Confusing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⣀⡀⠀⠠⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡄⢁⣽⣾⢲⢶⢳⣶⣒⣳⡤⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡢⢀⣼⡦⢨⣽⣿⣝⣾⣿⣽⣽⣶⣭⢆⡈⠻⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣣⣴⣟⢛⣻⣿⣿⣞⣿⢿⣬⣝⡞⣩⣷⣏⢤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢠⡧⢾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣟⣋⣻⣹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡌⣸⣷⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢸⠱⠜⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠅⠙⡍⣏⡲⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠐⡻⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⠐⢨⣷⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣏⠤⣣⢿⣥⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣇⠈⢿⣼⣷⢻⣿⣿⣯⣿⡿⣋⢠⡷⠏⠉⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⡶⠧⠤⣤⣉⡁⠂⠁⢙⡞⢻⣁⣀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠵⠠⡿⠒⠲⠆⠠⠁⠄⢐⠁⠈⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠁⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⠀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⠉⢆⢶⠶⡢⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠨⢤⡀⣘⡁⠀⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠉⠉⠈⠁⠀⠁⠀⠁⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠁⠈⠀⠀⠀⠁⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠟⠻⠎⠙⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠠⠐⠀⠁⠀⠀⠀⠈⠉⠒⠦⢀⣠⠞⠀⠀⠀⠀⠀⠒⠈⢷⣄⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠳⢤⣀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣀⣠⡤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠀⠀⠀⠈⣇⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⢉⡥⠤⠄⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇⠀⠀⠀⠀⠀⢰⠋⠀⣠⣴⡆⠈⢳⠀⠀⠀⠀⡴⢉⣤⣤⠀⠈⢢⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⡶⢸⡇⠀⠀⢰⠀⣿⣿⣷⣶⠀⠀⡇⠀⠀⠀⠀⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⠀⠀⠘⠲⠤⢌⢛⠋⣁⠜⠀⠀⠀⠀⠣⠙⠛⣛⢋⢀⡼⠁⠀⠀⠀⢀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣄⡀
⠀⠀⠀⠀⠈⢧⡈⠙⠦⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡤⠖⠋⣠⠟
⠀⣠⠤⠤⠶⠶⠞⠓⠀⠈⠙⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠙⠂⠀⠀⠀⠀⣠⢞⡟⠉⠀⡀⠛⠷⠶⠤⢤⢤⡀
⣾⣃⣈⠭⠅⠀⠀⠈⠉⠙⡆⣜⠀⠀⠉⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⢘⡇⡔⠉⠉⠀⠀⠀⢭⣭⣁⣙
⢯⠁⣀⣀⣀⣀⣀⣠⣤⠴⠃⢹⡀⠀⠀⠀⠀⡽⠓⣶⢤⣤⣄⣀⣀⣀⣤⣤⡴⠶⣏⠁⠀⠀⠀⣸⠃⠳⢤⣤⣄⣀⣀⣀⣀⡀⢨
⠈⠉⠉⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⣀⣀⣠⠞⠁⠀⣿⢢⡀⠴⣿⣿⡷⢄⡌⣿⠀⠙⢦⣄⣀⣠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠀⠀⣠⠞⣯⠀⠀⠀⢨⣽⡀⠀⠀⢸⣦⡀⠀⠀⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠤⠖⠚⠁⠀⡃⠀⠀⠀⠈⠛⣇⠀⠀⠈⡇⠉⠓⠦⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡿⠃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠒⢲⡆⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢰⠀⢸⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡴⠋⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢯⡀⠀⠀⠀⠀⡹⠂⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣦⣤⣤⣷⣄⣀⣠⣾⣥⣤⣤⣴⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡠⠖⠚⣋⣽⢛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣲⣤⠉⠙⠒⠋⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡳⠄
⠀⠀⠀⠀⠀⠠⡯⠖⠒⡺⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠥⢶⡄⠀⢹⠳⢤⣀⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠀⠀⠈⠉⠁⠈⣙⠓⠦⢤⣀⡀⠀⠸⣖⠲⠤⢤⣀⣀⡐⠻⢟⡛⠓⠒⠲⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣼⠀⠀⠀⠀⠀⡩⠖⠶⢤⣄⠀⠉⠉⠓⠛⠃⡀⠀⢷⡈⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡏⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠳⣄⠀⣠⠴⠒⠛⢇⠈⢧
⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⢠⢃⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠘⡄⢀⡷⠲⣄
⠀⠀⠀⠀⣾⠁⠤⣤⢤⡉⠳⡞⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⣝⢃⣙⡆
⠀⠀⠀⠀⠹⣄⠀⠈⠓⠛⠀⠁⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⡤⣄⣸⢠⢲⣶⠀⠀⣼⠀⠀⠘⠢⣌⡵
⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢶⡀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠤⣄⣛⣿⠋⠙⠻⠿⠤⠞⢁⡴⠊⠑⡄⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⣀⡴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⢀⠀⣠⠴⠒⢺⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠁⡜⠀⠀⠀⠀⡟⠉⠓⢶⣒⡲⣧⣤⠥⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡧⢠⠇⠀⠀⠀⠀⡿⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢏⠙⢾⠀⢸⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⠅⠀⢀⡎⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣙⣋⣉⣀⣀⣀⡤⡤⠶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠉⠉⠀⠀⡇⣷⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠐⠘⠛⡟⠃⢀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠤⠤⢤⣤⢶⠞⡏⢉⣻⣤⣼⠇⠀⠀⠀⠀⠀⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣗⣒⣒⣚⣓⣛⡋⠩⠝⠚⠉⠁⠀⠀⠀⠀⣤⣶⣶⣶⡶⠒⠀⠀⠀⠩⠍⠉⠙⠻⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠶⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⡿⣶⣦⣶⣦⠉⠉⠁⠀⠤⣤⣤⡀⠀⠀⠀⠀⠈⠙⠋⠀⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠘⠿⠃⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠙⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⣠⣶⡇
⢀⣤⣴⢤⣤⡀⢀⡀⠐⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠘⠿⣦⠀⠀⠀⠒⠂⠉⠻⠿⠛⠛⠂⢠⣤⠀⠀⠀⠀⠀⣀⠐⠋⠁⠀⠛⢢⣄
⠈⠛⠟⠀⠈⠀⣀⠀⠐⠲⡶⠿⠂⢠⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠈⣷⣦⡄⠚⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⢁⡿⢧⣀⠀⠀⠀⠀⠀⠀⠻⣤⡀⢀⣀⡀⠀⢾⣿⠶⠆⠀⠈⠉⣷
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠘⠀⠀⠙⢳⣄⡀⠀⠶⠦⠀⠙⠿⣏⠉⠁⠀⠀⢡⡄⠀⠀⠀⠀⠻
⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⢼⡟⠀⠀⠀⣰⡦⠤⠄⢠⡾⠿⢿⣷⣤⣄⡀⠀⠀⠙⢷⣄⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉
⠀⠀⠀⠘⠋⠀⠀⠈⠁⠀⠀⣻⡤⠈⠉⠛⠀⠀⢠⡌⠀⠀⠈⠋⣀⠈⠻⣶⣄⢠⣤⡼⢷⣤⣀⣹⣿⠆⠄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣧⠀⠚⠀⠀⠀⢸⡇⠀⠀⠀⣰⡿⠃⠀⠉⢁⠀⠀⠀⢀⡘⠛⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⡇⠀⠀⠀⠀⠸⣧⣀⠀⠂⠀⠁⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠈⣽⠛⠛⠒⠀⠀⢠⡤⠀⠒⠒⠊⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⠀⠈⠻⠀⠀⠀⠀⠀⠈⠻⠷⣀⣀⣠⣿⠆⠁⠀⠐⠀⠀⠀⠀⠀⠀⠈⣿⣀⠀⠀⠀⠀⠀⠀⠲⢦⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⢉⣄⠀⠀⠀⠿⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⣴⣎⣀⠀⠁⠀⠀⠀⠈⠛⣀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⣀⠀⠀⠀⠘⠃⠀⠀⠀⠠⡤⢤⣾⠉⠉⠉⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠛⠃⠈⠛⠛⠛⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠶⡶⠦⠄⣀⠀⠴⠶⠤⠀⠉⠉⠘⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠐⠃⢠⡄⠀⠀⠀⠀⠀⠀⠈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢂⣄⠀⠀⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⣀⡀⠀⠀⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⣄⡀⠸⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⣾⣇⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣧⣤⣤⣄⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣠⣤⣄⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠋⠘⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢄⠀⠀⣠⠆⠀⠄⠲⣶⠤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢠⡜⢀⣸⣷⡾⢋⡗⠂⠒⠊⠛⢿⡹⢿⢷⣄⢀⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣛⠈⠭⢉⡽⠻⠁⠀⠉⠉⠓⠈⠧⢄⣛⡋⢌⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢉⠛⡀⠀⠇⠀⢀⣠⣤⣶⣦⣤⣀⠀⠀⢉⣷⠤⠛⠋⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠀⣰⠁⣀⠀⠀⢀⣾⣿⣿⠟⠻⣿⣿⡇⠀⠈⠀⠋⡀⠠⢦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡁⣾⣛⠛⠃⠀⠀⠘⠛⠛⠋⠀⠀⣿⣿⡟⠀⣱⢖⡀⡹⠀⠀⠐⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠮⠑⠆⠀⠘⡠⠄⣸⠤⠂⣠⣾⣿⣿⠃⠀⠈⠀⡦⠰⠶⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠽⠀⠹⣂⣼⠁⣤⠅⠀⣰⣿⣿⡟⠁⠀⣀⣦⣼⡀⠀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⢶⢃⠙⢾⣪⡷⠄⠀⠿⠿⠿⠀⢀⣀⣉⠠⠟⣬⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠌⣿⣶⡖⠀⣤⣤⣶⠉⠻⢂⢀⡒⠀⠙⠴⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⢰⠀⣾⢿⣻⣆⠀⠿⠿⠿⠀⣰⠒⠉⣭⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠽⣧⣹⠿⠌⡀⠀⠐⠒⠋⠛⠉⣉⠉⠁⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠻⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⡀⠀⣀⣀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⢶⠄⠀⠠⣦⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣴⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢉⣉⣉⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠰⠋⠉⠉⠳⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⠾⠀⠀⠀⣠⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⣁⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠀⠒⠋⠙⠂⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⢘⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢙⣒⠀⠀⠀⠀⠀⠀⣠⠶⠶⣾⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢸⠀⠀⠀⠀⢀⡀⠣⣤⠤⢤⠀⠀⠀⠀⠂⠀⠀⣀⠤⠤⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⢄⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠛⢹⡆⠀⠀⢸⠀⠀⠀⠐⠂⠀⠘⣷⣢⡅⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⠤⣀⢡⣀⣀⣼⠇⠀⠀⠀⠀⠘⠛⠒⠒⠃⠀⠾⠤⣴⢶⣾⠀⠀⠀⠀⠂⠀⠀⢟⠦⠄⡜⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⣆⡜⠀⠀⠀⠀⠈⠃⠤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⢇⠀⠀⠀⠀⠀⠀⢀⠴⣷⣮⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠴⡌⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⠤⠀⠤⠔⠊⣡⠄⣼⣇⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⡖⠒⢦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠚⠉⢸⢠⡏⣻⠀⠀⢠⢧⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⡀⣠⠶⠒⠦⠘⠣⠄⣶⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⡯⣸⠂⠀⢸⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠙⡟⠛⠠⣴⣃⡀⠀⢰⣿⠃⠀⡿⠀⣀⠤⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠈⠁⠀⠀⢸⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⡶⠁⠀⢀⣀⡉⠉⠛⠛⠁⢙⡻⠙⠉⠀⠀⠣⡀⢀⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢤⣤⣤⠤⣼⠀⠃⡇
⠀⠀⠀⠀⠀⠀⢠⠤⠒⠒⠃⠈⠉⠁⠀⠈⡇⠀⠀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠉⢰⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢉⠉⠉⢹⣠⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣤⠶⠿⠀⠀⢳⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡄⠀⢸⡾⠟
⠀⠀⠀⠀⣀⠤⢄⢸⡀⠀⠀⠀⠀⠘⢇⣀⠤⡆⠀⠈⠾⠋⠀⣸⠀⣴⠚⠲⡀⢀⣠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡇⠀⠸
⠀⠀⠀⠀⡁⠀⠀⣥⣤⠀⠀⢠⡴⠶⢦⡀⠀⢸⠀⠀⠀⠲⡉⠁⠀⠻⣄⠰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢣
⠀⠀⠀⠀⠳⠤⠾⠃⠈⡄⠀⠸⣄⡀⢨⣧⣤⠴⠆⠀⠀⠀⢧⡠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠋⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠠⣤⣤⣤⣤⣤⠀⣀⣼⣲⣷⡴⣇⡀⣤⣤⣤⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠿⠋⠀⠀⠈⠻⣦⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⡤⠖⠛⢷⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠉⠉⠉⠀⠀⣀⣠⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⠶⠶⠞⠛⣉⣥⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠉⠀⠀⣼⡟⠉⠁⢠⣼⣿⢿⣯⠉⠛⠛⠻⠿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠿⠿⠀⣿⡆⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣶⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠈⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⡀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣼⠇⠀⠀⠀⠀⣼⡟⢀⣀⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠈⠀⠀⠀⠀⠀⠀⣿⡇⠈⣻⡷⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙⠛⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠈⠛⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣦⣀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⣀⣴⡾⠟⣻⣿⠀⠀⠀⠀⢠⠏⠉⣽⠏⠉⢩⣿⣏⠉⠉⠉⣿⣇⠀⠀⣿⠀⢻⣯⠻⢷⣦⣀⠀⠀⠈⢿⡆
⢀⣤⣶⠿⠋⠁⠀⢀⣿⠇⠀⠀⠀⢠⠏⠀⠀⣿⠘⣄⣾⠀⢻⣄⠀⣰⠇⢹⢀⡴⢹⠂⠈⣿⡆⠀⠉⠛⠿⣶⣦⣾⠟
⠛⠿⣦⣄⡀⠀⠀⣸⡿⠀⠀⠀⢀⣞⡀⠀⠀⢿⠀⠈⠃⠀⠀⣹⣿⣏⠀⠘⠋⠀⢸⠀⠤⣼⣿
⠀⠀⠀⠙⠻⣦⠀⣿⡇⠀⠀⠀⠹⣧⠀⠀⠀⢸⡀⠀⠀⠀⣰⡟⠀⠙⣦⠀⠀⠀⢸⠀⠀⡾⣿⡇
⠀⢀⣀⣀⣠⡿⢱⣿⠀⠀⠀⠀⠀⠈⢳⣄⠀⢸⡇⠀⠀⣰⡟⠀⠀⠀⠘⢧⡀⠀⣾⢀⡼⠁⢹⣷
⠀⢾⣿⣿⠟⠁⣸⡟⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⡇⠀⢰⡿⠀⠀⠀⠀⠀⠈⣷⠀⣿⠞⠁⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀⠘⠿⢶⣤⣤⣤⣴⠞⠋⠀⡟⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⣶⣿⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣴⣧⣤⣶⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⡍⠉⠉⠉⠛⢷⡀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠉⠉⢡⠁⠈⢙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣧⡤⠶⠺⣧⣀⣻⡄⠀⠀⠀⠀⠰⣯⣀⣼⠿⠶⠶⠶⠶⠶⠟⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⡈⣉⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠋⠉⠉⠉⠉⠙⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡄⠀⠀⠀⠀⢠⣶⣶⣶⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⢐⡜⠛⠠⡄⠀⠀⠈⠉⠉⠉⠉⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡤⠞⠉⠁⠀⠀⠀⠁⠀⠙⠛⠒⠲⠶⠶⠚⢯⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠒⡇⠀⠀⠀⠀⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢲⣭⣧⣶⠀⡀⠀⠀⣯⣫⣿⣿⣇⡦⠀⠀⢸⣏⠀⣉⢀⡇⠀⠀⠀⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠂⢀⡾⢤⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠐⠂⠛⠿⠗⠀⠇⠀⠀⠆⠐⢶⠶⠄⠀⠀⠀⠈⢇⠌⣀⠀⠇⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⢀⡀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠡⢰⠆⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠚⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⠐⠒⢢⣄⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸⡏⢉⣉⡀⢀⠀⠈⠉⠷⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣤⣤⣤⣹⣄⠱⣄⠀⠀⠀⠀⠙⠳⢤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⢀⡰⢋⡽⠀⡀⢀
⠀⠠⠟⠒⠒⠀⠀⠐⠢⡈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡹⠟⡋⠛⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⠌⠁⠉⠒⠫⢻⡄
⠀⠀⠓⠒⠒⠒⠤⠤⡤⠛⠑⣄⠀⠀⠀⠀⠀⣠⡴⠲⢺⣥⣾⡄⢀⡴⠳⠦⢄⡀⠀⠀⠀⠀⠀⠀⡼⠶⣅⣀⣀⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⠔⠙⢦⡀⠀⢀⡴⠻⡇⠀⠀⣼⣿⢉⠉⠀⠀⠀⡾⠙⣆⠀⠀⠀⢀⠾⢄⡀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⢲⠞⠀⠀⡅⠀⢸⣿⡿⠀⠀⠀⠀⣨⡁⠀⠈⢳⣠⠆⠁⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢸⠀⣠⠞⣇⠀⢸⡿⠁⠀⠀⠀⣸⠁⠙⢦⡀⠀⣿⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠛⠁⠀⣿⠀⠠⠁⠀⠀⠀⠀⡇⠀⠀⠀⠙⠲⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢰⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡼⢣⣀⣀⣀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⢳⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢹⣀⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠉⠛⢢⡼⠛⠉⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⢤⣠⢧⣿⠫⠭⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡼⢬⣿⠟⠁⠀⢠⢿⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡰⢲⣲⡮⠞⠋⠉⠉⠁⠀⠀⠀⠸⠋⠀⠀⣠⢶⣿⣿⣿⣿⣷⣶⠦⢄⡀
⠀⠀⠀⠀⢀⣴⣿⣶⣤⣽⠃⠀⠀⣀⣤⠴⠖⠒⠛⠿⠻⣯⡙⠛⠛⣛⡻⡿⢽⣷⣭⣙⠒⠤
⠀⠀⠀⣠⣾⣿⣿⣿⡿⠁⣠⠶⠋⠁⠀⠀⢀⡤⠤⠤⠶⠾⠄⠀⠀⠉⠀⠻⡆⠀⠉⠛⠿⣶⣄⡀
⠀⢀⣴⣿⣿⣿⣿⡟⢠⡞⠁⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠙⢿⡄
⠀⠘⠿⢿⣿⣿⡟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⣀
⠀⠀⠀⠀⠙⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡵⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡠⡏⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⣀⠀⠀⣀⣀⣠⠤⠴⠼⠮⣍⠒⠃⠋⠁⠚⠐⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠼⠦⠬⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣛⠂
⠀⠀⠀⠀⠀⠀⠶⣶⠦⠴⠞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣤⣤⣤⣤⣀⠈⠙⣆
⠀⠀⠀⠀⣠⠤⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡘⢾⡜⣡⠖⠋⠁⠀⠀⠀⠀⠈⠳⡄⠀⠑⢄
⠀⠀⠀⠙⠓⠒⣦⠖⠁⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠙⢾⡟⠁⢀⣄⣀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢳⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⠳⣤⠀⠀⠀⠀⡇⠀⠀⢻⠁
⠀⠀⠀⢠⣣⢴⠆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠉⠳⣎⠁⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠋⠁⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⣄⣀⡀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⡋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢍⡁⢀⡇
⠀⠀⠀⠀⠀⢸⠈⠩⠭⣷⠀⠒⢶⠶⠶⠾⠟⠛⠋⠉⠀⠘⠿⠂⠀⠘⠗⠀⠀⠀⠀⠀⢠⡿⠀⢠⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣾⠀⠀⠀⡾
⠀⠀⠀⠀⢀⣀⣸⡄⠀⠈⡆⠀⠀⠈⠛⢦⣤⣀⣀⣤⣤⡶⠂⠀⠀⣀⠀⠀⠀⠴⢾⡯⠀⠀⠀⣇⠀⣀⠴⠗⢒⢶⡄
⠀⠀⠀⣴⠋⠉⢀⠈⠓⠊⠁⠀⠀⠀⠀⠀⠀⠠⠴⠿⠋⠀⠀⠀⠘⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⢾⡉⠀⢹⡄
⠀⠀⠀⣇⠀⠞⢩⡿⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢻⠇⠀⢸⡇
⠀⠀⠀⠹⣄⠀⠘⠀⠹⠀⣧⠀⠀⠀⠀⢀⣤⣖⡋⠉⠉⠉⠉⠀⠀⠈⠉⠉⢙⣶⣄⠀⠀⠀⠀⢀⣷⣄⠀⠉⠀⣀⡾⠁
⠀⠀⠀⠀⠈⠳⠦⣤⡤⠞⠹⡆⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣶⣶⣿⣿⣿⣇⠀⠀⠀⣼⠃⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢟⣿⠿⠿⠭⢌⣙⣉⣩⠿⠿⠟⠻⣿⣿⠏⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠒⠦⠤⠤⣄⣀⣠⣤⣤⠤⠖⠋⠁⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢿⠇⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣠⣭⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⣠⡾⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠙⣿⣆
⠀⠀⠀⠸⣿⡀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠟
⠀⠀⠀⠀⠈⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠑⠢⣄⡀⠀⣧⠙⢦⣀⠀⢠⣄⠀⠀⠀⢠⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠲⡖⠒⠚⠁⠀⠀⠀⠉⠉⠁⠀⠀⠈⠓⠚⠈⠳⣄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣠⠚⠉⠛⠢⡄⠀⠀⣀⣀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡇⠀⠀⠀⠀⢹⡀⡮⠄⠀⢱⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢤⣠⠏⠀⠀⠈⡇⠀⠀⠀⠀⢾⠁⠳⣀⢀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠈⢛⣓⣀⠀⠀⠀⠀⠘⣄⠀⠀⢀⠎⠀⠀⠈⢉⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⣆⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠠⢀⡠⠇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⠲⢤⣀⣀⠀⠐⠂⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢇⣀⡜⠀⠀⠀⠀⡏⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢾⠏⠀⡏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣭⠀⠀⣸⡀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠋⠁⢈⣙⡓⢲⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢿⠒⣶⣤⣴⠧⢶⡟⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠭⠽⠛⠉⠙⠚⠭⠷⠾⠝⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢶⣶⡄⠀⠀⠀⠀⠘⢩⡿⠀⢀⣀⣤⠤⠄⠀⠀⣀⣀⣻⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣀⣿⣿⡠⠴⠒⣀⠤⠶⠖⠉⣁⣤⠴⠖⠚⠉⠉⠁⠀⠉⠁⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠏⢁⡤⠖⢋⣠⣤⣶⣾⣿⣥⡄⣀⣀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⢰⣿⠞⣡⣴⣾⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣷⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠞⢁⣤⣾⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠙⢻⡟⢿⣿⣷⡄⢞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠋⣠⠖⠉⣿⣿⠟⣿⣿⠟⠀⠀⣒⠲⢚⣩⠄⠀⠛⠀⢹⠋⠁⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠎⡠⠊⣁⣀⠀⢻⡇⢰⣿⠃⠀⠈⣁⣈⡉⠋⢀⣴⣶⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢸⠞⠀⠈⢩⠿⠃⠸⣧⠈⠃⠀⣰⡿⠟⠻⡇⠀⠟⠉⠙⠃⠀⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⡞⠳⢤⠀⠺⠃⢀⣀⣿⠀⠀⠀⠁⠀⣀⠀⠀⢲⠀⢠⣦⠀⠀⣿⡖⢺⡇
⠀⠀⠀⠀⠀⠀⠈⢧⣄⡀⠀⠀⢰⡏⢩⢿⣇⠀⠀⠀⠀⠻⢃⡀⠈⣧⠈⣉⠀⢠⣿⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⣇⠀⠀⣿⡄⠀⠀⠀⠠⠊⠀⠀⢸⡄⠈⠃⠈⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣹⡗⠀⠀⠀⠀⠀⠈⣿⠚⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⠀⠀⠀⣨⣤⡄⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢋⣟⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⠉⢻⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣞⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣤⣍⣉⣭⣅⣠⣴⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⠛⠿⠟⠛⠛⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣒⣀⡢⢀⠀⠀⠀⠀⢘⡟⠀⠀⠀⢀⣤⣤⡭⣛⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠗⣐⣻⠿⣗⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⢿⠷⠶⠶⢿⣿⣿⣿⠇⠀⠀⠀⣠⣤⣄⣸⡆
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀⠀⠈⢿⣿⠟⠉⠉⠈⠙⢃⡄⠀⠐⣾⠁⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠈⣛⡟⠀⠀⣰⣿⣿⣟⣋⣿⠁
⠀⠀⠀⠠⡀⣾⡿⢛⣻⣿⣿⡀⠀⠀⢱⣀⠀⠀⠀⠀⠀⢻⡆⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠃⠀⢠⣇⢀⡀⢹⡟⠁
⠀⠀⠀⠀⠙⢿⣷⠋⠀⠐⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⢸⠉⠑⠒⠊⣳
⠀⠀⠀⠀⠀⠸⠛⠆⠀⠀⣸⠀⠀⠀⠲⠶⣤⣄⡀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⣠⡤⠤⠶⢾⡟⢁⣀⡀⠀⠸⡀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢉⣤⣤⣤⠟⠈⠙⢦⡀⠀⠀⠀⢻⣿⡀⠀⠀⠀⡏⢰⠠⡀⠀⠙⠛⠙⠿⠴⠶⠝⡗⢠⡞⠁
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠐⣿⣶⠿⠟⣋⣤⠶⠶⠤⣄⡙⢀⠀⠀⢹⣹⣧⠀⠀⠀⠀⠸⡄⠀⠈⠀⠀⠀⠀⠀⢠⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⣿⠁⢠⠞⠉⠀⠀⣀⣀⡀⠈⠿⣆⠀⢀⡿⠈⢧⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡀⠀⠀⢀⡴⠚⣉⣠⢤⠠⡲⠁⢀⣼⠃⠀⠈⢷⡀⠀⠀⠀⠀⣉⡛⠛⣛⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⡋⣰⠟⠋⠉⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⠉⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⡀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣤⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠈⠉⠙⠛⠛⠿⢷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠶⢦⣤⣄⣀⣿⣦⣀⣀⣀⣀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⡟⠛⠿⡻⡙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠑⠱⠀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⣦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠄⠄⣸⣯⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠙⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠟⠻⣿⣿⣿⣶⣶⣾⡇⡀⡀⠀⣸⣿⣼⣤⣿⣷⣴⣜⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢴⡿⠛⠁⣀⣤⠼⠶⠴⠷⢭⡻⣿⣿⣷⡈⡦⢸⣿⣿⣽⡿⠉⡻⢈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠐⠶⠝⠐⣋⣡⣤⣶⣾⣿⣿⣶⣽⣿⣯⡉⠛⠄⢽⣿⣿⣵⣶⣶⣶⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠛⡟⠁⣿⣿⣿⣿⣿⣿⠟⢩⠉⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣤⣾⣯⡉⠳⡄⠀⠀⢣⠀⠀⠀⠀⢀⠤⠊⠀⡴⠋⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣤⣴⣾⡆
⠀⠀⠀⠀⠀⣾⣧⠈⠀⠈⠀⢰⠀⠀⢸⠀⠀⠀⠂⠁⢀⡠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡈⠙⣿⣷
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⡇⠀⠀⡠⠜⠁⢀⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡛⣵⣼⣿
⠀⠀⠀⠀⢀⣤⣿⣇⠀⠀⣇⣴⠋⣀⠴⡎⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣄⣠⣴⣶⣤⣀⠀⣾⣷⣽⣿⣿
⠀⠀⠀⢀⣾⣦⣄⠉⢢⡀⣿⠁⡜⠁⢸⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠉⠛⠋⠙⢻⣿⣿⣿⣿⣿⣷⣽⡟
⠀⠀⠀⢸⡟⣼⠀⠁⢀⡑⢼⣸⣧⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢈⣿⠏⢻⣿⡙⣿⡿⠁
⠀⠀⠀⢸⣷⢿⠀⠀⠀⠉⢻⠡⣽⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀⣠⣤⣞⣧⣶⣌⡻⣩⣿⣧⣶⣘⣿⠟⠁
⠀⠀⠀⠀⢿⣾⡀⠀⠀⠀⡏⠻⣿⣷⣦⠈⢆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠛⠉⠉⠀⠈⠙⣿⡏⠙⣻⡿⣹⠏
⠀⠀⠀⠀⠸⣭⣿⡄⠀⠀⡇⢀⢻⢻⣯⡧⠈⢦⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⣦⣤⣤⣤⣽⣷⣾⣿⣳⠏
⠀⠀⠀⠀⠀⣿⡦⢣⡀⣀⡀⠀⣼⠘⣿⡇⢠⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⢿⢻⣿⡟⠋
⠀⠀⠀⠀⠀⠈⠻⢿⣦⣿⡥⠞⠁⠀⢻⡟⢦⣕⣦⡀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣯⠉⠁⠀⠀⠈⠙⠻⣶⣦⣤⣀⡀⠀⠀⡀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠻⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢲⢰⠃⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢵⣏⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⣤⣶⣦⡄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡟⠋⠉⠻⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣾⡿⠋⢿⣿⣿⠏⠻⣿⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⢀⣴⣄⠀⠀⢀⣦⡀⠈⠻⣿⣿⣿
⠀⠀⠀⠻⠿⣿⣷⣶⣤⣭⣥⣴⣶⣿⡿⠿⠃⠀⠀⠀⣿⣿⣿⣧⣀⡀⠈⠉⠛⠓⠚⠛⠋⠁⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⡀⢉⣿⣿⣿⣿⣿⣏⠁⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡼⠉⠉⠀⠀⢸⠀⠀⠈⠉⠹⡄⠀⠀⠀⠀⣿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣾⣿⣿⣿⣷⡹⣿⣿⣿
⠀⠀⠀⣼⣧⣤⣒⣒⣒⣼⣔⣒⣒⣢⣤⣿⡄⠀⠀⠀⣿⣿⣿⡟⠸⠿⠿⠭⠭⠟⠹⠭⠭⠿⠿⡇⢹⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠉⠉⠁⠒⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠀⠙⢆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⡀⡰⠁⡴⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠾⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⢀⡵⣕⠀⠀⠀⠀⠈⢢⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡏
⠀⠁⠢⠀⠀⠒⠄⡀⢀⠔⠀⠈⠊⠐⣈⡻⠃⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⠁
⠀⠈⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠌⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡇⠀⠀⠀⠀⢸
⠀⢰⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡠⢂⡔⠛⠃⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⡀⢀⡠⠃⠀⠀⠀⢀⠤⣚⡐⢛⣤⠤⣀⡀⠀⠈⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠀⠀⢧⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠞⠁⠄⠀⠣⠄⢠⠤⠊⠉⠓⠢⢤⠴⠃⠀⠀⠀⠀⢀⣀⡤⡞⠁⠀⣸⠀⠀⠈⠳⢤⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠒⢉⣉⡀⠔⠀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠀⡸⠀⠀⡱⠦⠴⡄⠀⠀⢰⡆⠠⣥⠀⢀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣇⣀⣀⣧⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⢸
⠀⠀⠀⠐⠲⢄⣄⣠⢶⠊⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣄⠀⣰⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣾⣶⣬⣻⣿⣿⡆⠀⠀⠀⠙⢷⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠆
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠂⠀⠹⣿⣿⣿⣿⣿⠛⠉⠉⠙⢿⣿⣿⣿⠀⠀⣀⣀⣀⡈⠛⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡿⠁⠀⣀⣀⠀⠉⢻⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⡇⠾⠿⠿⢿⣿⠆⠀⠸⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠁⣰⣿⡿⠿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⣀⠀⠉⢻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⣿⣷⣝⣿⣿⠀⠀⠀⠀⠈⠙⢻⣿⣿⣷⡶⢾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⢀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣷⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠐⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠆⠂⠀⠐⠄⣀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠠⠀⠀⢀⠀⠘⠖⠀⠀⠀⠰⠐⡂⠐
⠀⠀⠀⠀⠀⠀⠤⡌⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⡄⠀⠐⠈⠒⠉
⠀⠀⠀⠢⠂⠀⠀⡄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠤⠩⠀⠀⠀⢄⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⠀⠠⠈⢁
⠀⠠⡀⠀⠀⠀⢀⠀⢈⠁⠀⠀⠀⠈⠀⣤⠄⠀⠘⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠂⠈⠀⣀⣁⠈⠀⠀⠘⠁
⠹⠆⠀⠀⠐⠀⣁⣠⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢨⣤⠠⣄⡖⠢⠀⣀⠀⡀⠀⠈⠹⢆⡀⠀⠀⡀⡐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡦⢀⠄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠆⠈⠀⠁⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠳⡂⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠛⢄⡀⣀⠀⠛
⠀⢘⢀⠀⠀⡼⡏⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⡀⠐⠂⠀⡓⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠦⠄
⠀⠦⠀⠡⠔⠀⠸⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠈⠁⠗⠀⢦⡀
⠀⠠⣄⠓⠀⣆⠸⢧⢀⣀⣀⣀⠸⠏⠁⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠢⠄⠐⠿⠀⠀⢠⠀⠀⠀⠀⠰⡦⠃
⠀⠀⠈⠁⠈⠁⠀⠤⠴⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠴⠆⠀⠰⠦⠆⠈⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⢁⡁⠀⣰⣆⠀⢰⡖⢀⡀⣀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠐⣀⢠⢤⣀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⢀
⠀⠀⡄⡀⠠⠀⠀⠠⠀⠠⠀⠀⠀⠄⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⢨
⠀⠀⠁⠁⠁⠀⠀⡄⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⠁⠀⠡⠀⠀⠀⠀⠄⢀⣀⠀⠈⠀⠐⠀⠀⡀⠀⡠⠀⠀⠀⠀⠁⠰⡅
⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠄⢀⠀⠀⠈⠀⠂⠀⠐⠄⢀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠠⠀⠁⠀⠀⠄⠀⠀⠐⠂⠀⠐⠠⠀⠀⠀⠀⠓⣀⠀⠊⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⡇⠈⠀⠀⠈⣀⢨⡀⠀⡌⠉⡁⣀⠉⠁⠀⠂⠀⠐⠀⠀⠁⠀⠀⠠⢀⠀⡄⠀⠀⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠠⠰⠐⠈⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠄⠠⡶⡶⡦⢶⢤⡌⠀⠂⠀⡀⠀⠀⡀
⠀⠀⠀⠀⢠⡀⠀⠈⠐⠂⠈⠀⠂⠀⠀⠀⠀⠀⠀⢀⣾⡻⢃⣹⡷⠇⠠⠯⣦⡀⡀⠐⣁⠔⠰
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡋⠀⠀⠀⠀⠀⠀⠚⡞⡆⠠⠉⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠐⢦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠲⠒⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠠⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡾⣇⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣾⣷⣤⣀⣠⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡈⣿⣿⣿⣺⣋⣻⡷⣽⣿⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣽⠯⢶⣟⣿⣿⣿⠀⠀⠀⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⣀⣀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⢀⠤⠂⠈⠁⠀⠀⠀⠉⠑⠢⡀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⣇⣠⣾⣥⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⡇⠀⠀⢀⠀⢸⢧⡀⠀⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⢰⣷⢀⣆⢸⠷⠿⣄⢳⡀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠲⠿⠤⠐⠃⡾⠚⠙⠟⠀⠀⠙⡀⢃⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⢀⣀⣠⣤⣤⡶⠟⠁⠀⠀⠀⠘⢷⣦⣤⣤⣀⣀⣀⠀⠀⠀⣇⢸⡀⠀⠀⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠿⠀⠀⠀⠀⣨⠭⠄⠤⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡉⠁⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⢺⡟⠁⠀⠀⠀⠀⡞⠁⢀⣴⣶⠂⠘⣆⠀⠀⠀⢀⡜⣡⣤⡄⠀⠉⢦⠀⠀⠀⠛⢾⣇
⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠸⠁⠀⢸⣿⣿⣿⠇⢸⠀⠀⠀⢸⠸⣿⣿⣷⡶⠀⠘⡇⠀⠀⠀⢸⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠾⣇⠀⠀⠀⠀⠀⠒⠤⢤⣉⣙⣁⣠⠆⠀⠀⠀⠘⢆⠙⣛⣛⣀⣀⡴⠀⠀⠀⠀⣼⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢿⡉⠛⢦⣀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣠⠖⢶⡀
⠀⣀⠀⠤⠤⠄⠝⠲⠀⠈⠑⢄⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠞⠁⠀⡠⠔⠛⠉⣠⡐⠛
⣼⢛⣛⣛⡃⠀⠀⠀⠛⠓⣆⣸⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⢰⡃⣠⠶⠦⠈⠉⠙⣓⣒⡦⣄
⢯⠉⠀⠀⣀⣀⣀⣀⣀⣠⠟⢸⡀⠀⠀⠀⠀⢈⡟⣿⠒⠶⣤⠤⠤⠴⢴⡶⠛⣯⢳⡀⠀⠀⠀⠀⣼⠱⣇⠀⠀⠀⠀⠀⠲⠬⣭⣻⡆
⠈⠛⠋⠉⠉⠉⠉⠉⢹⡄⠀⠈⢧⠀⠀⠀⣠⠟⠀⡇⠀⠀⠈⠙⠒⠚⠋⠀⠀⢸⡌⠳⣄⠀⢀⡴⠃⠀⢈⡿⠓⠲⠶⠤⢤⣀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠙⠚⠋⠁⠀⣸⠇⠀⠀⠀⠚⠻⣿⣦⠀⠀⠀⣧⠀⠈⠉⠉⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⡤⠞⢹⠀⠀⠀⠐⣶⣿⣿⡿⠁⠀⠀⢸⡶⠤⣄⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠤⠤⠤⠤⠶⠶⠶⠶⠖⠒⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢲⡟⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠘⠁⠈⠉⡟⠒⠒⠒⠂⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣄⣀⣀⣀⣧⣀⣀⣤⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠾⢧⡈⠉⠀⠀⢹⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⣀⣀⣿⠀⠀⢀⣇⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦
⠀⠰⠿⠶⠊⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⠀⠀⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⣴⡀⠀⢀⣠⣴⣤⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢳⣦
⠀⠀⠀⠀⠀⠙⠿⠛⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣿⣿⣷⠀⠀⠀⣀⣤⣶⣾⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⡿⠿⣿⣿⣧⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣥⡶⣾⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣷⣝⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣋⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⢽⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠲⣄⣀⣠⣤⣾⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⣦⣿⣿⣿⣿⣿⣷⣝⣻⣿⣿⡏⠀⠀⠀⠀⠈⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣾⠟⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⡉⠉⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣶⣦⣄⡈⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⣶⣶⣶⣶⣶⣶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣳⣶⣾⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡄⠀⠀⠀⢠⡾⣻⠏⣿⢻⣇
⠀⠀⠀⠀⢀⣸⢃⣿⠀⣿⠦⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⢏⠹⡇⡹⡆⠋⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠋⠸⠟⠀⣴⣿⣿⠛⢿⣿⣦⡀⠀⠀⠀⠀⡄⡆⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡟⠀⠈⢻⣿⣿⣦⡀⠀⢀⡡⠐⠊⠁⠀⠀⢀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣷⠀⠀⣀⣹⣿⣿⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⠀⣠⣄⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⡄⠀⠀⣀⠀⠀⢸⣿⣿⠿⢐⣇⣈⡄⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⢿⣿⣿⠦⣀⠀⢀⣠⠞⣿⡿⠀⠘⠉⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠛⠉⠁⠀⠀⠀⠃⠀⡀⠠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⣿⠀⠠⠄⠀⠄⠄⠤⠂⠈⠀⠀⠀⠑⣄⢚⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣇⡀
⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠋⠘
⣿⣶⠀⡀⢀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⣠⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠒⢛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠛⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣤⠶⠶⣶⢦⣄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡇⠀⠀⡀⠀⠀⡀⠀⠀⠀⠠⠄⠠⠔⠀⣰⠟⠁⠀⠀⠈⢳⡀⠀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⠀⡀⢣⠘⣦⡈⠑⠒⠂⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⢷⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠑⢺⣶⡿⢋⣹⡷⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⢸⡉⣡⣾⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣤⢸⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⡿⡿⠋⣁⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣭⣝⡻⠟⢸⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⠀⡇⢀⡞⠁⠀⠀⠈⠙⢷⡀⠀⠀⠀⣰⠋⠀⠀⠈⠻⡄⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⠻⣆⣇⡾⠀⠀⠀⠀⠠⣦⠈⣧⠀⠀⠀⡟⠀⠀⠘⠇⠀⢹⣸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠲⣄⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⣿⣠⠞⠋⠙⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⠞⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢳⡀⠀⠀⠀⢀⡾⠈⠋⣠⡒⠓⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡻⣄⡁⠀⠀⠘⢦⣀⡀⠀⢀⣠⡾⠁⡴⠒⣶⡄⠉⠓⠶⠖⠋⠀⠀⣸⠈⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣥⣼⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⠁⠸⠁⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠲⠶⠖⠚⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠉⠉⠉⠉⠻⢶⣄⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠉⠁⠀⠀⣠⡶⠶⢦⡀⠀⠀⠻⣦⠀⠀⢀⠏⠠⠀⠉⠓⠶⠤⣀⣠⠞⣉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠙⣆⠀⠀⠹⣇⠀⡞⠀⠀⠀⠀⠀⠀⢀⡼⡁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠀⢠⡶⠾⢶⣄⠀⠀⠀⠈⢧⠀⠘⣧⣤⠼⠄⠀⠀⢹⣾⠁⠛⠀⠀⠀⢀⡴⠋⠈⠃⠀⠀⠀⠀⠀⣀⣹⠶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠀⡆⠀⢻⡄⠀⠀⠀⠈⠳⠟⠋⣀⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣀⡤⠴⠚⠋⣥⠀⠀⠁⠀⢣
⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⠀⣿⣀⣬⡅⠀⠀⠀⠀⠀⠠⢋⣤⣶⡦⠀⠀⠀⠈⠻⣄⣠⠎⢀⣀⡤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠡⠞⠋⢉⣁⣀⣀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣳
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢋⣵⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⡌⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡜⢀⣿⡏⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠂⣠⠏⠀⣸⣿⠃⠀⠀⠀⠀⠠⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠲⠤⠃⠀⣀⣾⡿⠁⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡆⠀⢰⠋⣀⣀⣀⣉⣀⣀⣀⣤⣴⣾⣿⡿⠁⠀⣴⡟⡸⠀⠀⢀⣤⡴⠶⠟⠻⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠙⢦⡘⢦⣄⡉⠉⠉⠛⠿⠿⠿⠿⠛⠋⣀⣴⡿⠋⢠⠃⢀⡼⠋⠁⠀⠀⠀⣠⠄⠀⠀⠉⠛⠷⣶⣤⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠓⠪⢝⡛⠶⠶⣦⣤⣴⡶⠶⠟⠋⠁⠀⠀⡞⢠⡟⠁⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⡰⢳⡾⠁⠀⠀⢤⣄⣛⣁⣤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣮⡑⠢⢄⣀⣀⡤⠚⠁⣼⠁⠀⠀⢀⣀⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣬⡳⠀⠀⠀⠀⠀⠀⢺⣆⠸⠏⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⢀⡤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠀⠀⠀⠀⣼⠃
⠀⠀⠀⡞⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣠⣶⠏⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣍⠢⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠹⣄⠀⠀⡇⢀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⡇⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠘⢆⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠼⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠀⣠⠚⠉⠉⠓⠒⠦⣵⣒⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠈⡆⢇⠀⠾⠿⢿⣿⣿⣶⣌⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢀⡼⠈⠑⠲⠦⣤⣀⠉⠛⢿⣷⡄⠈⢷⡄⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡀⠀⣉⣵⠚⠁⠀⠀⠀⠀⢤⡄⣠⠋⠀⣇⠀⠀⠀⠀⠉⠛⠶⣄⡈⠃⢀⣼⠇⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠚⠁⠈⠳⢄⡀⠀⠀⠀⢀⡼⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠉⣛⡿⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡤⠋⠀⠀⠀⠀⠀⠙⢦⣀⡀⣀⣠⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣐⣦⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣾⣾⣿⡏⠉⣿⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⣿⣿⣷⠀⣀⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣿⣦⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢀⣤⡄⠀⠀⠀⢠⣤⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⡷⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣀⣶⣾⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⡷⠄⠀⠀⢤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⠉⠀⠉⣹⣷⣶⣀⣤⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⢀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⡁⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠛⣣⣼⣦⣤⣼⣿⣿⣿⣏⠁⠀⠉⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣆⣀⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣤⣤⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠀⣀⣰⣾⢿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢸⡟⢻⣷⣴⣄⣻⣿⣆⠀⢠⣿⠛⣿⡄⣿⣿⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣿⢿⣿⣿⣿⣿⡿⣿⣦⣾⡏⠀⣿⣇⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⡇⠈⣿⡇⢻⣷⠀⠘⣿⠇⠀⠀⢹⣿⡿⠿⠇⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠿⢷⣤⣴⣶⣬⡟⢃⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⣤⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣀⣾⡟⠉⠉⢻⣿⣾⡟⠀⠀⠀⠀⣤⣄⣀⣾⡿⢿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠋⢿⣧⣀⣀⣼⣿⠻⣿⣄⣀⣀⣤⣨⣿⣿⣿⣥⡄⣈⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢠⣤⣽⣿⣟⣿⣥⣶⣾⠛⠛⣿⣯⣿⠟⢿⣿⠛⣋⣿⡛⠛⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⢸⣿⣇⣹⣿⢿⣿⣀⣀⠀⢀⣿⡋⣿⡇⢸⣿⣾⣟⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⢀⢹⣿⣿⣿⣁⠸⣿⡟⠉⠀⢸⣿⠿⣿⣧⢸⣿⠘⣿⣿⠛⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⡇⠙⢿⡷⣿⣷⣿⠿⣿⡯⠀⢚⣿⣼⣿⠀⠘⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⠛⠿⠿⣦⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠉⠛⠛⠛⠛⠛⠉⣡⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⢀⡀⢀⠀⡔⠀⠢⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⢰⠄⢰⠂⢀⠆⠀⢲⠀⣀⠀⠀⠔⠒⠒⡄⠀⣀⠀⠀⡠⠄⠤⡀
⠘⠁⠃⠀⠀⠁⠀⠀⠀⠄⠘⠀⠀⠑⠂⣤⡈⢿⣵⣮⠣⡈⣄⠾⠲⣤⣘⡠⢃⣀⠀⠀⠀⠀⠘⠨⠁⠀⠈⠀⠀⠀⠸⠀⠀⠀⠉
⠀⠤⢄⠀⠆⠉⠁⠀⠀⠀⢀⠀⠰⠃⠀⢻⣝⣶⣇⣉⢦⢋⣤⣶⣶⣄⣈⡶⣋⠏⣄⠀⠴⠤⠀⠔⠀⠀⠈⢢⠠⠄⠀⠂⠈⠁⠂
⠀⠤⠄⠀⠀⢂⠀⠘⠁⠀⠀⠀⠠⡔⢂⢦⣽⣿⣿⣄⣶⠸⣿⣟⠛⠛⣇⡶⠧⠾⣥⣄⣀⠀⠀⡀⢐⠈⠉⠀⠀⠀⠀⠉⡀⠀⠁
⠀⠀⣠⠴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠙⠣⠿⢿⠛⠛⣏⣉⠭⣿⣶⣾⠟⠃⣸⠒⢾⣿⣿⣿⣷⠄⠀⠀⠱⣠⣶⣶⣾⣿⣳⣶⣤⡀
⢠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣛⣀⡤⠞⣹⠉⡸⣧⢴⣇⣴⡦⠻⣎⢙⠉⠙⠈⠛⢯⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡽
⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠐⠃⠚⠅⡾⢳⡈⠁⠈⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣄⠀⠀⠀⠀⢠⠞⠀⠀⠙⣄⠀⠀⠀⠀⢠⣴⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⠋⠀⠀⠀⠀⠈⢦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠸⡻⠟⠋⠹⡄⡴⠁⠀⠀⠀⠀⠀⠀⠈⢧⢀⠟⠉⠛⠛⡏⠉⠛⠛⠛⠛⠛⠋⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀⣳⡀⠀⡇⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⡀⠀⠲⣭⣯
⠠⣶⣦⢠⣤⣄⢀⣄⡀⠙⠿⠋⢀⡀⣧⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⢾⠁⠀⠀⠀⡏
⠀⢹⠇⠂⠻⠃⠘⠿⠃⠒⠚⠒⢻⠟⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⣇⣀⣀⣠⣤⣤⠴⢻⠲⠤⠒⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⠉⠀⠐⠀⠐⠒
⢠⣀⣀⣄⡄⣀⢠⣀⣀⣀⣤⣤⠤⠖⣺⡆⠀⢨⡴⣖⣋⠉⠉⠉⠉⠉⠉⣓⣲⢤⢰⠀⠀⣼⠆⣄⡀⡀⣀⣀⣀⠸⠴⡇⠀⠤⠤
⣼⣿⣿⠿⠿⠟⠛⣋⡉⠀⠢⠃⠫⣯⢽⢳⠀⡿⢸⣏⡛⠻⠿⠿⠿⠿⠛⣋⣿⡜⣿⠀⢠⣿⠈⣐⡪⣳⠐⢚⡀⢀⠐⠀⢀⠊⢰
⢀⢢⢤⠤⣷⡉⠉⢤⠐⣾⢫⡶⡂⢠⢸⡘⣷⠇⢸⣿⣿⡆⠀⠀⠀⢠⣾⣿⣿⡇⢻⡄⡼⢸⢰⢢⠢⠄⠡⠠⣤⠳⣞⣀⡸⠱⣅
⠐⢽⡉⢡⣈⡟⣉⣉⣇⣼⠐⠀⠅⣀⠘⣷⡇⠀⠘⠿⢿⣧⣶⣤⣦⣼⣿⣿⡿⠁⠀⢻⡇⣾⢀⠝⢁⡂⣸⡀⠨⠤⠏⠋⣠⣀⣤
⠰⣄⡈⠣⡜⡷⣨⠃⡦⢤⠼⠲⠠⠁⠄⣟⠧⣴⣶⣾⡿⠿⠿⠿⠿⠿⠿⣿⣷⣶⡦⠞⢡⡇⡜⠋⢯⢔⡹⠈⠞⠆⢒⠫⣥⡽⠥
⠀⡁⢈⠀⢿⢻⡁⡈⢤⡾⣤⢺⡜⡼⠀⡜⢦⡀⠉⢪⡻⠭⠭⠭⠭⠭⠭⢋⡞⠁⠀⣠⠏⠄⢧⠆⣸⣁⡄⠁⡘⠧⣾⠤⢃⠰⢰
⠀⡧⢸⠎⠉⢸⡈⢣⡘⠿⠛⡯⡠⠃⡂⠹⣄⠳⢄⡀⠳⣄⣀⣀⣀⣀⣠⠞⠀⡠⢚⡁⠐⣞⡎⢉⠓⢴⠘⣒⢡⣥⡌⣢⢌⠄⢛
⠀⠎⡆⢼⠫⣳⠙⡼⣗⠓⢊⡅⡀⠼⣡⠀⡏⠳⣄⠉⠓⠦⣍⠉⣉⠭⠖⠒⠚⠱⡱⠀⠆⢻⠘⢤⡾⠀⡣⣠⠸⣍⡆⠣⡜⢢⠐
⠈⡄⡱⠼⣥⡥⡜⢫⣘⢾⠄⣹⠁⡄⠀⡴⡁⠸⡈⣉⠙⢲⢬⡛⢁⡴⡞⠛⡩⢠⠁⣶⠀⣟⢉⡌⠩⢹⢴⠈⢏⢸⠰⣃⡨⢶⢸
⠀⠻⠆⠲⠑⠃⠣⠇⠋⠖⠈⠻⠄⠫⠁⠠⠅⠸⠰⠇⠎⠀⠰⠟⠻⠴⠁⠘⠓⠚⠷⠠⠆⠨⠉⠃⠰⠚⠖⠖⠉⠾⠰⠡⠰⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⠖⠒⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠋⠉⠉⠓⠦⣄⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣁⣠⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⢀⡴⠶⠶⢤⣀⠀⢀⣀⣀⣀⣀⡟⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡾⠀⠀⠀⢰⡏⠀⠀⣴⣚⠉⠉⠻⢧⡀⠀⠈⠉⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⣼⠁⠀⠀⠀⠈⢷⡀⢸⡇⠈⠙⢦⠀⠈⢷⠀⠀⠀⠀⠘⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠓⠦⣤⠞⠀⠀⣸⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠲⢤⣀⡀⠀⠈⣧⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡞⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣘⡇⠀⠀⠈⠉⠛⢲⡇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⣸⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢈⣩⠷⠒⠒⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⠙⣳⠖⠛⠻⣍⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⢠⡟⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡟⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⣾⠃⣀⡤⠶⠒⠛⢛⣋⣩⡽⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣷⣸⣾⢗⣋⡤⠴⠖⠚⠋⠉⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡿⢟⣉⣠⣤⡤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣷⣦⠀⠀⠀⠀⣠⠞⠛⠳⢦⣤⠿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠙⢿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠿⠟⠋⠀⠀⠀⠀⠈⠳⠶⠞⠋⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠛⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛⣤⣤⣤⣤⣤⣤⡄⠀⠀⢀⣤⣤⣤⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣠⡴⠶⢦⡀⠀⠀⠀⠀⣠⣴⣶⣤⣀⣀⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠳⢦⣤⡴⠋⠀⠀⠀⠀⠻⢿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠣⠤⢲⠀⠀⣀⠄⡀⠀⢰⠒⠤⠂⠀⠘⠤⠔⢦⠀⠀⡀⢄⠀⠀⡔⠢⠤⠁⠀⠱⠤⠒⡆⠀⢀⠠⡀⠀⠀⠖⠤⠜
⢀⣀⣀⣘⠀⠀⢣⢠⡃⠀⢨⣀⢀⢀⠀⣀⣀⣀⣄⠀⠈⡆⢰⠁⠀⣁⣀⣀⣀⢀⡀⣀⣀⡇⠀⢸⡀⡜⠀⢀⣃⢀⣀
⢸⠀⠀⡈⠀⠉⠁⠀⠉⠁⠈⡄⠀⢸⠁⢡⠀⠀⠃⠈⠉⠁⠈⠉⠁⠸⠀⠀⡞⠈⡇⠀⢰⠀⠈⠉⠀⠈⠉⠀⢁⠀⢠
⠉⠀⠀⠓⠒⠓⡄⠀⠐⠓⠒⠃⠀⠀⠁⠁⠀⠀⠓⠚⢲⠀⠀⡖⠓⠚⠀⠀⠈⠈⠀⠀⠘⠒⠒⡆⠀⢠⠚⠒⠚
⠲⠀⠀⠋⠉⠊⠀⠀⠈⠒⠉⡇⠀⢠⠒⢢⠀⠐⠋⠑⠋⠀⠀⠙⠊⢙⠀⠀⡔⠒⡄⠀⢸⠉⠒⠁⠀⠀⠑⠉⠑⠀⢀
⠸⠀⠤⠴⠄⠒⢦⢠⠖⠂⢠⠤⠄⡸⠆⠧⠀⠤⡧⠀⠒⡆⢰⠒⠀⠼⠤⠀⠵⠰⠇⠠⠬⡄⠐⢲⠄⡴⠒⠠⡦⠤
⠀⢀⣀⢸⠀⠀⢇⣀⠇⠀⢸⠀⣀⠀⠀⠀⣀⡀⢠⠀⠐⣅⡨⠀⠀⡆⢀⣀⠀⠀⠀⣀⠀⡇⠀⠸⣀⡼⠀⠀⡃⣀⡀
⠀⢇⣈⣭⠀⠀⠀⡀⠀⠀⢈⣍⣀⡅⠀⠰⣁⣉⣅⠀⠀⢀⠀⠀⠀⣨⣁⣈⠆⠀⢊⣀⣩⡁⠀⠀⢀⠀⠀⠀⣭⣁⡸
⠀⠀⠀⢸⠀⠀⢎⠈⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡈⠀⠰⡃⢸⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⡱⠀⠀⡆
⢸⠉⠁⠚⠒⠒⠚⠘⠒⠒⠚⡃⠉⢹⠂⢏⠉⠁⠗⠒⠒⠃⠘⠒⠒⢺⠈⠉⡹⠐⡏⠉⢘⠓⠒⠚⠁⠓⠒⠒⠃⠉⠉
⠘⠀⠀⢧⠠⠤⡀⠀⢠⠤⢤⠇⠀⠘⠀⠊⠀⠀⣄⠤⢄⠀⠀⡠⠤⣠⠀⠀⠓⠐⠃⠀⠸⡠⠤⡄⠀⢀⠤⢄⡤⠀⠈
⢄⠀⠀⠴⠢⠴⠁⠀⠐⠤⠒⡆⠀⢀⠤⣀⠀⠀⠖⠤⠜⠀⠀⠣⠤⠲⠀⠀⡀⠤⡀⠀⢰⠂⠤⠃⠀⠘⠤⠔⠦
⢰⠁⠀⣀⣀⣀⣀⢀⣀⣀⣀⡃⠀⢸⡀⡜⠀⠀⣄⣀⣀⡀⢀⣀⣀⣰⠀⠀⣣⢠⡇⠀⢘⣀⡀⢀⠀⣀⣀⣀⣄⠀⠈
⠈⠉⠀⢨⠀⠀⡞⠈⡆⠀⢸⠁⠈⠉⠀⠈⠀⠀⠃⠀⢠⡃⢘⠄⠀⡈⠀⠈⠁⠀⠉⠁⠈⡇⠀⢰⠁⢣⠀⠀⡇⠀⠉
⠀⡖⠑⠚⠀⠀⠈⠉⠀⠀⠘⠒⠈⠂⠀⢠⠊⠒⠊⠀⠀⠉⠉⠀⠀⠓⠒⠑⡄⠀⡔⠑⠒⠃⠀⠀⠉⠁⠀⠀⠓⠊⢢
⠀⠙⠊⢹⠀⠀⡔⠒⡄⠀⢸⠉⠑⠁⠀⠀⠑⠉⠱⠀⢀⠖⠢⠀⠀⠏⠉⠊⠀⠀⠈⠊⠉⡇⠀⢠⠒⢢⠀⠀⡋⠑⠉
⢠⠂⠤⠼⠤⠤⠵⠰⠥⠤⠸⠤⠄⢠⠄⡔⠀⠄⡦⠤⠤⠇⠸⠤⠄⢴⠠⠀⢦⢠⡖⠠⠤⠧⠤⠬⠆⠧⠤⠤⠧⠤⠐
⡨⠀⠀⡄⠀⣀⠀⠀⠀⣀⠀⡇⠀⠸⣀⠼⠀⢀⡁⢀⡀⠀⠀⢀⡀⢘⠀⠀⠇⣀⠇⠀⢸⠀⣀⠀⠀⠀⣀⡀⣀⠀⠐
⠀⠀⠀⣨⣅⣀⠆⠀⢨⣀⣩⡁⠀⠀⠀⠀⠀⠀⡭⣁⡸⠀⠀⢅⣈⢭⠀⠀⠀⠀⠀⠀⢈⣍⣀⡇⠀⠰⣀⡨⣅
⢹⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠁⡱⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢎⠈⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠒⠂⢛⠈⠉⡹⠐⡍⠉⢸⠃⠒⠚⠁⠓⠒⠂⠏⠈⠉⠇⢸⠉⠁⠙⠐⠒⠚⠈⠓⠒⠘⡇⠉⢹⠂⢏⠉⠁⡇⠐⠒
⠀⡠⠤⣼⠀⠀⠑⠐⠃⠀⠸⡤⠤⡄⠀⢀⠤⢤⡴⠀⠈⠂⠘⠀⠀⢧⡤⠤⠀⠀⠠⠤⢤⠇⠀⠘⠀⠊⠀⠀⣥⠤⢄
⠀⡁⡁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢲⠁⠐⠋⠀⣀⡀⠉⢷⠉⡴⢟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⢀⣎⣀⢠⠔⠀⠀⠀⠀⡀⠀⠀⢁⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⠉⠎⡉⠣⠀⡀⣤⠔⠒⠉⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠘⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠚⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠰⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢛⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⣀
⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⣀⠀⠈⠁⠸⣲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠈⠙⠲⣄
⢀⡴⠋⠀⠀⠀⠀⢀⠀⠀⢀⣠⠬⠗⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⠿⠳⠿⠉⠉⠉⠉⠉⠉⠉⠛⠛⠒⠒⠺⠥⣄⡀⠀⠀⡀⠀⠀⠀⠀⠙⢦
⠺⠤⠤⠤⠤⠖⠚⠙⢦⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡴⠋⠓⠲⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡤⠤⠖⠒⠒⠛⠋⠉⠉⠁⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠈⠉⠉⠙⠛⠒⠒⠲⠤⢤⠀⠀⠹⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⢰⠀⠀⠀⠀⢀⣀⣠⡤⣴⡖⠚⡇⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢸⠓⢲⣦⢤⣄⣀⡀⠀⠀⠀⠈⡆⠀⠀⢱⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠔⠐⣆⠉⢿⣿⣿⣦⣾⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠸⣷⣴⣿⣿⡿⠉⣰⠒⢢⡇⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⣇⠀⠘⢆⠈⠙⠛⠛⠉⢀⡴⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⢦⡀⠉⠛⠛⠋⢁⡰⠃⠀⣸⠇⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠹⣧⣀⠀⠙⠒⠲⠒⠚⠉⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⠓⠒⠒⠒⠋⠀⣀⣼⠏⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠙⠳⠦⠤⠤⠤⠔⠚⠁⠀⠀⠀⠀⣤⣶⣛⣛⣷⣦⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠴⠚⠛⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣛⡉⠉⠉⠁⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⢉⣛⠠⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢀⣞⠀⢰⠀⠀⠀⠀⡆⠀⣳⡀⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡼⡉⡀⠀⢸⠀⠀⠀⠀⡇⠀⢀⢉⢧⢀⢳
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣾⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⢀⣴⣿⣦⡀⠀⠀⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣿⣿⣿⣿⣿⣦⣴⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠙⢿⣿⣿⡟⠉⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋⠲⣄⠀⠀⡠⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠙⠋⠀⣀⣤⣾⣿⣿⣿⣿⣿⡋⠀⠀⠀⠈⠓⠐⠁⢀⡀⠌
⠀⠀⠀⠀⠀⢀⠔⠒⠄⠀⠈⢂⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⣅
⠀⠀⠀⠀⡔⠁⠀⠀⠑⠠⠔⠃⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠹⢿⡿⠃⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠠⠂⠐⢄⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠘⠿⢿⣿⣷⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠡⢀⡀⠈⠢⠒⠁
⠀⠀⠀⠀⡔⠁⠀⠠⠒⠢⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣄⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠘⠢⠤⠊⠀⠀⠈⠢⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣿⣷⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠁⠉⢻⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀⣠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⣀⣤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣇⢸⣻⣿⡇⠙⢶⡀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠈⣏⠟⠓⠲⣾⣿⣷⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⡀⢐⡶⢿⡗⢠⡄⠀⠙⢻⡟⣉⣉⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣨⣃⡈⠙⠊⢱⠀⢠⡄⢀⡬⡟⢿⡟⠷⠀⠀⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠬⢭⣀⠀⠀⢢⠀⠀⣈⣿⡟⡮⢁⣄⠐⣜⣳⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣿⢽⣛⡟⠡⠴⠷⣾⣿⣿⣎⠝⠋⠀⢀⡜⠿⢽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣾⣧⣞⠉⠀⢤⢞⠀⠀⠈⢉⣀⡤⡄⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠈⠋⠤⠴⠿⠿⢟⢵⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣽⣿⣷⣦⠀⢀⡀⠀⣀⠜⠫⠄⠂⢈⣷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⡯⢾⡟⠉⠀⠀⡐⢈⢂⣾⣿⣮⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠙⢳⣸⠃⣍⣷⣤⣤⠾⠛⠁⠈⣻⠟⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠟⠛⠋⠉⠀⠀⠀⠀⠼⠣⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠰⠄⠀⠀⠀⠀⠈⠻⣿⠿⠀⠐⠾⣻⢓⣧⠀⠀⠀⢠⠤⢀⠀⠀⠀⠀⣀⠒⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢤⡀⠰⠦⠐⠓⠸⠃⠶⢰⠦⠒⠘⠛⢶⣶⣿⡄⡀⡍⡉⡁⠰⠃⠀⠀⠀⣴⣦⡤⠀⠀⠙⣉⣿⣿⠏⠁
⠠⢊⣠⠀⠀⠀⠤⠀⠆⠐⠂⠛⡀⠛⢠⣮⣤⠆⠀⠀⠀⠈⢹⠇⠆⠻⠃⠓⠀⠀⠀⠀⠀⣿⡟⠁⠀⠠⠾⠟⠛⠁
⠀⠈⠀⠀⠰⢠⡄⠰⢂⠐⠃⣈⠁⠶⠂⣈⠙⠀⠀⠀⠀⠀⣾⠀⠀⣀⣀⠀⣵⣦⡤⣴⢶⣿⠈⠠⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⡄⠗⠈⢁⣄⠋⡀⠒⠀⠉⣀⠉⠁⢠⡤⠚⠽⣏⣻⠟⣡⣼⣿⣿⣿⡇⣓⠿⡻⠆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠋⡀⠛⣀⠁⠘⠋⣠⣏⣭⣽⢛⣛⠭⠥⢲⣿⠿⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠛⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⡒⠪⢀⠀⣸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢍⡘⡖⣉⠁⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣅⠈⠀⠀⠀⠘⠈⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠈⢿⣿⡄⠈⠁⢀⠆⢀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠆⠀⠀⠀⢸⣿⣷⣄⠀⢀⣴⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠨⢰⠑⣡⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠨⠠⣼⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣶⣤⣀⡀⠀⢃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠗⠂⠄⣈⠿⠇⡀⠀⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⠃⠀⣾⣿⣿⣿⣿⠟⠉⠈⠐⠄⠀⠸⠤⠤⠤⠤⠤⢀⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣁⡀⠀⡠⠛⢿⣿⣿⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡡⠬⢐⡉⠥⠤⠤⠄⣀⢱⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠖⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠊⡠⠂⠁⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠓⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠀⢠⠞⢉⢤⡈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢠⡏⠹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⢀⠉⠀⠀⠀⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣠⡄⢰⣅⢀⡀⠀⢀⠙⠀⠀⠀⣠⠀⠀⠀⠀⠂⢹⠃⢀⡾⠁⠀⠛⠍⠀⠀⣀⣷
⠀⠀⠀⠠⢀⡸⠀⡠⠆⡠⠼⠿⠨⠦⣤⣄⡙⠲⣼⡄⠀⠂⣤⣤⣿⠶⠯⠴⠿⣿⠶⢤⣤⣤⣭⠟
⠀⠀⠀⠀⠙⠀⠀⠇⣀⠃⢀⣨⣤⡶⠶⣿⣿⣷⡘⣿⣆⣼⡿⠛⠉⠐⠀⠈⡀⢈⣳⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡸⠋⠀⠁⡀⣀⡀⠈⢿⣿⣾⣿⢏⣴⠶⠛⠛⠓⢒⡀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠻⠆⡮⠚⢿⡰⣶⠀⠙⣿⣿⡟⢀⣠⠘⡄⠁⢈⣉⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠋⡀⠉⠁⠂⠀⢘⣿⠇⠐⠂⠁⠀⠀⠉⠘⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡿⣹⡆⠀⠉⠀⠈⠀⢨⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠄⣸⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠟⡁⠀⣼⠞⣧⡤⢸⣦⠀⣳⡶⠶⠀⣬⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⡸⡝⠀⣈⣵⡄⠈⢬⠃⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠘⣤⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠶⠖⠛⠉⠉⠉⠙⡆
⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠋⠀⠀⠀⠀⠀⣤⣶⣶⣅
⠀⣠⣴⠿⠛⠋⠉⠙⢿⣿⢟⣛⣵⣿⣿⣿⠟⠛⢿⣿⠀⠀⢀⣀⡤⠼⣿⣿⣿⣿⣷⣄
⢰⡿⠁⠀⠀⠀⠀⠀⠘⣿⠏⢁⣈⣿⣿⣿⣤⣶⣤⣽⣧⢰⡏⠁⠀⢠⣾⣿⡿⣿⣿⣿⣷⣦⣤⣄⡀
⠈⠿⣦⣤⣤⣤⣤⣤⣄⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠦⢤⣿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠉⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⣿⣿⡟⠋⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢿⣿⡿⠋⠉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⢋⣤⣴⣶⡶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⣀⡹⣷⣠⣾⣟⣿⣿⣿⡿⣿⡏⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢷⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠻⠶⠾⠛⠉⠙⣿⢿⣿⣿⣿⣿⣿⠇⣿⣇⠀⠈⠻⠿⣿⡿⠿⢿⣿⣿⠏⠘⣧⣀⠀⣀⡤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠙⠛⠛⠛⠁⢠⣿⣿⡀⠀⠀⠀⣀⣤⣾⠟⠋⠀⠀⠀⠈⠉⠉⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠐⠂⠤⠀⠀⠀⠤⠐⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠈⠑⠒⠀⠀⠀⠒⠚⠀⠌⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣾⣿⡿⣣⡿⠛⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠙⠿⢻⣜⣷⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠿⠋⠞⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢉⣉⣉⣢⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠢⡄⠀⠀⡇⢰⠉⠀⢠⠃⡴⡵⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠘⡄⠀⠇⠈⠀⠀⢣⣸⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠉⠀⠀⣀⣤⠤⠤⠀⠱⣀⠆⢀⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢄⡀⠀⠀⣀⠔⠈⠁⠀⠀⣀⣀⡀⠰⠃⠀⢀⣀⣀⠀⢇⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠲⢅⡸⡄⠀⠀⢠⠞⠉⠀⠀⠀⠀⢰⠋⠉⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⣠⠶⠂⠀⠀⠑⢌⢢⠀⠉⠀⣠⡶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡜⠀⠀⢸⡇⠀⢠⡶⠋⠀⠀⠑⢵⢄⠀⠋⠀⠀⠀⠀⢒⣡⠶⣚⠳⠆⠰
⠀⠀⠀⢠⠊⠀⠀⣀⡈⠁⠀⠸⠁⠀⠀⡞⢄⠈⢻⠳⣄⠀⠀⢠⢞⠭⠒⠉⠀⠀⠀⡇⠀⠀⠀⠀⢀⠔⢖⠀⠀⠐⠢⣄
⠀⢀⠔⠁⠀⢀⡞⠁⠀⣀⡄⠀⠀⢰⣰⠃⠈⢇⠀⢃⠈⠓⢄⠘⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡰⠁⢣⠈⢆⠀⠀⠀⠈⠆
⠀⢈⠀⠀⠀⠸⡇⠀⣸⠋⠀⠀⠐⣵⠋⠀⠀⡘⠀⠘⡀⠀⠀⠉⠐⠂⠤⠤⠤⠚⠁⠀⠀⢀⡴⢣⠀⠀⠡⡈⢣⠀⠀⠀⡙
⠀⠀⠉⠒⠤⣀⡀⠀⠙⠀⠀⢤⡚⠁⠀⣀⠔⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠐⡄⢣⡀⠀⠑⡄⠱⣄⡰⠁
⠀⠀⠀⠀⠀⠀⡇⢙⠒⠢⠤⠄⣀⣉⣁⣀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠘⣦⡱⠤⠤⠬⠶⠊
⠀⠀⠀⠀⠀⠀⠡⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢁⠠⢤⡀⠀⠀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠿⣔⠒⠒⠒⠂⠐⠢⡀⠀⠀⠀⠀⠀⣠⠒⢁⡠⣒⣵⢞⡳⣊⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠥⡻⠃⠀⠀⣀⠔⠊⠉⢆⢷⠹⠯⡢⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⣁⠔⠊⠀⢀⡤⡊⠀⠀⠀⡠⠔⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⢀⠠⠒⠁⠳⣘⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡠⠔⠈

⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣃⣤⣶⣦⣤
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⠀⠾⠃⣀⣠⣄⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣧⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣁⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣤⣤⣀⣠⣬⣽⣿⣿⠟⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣦⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⣙⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⡿⠿⠿⠿⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⠉⠀⠉⢿⣿⣿⣶⣾⣿⣿⣿⣿⠟⠉⠀⠉⠉⠙⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⢣⠃⠀⠀⢀⣸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⡇⡇⠀⡌⠀⠀⣛⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠃⢰⠀⠀⠀⠸⣿⣿⡗⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⣽⡄
⠄⠀⠀⠀⠀⢻⡀⢰⠀⠀⠀⠀⣻⣿⣿⣄⠀⠀⠀⣿⣦⡀⡀⡀⣾⡟⠀⠀⣠⣼⣿⣿⣧
⣧⠀⠀⠀⠀⠀⢳⡀⢆⠀⢀⣶⣿⣿⣿⣿⣤⣤⣤⣻⣿⡿⣷⣿⣿⣅⣶⣿⣿⡟⣿⣿⢯⢃⡀
⣿⣧⡀⠀⠀⠀⠀⠙⢌⢲⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⡿⡌⠛⢸⣿⡿⠉⠙⠜⢋⣵⣿⣿⣷
⣿⣿⣷⣶⣦⣄⣀⢀⣼⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣾⣤⣼⠿⢤⣤⡴⣚⠛⢛⣛⡿⠟
⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠛⠀⠀⠈⣿⣿⣯⣿⠿⣿⣿⠁⠀⠀⠉⢅
⠀⠀⠀⠀⠅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⣠⣿⣿⣟⢃⣶⣤⣭⣔⢦⣄⠀⠀⠱⡀
⠀⠀⢠⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⢫⣿⣿⣿⢿⣿⣷⡄⠀⠐⡀
⠀⠀⢼⢷⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠙⣿⣿⣿⣿⣿⣟⣿⣿⣿⣦⣾⣿⣿⢹⣿⣿⣿⠛⠀⠀⠱⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⠉⠻⢧⣅⣈⣿⣿⣤⣿⣿⠃⠀⢀⣴⣶⣿⠇
⠀⢠⠷⣿⣿⣻⣿⣿⠟⡃⠀⠀⠀⠀⠀⡿⠛⠃⣥⣿⣧⡄⠀⠀⡀⢰⣼⣿⣿⣿⣹⣾⣟⠞⣻⡿⡏
⠀⠀⢠⠟⢿⣿⣿⣧⣦⢉⠁⢀⠆⢸⣾⣃⠀⠀⠉⠿⠏⠁⠀⣼⠇⣸⣿⣿⣿⣿⣶⠁⠈⠉⠁⠀⡁
⠀⢰⣧⣦⣶⣿⣿⣻⠇⠘⠐⣿⠀⠀⢻⣿⢷⢦⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠋⣠⡖⠀⠀⠀⠀⠀⠃
⠀⢰⣿⣿⣿⣿⣿⡁⠀⣆⢤⠉⠀⠠⣾⣿⣅⣁⢡⠀⠀⢀⣤⣆⢀⣙⠋⠉⠀⠁⠀⠀⠀⠀⠀⠰
⠀⠈⠇⣿⣹⣿⣿⣿⣦⡘⣤⡀⠀⣼⣊⣿⣝⠈⠳⠀⠀⣿⡻⣿⠇⠀⠀⠀⠠⣀⢠⣀⠀⠀⢠⠁
⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⢛⣿⠛⠿⣿⣿⣿⣆⠀⠀⠐⣿⡿⠯⠀⠢⠀⠀⠀⢽⣿⣿⣷⣶⣧⣤⣀⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠆⢤⡤⢘⠻⣷⣄⡀⠀⠀⠙⣷⢂⠀⠈⠢⡀⠀⠀⢋⠟⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⢰⢿⢿⠿⣿⣫⣿⣿⣿⣿⣆⣿⣿⣾⣿⣿⣦⣈⢿⣿⣿⣆⡀⠀⠀⡡⠖⡁⠀⠀⠈⠈⠙⢿⣿
⠀⠀⠀⠀⢸⣆⡴⣷⡿⣿⣿⣿⣟⢿⣿⣿⡿⣿⡝⡿⣿⣿⣿⣿⣿⣿⣶⡶⠉⠀⠈⢊⠲⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠟⢰⢻⢹⢻⢉⣎⡾⢿⣿⣿⠻⢿⡿⡸⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢃⠙⣆
⠀⢤⠄⠀⠀⠀⠘⡆⡸⣼⠞⠋⠀⢠⢏⡿⠀⠀⠙⣧⡼⠏⠉⠀⠈⠹⣿⣿⡇⠀⠀⠀⠘⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢼⠃⠀⠀⠀⢸⠞⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢰⠀⢠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣿⣿⣯⡅⠀⠀⠂⠀⡌⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠀⠀⠀⠀⠈⠓⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠠⢤⣀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠴⠊⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠁⠀⠲⢄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⡈⢀⠴⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠈⣀⣀⡀⠼⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⢪⡁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⢄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠂⢢⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠈⣤⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⡐⠂⠀⠂⢴⠂⠉⠀⠀⠀⠘⠿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⡇
⠀⡇⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠙⠒⢳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣰⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠒⠻⣁⡠⠊⠉⠳⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠂⠀⡐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⡜⣸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⡜⢀⠇⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⠴⢋⠔⠊⠀⠀⠀⡘⡠⠎⠀⠀⠀⡴⠁
⠀⠀⠀⢀⢀⣀⣀⣀⠠⠄⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⢄⡀⠀⠀⠀⠀⠘⡅⠀⠀⠙⠢⠴⣅⠴⡴⠋⠀⠀⠀⠀⢸⠁
⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠚⠉⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠸⢆⡠⠀⠀⡀⣠⠏
⠀⠀⠸⢅⣀⣤⠤⣤⠤⠤⠠⠤⠔⠒⠒⠚⠛⠉⢉⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⢀⡀⣀⡤⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠰⠒⠲⠆
⠒⠒⠀⠀⠐⠂⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂⠂⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⢀⠤⠄⠀⠐⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠔⡤⠤⠎⠀⠀⠀⠀⠀⡇
⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠏⠉⠉⠉⠉⠉⠉⠉⠉⢟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠀⠈⠀⠀⠄⠶⠂⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠠⠀⠀⠀⠀⠀⢀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⣭⠂⢠⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢠⠀⠀⠀⡐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⡴⠂⠀⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠉⠀⠀⡘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠤⠴⠈⠁⠀⠀⠈⠀⠀⠁⠈
⠀⠀⢰⠀⠀⠀⠔⠀⠐⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⡐⠢⠀⠀⠠⠰⠀⢀⠔⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⡐⠀⠰⠂
⠀⠀⢸⣤⡸⣌⢀⡀⠀⠈⠀⠈⠉⠐⠃⠐⡆⠀⠀⡇⠀⠀⠀⠒⠁⠁⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⢀⠈⢀⠀⡐⠀⠈⠲⠒⠀⠠⢤
⠀⠀⠘⢆⠀⠀⠀⠨⠓⢄⠀⠀⠀⠀⠀⢊⠈⠁⠈⠰⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢰⠉⢱⠀⠀⠀⠀⠀⠀⠁⠀⡀⡄⣀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠈⢦⡀⠐⠀⠀⠀⠑⠠⠀⡀⢱⣎⠀⠀⠀⠀⣁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠁⢀⡆
⠀⠀⠀⠀⠀⠉⠒⠪⠥⠒⠂⠀⡂⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⠈⢎⡅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠊⠀⠀⠀⠐⠈⠈⢢⠀⣤⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⠸⠁
⠀⠀⠈⠀⠀⠀⠁⠁⡀⠀⡠⠉⡏⢈⣡⠭⠅⠤⠀⠀⠠⠤⠛⣿⠉⠉⠉⠀⠀⠀⢀⠡⠠⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠈⠠⢀⡀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠰⠂⠑⠒⠃⠀⠀⠀⠀⠡⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠢⡀⠤⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⣆⠤⠈⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⣂⡆⠸⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠆⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡌⡁⠀⠀⢀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠓⠶⣎⠀⠀⣀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢯⠀⠀⢀⣀⣀⠀⣀⣀⡞⠁⠀⠀⠀⠀⠀⠈⡷⠋⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠚⠉⠀⠀⣿⡄⣈⠃⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢤⣄⣠⡄
⠀⠀⠀⠀⠀⢀⡠⠖⠚⠛⠒⣾⠀⣀⢤⡀⠀⠈⠉⠁⢀⠆⠀⠀⠐⠚⢛⣶⣤⠤⠦⠴⣾⢤⣀⡀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠳⡾⠷⠚⠁⠀⢰⣋⡵⣏⠀⠀⠀⢠⠖⠋⠀⠈⡇⠀⣠⢼⡶⠷⡗⠦⠴⠖⠋
⠀⠀⠀⣀⠼⠶⠿⠂⢀⡤⠖⠢⡌⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠟⠒⠦⠖⠚⠁⠘⠒⠋⠀⢀⣇⡠⠔⠒⠒⠲⣄
⠀⢠⠞⠁⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⢀⡜⠹⡀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⢀⡀⠀⠀⠀⣠⠞⠁⠀⠀⡇⠀⠀⠈⡇
⢠⠃⠀⠀⠀⠀⠀⣠⠟⠛⠁⢀⣀⡴⠋⠀⠀⢣⠀⠀⠀⠀⠈⠳⠤⠤⠤⠖⠻⠀⠀⠀⠈⠻⡄⠀⠀⠀⠈⠛⠋⠀⡟
⢸⣀⠀⣀⠀⠀⢰⠃⠀⡀⠀⣸⠁⠀⠀⠀⠀⠀⠳⢄⣀⣀⣰⡆⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠎⠀⠀⠀⠀⠀⢀⡼⠁
⠀⡽⡟⠁⠀⠀⠈⠛⠋⠁⡰⠃⠀⠀⠀⣀⠀⠀⢀⣀⠬⠥⠤⠼⠶⠶⡆⠀⠀⠀⠀⠉⠉⠁⢀⣠⣤⡤⠖⠚⣉⣀⣤⡤⣀⡀
⡜⠀⢣⠀⠀⠀⠀⠀⠀⠊⠀⣷⠒⠉⣉⡀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⡇⠀⠀⢀⠞⠀⣠⡔⠁⠀⢀⣹⠀⠊⠁⠀⠀⠀⠀⠈⢳
⠱⠤⠴⠛⠒⠶⠖⠀⠀⠀⠀⢸⠀⠀⠘⠃⠀⠠⠆⠀⠀⠈⠁⠀⠀⠀⢱⠀⠀⠈⠳⠚⠁⠙⠒⠚⠋⠉⢧⠀⠀⠀⠀⠀⠀⠦⠤
⠀⠀⠀⠀⠀⠳⣄⣀⡤⠊⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠀⠘⠓⢲⠄⠀⠀⡤⠒⢄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠐⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⡖⠋⠀⠀⠀⠙⠦⢼⡦⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠲⡀⠀⠀⠀⠀⡇⠲⠤⠾⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠳⣄⣀⡤⠞⠉⠉⢁⣯⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡼⠯⠭⠭⠭⠭⠭⠭⠍⣽⠵⢚⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⣌⣹⠗⠒⠒⠒⠒⠒⠒⠒⠒⡷⢚⡩⠤⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠑⢦⣠⡟⠒⠚⠛⠛⠛⠛⢉⣉⣹⡏⣁⡤⠖⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀⣹⠓⠒⠋⠉⠉⠉⠉⠉⠀⣸⢋⣡⠤⠒⠒⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢨⣟⣛⣳⡎⢉⡹⠒⠻⣭⠉⠻⣤⠤⠶⠖⡶⠒⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠁⠉⣉⡩⠤⢶⡉⡉⠉⠓⠚⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠶⠒⢉⣙⣉⣉⣁⣈⣙⣓⣒⣦⣤⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠘⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠂⠐⢢⠀⠀⠀⢀⡠⠤⠖⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⢦⠀⠢⡖⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⠏⢀⡴⠒⠒⠦⣤⣘⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⣤⠶⠒⠒⠀⠈⢶⠚⡇⠀⠀⠀⠀⣀⣤⣀⠀⠀⢀⣤⠶⠶⢤⣀⠀⠀⡇⠀⢸⠀⡸⠀⠀⢠⠔⢁⡠⢟⡠⠤⡀
⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⡟⠁⠀⢀⣀⣤⡄⠈⢆⢣⠀⠀⡴⠛⠉⠉⠉⠑⠀⠈⠀⠀⠀⠀⠈⠁⢠⣃⡤⠃⢠⠇⠀⠀⣇⣰⡯⠚⣁⠤⠒⠋
⠀⢀⠞⠉⠀⠀⠀⣠⡶⠖⠒⠀⠀⠀⢰⡟⠉⠀⠀⠀⠘⣎⡆⠀⠀⢀⣠⣤⣤⡀⠀⠀⢠⠶⠿⠷⠦⠀⢸⣁⣀⡤⠋⠀⠀⠀⠈⠑⠒⠉
⠀⠘⣄⠀⠀⠀⢰⠏⠀⠀⢀⣀⡀⠀⠈⠀⠀⠀⣠⢦⠀⠸⣹⡀⠀⠛⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠣⡀⠀⠈⠀⠀⣼⠟⠉⠁⠀⠀⣠⢃⡴⠃⠘⡆⠀⡏⢳⠀⠀⠀⠀⠀⠐⠤⠤⠂⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠈⡳⢄⡀⠘⠃⠀⠀⠀⢀⣩⡶⠋⠀⠀⢀⠇⠀⡇⠀⢣⠀⠀⣠⠴⢖⣻⣛⣛⣛⣛⣳⡀⢠⠃
⠀⠀⠀⠀⢀⠃⢠⠟⢦⡀⠀⠰⢟⡉⠁⠀⠀⠀⣠⠎⠀⠀⡇⠀⠀⢣⡀⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⢸⡀⡎⠀⠀⠈⠓⢄⡀⠉⠑⠒⠒⠋⠁⠀⠀⡰⠃⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⢣⡧⣀⡀⠀⠀⠀⠈⠙⠒⠒⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠙⢤⣉⠓⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠘⡆
⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⣒⡪⠝⠁
⠀⠀⠀⠀⠀⠀⠷⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣧⡀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⢿⣄⠀⠀⠀⠀⠀⡉⢠⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⢻⣦⠀⠀⠀⡰⠁⣾⠃⠀⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠛⢀⡠⠀⠈⢿⡄⠀⢻⣧⠀⢰⠇⣸⡏⠀⢸⣿⠀⠀⠀⢂⠄⠉
⠀⠀⠀⠀⠻⣿⣛⠛⠻⠷⢶⣤⣄⡒⠉⠲⣄⠘⣿⡀⡄⢻⣆⠈⢰⡿⢀⠆⣼⡇⠀⣠⠔⠁⠀⣀⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠈⠉⠻⢷⣤⡈⠳⣼⣧⠰⠈⣿⣧⣿⢁⡞⣠⡿⢀⠜⣁⣤⡶⠟⠋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠠⣀⠉⠻⣦⡙⣿⡆⠃⢸⣿⡇⠎⢠⣿⣷⡷⠟⢋⠁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡙⢦⡈⠻⣿⣷⣿⣿⣿⣿⣶⣿⠟⢋⡠⠖⣁⣴⠿⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⢲⣿⣿⠏⣁⠉⠻⣿⣿⡎⣁⣤⣾⠿⠥⠖⠚⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠒⢂⣴⣿⣿⣿⡏⢀⣭⠖⢀⣿⣿⣿⠿⠿⠿⠶⠶⠶⠶⢶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠁⠀⢀⣤⣾⠟⠋⡩⣿⣿⣷⣤⣥⣤⣾⣿⡿⠉⠈⠛⠒⠀⠀⠂⠀⠀⠀⠀⣉⣉⣛⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⠿⠋⠔⣪⣵⠞⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣤⡶⠛⠉⢀⣴⣿⢃⠏⣸⣿⣿⢰⠀⢿⣿⣌⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠞⠋⠁⠀⠀⡠⠊⣼⡏⡎⢰⡟⢸⣿⡀⠆⠸⣿⢻⣆⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⢀⠜⠁⢰⡿⡘⢠⡿⠀⡟⢻⣧⠘⡀⢿⡄⢿⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠑⠀⠀⣾⠃⢡⡿⠁⢠⠇⠈⣿⣆⠀⢸⡇⠸⣷⠀⠀⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡿⢠⡿⠁⠀⡞⠀⠀⠘⣿⡄⢸⡇⠀⣿⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣾⠁⠀⠰⠃⠀⠀⠀⠹⣿⣸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣼⡇⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢷⢀⣿⣡⠞⠫⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢸⣿⡿⠋⠆⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣸⣿⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣧⡾⠋
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀
⠀⢈
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠄⠒⠒⠒⠒⠚⡗⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⣄⣀⣀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠤⠒⠉⠉⠹⡀⠀⠈⠑⣄⣎⡠⠤⢄⣀⣀⣠⡤⣖⠉⠉⡇⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠁⠀⠀⠀⠀⠀⠙⠢⢤⡶⡿⠛⠈⠉⠀⡠⠊⠁⠉⠉⠳⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠱⡀
⠀⠀⠀⠀⠀⢀⡎⠀⢰⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⠎⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠼⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⡘⠀⠀⠀⢣⠀⠀⠀⢀⡿⠁⠀⣠⠧⠴⠒⠒⠒⠒⠢⣄⠉⠒⠊⢁⣸⠴⠆⠦⣖⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠣⡀⠀⢸⢃⣴⠟⠁⠀⠀⠀⢀⠔⠉⠁⢸⠉⢢⡔⢩⠃⠀⠀⠀⡼⢢⢀⠤⠒⠉⠉⠑⢾⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣾⠉⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡸⢀⠏⣳⠃⣀⠤⠒⠢⡆⡼⠁⠀⠀⠀⠀⠀⡇⠙⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⢠⢃⣸⢖⡷⠊⠀⠀⠀⣸⣿⡿⠀⠤⢄⠀⠀⢠⠃⠀⢰
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠉⠁⠚⡖⠒⢲⠋⣡⠼⣡⠃⠀⠀⠀⡰⠋⡿⢆⠀⠀⠀⡇⢀⡇⠀⠀⠰
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠃⢡⠀⠀⠀⠀⠀⠀⠀⠈⡲⣁⠞⠁⢠⢇⠀⠀⡠⡾⢁⢼⠃⠈⠳⢄⠀⠇⡜⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⢢⠀⠀⠀⠀⠀⣠⠎⡰⠋⠁⡲⠃⠜⢖⠈⠀⡧⠋⠸⠀⠀⠀⠀⢹⠟⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⠀⠀⠀⠱⣄⠀⡠⠚⠁⡐⠁⢀⠔⠁⠀⠀⢀⡱⢞⡇⠀⡇⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⡆⢀⣀⠤⠚⠛⢄⡀⣰⡡⠔⠁⠀⢀⡠⠖⠉⠀⠀⠟⠲⠂⠒⠒⠉⡸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⠤⠄⠒⠒⠃⠉⠉⡛⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠢⡀⢀⠆⠀⠀⠀⢀⡠⠊
⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢈⠟⠒⠒⠒⠊⠁
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠎
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣈⣢⣀⡠⠤⠒⠁⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⡠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⣉⣭⠭⠽⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠊⠁⠀⠀⠀⢠⡤⠒⠛⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠅⢐⡈⠉⢇⠀⠀⠀⠀⠀⡠⠒⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢰⢃⡤⢬⠣⡀⠈⡄⠐⡡⣆⡜⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢵⡄⠰⡎⠀⢈⣧⣀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⡗⠈⢱⣟⣛⣉⣴⣊⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠪⠄⠮⠻⠃⠈⡒⠟⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢒⡖⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⢸⣼⡲⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣈⣉⣈⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠸⡅⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠛⢆⠈⠢⡀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢠⡚⢦⣀⠀⠀⡔⠒⢄
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⢣⡀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⠳⢞⠀⠐⠈⠳⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠱⣄⠀⠈⠑⢄⡀⠀⠀⠀⣠⠊⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣞⣀⡀⠀⠀⠀⠐⡀⠈⢦⡀⠀⡼⠁⠀⢹
⠀⠀⠀⠀⣸⠉⡀⠀⠀⠀⠀⠀⠘⢦⠀⠀⡰⣿⠖⠢⣴⣻⠓⣤⢀⣀⡏⢇⡀⠀⠐⠀⠀⠠⠀⠈⠉⠓⢽⠦⣀⠀⠠⠠⠀⠙⠚⠀⠀⡼⠁
⠀⠀⠀⡜⠁⠸⣀⣀⡀⠀⠀⡆⠀⠀⠳⠊⠀⠀⣧⣰⠃⢠⠀⢸⣀⠤⢆⣄⣾⠂⠔⠁⠀⠀⠀⠀⣠⠖⠉⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⣎⣀⡀⠀⡏⠙⠛⡟⠉⠀⠀⠀⢀⣀⣀⣤⠏⠘⣦⠈⢇⠉⠀⢀⠜⡋⠉⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠸⡄⠈⠉⡇⢀⡾⠢⠤⠤⠤⠀⣀⣀⣠⠊⠀⠀⠈⢆⣠⡆⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠫⠼⠗⠋⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀⢀⠴⠚
⠀⠀⠀⢇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⢤⣀⠀⡠⠊⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣈⠑⠒⠶⠿⠖⢺
⠀⠀⠀⡟⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⡎⢸⣙⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠠⠔⠁
⣄⠠⡴⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⡴⠃⣠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸
⠀⠀⠀⢰⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⠀⠀⠀⢠⠋⠀⠀⠈⠐⠁
⠀⠀⠀⠸⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⠀⠀⠀⠘⣄⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠲⡄⠀⠀⡌⣯⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣠⠞⠉⠁⠈⠉⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠊⠉⠀⠀⠀⢸⠃⢀⠼⣦⣌⢮⠫⠹⣦⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢒⣒⣛⣿⣂⢃⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⠳⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠁⢄⣺⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⢠⠚⣧⣀⢀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⢻⢒⠲⠲⠲⢶⠶⢶⣻⠃
⠀⠀⠀⠀⠀⠈⠓⢀⣊⢿⣬⢊⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣢⣡⣠⢠⢡⢂⣶⠁
⠀⠀⠀⠀⠀⡼⠋⠉⠁⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡬⠛⠛⢛⣛⠻⠄
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠥⠒⠋
⠀⠀⠀⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⢏⢫⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⡟⡸⡷⣤⣀⢀⢀⣀⣤⢞⢧⣇⢀⠦⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⣠⣴⡧⠲⢄
⢠⠭⠸⣧⡑⡑⡑⡘⡉⠍⣌⠆⢌⡿⠿⣿⠌⠘⠞⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣀⣤⣶⠿⠛⠁⠀⠀⠀⠑⢄
⢘⣃⣀⢘⣳⣽⣐⡈⡀⣈⣋⣼⣟⣉⣉⣿⡌⠎⡜⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠸⣷⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠐⠠⠤⠀⠉⠛⠿⠿⠿⠯⠵⢦⡴⠒⢺⡷⡐⡠⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠈⠉⠀⠂⢩⣥⡬⠍⠉⠀⠀⠀⠉⣷⠱⡁⣱⣿⣤⣤⣤⣤⣴⣶⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⡩⠳⡶⡤⢤⡤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠠⠀⣻⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡥⢥⣁⡙⡱⡀⠃⣸⠃⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠉⠭⠿⡿⡏⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣚⣋⢽⠿⢶⣷⣽⡏⣰⠇⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⢨⢽⣏⣬⠺⣇⠀⠀⠀⠀⢠⡾⡋⠠⠡⠀⠉⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢹⡁⠉⠙⠛⢫⠩⠭⣰⠟⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⣿⣣⠐⠹⣆⠀⠀⠀⣼⣵⣶⣥⣥⣤⣠⠄⢄⢾⡆⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣐⣒⠘⣷⣠⠀⠜⠷⣄⣠⠯⠥⢶⠶⠿⠿⣿⣆⠆⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡒⠚⢧⣆⠊⢌⣼⠃⠀⠀⠀⠀⠉⣈⣉⣿⣾⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠛⠋⠁⢠⡞⠉⠙⠂⠒⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⢤⠶⠶⠚⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢣⣶⠆⢠⠎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣻⡙⠘⠀⠂⠀⠌⡌⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠂⠀⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⡀⠀⠀⠈⠉⠙⠛⠶⣾⡾⡚⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣀⢻⣆⢌⡘⠙⣦⡀⠀⠀⠀⠀⠀⠀⣀⢴⠞⢋⢃⢃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⠀⠹⢿⡄⠀⠈⠟⣦⡀⠀⣠⡴⡟⠉⢀⡀⣦⢾⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠬⢿⣎⠌⡐⡙⡝⠛⠱⠐⣐⣰⣾⢛⣋⣹⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢙⣾⣝⣐⣄⣠⣤⡷⠛⣉⢭⠥⠄⣿⢇⢞⢳⣤⣀⣀⣀⣀⣤⡴⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠤⠀⠚⢛⡛⠉⠙⠋⠁⠈⠘⠑⢛⣛⣿⣦⢧⢠⢩⢁⢉⢋⣦⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠤⠶⠖⠒⠚⠀⠀⠀⠀⠀⠀⢀⣒⣛⣛⣛⣿⠷⠞⢋⣉⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠩⠭⠥⠤⠴⠖⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠔⠂⠉⠉⠉⠙⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠰⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⣀⠤⠼⡖⠒⠠⢄⠀⡰⠁⠀⠀⠀⠀⠀⢀⡠⠼⠖⠒⠒⠒⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢘⡠⠚⠁⠀⠀⠀⠑⢄⡀⣀⣷⠶⠭⠉⠒⡲⠞⠛⠳⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢠⢎⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠇⠀⠀⠀⡜⠀⠀⠀⠀⠈⡝⢢⠀⠀⠀⠀⠀⠀⠀⠀⠗⢄
⠀⠀⠀⠀⠀⠠⠁⢸⠀⠀⠀⠀⠀⢠⡞⠁⠀⡜⠀⠀⠀⠀⢇⠀⠀⠀⠀⣰⠁⠀⢡⠀⠀⠀⠀⠀⠀⠀⢠⠈⢆
⠀⠀⠀⠀⢀⠃⠀⠀⢧⠀⠀⠀⢰⡟⠀⢀⡌⠤⠄⠐⠒⠂⢄⠑⠒⠒⠈⣸⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠣⡀⠀⡞⣠⠾⠁⠀⠀⠀⢀⠔⠉⠀⡏⠱⡔⢊⠃⠀⠀⠀⠗⣀⡠⠒⠈⠉⠐⣦
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⢲⡏⠁⠀⠀⠀⠀⢠⠃⠀⠀⢀⠃⡌⣰⢂⡠⠔⠒⢲⢠⡏⠀⠀⠀⠀⢀⠃⠱
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠀⠑⠢⠄⣀⡀⢸⠀⠀⢀⣎⡠⣗⡝⠁⠀⠀⢀⣾⣿⠒⠒⠢⡀⠀⡸⠀⠀⢳
⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⢀⠹⠀⠀⠀⠀⠀⠀⠉⢇⢉⠍⡠⠊⢧⠁⠀⠀⢠⠎⣸⠛⢄⠀⠀⡁⢠⠃⠀⢀⠛
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⡠⢛⠾⣁⣠⠛⣄⡠⠔⠏⡔⠋⠀⠈⠑⠤⣧⣆⡀⠔⠋
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠣⡀⠀⠀⡠⠎⢠⠃⠀⡰⠉⠉⠙⢄⣠⠋⠀⠇⠀⠀⠀⡸⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⠀⠀⠀⣈⠤⡊⠀⢠⢃⡠⠊⠀⠀⣀⠔⠊⠑⡦⣼⢀⡀⠤⢊⠃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣖⣈⠩⠤⠤⠘⠓⡾⠥⠤⠤⠒⠈⠀⠀⠀⠀⢱⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⢀⡠⠤⠒⠈⠁⢱⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠱⣄⠀⡰⠀⠀⠀⠀⣠⠊
⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠹⠓⠂⠐⠒⠈
⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠘⡄⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠌⢦⡠⠤⠒⠁⠀⠀⠀⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠤⠤⠤⠤⠒⠒⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢀⡠⢲⣀⢮⠙⠓⢶⣄⢇⠰⠁⠈⠑⠢⠤⠄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠞⠁⠐⢺⠀⠀⠉⠉⠀⠀⠙⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣀⣀⡠⠤⠤⠄⠤⠤⠤⣀⡘⢄⠀⠀⠀⣘⣀⣀⣀⡀⠀⠀⢠⠃⠴⠭⢄⣱⠀⢀⣔⣂⣄⠀⢰⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠂⢴⠁⠀⠀⠀⠈⡆⢠⠃⠀⠀⠀⠀⢸⠉⠉⠉⠉⠛⠓⢺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡸⠔⠊⠉⠉⠉⢁⠇⡏⠉⢲⢶⡊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⠒⠤⣀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢀⡠⠊⠀⠈⢆⠘⡄⠈⠑⠒⠒⢊⠇⠀⣠⠎⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘⡄⠙⠤⣀⣀⠴⠃⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣷⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡼⠃⠘⢧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢺⡀⠀⠀⢀⡗⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣄⣀⠀⣿⠀⠀⠀⠀⠀⠈⠳⠦⠴⠞⠁⠀⠀⠀⠀⠀⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿
⠀⠀⠀⢠⡟⠁⠀⠙⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠁
⠀⠀⠀⠘⣧⡀⠀⣠⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡀⠀⣀⣼⣿⣿⣿⣿⣿⣧⣀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣹⣿⣟⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣽⣿⣏⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠉⠀⠉⢻⣿⣿⣿⣿⣿⡿⠉⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋⠁⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣄⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⣿⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢳⡄⠀⡼⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⢿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣃⠀⠀⠀⠀⠀⠙⠋⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠘⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠙⠀⢀⠈⠁⠀⠺⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢛⢫⡀
⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢀⡀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠉⠁⠛⠑⢯
⣶⣼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡀⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⡶⠖⠒⠀⠀⠀⠸⠆⢀⡀⠤⠀⠒⠐⠒⠂⠠⢸⠁
⣎⣿⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⠇⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣍⣩⡆⠀⠀⠀⠀⠀⠴⡀⠣⡀⢠⡄⠀⠀⠀⢴⡄⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠠⣀⣤⡀⠀⠀⠀⠸
⠉⠀⠀⠀⢀⠀⢀⡀⠈⠅⠀⠀⢀⠀⢠⠼⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠋⠁⠀⠀⠀⢀⡀⢐
⠀⠀⠐⠇⢀⡠⠀⠀⠀⠀⢀⡀⠛⠛⠛⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⢒⣶⠶⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⡀⡠⠀⠠⢰⡀⣴⠶⠶⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠪⠟⠷⢆⣤⠦⣀⣤⠂⠀⢦
⠀⢀⣤⠀⠀⠀⠓⠀⢤⠀⣌⡁⠀⠀⢊⣡⡍⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣴⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⣄⠀⠀⡀
⠀⠈⠙⣄⢀⠀⠈⠁⠀⠀⡏⠉⠀⠀⠨⠉⠹⠶⣤⣿⣤⣴⠆⠠⠲⢲⠚⠧⠤⠤⢀⣀⠀⣿⢀⢀⡄⣀⡀⠢⣠⡏
⠀⠀⠀⠍⣧⢀⠀⡈⠁⣁⣁⠀⠀⠀⠀⠀⠁⠀⠈⡈⠁⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⢈⡧⠒⠻⠙⣷⠉⠻⣏⠑⠂
⠀⠀⢠⠆⠁⠘⠉⠉⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠡⡀⠀⢈⠁⡈⠐⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡟⢿⡄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⢾⠋⠩
⠀⠀⠀⠈⠉⠀⠀⢉⠖⠤⠀⢃⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⠋⠀⠀⠹⡄⠀⠀⢀⠶⠦⠐⡀
⠀⠀⠀⠀⠀⠙⠀⠀⢟⣿⠶⣾⡄⠀⠰⡖⠋⢹⠀⢀⣴⠁⣠⡄⢀⡀⢰⡀⢠⠿⠀⠂⡐⠉⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢠⠒⠒⠉⣿⣾⡟⢼⡧⠤⠧⠀⠺⣤⠟⠁⠚⠛⣣⠾⠿⠈⠛⠋⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣴⣤⠈
⡀⣀⣠⠀⠀⣤⡄⠀⠀⠙⠛⠻⠦⠄⠰⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠈⠛⠷⠚⠀⠀⠀⠀⠀⠸⠋⠠⠤⠀⠂
⠅⠈⠀⠂⠀⠼⠤⠊⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠖⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡠⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠂
⠀⣶⠄⠁⠀⣀⣥⠰⠃⠀⠈⢡⠀⠌⠀⠀⠀⠀⢀⣀⢀⢀⣠⣴⠶⢶⡀⢀⡀⠀⠀⠀⠀⠀⠰⠀⠶⠂⠀⠀⠀⠀⡀⠀⠀⠓
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉

⣿⣿⡿⣿⣿⢿⣿⣿⣿⡿⣿⢿⣿⡿⣿⣿⣿⢿⢿⡿⣿⣿⡿⣿⢿⡿⢿⡿⣿⡿⣿⣿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⢛⣿⣿⣿⣿⣿⣿⣛⠛⠛⠯⠭⠭⠿⢟⣛⣻⣿⣿⣿⣿⣿⠿⠭⠽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡿⡿⣿
⣿⣷⡇⣿⢧⡏⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡘⣇⣿⡇⣧⣿
⣿⣿⢻⣽⡼⣸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⡇⡇⠈⡇⠃⠿⠃⢹⠹⢹⢿⣿⣿⣿⣿⣿⣿⣿⣎⢧⢻⢸⣧⣿⣿
⣿⣿⣿⣿⢳⣿⣽⣿⣿⣿⣿⣿⣿⠟⡇⠏⢸⠀⠃⠁⠀⠁⠀⠀⠀⢸⠀⠸⠀⡇⡿⣿⣿⣿⣿⣿⣿⣞⣾⣾⣺⢸⣿
⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠾⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⡀⡀⣠⢀⣀⡄⡀⡀⣀⣀⢀⣀⢀⢀⣀⡀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄
⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⡀
⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡀
⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧
⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇
⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟
⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟
⠀⠀⠀⠈⢿⣿⣿⣿⣦⠀⠀⠀⠀⢾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⣠⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⢰⡇⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣾⣿⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⣡⣾⣿⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣴⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣄⢠⢣⣿⣿⣿⣿⠟⠋
⠀⣸⣦⡄⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⡤⢊⣡⣴⣶⣿⣿⣿⣿⣶⣝⣿⣿⣿⠟⠁
⠀⢿⣿⣿⣿⣿⣷⣦⣭⣑⣒⣲⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣤⣥⣵⣿⣿⣿⣿⣿⣿⣿⡇⠀⡰⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠉⠛⠙⠛⠉⠉⠀⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣿⣿⠏⠀⣿⣿⣿⣝⣿⣿⡟⣿⣿⣬⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣇⠀⠐⣿⣿⡿⢿⣿⣿⣿⣝⠏⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡞⣿⣿⣿⣿⣿⣷⢠⡀
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣯⠝⠋⡀⠀⠹⣎⣛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⢸⠁⣽⣿⣿⣿⠹⡟⢰⡇
⠀⠀⠀⠀⠀⠀⠸⠛⣿⡿⠇⠀⠐⠀⠀⠀⠹⠿⠟⠻⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⡟⠀⢱⣿⠻⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⡌⢠⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡸⠁⠀⠀⢳⡀⠙⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠻⠿⠿⠃⢀⠜⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⠁⠀⠀⠀⠀⠙⢦⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠲⡟⠲⡞⢇⢀⣼⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡄⠀⡘⣦⡙⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⡿⣉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⡼⣿⣿⣿⣿⣿⣧⢻⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢤⣴⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣎⠭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠘⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⠿⢿⣛⣻⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠾⣄⣀⡰⠤⠜
⠀⠀⢪⡀⠀⠀⠀⣀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠛⠉⢩⢤⡍⠘⠩⠞⠁
⠀⠀⠀⠈⠉⠓⠚⠁⠰⡀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠼⠤⠂
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣄⠀⠀⡸⠀⠀⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡁⢀⠘⠦⠔⠁⠀⡎⠀⠀⠀⡖⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡸⠀⠀⢣⣀⡀⣀⣠⡀⠀⠀⠀⠁⢙⠆⠀⠀⠀⠈⠢⠤⠴⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⢡⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠒⢦⠀⠀⠀⠀⢠⠒⠒⠦⡸⠀⠀⡞⠁⠀⢠⠒⠒⠦⡀⠀⠀⠀⠀⠈⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠙⠦⣀⡴⠀⠀⢀⠇⠀⢠⠔⠢⡄⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠲⠤⠜⠁⠀⠀⠀⠈⠓⠒⠁⢸⠀⠀⠀⡠⠤⣀⠠⣎⡁⠀⢠⠃⠀⠀⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠘⣄⠀⡸⠀⠀⠉⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠉⠉⡇⠀⠀⠺⡉⠉⠉⢹⢄⣀⣀⣀⡸⠀⣇⣀⣀⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⡀⠀⠀⢀⡵⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠶⢄⣀⠞⠀⠀⠈⠁⠈⠉⠀⠀⠀⢇⣀⡠⢦⡀⠀⠀⠀⢠⠊⠉⠲⠤⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠀⠀⠀⢸⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠊⠙⢦⠀⠀⢀⠴⠶⠦⢄⠀⠀⡃⠀⠙⠚⠀⠀⠀⠀⠀⠙⠒⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢣⡀⠀⠀⡸⠀⠀⡇⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠂⠔⠃⠀⠘⠣⠤⠴⠚⠉⠀⠀⢘⠄⠀⡏⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⢀⣠⠴⠶⠶⠤⣄⡀⣼⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⣿⡏
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠉⠀⠀⠈⠙⠛
⠀⠀⢻⣷⣄⣀⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠛⠛⠛⠛⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠛⢿⣦⠀⠀⠀⠀⠈⠙⠒⠒⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣄⣀⣀⣀⣀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢠⣾⣁⣀⣀⡀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⠿⠿⠿⠏