⠟⠁⢰⠇⢸
⠘⣧⠀⢻⠘⢧⠀⡏⡜⠁⠀⠀⠁⠀⢹⣮⣉⣉⣉⣡⠞⡡⠊⠀⢧⠑⠦⣄⠀⠈⡌⢄⣈⠆⡏⠳⡄⠀⢸⠀⣾⠀⢸⡀⠈⡄⠀⠈⣧⢳⠀⣇⠀⢀⡞⠀⣾
⠀⠹⣆⠀⢧⠀⠑⢿⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡀⠔⠀⡠⠒⠚⠛⠛⢶⡞⠀⠀⠈⣢⠤⠶⠡⢄⡈⠢⡈⢇⠹⣄⠈⢣⡀⠡⠀⢀⡟⣸⣠⠏⢀⡞⠀⢰⡟
⠀⠀⠹⣆⠈⢳⡀⠈⠳⣄⣀⠀⣀⣠⠞⢀⠔⠈⠀⠀⡌⠀⠀⠀⠀⠀⠀⢻⡆⢠⢊⡤⠞⠉⠙⢦⡙⣆⠈⠻⣗⠉⠀⠀⠈⠓⠻⠷⠚⡵⠁⠀⣼⠁⢠⡿⠁
⠀⠀⠀⠙⣧⡀⠙⣄⠀⢀⡏⠉⠉⠀⠐⢁⣄⡀⠀⠀⢇⠀⠀⠀⠀⠀⢀⢿⡇⢂⢸⡀⠀⠀⠀⣠⠷⠞⠲⠶⣌⡓⢄⠀⠀⠀⠀⡤⠖⠁⠀⢰⠇⢠⡿⠁
⠀⠀⠀⠀⠈⢷⣄⠈⠳⣄⠣⣄⣀⣀⠀⡎⠸⠁⠀⠀⠈⠢⣈⡂⠀⣒⡽⠋⡇⠈⠋⠀⠀⠀⡞⠡⠂⠉⠉⠑⠢⢷⡀⠑⢄⠀⢀⠇⠀⠀⣰⠋⣰⠟
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⠓⢤⡀⠈⠦⣱⡘⠤⣄⠀⠀⠀⠀⠉⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡧⣠⠞⠙⠄⠀⣠⠞⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠙⠢⣄⠀⠙⢦⣘⠶⠖⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⣀⣴⠏⠀⠀⠀⢀⡤⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠈⠑⠦⣄⡈⠙⢯⣅⣤⠴⠶⠦⣀⠀⠈⢀⣠⠞⠉⠓⠶⠤⠴⠋⠉⠉⠀⢀⣠⠴⠞⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠉⠓⠶⠤⣄⣀⣀⡀⠈⠉⠛⠉⠀⣀⣀⣀⣀⣤⠤⠤⠶⠒⠋⠉⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣄⣀⠀⠀⠈⠉⠉⠉⠹⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⠂⠀⠀⠐⡀⠐⠂⠘⠀⠒⠒⠒⠦⠤⠤⠧⢈⣁⡀
⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⢀⠄⣡⠖⠋⠁⠀⠀⠀⢀⣡⠐⠀⠃⡆⢂⠀⠀⠀⠀⠐⠒⠂⠐⠛⠉⠑⢤⢀⣃⠐⠂
⠀⠀⠀⠀⠘⠀⠀⡿⠀⠈⠄⠉⠈⣁⢩⣈⠁⠂⠀⠀⠀⠱⠤⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡥⠄⠀⠉⡑⢆⠈⠑
⠀⠀⠀⠀⡆⠀⠰⠃⡄⠀⠠⠀⠀⠈⠒⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⡠⠀⠀⠀⠀⢀⡀⠀⡌⠁⠃⠠⢷⠂⠀⠂
⠀⠀⠀⠀⢟⠀⠀⢱⡄⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠄⡝⣦⣳⠗⠖⠀⠈⠄⢀⣀⡀⠀⠀⠐⠀⠐⠀⠞⠋⠀⡰⡇⠀⠘⡆
⠀⠀⠀⠀⠈⢦⡀⠈⠁⢡⣶⡀⠒⠀⡀⢠⣄⣶⠠⣔⣶⣿⡄⠃⠁⠀⢀⠀⠠⠞⡀⠈⠁⠀⠈⠀⢀⠁⠀⠀⠀⠀⠈⠏⠁⠀⣘
⠀⠀⠀⠀⠀⠈⢳⣄⡈⠀⢰⡷⠶⣶⡿⣮⠿⠚⠁⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⡀⠁⠀⣈⠄⠀⣀⡤⠔⠀⢀⠠⠬⠂⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠀⠀⠀⠀⠀⠉⣥⠤⠃⠀⠂⠀⠈⠠⠠⠄⠀⠀⠀⠠⡈⠁⢉⢉⠀⠀⣠⡆⠁⠀⠀⠀⢢⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠇⣴⠀⠀⠀⠀⠀⠀⠈⠐⠉⠉⠀⠃⢰⡖⠒⠒⠒⢻⠍⠀⠀⠀⠀⠁⠁⢀⡀⡴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⠄⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡄⠤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠐⠒⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡤⠤⠤⢤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠲⣄
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⠓⠦⡤⠤⠴⠾⠇⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣻⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢰⡏⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢰⡏⠀⠀⣻⣿⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡄⠸⠄⠀⠀⠀⢸⣷⣦⣶⠋⢻⡿⠀⠀⠀⠀⠀⢸⣿⣶⣶⠉⢹⡿⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠙⠿⠿⠶⠟⠁⠀⠘⠄⠠⠀⠀⠙⠻⠿⠷⠛⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢡⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠀⠀⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠻⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠀⠂⠀⠀⠀⠀⢀⡶⠀⠀⠀⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠄⠀⠂⠀⠀⠀⢠⠞⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠⠀⠀⠀⠀⡷⠋⠀⠀⠀⠈⣝⣩⡟⠧⣤⣭⡼⠿⠿⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡰⠒⠀⠀⠀⠀⠀⠀⣟⣱⣞⣻⣦⠙⣼⡛⣷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣿⡃⣛⠈⣛⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣚⡻⠋⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⢨⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡿⢊⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⣤⣤⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡖⠲⢄⠉⠉⠑⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠈⢳⡄⠒⠠⠤⠜⠀⠀⠀⢀⣸⣟⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠁⠀⣀⡀⠲⣄⠀⣎⠀⠈⣛⠇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀⠀⣀⠀⠯⣁⣀⡤⠃⠈⠓⠚⠃⠀⠀⠂⠀⠙⠳⣀⣤⢖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⢛⡏⠀⡉⣹⠀⢀⢄⣤⡖⠀⢀⡔⠊⠍⠙⢲⠀⣀⠤⠜⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢬⢶⡶⠒⠁⠀⠈⠉⠛⠃⠀⠀⠹⠦⠶⣾⡾⢞⡡⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠊⣀⡗⢀⡔⠒⠓⣢⠀⠀⠀⠀⠀⠀⢀⠜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠁⠀⠈⢇⣨⣤⡼⠁
⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠘⠃⠂⠖⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⣠⣴⣊⣭⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠉⠛⠒⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡷⣄⡀⡀⠀⠀⠀⠀⠈⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢈⡛⠿⠷⠷⣧⣠⠀⡀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠰⠥⠃⠀⠀⠀⠈⣝⠳⠷⠦⣥⣠⡠⣀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣠⣤⣤⡤⠤⣌⡁⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡴⠋⠊⠁⠀⠈⠉⠒⠙⢦⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⡇⣀⠤⢤⠀⠀⡴⠶⢤⡼⠀⠀⢠⢖⡦⠘⢮⡰⣠⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⣀⠀⠀⠛⠗⠚⡾⠀⠀⣿⠛⠋⠁⠀⠀⠀⠁⠀⠀⠀⠙⢮⣓⠂⢤⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⡌⢳⡀⠀⠀⢰⡁⣀⣀⢈⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠈⠉⠓⢦⡴⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠒⠛⠀⡇⠀⠀⠀⠙⠒⠛⠋⠀⠀⢀⡤⢂⠍⠀⠀⠀⠀⠈⠉⠛⢦⡄⠀⠳⡗⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠰⠧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠒⠁⠀⠀⠀⠀⠀⠁⠀⠹⡆⠀⣸⠄⠸
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠠⡀⠀⠀⣠⠃⠀⠀⠀⠤⠴⠀⠀⠀⡎⠀⠀⣠⡀⠀⠀⠀⢰⠁⢀⠄⠀⠀⢿⢰⡗
⠀⠀⠀⠀⠀⠀⣰⠃⠳⠖⢃⡠⠖⠁⣠⠤⣀⣀⠀⠀⠀⠀⠸⡇⠀⠀⡀⠀⠀⢀⡀⠀⠉⠁⠀⠀⠀⡾⣸⡤
⠀⠀⠀⠀⠀⣰⠛⠒⠂⡽⠛⣖⣄⢸⡄⠉⠉⠙⣻⠀⠀⠀⠀⢷⡔⢉⠄⠀⠐⠒⠃⠀⠀⠰⡅⢀⣴⠃⡿⣿
⠀⠀⠀⠀⣰⠃⠀⠀⠐⣇⠀⠻⠿⠟⠀⢀⡞⡉⠁⠀⠀⢀⠀⠈⢿⣥⡂⠀⠀⠀⠀⠀⢀⣀⣤⠞⠁⢰⣧⠿⢶⢦
⠀⠀⠀⢠⠃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⠿⠿⣧⠀⠀⠈⠀⠀⠀⠉⠛⠛⠓⠒⠚⠛⠋⢉⣀⣀⣠⡾⠑⠀⠆⠮
⠀⠀⢠⠏⠀⣠⠄⢄⠀⠈⠳⣤⣀⠀⠀⠠⣂⡴⠃⠀⢀⣀⣀⣤⣤⣤⣶⣶⢶⠾⠿⠻⠛⠟⠙⠁⠁⠀⠀⣀⣀⣀
⠀⢀⠏⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⣉⣩⣭⣵⣶⣿⢿⠿⠻⠛⠋⢋⣈⣀⣡⣤⡤⠤⠶⠶⠒⠚⠛⠛⠉⠉⠉⠉⠉
⢀⡞⠀⠀⠀⢀⣀⣠⢤⠴⠖⠚⠛⢋⣙⣁⣠⣥⠤⠶⠖⠒⠛⠋⠉⠉⠁
⣾⡄⠒⣊⣉⣩⣥⠥⠴⠶⠒⠛⠋⠉⠉
⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠠⢪⡞⣡⣶⡏⣸⢁⣨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣭⠴⠒⣛⣛⣛⣂⠀⠀⠀⠠⢏⣾⣿⣿⡇⠋⣈⣤⣤⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣡⣴⠾⠟⠛⠛⠛⠛⠻⠷⣶⣄⣸⣿⣿⣿⣣⣾⣿⣿⡏⡾⠀⢀⣀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣏⠁⠀⠀⠀⠀⣴⣦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⢷⣇⣤⣭⣭⣶⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⡿⠛⠀⠀⠀⠀⠼⠛⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣟⣷⠟⣡⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣸⡿⠏⠀⠀⠀⢰⣿⣷⢸⣿⣿⣧⡀⠀⣾⣿⣿⣿⣻⣿⣯⣥⣤⣀⡀⠀⢤⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠐⠛⠋⠋⢸⣿⣿⣿⣷⠀⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣦⣄⠉⠢⡹⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⣿⡿⠀⠀⠀⣴⣦⡄⣦⣀⠀⠀⢀⣿⣿⣿⣿⣿⣇⡿⠋⡡⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠙⣎⠆
⠀⠀⠀⠀⢀⡎⢠⣿⠁⠀⠉⠉⠀⠀⠀⠰⠿⠛⠁⠹⣿⣷⣶⣬⣍⣉⣙⣻⣿⣟⣄⠈⡄⢀⠀⠀⠁⠀⠀⠄⠀⠀⠘⢿⣷⡀⠘⡆
⠀⠀⠀⢀⡞⢀⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡿⠿⠛⠁⡃⠀⣤⡉⠲⠤⣄⣀⠀⡀⠀⠀⠀⠠⠀⠈⢿⣷⡀⠘
⠀⠀⠀⣾⡇⣸⣿⣿⠇⢠⡿⠗⠀⠀⢀⣤⡄⠀⠀⠈⣿⣿⠟⠋⠀⠂⠘⠃⡇⠻⣿⣷⣄⠀⠸⣍⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠻⡇⣿⡏⠁⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠀⢸⣿⠃⠀⠀⠠⠀⠀⡄⢄⠀⠙⢿⣿⣄⠀⠈⡟⠗⠀⠀⡀⠀⠀⠀⠀⢹⣿⡄⢠
⠀⠀⠀⠀⣇⢹⣧⢠⣿⡷⢀⣤⣶⠀⠀⠀⢀⣀⡀⣿⣿⠀⠀⠀⠀⠀⢠⠀⣀⢇⠀⠀⢻⣿⣧⠀⢳⠃⠐⠃⠀⠀⠀⠀⠘⠀⣿⣧⠈⡇
⠀⠀⠀⠀⠘⠈⢿⣆⠁⠀⠈⠛⠉⠀⠀⠰⠿⠿⠃⢻⣿⡀⠀⠐⠊⠀⠀⠀⠁⠀⡑⢆⠀⠻⣿⣇⠀⡄⠶⠀⠁⠀⡀⠀⠀⠀⣿⣿⠀⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣾⠿⠆⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠓⢄⡈⠻⣆⠡⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠸⠂⣀⠘⠁⢈⡲⣝⠆⢃⠰⠆⠀⠀⢀⠀⠀⣿⣿⠀⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⣍⣉⣉⣉⣀⣀⠀⠙⣿⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡂⣀⠀⠀⠀⠐⢀⣿⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠀⠀⠀⠈⠻⣿⣦⣄⠀⠈⠀⠀⢀⠀⠀⠀⠛⠁⠀⠆⢉⢉⠀⠀⠀⠀⣼⣿⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⣼⡿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣦⣤⣀⣀⠀⠀⡀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣉⠙⠛⠿⠿⢿⣿⣿⣷⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡉⠓⠢⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣴⣶⣶⣶⣖⡒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠓⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⣤⣤⣴⠶⠿⠟⠛⢋⣉⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣛⣫⣇⣻⠏⠀⠙⣋⠧⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢒⣒⡩⠭⠀⣀⣤⣶⡿⠛⠁⠀⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠂⠁⠀⠀⢃⡾⢻⡄
⠀⠀⠀⢀⠤⢒⣊⣭⣴⡶⠟⠋⣁⣤⣶⣿⡿⠛⠁⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⣟⣻⡽⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⠇⣈⣀⣀
⠀⠀⢀⠁⡼⣎⣽⡟⡉⠀⠀⠉⠙⠛⠛⠁⠀⠀⠴⣾⣿⣿⣿⣿⣿⣿⣫⡵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠰⠂⠀⠀⠀⡼⠁⠐⢿⣿⣿⣿
⠀⠀⢸⡇⠣⢻⣿⠐⡷⠀⡀⣨⣁⣐⡒⣒⠒⠂⠀⠠⠤⠄⠀⢴⣾⠟⠉⠀⠀⠴⣠⣴⣦⣄⠀⠀⠂⠀⠀⠀⣴⣿⠟⠛⢲⠀⠀⠀⠀⠀⠠⠎⠀⢀⠰⢸⣿⣿⡿
⠀⠀⠈⠙⠛⠁⠙⠀⢀⠀⠈⠟⠿⣿⣧⡿⣾⢲⢃⡏⡠⠀⠀⠘⠁⢠⠻⡆⠈⢰⣍⣙⡍⢿⠶⠁⠀⠀⠀⢐⠟⠁⠀⠀⣼⠀⠀⢀⣤⣾⣷⣤⣤⣾⠀⣾⡿⠋
⠀⠀⠀⠀⠀⢀⡒⠶⢴⣾⠷⢶⣤⣤⣬⣭⣭⣭⣌⣁⣁⠀⠀⠀⠢⣄⡻⠁⣀⠠⢿⡛⢁⡿⠀⠐⠏⠀⠀⠂⠀⠀⠈⣴⡇⣴⣾⣿⣿⣿⣿⣿⣿⣿⡷⠋
⢀⣴⣿⣶⣶⣦⣽⣷⣀⠌⢑⠒⠒⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⡶⠶⢶⣤⣽⣶⠶⠾⠫⠇⠀⠀⠀⢀⠍⠀⠀⢰⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣉⣉⣐⠒⢶⣶⣶⣶⡂⠀⠀⠤⠍⢉⡉⠀⠒⠀⠀⠀⠀⠁⠀⠀⡠⠊⠀⢰⠰⢸⡟⣸⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣖⣒⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⣠⡴⣀⠀⡀⢠⣀⡿⢃⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣦⣧⢸⡏⠀⣼⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢻⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⢸⡇⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⣠⡤⣄⠈⣧⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⣯⣀⣸⠇⠈⠛⠶⣤⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠛⠁⠀⠀⠀⣠⣤⣤⣤⣀⠉⠁⠀⠀⠀⠀⠈⣧⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⠀⢿⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⢿⣤⣤⣄⠀⢸⡋⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⢠⡞⠛⢦⠀⠀⠀⠀⢿⣀⣨⡇⠀⠀⠀⠀⣰⠞⠳⣆⠀⠙⣦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠷⠤⠟⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⢹⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣤⣄⠀⠀⠀⠀⠀⠀⢸⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⣀⣀⠀⠀⣼⠁⠀⠀⢀⣤⠿⠃⠀⠀⢀⣤⣀⠀⠀⢠⡞⠁⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠘⢧⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣾⠉⢙⡇⠀⠛⠖⠺⡆⠈⢷⠀⠀⠀⠀⣏⠀⣹⠆⠀⠀⠙⠳⡆⠀⠀⣀⣀⣹⡄⠀⠀⠀⠀⠀⠙⣆⢿
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠻⠶⠋⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⣸⠃⠀⣸⠉⠉⠉⠀⣠⠶⢦⡀⠀⢀⡟⢸⡆
⠀⠀⠀⠀⣼⠛⠒⠒⠒⠶⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠋⠀⠀⠀⠀⢿⣄⣼⠇⠀⣸⠃⢸⡇
⠀⠀⠀⠀⠙⠶⠶⠤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠒⠲⠰⠶⠦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠹⣄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⠛⠛⠛⠒⠶⠶⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠓⠶⠶⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠒⠶⠶⠶⠦⢤⣤⣤⣤⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣧⣤⣿⣙⡐⠲⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠙⠒⠲⢤⣷⣠⣾⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⢠⣄⡀⠀⠀⠈⠉⠙⠷⢿⡅⠈⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⢀⣤⣴⡾⠛⢿⣿⣟⣷⣆⣘⠁⠀⠀⠈⠛⢿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢁⡤⢬⣿⣿⣟⠛⣿⣛⣿⣿⣿⣏⣀⣀⣠⡀⠀⠀⠈⠻⣴⣷⡞⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⡿⠻⣶⣦⡀⠀⠀⠈⠳⣶⡏⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⡌⠣⣤⡀⠀⢀⣿⢿⣟⣹⣿⣧⣀⠀⠀⣿⣿⣷⣶⣿⣿⣿⠂⢀⠀⠀⣸⠿⠟⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣿⣷⠀⠈⠙⠳⣾⣷⣿⣿⣿⣷⣾⣿⣧⣤⣿⣿⣿⣿⣿⣿⡟⠀⠈⣱⠆⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣻⣿⣿⣏⠀⠀⢀⣠⣿⣿⡈⢿⣿⣿⣿⣿⣿⣧⠤⠝⠓⠟⠛⠛⢓⡴⠂⠡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠟⠛⠛⠛⠉⠁⠀⠛⠍⡛⣿⣿⣿⣿⣿⡿⠿⠿⢦⠀⠀⣀⠤⠆⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣤⡤⣶⣾⣷⣶⣦⠀⠉⠁⠉⠉⠀⠀⠀⢀⣠⠃⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣣⠀⠀⢀⣀⣼⣿⣿⣿⣤⣿⣿⣿⣆⠀⠀⠀⠀⣀⠶⠛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣶⣶⣦⣀⠉⣿⣏⣹⣿⣿⣿⣿⣛⣀⡤⠐⠈⠡⠂
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡙⣿⣿⣶⡼⠿⢿⣿⣿⡿⠏⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⣽⣿⣿⣿⠿⠿⠗⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣤⠴⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠈⠉⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡤⠤⠤⣄⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣴⠋⠀⠀⠀⠈⠳⡀⠀⠀⡤⢄⡀⠉⠳⢤⡀⠀⠀⠀⠀⠘⠻⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢃⠀⠀⠀⠀⠀⣠⠇⠀⠾⠀⣀⡵⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⢴⡄⠀⠑⠒⠲⠖⠚⠁⠀⠀⠀⣠⠤⠤⣤⣄⣀⡀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡀⠀⠳⠞⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣼⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⣠⠖⠒⠋⠉⠙⢦⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠈⣳⣄⣤⡤⠶⠛⣁⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠏⠀⠀⠀⠙⠦⣀⣀⣀⣴⠏⠀⠀⠀⠀⠁⠠⠤⢤⣤⡤⠴⠞⠁⠀⠀⢀⣠⠾⣯⣄⣀⣠⡤⠞⢋⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢰⣒⣒⣦⡀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠀⢀⣿⣧⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡴⢚⡶⠀⠀⠀⣀⡤⠴⠶⠶⠤⢤⣀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠉⠀⠀⢀⣠⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⢋⡴⠋⠁⢀⡴⠋⠁⠀⠀⠀⠀⠀⢀⣀⡽⠶⠚⠋⠉⠀⢀⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠏⠀⠀⢀⡟⠀⠀⢀⣀⣤⠴⠒⠋⠉⠀⠀⣀⣠⡴⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠀⠀⣀⣼⠷⠖⠛⠉⠁⠀⢀⣀⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⢰⡇⠀⣀⣤⡴⠶⠚⠋⠁⠀⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠘⣷⠚⠉⠀⣀⣠⡤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉