Get well soon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡇⠀⠀⠀⠀⣠⡶⣦⠀⠀⠀⣀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢞⠻⣄⠀⠀⢰⣿⠁⠉⠀⣀⣀⠀⣿⡇⠀⠀⠐⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠃⠤⣀⠀⢸⣿⠀⣿⢰⣿⣫⠆⣿⡇⠠⢖⣸⣿⢂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣻⣷⣧⢀⣨⡉⠸⣿⠀⣿⢸⣿⠋⢠⣿⣀⠆⡎⢀⣈⡆⣣⣨⣄⡎⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣧⣭⣔⣁⠙⠦⠟⠈⢿⡴⠋⠙⣋⣀⣘⣯⣟⣭⣄⡀⢀⠈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣀⣘⣒⡂⠉⢩⡉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⣉⠉⠉⠉⢐⣒⣢⣬⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠾⠀⠀⢸⡇⣾⢀⡇⣿⠛⠃⣶⡆⠀⢸⣿⠀⠀⠀⠐⠷⣺⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡯⠭⠀⠀⢸⣧⡟⣿⠁⣿⠂⠀⣿⡇⠀⢸⣿⠀⠀⠀⠈⠭⢽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠥⠀⠀⠀⣿⠀⠻⠀⠿⠤⠄⠸⠧⢤⠘⣿⣀⠀⠀⠀⠬⣽⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⢭⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⢤⣤⣤⣤⣭⣅⣀⣀⡭⡏⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⣴⠦⢀⣤⣠⠀⣠⢤⡀⣴⣤⣶⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢀⠀⠘⢿⣄⣾⡇⢙⢿⡟⠈⡟⣿⠃⣿⢀⠀⠀⡀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⣾⣿⠈⠓⠊⠀⠙⠚⠁⠙⠀⠻⠊⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠔⡫⠊⠀⠑⠝⠂




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⠀⠀⣀⣀⡀⠐⣾⣿⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢨⣿⣿⡀⣼⡟⢀⡿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣥⡟⢸⣿⣷⣿⡷⠚⠁⣸⣿⣿⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡞⢹⣿⠀⠙⠷⠤⠞⠁⠻⣿⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧⡾⠃⢀⡀⣀⣀⡀⢀⣀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⢠⣿⡇⠀⢸⣿⠄⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⣶⡀⢰⡏⢸⣿⠗⠂⢿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡏⢿⣇⣼⠃⢸⣿⣀⡀⢸⣿⢀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠈⠛⠋⠀⠀⠉⠉⠁⠈⠉⠉⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⢻⣶⠀⠀⣤⡶⣦⠀⠀⢀⣶⠶⡄⢀⣤⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⡿⠀⣴⣿⡇⢸⠀⣀⣼⠿⣧⣿⢾⣿⠀⣰⢃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡀⢀⣼⣿⡟⠻⢾⠿⣿⡏⠀⠀⣿⢸⣿⣠⡇⢸⣿⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡏⠘⣿⣇⢀⡿⠀⢿⣧⣀⣰⠇⠈⢿⣿⠁⠈⣿⣧⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⡇⠀⠈⠙⠋⠁⠀⠀⠉⠉⠁⠀⠀⠀⠁⠀⠀⠈⠻⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⡇⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣾⡟⣻⡷⠀⠀⠀⣠⡶⢶⣦⠀⣠⣴⢬⠛⢻⡟⠉⠁⠠⠷⠐⢿⣶⡄⠀⣷⠀⢠
⠀⠀⠀⠀⠀⠻⠿⠿⢋⣤⡀⣾⡟⠀⢸⡇⣼⣿⣁⠴⠁⣼⠃⠀⡦⠘⢳⠀⠀⠀⣤⣴⠿⡀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠉⠁⣿⣧⣠⣾⣧⠘⢿⣄⣠⠎⠹⣇⡜⠁⠀⡼⠀⠀⠀⠀⠠⣤⡼⢏⠀⣴⠃
⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⢀⣬⠟⠉⢸⣿⠀⠀⠉⠀⠀⢀⣀⣠⡴⠛⠀⠀⠀⣤⠄⠀⠀⠲⠦⢿⠃
⠀⠀⠀⠀⠀⣾⡇⠸⡀⢠⡿⠁⢠⠃⢀⣿⣤⣶⠶⠿⠿⠛⠋⠁⠀⠀⣠⣜⢦⠀⠀⢀⣠⣤⣤⣀⠃
⠀⠀⠀⠀⠀⠹⠁⣠⠑⣿⡧⠒⢡⠖⠋⣿⠀⢀⡀⠀⠀⠀⠠⣤⣴⡾⡽⠊⢀⣤⠾⠛⠉⠉⠉⠻⣆
⠀⠀⠀⠀⠻⣶⡾⠏⠀⣿⡇⢠⠃⠀⠀⡏⠀⢸⠋⠀⠠⠖⠀⠙⠈⢀⣠⡴⠛⠁⠀⠀⠀⡀⠀⠀⡿
⠀⠀⠀⠀⢀⠀⢧⣴⡇⠘⣿⣜⠀⢀⠜⠁⠀⠈⠃⠤⠤⠤⠤⣖⡚⠋⠁⠀⠀⣀⠀⠀⡌⠈⣆⡴⠁
⠀⠀⠀⠀⠈⠛⠿⢿⠀⣴⠈⠻⣦⡀⠀⢀⣠⣾⠋⠑⣄⢀⣼⠉⢻⣶⢾⡷⠋⢈⡷⠀⠀⢰⡏⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢤⣌⣻⡟⠀⠀⠈⣿⣖⢩⣿⠁⠀⠁⣹⢸⠀⠀⢺⡿⢸⡇⠀⣾⠃⠀⢀⡾⢰⣿⣛⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠂⢀⠞⠀⢻⠈⣿⠀⠀⣠⠃⠸⡀⢀⡼⠃⢸⡇⢰⡇⠀⣠⠞⠁⠈⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⠞⠀⠈⠙⠊⠁⠀⠀⠉⠉⠀⠀⠘⠀⠀⠳⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠈⠛⠂⠀⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠿⢦⠄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⡑⠀⠀⢀⣤⡖⠢⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡔⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣿⠀⠀⣿⡇⠀⠀⠀⠘⠯⢉⠳⣼⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠊⠉⠙⠀⢠⠴⠛⠻⢿⠆⠀⠀⠀⠘⠦⣸⣿⢀⠠⠃⠀⠀⢀⡈⠁⠊⢵⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⠛⠅⡀⢰⡏⠀⠀⣤⡄⠀⣠⣾⠟⣳⠀⣿⡏⢀⡀⠀⠐⠀⣬⣴⣖⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣀⣤⠀⢾⣧⣀⣰⣿⣷⠀⣿⣯⠔⠃⡘⣿⡇⠘⢿⠀⠶⠺⢷⠴⠏⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠘⠿⣿⡿⠹⣿⡟⢿⣷⣀⡠⠀⠘⠷⠤⠃⠀⠀⠘⠂⠀⠋⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣀⡀⠀⣠⡖⠀⠀⢢⠀⡔⣿⡇⠀⣉⣭⣴⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢻⡣⡀⣿⡇⠠⣶⠟⡘⠀⢸⠃⣼⡏⠋⠛⢸⢋⣈⡏⣿⡏⣿⣷⠀⠀⠉⢠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠻⣇⢻⣧⡀⠀⠀⠣⢀⠟⠀⠻⣷⣼⣦⣾⣦⣿⣧⣬⣧⣭⠟⠀⠀⠀⠀⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣉⡈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢛⣛⣛⡉⠀⣠⡀⠀⣀⡀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⢿⡷⢦⠈⠻⢿⣦⡀⠀⠀⣠⣶⡟⠲⣄⢴⣿⠋⠀⢹⡞⢹⣿⠋⠙⣿⠀⠐⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠰⢷⣴⣏⣢⠀⠀⠀⠙⣿⣶⠊⣿⡏⠀⠀⢹⢸⣧⠀⠀⢸⠀⢸⣿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠡⠃⠀⢰⡷⠆⡠⠛⣿⡇⣿⡇⠀⢀⡜⠘⢿⣷⡴⠋⠀⢸⣿⠀⣸⠃⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠁⠀⣿⠃⠙⠻⠶⠊⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⡟⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠘⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⣨⠉⢵⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠂⠀⠀⠀⢄⠀⠀⢀⢢⡀⠐⠚⣦⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣷⠀⠀⠈⠘⣦⣀⠀⠤⢷⠆⠀⠨⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠠⣤⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡁⠑⠀⡀⢀⠀⠐⣉⠹⠎⣉⡽⠠⡼⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⣧⡠⠛⣳⠚⢣⢠⣵⣜⠉⡤⣐⣺⣗⠀⢀⣠⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣐⠷⠟⢤⡷⠚⣷⠒⣇⣾⣴⣧⠔⣵⣾⣿⣯⣧⣼⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢪⡾⢿⡰⠉⠛⠛⣠⡉⢩⠍⠑⡶⠀⠀⠀⠀⠀⠉⠺⠟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠼⡆⣀⣀⠀⠀⠐⣇⡆⢸⡂⢀⣇⡀⣐⠀⢆⡤⣀⣀⠄⠐⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢧⣷⡴⣲⡦⠄⣴⠤⠄⢲⠏⡄⢋⡯⠻⣠⢋⡥⠂⠚⢃⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢾⣾⣿⣿⡿⠦⠮⠾⠛⢚⠉⠛⡟⠛⠛⠷⢿⣾⣶⡆⣀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⢳⡎⠀⣄⡆⠀⠀⣆⣆⡤⢀⣏⠀⢸⡀⠀⣇⡀⠀⠀⠀⠈⠛⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠭⢴⣤⣞⡇⠀⠀⠸⠙⢃⠈⠓⢀⠤⣭⣖⣴⣅⡠⣀⣠⡀⣯⠔⡀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⣌⣿⠿⣿⣷⡂⠀⠐⠚⠑⠶⣋⡻⣿⡿⣷⣞⠋⣵⣮⣤⡷⣶⠲⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁⢺⡍⠁⠀⠸⣙⠠⡏⡧⢠⠖⡝⢈⡍⡍⠉⠓⠛⢺⠖⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠐⣋⣀⣙⣁⡘⠶⠃⠸⠟⠇⠀⠀⠀⡄⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠘⣯⣾⢿⣍⣚⣉⡀⠠⠹⠖⠲⠆⢤⠤⣤⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠦⣬⢹⣋⣷⣤⣶⣀⣀⠽⠶⡶⢺⠟⠳⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠃⠀⠉⠎⠉⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣠⣴⣿⡷⠶⠒⠒⠒⠦⡄⠀⠀⠀⠀⠀⠀⣰⣿⠃⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢉⣉⠉⢩⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⡟⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠂⠀⣰⣿⣻⠃⣾⡟⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣿⡿⠁⢰⡟
⠀⠀⠀⠀⠀⠀⢰⡟⣡⣾⣿⢰⡿⠛⠁⢸⣿⠀⠀⢠⣿⠋⠀⠀⣶⡆⣠⣾⣿⢂⣾⡿⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠷⢋⣿⡿⢻⡏⢀⠀⢸⡇⠀⠀⣿⢏⣾⡆⢰⣿⢡⣿⡿⠋⢸⣿⠃⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⠁⠀⠉⠉⠀⠀⠈⠀⢸⣿⣾⣿⢃⣿⠇⢾⣿⠁⣠⢿⣿⠀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⣼⠃⣾⡇⠀⠀⣀⣤⣴⣦⡀⠀⠸⡿⢹⣿⣿⠏⠀⠈⠻⠾⠃⠸⣿⠾⠛⣿⡇⣠⠏⠀⣼⡗
⠀⠀⠀⠀⠀⢰⡏⣸⡟⠀⣠⣾⣿⠿⠛⠛⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠈⠛⠋⠀⢸⣿⠟⠁⢀⣀⡀⠀⠀⣠⣶⣦⠀⠀⣠⣾⣷⡀⢠⣶⣆⣴⣦⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠛⠉⢀⣾⣦⣾⡿⠛⡹⢀⣾⡿⠋⣼⣧⣿⣿⢫⣾⠏⠀⡀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⣰⣿⡿⣿⡟⢁⡾⠁⢸⣿⢁⣾⠏⣸⡿⠁⣿⡏⠀⣰⡇⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠶⢦⡴⠶⠟⠛⠉⠀⠙⠓⠋⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⣿⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣴⠏⡈⣠⡔⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡈⣠⡖⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠈⠻⢸⠟⣿⡁⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⠟⢿⡁⢻⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣀⢁⣴⠂⣹⡟⠁
⠀⠀⠀⠀⠀⣧⢰⠆⣃⣴⢠⡿⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠆⣦⡤⢰⡟⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⡿⢹⣏⠀⢻⠁⢀
⠀⠀⠀⠀⠀⠛⣘⣃⣘⣃⣘⣃⣻⡀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠻⠘⠆⠘⠇⠺⠃⣿⠀⣴⠀⠀⠀⠀⠀⠐⣦⢰⡆⠸⢠⡤⢰⡿⢰⡟
⠀⠀⠀⠀⠀⣿⣝⣏⣽⣏⣿⣉⢩⣿⠀⠀⠀⠀⠀⠀⠈⢻⣆⣾⠃⢲⡟⠰⣿⢷⡗⠠⠇⠀⠀⠀⠀⠀⠀⢿⡼⣇⠀⢿⡁⢾⡇⣿
⠀⠀⠀⠀⠀⠉⠉⠉⢉⢉⢉⡉⠍⠉⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠁⠀⠁⠀⠉⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣦⢤⣤⡤⣶⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⣀
⠀⠀⠀⠀⠀⣴⡖⠐⢀⣴⠂⢻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣾⠏⣀⣠⡖⣹⡟⢠⣄
⠀⠀⠀⠀⠰⣿⣠⡷⠸⡇⠠⣿⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⣿⠋⣠⣀⣶⠏⢩⣿⠏⠀⠀⠀⠀⠀⠀⠀⣙⠸⣏⢙⠀⠿⢠⡬⣩⡄
⠀⠀⠀⠀⠀⡀⠉⢸⡆⡿⢰⣴⢂⡿⣸⠃⠀⠀⠀⠀⠀⠀⠈⠋⠸⠛⠘⠯⠐⢙⡛⢈⡀⠀⠀⠀⠀⠀⠀⢸⡆⡏⠸⣾⠇⣾⢃⡟⠀⠄
⠀⠀⠀⠀⠀⢠⡄⠜⣃⠛⣀⠓⣘⢃⠿⠀⠀⠀⠀⠀⠀⢹⣧⢸⡇⠸⣴⡖⢠⣿⢡⡿⠁⠀⠀⠀⠀⠀⠀⡨⠇⣛⡀⢉⢄⣹⣘⡇⢠⡄
⠀⠀⠀⠀⠀⡈⢻⢸⡃⠱⡏⠹⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠷⠀⠙⠃⠹⠇⢺⡇⠀⠀⠀⠀⠀⠀⠈⠻⡦⣏⠈⢿⠈⣿⢻⠃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⡴⣿⠒⠲⠤⣀⣀⣼⠇⠀⢀⣀⠀⠀⢀⣼⠃⢠⡟⠛⠉⠛⠳⢦⣄⠀⢀⡤⢄⠀⣠⡶⡆
⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠈⠚⠋⠀⣀⣀⠀⣽⡟⠛⡛⠉⠁⠀⢠⣿⠃⠀⠀⠀⡶⣦⠀⣀⣤⡈⣹⡟⠓⢫⣾⢋⡼⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠰⢲⠖⣾⣃⡾⢰⣿⠀⠀⣿⠀⠀⠀⣿⠇⠀⢠⡾⠀⢹⠗⣾⢏⣴⢳⡿⠀⠀⣿⠛⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣆⣀⣠⠞⠘⣿⡉⣠⠾⣿⣀⣰⠏⠀⠀⠀⣿⡀⣠⠻⡇⣠⠏⠈⢿⡉⣠⠾⣇⣠⠜⢿⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠀⢀⣬⠭⢄⠀⠀⠀⠀⠈⡉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡴⢦⣀⠔⣦⠀⠀⠀⣰⡟⣱⠒⣺⠷⢤⣄⣤⡴⠇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣰⠋⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⢻⠀⢸⠀⠀⠀⢹⣧⠀⠛⠉⢀⣀⡀⠀⢀⣠⣄⠀⣠⡗⢠⠞⠉⣼⡇⠀⠀⢠⡇⣰⠟⢉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠁⣸⠀⠀⢀⣀⠹⣧⠀⣰⡟⠙⣿⢶⣾⠋⢹⢋⣿⡵⠃⠀⣼⡟⠀⡄⠀⢸⡇⢁⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⣾⠁⢠⣿⠀⣿⠁⣰⠇⢾⡇⢠⠏⢸⣿⠃⠀⠀⣿⡇⣸⠇⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⠀⠈⠛⠁⠀⠈⠓⠋⠀⠀⠛⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢄⣄⡀⡀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡤⣄⠆⡭⠶⠞⢭⠟⠁⠼⠬⣍⡺⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⡵⢖⡒⠍⠀⠁⠁⠈⠀⠀⠀⠈⠁⠂⠇⠊⢉⢤⣁⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡦⢖⠞⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡌⡪⣳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⣡⠞⢥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡬⣄⢂⣀
⠀⠀⠀⠀⠀⠀⢀⣐⡂⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⢷⢲⡂
⠀⠀⠀⠀⠀⣤⢻⡥⠧⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠒⠢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠚⠦
⠀⠀⠀⠀⠘⠦⡟⠌⠁⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⠀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⡲⡞⣥
⠀⠀⠀⢀⣸⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠰⠖⠲⢶⠚⠀⣿⡔⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡛⣶⠂
⠀⠀⢠⡛⡵⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⢀⡼⠀⠀⠈⠛⠋⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠺⠄
⠀⠀⠲⢹⡣⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢱⡔⣂
⠀⠀⢐⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣎⢗⡭
⠀⠐⣟⡜⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠈⢿⡇⠀⢹⣯⠀⠈⡛⠁⠀⠀⠀⢸⡏⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡁
⠀⢙⣰⡧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠈⣿⡄⡌⢻⣇⢠⠁⣰⠋⡿⠃⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣠⠄
⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢿⠇⠀⠹⣧⡤⠀⠸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⢥⡓
⠀⢀⣼⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡝⠁
⠀⢨⡑⡧⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢉
⠀⠐⠒⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠒⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⣟⢨⡅
⠀⠀⠀⣱⠆⡀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⡀⠀⠀⠀⠀⡤⠶⣄⠀⢀⠴⢦⡀⢠⣆⣠⣆⠀⠀⠀⠀⠀⠀⠀⠐⢪⡵⠓
⠀⠀⠐⡳⢥⢔⡂⠀⠀⠀⠀⠀⢀⠀⠉⠉⠛⠛⢷⡄⢸⡇⠀⣿⠀⣿⠀⢸⡇⢸⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠂
⠀⠀⠀⠩⠘⠮⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⢀⠇⠀⠙⠊⠁⠀⠈⠛⠉⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠬⢱⢃⡓
⠀⠀⠀⠀⠐⣱⠄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣡⠷⠁
⠀⠀⠀⠀⠀⠿⠸⡜⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢢⠘
⠀⠀⠀⠀⠀⠈⠥⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢓⡴⢣⡛
⠀⠀⠀⠀⠀⠀⠀⠀⢑⡇⣜⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠵⠞⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡜⢦⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⣩⠞⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠐⢲⡲⣕⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠤⢠⢀⢮⡭⡆⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡬⢙⠒⢡⡴⡫⣽⣘⣀⢀⣰⣡⣺⣛⢩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⠡⠖⠆⠈⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢀⠜⠁⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠄⠊⠁⠀⣰⡿⢁
⠀⠀⠀⢀⠤⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠒⠂⣀⡀⢸⣿⠁⠀⠀⠀⢠⣿⡧⠊
⠀⣠⠞⠁⢠⡶⠋⡦⢀⠀⠀⢀⣴⠶⡄⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⡴⠻⣷⠀⠀⢀⣤⠀⠸⣿⡇⠀⣰⡿⢁⠏⣿⣿⠀⠀⠒⠀⣾⣿
⣰⠁⠀⢀⣿⡇⠀⢣⣿⠁⢠⣿⠇⣠⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡄⠀⢸⣿⠀⠀⢙⡗⢺⣿⠏⠁⠀⣿⣿⠀⠀⠀⢰⣿⡇
⡇⠀⠀⢸⣿⡇⠀⢸⣿⢀⣾⣿⡋⠁⠀⣰⣿⣷⠀⢰⠁⠀⠀⠀⠀⠃⠀⣿⡇⠀⣼⣿⡀⠀⡼⠀⠘⣿⠀⠀⢀⣿⣿⡀⠀⠀⢸⣿⡇
⠛⠀⠀⠈⢿⣇⢠⡿⣿⡏⢸⣿⡇⠀⢠⠇⢻⣿⠀⡎⠀⠀⠀⠀⠀⠀⠀⠹⣿⢠⡏⢿⣇⣰⠃⠀⠀⠹⣆⢀⠞⠘⣿⣇⠀⠀⡼⣿⡇⠀⣸
⠀⠀⠀⠀⠀⠉⠋⣠⢿⣷⠀⠻⣷⣀⡞⠀⠈⢿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠴⠁⠈⠻⠴⠃
⠀⠀⠀⠀⠀⠀⣰⠃⠘⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⣄⠀⢀⡔⠈⠐⡄⠀⡞⠁⠈⠳⡀⠀⠀⠀⢠⠎⣹⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠚⠀⢸⢀⣀⠀⢸⠸⡇⣤⡄⠀⡇⢀⡀⢠⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠈⠓⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⣨⣿⡟⠀⢸⣀⣽⣿⠇⠐⡏⠀⣿⡏⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡊⠀⣿⡏⠀⡾⠁⢸⣿⠀⣰⠃⠀⣿⡇⠀⣸⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢻⡇⠀⠈⠳⠞⠁⠀⠀⠙⠚⠁⠀⠀⠈⠀⠀⣿⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡼
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣖⣶⠀⢰⣶⡄⠀⢀⣤⣤⣤⡀⠀⢰⣶⣶⣦⣄⠀⠀⢠⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⠅⢠⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣷⡀⢸⣿⡿⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⠃⢸⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⠀⢸⣿⠀⠘⢿⣿⣿⣿⡿⠁⢸⣿⡿⠟⠋⠁⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠈⠉⠀⠀⠀⠉⠛⠉⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⡴⣰⠛⢦⢠⡆⠀⢰⠀⠀⢰⠒⠒⣴⠒⠂⠀⡖⠒⠂⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡜⠀⣿⠀⠘⣾⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢿⠀⢀⡏⡇⠀⣼⠀⠀⢸⠖⠂⣿⠶⠆⠀⡷⠶⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠘⢦⠞⠀⠙⠖⠃⠀⠀⠸⠀⠀⠹⠤⠶⠆⠳⠤⠶⠘⠧⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢲⡀⡞⠛⠃⠘⠛⡟⠉⠘⠛⡟⠉⢰⠛⠛⠀⣿⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⡇⠀⠀⠀⢠⡇⠀⠀⠀⡅⠀⢸⠀⠀⠀⢿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢾⡁⡷⠶⠆⠀⠈⡇⠀⠀⠀⡇⠀⢸⠶⠖⠀⢹⣎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⠃⠹⠶⠒⠂⠀⠇⠀⠀⠀⠇⠀⠘⠦⠖⠒⠘⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢹⡟⠀⠀⢀⠀⣴⣆⠀⢠⢀⣾⢇⠀⠀⠀⠀⠀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢀⡾⠃⠀⠀⠋⢸⣿⢸⡆⠇⣸⣿⠘⡆⠀⣾⣇⢸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠞⠁⠀⠀⠀⡠⣿⣿⠀⡇⠀⣿⣿⠀⡇⠀⣿⣿⡟⠀⣿⡄⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⣠⠊⠀⢻⣿⢰⡇⠀⢹⣿⣰⡇⠀⢻⣿⠇⠀⢹⣇⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣾⡁⠀⠀⠈⢿⡿⠃⠀⠈⠻⠿⠁⠀⠀⠉⠀⠠⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣿⣆⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣿⡇⠀⡀⠈⣓⠉⠉⠉⠁⠀⠀⠀⠠⠞⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⣾⠇⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⣴⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⢀⣀⠀⣴⣶⣶⡄⢠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣰⣿⣿⢸⣿⣿⣿⢃⣿⣿⣿⡇⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣆⢹⣿⣿⠟⠘⢿⠿⢿⣿⣿⣿⣿⣆⠀⣿⣿⠇⢸⣿⣿⡟⣼⣿⣿⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⣿⣇⢀⣀⡀⠀⠀⣿⣿⠛⠻⠋⠀⣿⣿⣠⣸⣿⣿⢱⣿⠋⠉⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⡇⠸⣿⣿⣿⣿⠀⠀⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⠇⣿⣷⣄⢀⣿⣿⠃⠀⣰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⣁⡀⢹⣿⣟⠋⠀⠀⢸⣿⣿⡆⠀⠀⠻⠟⢻⣿⡟⣸⣿⣿⡿⣸⣿⠃⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣰⣿⣿⣿⣧⢻⣿⣦⣴⣶⡄⠻⡿⣃⣀⢀⣶⣶⣜⠛⢡⣿⣏⡀⢰⣿⠃⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢿⣿⣿⣿⣿⡆⢿⣿⣿⣿⠇⢀⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⣾⣿⣄⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠙⠛⣻⣿⡇⠀⣙⣛⠁⠀⠘⣿⣿⣿⣿⣿⡿⠋⠀⠀⢉⣛⣁⢿⣿⣿⡇⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣿⡿⣴⣿⣿⣿⣷⡄⠀⠈⠻⣿⣿⡟⠁⠀⢶⣄⢻⣿⣿⣇⠙⠛⠑⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢸⣿⣿⣿⣿⣿⠇⢀⣤⣤⡀⠙⢠⣶⣶⡸⣿⣮⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣏⠁⢠⣿⣿⣿⣿⠀⣿⡿⢻⣧⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣻⣿⡇⣼⣿⠁⢸⣿⠀⣿⡇⠈⣿⣾⣟⣛⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢁⣿⡏⠀⣾⣿⠀⣿⡇⠀⣿⡏⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⣿⡇⢀⣿⣿⠀⣿⣷⢸⣿⡇⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣼⣿⡟⠀⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠁⠀⠀⠙⠛⠋

⠀⠈⠢⣄⠈⠢⡀⠑⠄⠀⠀⢀⣴⡿⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤⣤⣴⣶⣿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀
⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠝⢦⡆⠀⠀⠀⠀⠀⠘⢄⡀⠀⣾⣿⣿⡿⠟⠉⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠐⠁
⠁⠀⣠⡄⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⢔⡡⠒⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⢀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠠
⣀⣴⡿⠁⠀⢀⡀⠀⠀⠀⠀⡤⢺⣤⡄⢡⣤⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠈⠳⢄⡑⠤⠀⢀⡈⠙⠛⣿⣿⣿⣿
⠈⠻⡀⠀⣰⣿⠏⠀⠀⠀⢀⢀⠀⠉⠀⠈⠛⠁⠀⢀⣆⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡄⠀⠀⠀⢈⡁⠀⣀⣨⠿⡀⠈⠿⡿⠏
⡄⠀⠈⠺⣿⠁⠀⠀⢀⡠⢊⡞⠰⣿⡆⠀⠀⠀⢀⠎⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⣷⣄⠀⠀⠻⠟⠀⠛⠛
⠓⡄⠀⠀⠈⠳⢄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⡀⠀⠀⣶⡶⠈⢎⠢⡄⠀⢀⣴
⢠⣾⣦⡀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠳⠀⣴⣿⣿
⠻⠋⠀⢈⣦⠀⠀⠀⠀⠉⠢⣀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⢀⣠⣾⣿⣿⠟
⠀⠀⣴⣿⠟⠳⡄⠀⠀⠀⠀⠈⠑⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⠟⠁
⢦⡀⠙⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠁
⠀⠉⠢⢄⣀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠨⠉⠀⠈⢉⠁⠀⠀⠀⠀⢠⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠐⠀⠀⠘⠀⠀⠀⠒⠃⠒⠑⠐⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄
⠀⠀⠀⠀⠀⡀⠤⠒⢈⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠢⠤⣀⠀⡴
⠀⣀⠤⠒⠉⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⢄⠀⠀⠄⢠⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠄⠀⠀⠀⡙⡳⠮
⠉⠀⢀⡘⠄⠀⠀⡀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠂⠀⠁⠂⠀⠘⠑⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣄⠀⢠⣶⡄⢀⢱⠁
⠀⠀⠀⠱⠘⠀⠻⠟⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠉⠀⠀⠉⣥⡈⠈
⠀⠀⠀⢀⠀⣴⣦⠀⣠⣄⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠄⠀⢿⡷⠀⠛⠑⡞
⠀⠀⠀⠀⠹⠀⠠⣄⠘⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠒⠀⠞⠀⠀⠀⠀⠀⡰⡳⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠎⠣⡀⠀⠀⠀⠀⠉⢉⠽⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠎⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⡠⠔⠊⠁⠀⠀⠀⠏⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠉⠢⣄⠘⠀⠁⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⢶⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣶⣾⣿⠿⠋⠀⣠
⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠙⡋⠉⠉⠉⠛⠛⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣴⣾⡿
⠀⣀⠔⠊⠀⠀⣠⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⠟⠀⡀⠸⠿⠀⢀⣀⣀⡀⠀⡁⠀⠀⠀⠀⠀⢀⠤⠒⢿⣿⣍⢳⣶⡦⢌⡓⠤
⠊⠀⠀⠀⢀⣼⣿⣿⡿⢿⣿⣿⣿⣿⣿⡄⠀⠀⢈⣤⣤⡀⠠⠶⠦⠭⠀⠘⡟⠀⠐⠭⠁⠤⠀⠀⠀⡇⠀⠀⠀⠀⣰⠿⣿⣦⣀⡿⠿⠸⠿⢥⣼⡟⠑
⣄⠀⠀⣠⣿⣿⡟⠁⠀⠀⠈⠻⢿⣿⡿⠃⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠚⠑⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠁⠀⠀⠹⡃⠀⠀⠀⠀⠀⠀⠁⠚
⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡀⠀⠀⢠⠃
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡋⠀⠀⠀⠀⡆⠀⢀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠑⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢈⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢑⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡤⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣠⠤⠠⢀⣀⣿⠀⠑⠠⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠞⠀⢀⣠⣀⢸⡏⠑⠒⠲⠚⢁⡆⣆⢀⡞⣴
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠁⡼⢸⡇⠀⠀⡀⠀⢸⠃⡇⢸⡇⡿⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⣀⡴⢃⠿⠮⠴⠊⠙⠒⢊⣁⠀⣿⢸⠃⢺⣠⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⢿⠁⣠⠀⠀⡠⣄⢸⡏⢈⡇⣿⠋⠀⣸⡇⠀⣠⠆
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⢸⠀⢿⠀⢀⠉⣾⠘⢷⣩⠴⠉⠓⠚⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣰⠏⠀⠈⠑⠈⠉⠁⣀⢀⣀⠤⣄⠐⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣤⠄⠀⢠⡖⠒⢦⡀⣾⠁⠀⢹⡄⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠀⠈⣩⠶⣖⢿⡁⠀⢈⡧⠻⣄⠀⠼⠁⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠐⣃⣴⠏⠀⠙⠂⠋⠀⢀⣀⠤⠐⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⢄⣀⣀⣀⡤⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠀⠀⠠⠀⠀⠠⠄


⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⢠⡴⢦⣄⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣀⣉⠙⠿⠇⠀⣿⡟⣷⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣤⠤⣼⣷⣴⡿⠿⣿⣿⡷⠀⢈⣛⠛⣁⣴⣿⡇⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢠⣶⣦⠁⢠⣾⠟⢁⣴⠆⣸⣿⠇⢀⣿⡿⠿⣿⡏⠈⣿⡶⠋⠁⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⣿⣿⠏⠀⣾⡏⠀⣨⣥⣾⣿⠏⠀⣼⣿⡇⠀⣿⡇⣰⣟⡤⢶⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠘⠿⢋⠀⢰⣿⣧⠀⠻⠿⠟⣃⡄⠀⣿⡿⢀⣼⣿⣾⣿⣶⠶⢦⣈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⠖⡋⠀⣛⠛⠻⣷⡶⠲⢾⣿⣷⣤⣭⣴⠟⢡⣶⢸⠟⢡⣶⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢠⠞⣡⣾⣿⠁⣸⠛⢿⣆⣼⡇⠇⢸⣿⡿⠿⣿⡏⢠⠟⣡⡟⠀⢟⣡⣿⠟
⠀⠀⠀⠀⠀⢀⡏⢰⣿⡿⠃⣰⡏⠀⣾⡟⢩⣿⠄⠸⠋⣴⠗⣸⠀⣴⣿⣿⠁⢰⣿⣿⠟⣷⡄
⠀⠀⠀⠀⢀⡼⣷⣌⣉⣠⣾⣿⠀⣸⡿⠀⣾⡟⢠⡇⢰⣶⣾⠏⠀⣿⣿⠏⠀⢸⣿⡿⢀⣿⡇
⠀⠀⠀⠀⠸⣧⣌⣉⣩⢿⣿⣿⡀⢉⣴⣦⣈⣴⣿⣧⣈⣋⣥⣾⡄⠙⣡⣾⣧⣈⣋⣡⣾⣿⡆
⠀⠀⠀⠀⣼⣉⣠⣾⠁⣾⠉⢩⣿⡿⢋⣭⡉⢿⡟⢩⣭⡙⢿⠏⠛⠖⠒⠒⣿⡿⣛⣋⣉⣿⢿⡄
⠀⠀⠀⠀⠈⠛⠛⠿⣶⣿⡆⠈⠿⠃⠈⠻⠇⠘⠃⢈⣛⡃⣠⠀⢀⣾⠏⢠⡿⣿⡌⢻⣍⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡞⢩⣴⠀⣿⠀⣾⡿⢂⣿⠀⣿⡿⢡⣿⠀⣾⡟⢀⣿⡇⣸⣇⣼⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣦⣉⣡⣾⡿⣷⣤⣴⣿⠿⣶⣤⣴⡿⣷⣤⣿⣷⣌⣉⣴⣿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠉⠁⠈⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣾⣿⡏⠀⠀⢀⣠⣴⣶⣦⣀⠀⠀⢸⣿⣿⣷⣿⣿⣷⣄⠀⠀⣠⣶⠟⢿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⣸⣿⣿⠃⢀⣴⣿⡏⠙⢿⣿⣿⡆⠀⣿⣿⡿⠀⠈⣿⣿⡿⢠⣾⣿⠃⠀⣼⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠿⣿⣿⣿⠀⢸⣿⣿⡁⠀⠈⣿⣿⡇⢠⣿⣿⣇⣤⣤⠿⠛⠁⣿⣿⣿⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⣿⣿⡿⠀⠀⣿⣿⣿⠀⢸⣿⣿⣧⠀⣸⣿⡿⠁⢸⣿⣿⠋⠉⠀⠀⠀⢸⣿⣿⣇⠀⠀⣀⣤⣤⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠻⣿⣿⡿⠟⠋⠀⠀⣼⣿⣿⠀⠀⢀⢤⡀⠈⢿⣿⡿⠷⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢠⠇⠘⠁⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⢀⡌⠁⠀⣀⣀⠀⣠⣴⠄⢀⡀⠀⠀⠛⠋⠁⠀⢸⠀⠀⣠⣤⢀⡤⡄⠀⣴⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢮⡴⠋⡇⢀⣼⢦⡼⠞⠡⣏⡴⢻⠇⠀⠀⠀⠠⠴⠒⡟⠋⢙⡟⣡⡾⠖⣡⢾⠋⣀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠈⠉⠀⠀⠀⠈⠀⠸⠄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠉⠁⠙⠊⠁⠘⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡇⠀⠀⣤⣤⠀⠀⣤⣤⢠⣤⣤⡄⢠⣤⣤⢠⣤⡄⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡇⠀⠀⣷⢾⣄⢠⡿⡤⠀⢸⡇⠀⢸⡏⠀⣾⣧⡤⢸⣇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞⠀⠀⠀⣧⣠⡾⠹⣇⡠⠀⠰⠁⠀⠰⡇⠀⣿⣥⡀⢾⡏⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠾⠁⠀⠀⢀⣰⣿⣷⢦⢀⣤⣤⣴⣿⠛⣶⣦⣤⣴⡶⣀⣴⠶⢟⣷⠀⠀⠀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠞⠋⠙⠶⣄⣤⠶⠋⠻⣤⣤⠞⠀⠀⠀⢲⣤⣤⠞⠀⠀⠀⠶⠋⠀⠀⢸⣧⡴⠞⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣶⣶⣶⡿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⡇⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢀⣤⣄⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡽⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠇⠀⠀⣴⣿⡟⡿⠀⣿⣿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢳⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢁⣼⣷⠀⣸⣿⠿⠞⠁⢸⣿⠇⠀⠀⢀⣾⣿⠃⠀⠀⢀⣤⡀⠀⣠⣾⢿⠄⣰⣿⡿⠁⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣠⡿⣿⣿⣠⣿⣏⠀⠀⠀⣿⡿⠀⠀⠀⣼⣿⢃⣄⠀⠀⣼⣿⠁⣾⣿⣯⡾⢠⣿⣿⠃⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⣰⣿⡟⠉⢿⡁⢀⠄⠀⢻⣇⡠⠀⢰⣿⢏⣾⣿⠇⢰⣿⡏⣸⣿⡿⠋⠀⢸⣿⡟⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⢀⣿⡿⠀⣿⣿⡇⠀⣴⣿⣿⡇⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⣿⡏⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⣿⢻⣿⣿⣾⡿⠁⠀⠹⣿⣧⡾⠁⢸⣿⣇⣼⠏⣷⣿⠀⠀⣾⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣼⡿⠁⠀⢀⣤⣶⣿⣿⣿⣿⠆⠀⠀⠈⠁⠸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠻⣿⡦⠞⠁⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⡿⠁⠀⣴⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⣸⣿⡿⠃⠀⠀⣀⣀⠀⠀⠀⢀⣤⣶⣶⡄⠀⠀⢀⣾⣿⣗⠀⠀⣴⣿⡆⣠⣶⣦⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠧⠶⠾⠛⠉⢁⣷⡄⣴⣿⣿⠿⢋⡗⢀⣴⣿⡟⠉⣼⡷⣸⣿⣿⠟⣵⣿⠏⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠁⣠⡞⠀⣼⣿⠏⢀⣼⡿⢳⣿⣿⠋⣼⣿⠏⠀⢀⣶⠀⠀⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⠋⣿⣿⢀⣴⠏⠀⠀⢿⣿⣠⣾⠟⠁⢸⡿⠁⢰⣿⡏⠀⠀⣾⡏⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⣶⠶⠿⠛⠛⠁⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢿⣿⡃⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣽⣽⣷⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣿⣾⣿⣿⣶⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⢠⡀⣛⣈⣵⣉⣛⡷⠟⣐⣋⡒⠋⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢋⣚⣙⠭⠇⠉⠏⠶⠸⠆⠓⠀⠀⠃⠤⢩⡑⡮⡱⠶⠂⠤⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⢔⢫⡁⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢋⡳⣦⡩⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠗⣛⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢇⡗⣽⢇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⣡⠞⠡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⢤⡘⢃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡄⠓⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡿⡔⢴⠆
⠀⠀⠀⠀⠀⠀⣀⢶⠛⣩⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⢓⣭⣅
⠀⠀⠀⠀⠀⢠⡙⣠⠏⢴⠅⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⣠⠤
⠀⠀⠀⠀⠀⢀⡁⠧⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣀⣀⣀⣀⠀⣴⠋⣻⠗⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⢷⢐⠒
⠀⠀⠀⠀⣠⡴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠚⠋⠙⠻⡟⠁⠀⣿⣖⠁⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡜⠸⡯
⠀⠀⢠⣌⠃⡵⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⣰⠇⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠧
⠀⠀⠰⡌⣼⠣⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢦⠐⠆
⠀⠀⠀⢤⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢾⣤⣛
⠀⠀⡰⡞⡗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⣶⣶⠀⠀⢶⣶⠀⠀⠰⣶⠖⠀⠀⠀⠀⢠⡶⠆⢠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢺⣐⠏
⠀⣠⡙⢰⡩⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⡄⠀⠘⣿⡆⠀⢠⠏⠀⣠⣤⣄⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠠⣅⢾⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⠀⠀⠸⣿⡀⡆⠹⣿⡄⡜⠀⣸⡏⡸⠋⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢻⣐⠶
⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢹⣿⠀⠀⠹⣿⣤⡄⠀⢻⡧⠀⢾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢹⢠⡛
⠀⠀⢠⡿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⡳⠉
⠀⠀⡻⢥⣋⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⠧
⠀⠈⣙⡸⣇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⡇⡰⠆
⠀⠀⠉⢁⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠀⠉⠉⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⣸⢣⣘⠃
⠀⠀⠀⢠⡟⣅⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣀⣀⠀⠀⠀⠀⣤⠚⢳⣦⠀⢠⡔⠛⣶⡄⠰⣶⡠⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠷⠉
⠀⠀⠀⢚⠦⣧⠔⡃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠛⠛⠻⣷⡄⠸⣷⠀⠀⣿⠀⢿⡇⠀⢸⡇⠀⣿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠙⠂
⠀⠀⠀⠉⣁⠸⣌⡁⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠳⠚⠁⠀⠈⠛⠒⠋⠀⠀⠛⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⣀⠃⡼⢈⠶
⠀⠀⠀⠀⠀⠠⢤⡀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⢦⠤⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠜⢳⡘⠃
⠀⠀⠀⠀⠀⠀⢼⠝⡜⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⠎⠋⠁
⠀⠀⠀⠀⠀⠀⢩⣅⢳⡅⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢎⡽⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠦⠙⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡡⢟⢱⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡕⣜⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠶⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢓⡘⢦⡘⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢓⡼⢃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⠴⠉⡣⣤⢀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠇⣒⡉⣤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣊⡳⢤⣘⢠⠀⠀⢠⢠⡄⣀⠀⠀⢀⠴⢘⣢⣝⡬⠐⢎⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⢂⡬⠉⠶⢟⡵⢒⠶⠤⠶⢰⡼⢧⣮⡇⣴⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠾⠱⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣾⣿⡏⠀⠀⢀⣠⣶⣶⣦⣀⠀⠀⢸⣿⣿⣷⣿⣿⣷⣄⠀⠀⣠⣶⠟⢿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⣸⣿⣿⠃⢀⣴⣿⡏⠙⢿⣿⣿⡆⠀⣾⣿⡿⠀⠈⣿⣿⡿⢠⣾⣿⠃⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠿⣿⣿⣿⠀⢸⣿⣿⡃⠀⠈⣿⣿⡇⢠⣿⣿⣇⣤⣤⠿⠛⠁⣿⣿⣿⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⣿⣿⡟⠀⠀⣿⣿⣿⠀⢸⣿⣿⣧⡀⣸⣿⡿⠁⢸⣿⣿⠋⠉⠀⠀⠀⢸⣿⣿⣇⠀⠀⣀⣤⣤⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⣿⠀⠀⠻⣿⣿⡿⠟⠋⠀⠀⣾⣿⣿⠀⠀⢠⢤⡀⠀⢿⣿⡿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢠⠇⠘⠃⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⢀⡌⠁⠀⣀⣀⠀⣠⣴⠀⢀⣄⠀⠀⠛⠋⠁⠀⢸⠀⠀⣠⣤⢀⡤⡄⠀⣼⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢮⡴⠋⡇⢀⡼⢦⡼⠞⠡⣏⡴⢻⠇⠀⠀⠀⠠⠴⠒⡟⠋⢹⡟⣡⡾⠖⣡⢾⠋⣀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠈⠉⠀⠀⠀⠈⠀⠸⠄⠀⠀⠀⠀⠀⠠⠇⠀⠀⠉⠁⠙⠊⠁⠘⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡇⠀⠀⣤⣤⠀⠀⣤⣤⢠⣤⣤⡄⢠⣤⡤⢠⣤⡄⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡇⠀⠀⣷⢾⣅⠀⣿⣤⠀⢸⡇⠀⢰⡇⠀⢸⣧⡄⢸⣇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞⠀⠀⠀⣧⣠⡾⠀⣧⣤⠀⢸⠇⠀⢸⡇⠀⣿⣤⠀⢸⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠾⠁⠀⠀⢀⡰⣶⣶⣦⣀⣀⣤⣼⣏⣙⣳⣤⣤⣤⣤⢀⣤⠶⠚⣷⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠞⠋⠙⠶⣄⣤⠶⠛⠻⣤⣤⠟⠉⠁⠈⢷⣤⣭⠟⠁⠀⠀⠿⠋⠀⠀⢸⣧⡴⠖⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠙⡆
⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⣠⠃
⠀⠀⡠⠚⠁⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢀⡴⣁⣀
⠀⡜⠁⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⢠⣿⠇⠈⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⠠⠐⣡⣾⠋⢠
⣼⠀⠀⠀⠀⠀⠀⠀⠸⠼⠟⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⡀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⣸⣿⢇⠴⠁
⣿⠀⠀⣠⡶⠓⡆⣀⡄⠀⣠⡶⢦⠀⣿⡏⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣾⠃⣻⠀⢀⣤⠶⣄⣿⣿⠀⠈⢲⣿⡟⠁
⠛⠀⣸⣿⠁⠀⣿⣿⠁⣾⣟⡠⠋⢰⣿⠇⠀⡀⠀⠀⠀⢰⣿⠀⢠⣾⠘⣿⢀⡇⣰⣿⠃⡰⢻⣿⡇⠀⠀⣼⣿⠇⠀⢀
⠀⠀⣿⣿⠀⢀⣿⣿⢼⣿⡏⠀⢀⣼⣿⠀⣸⠁⠀⠀⠀⣾⡿⠀⣿⡿⠀⠙⡿⠜⣿⡟⠉⠀⣸⣿⡇⠀⠀⣿⣿⠀⢀⠎
⠀⠀⠹⣿⣀⡞⣿⣯⠈⣿⡇⢀⡞⢸⣿⢠⠇⠀⠀⠀⠀⢸⣷⣰⢿⣿⢀⡜⠀⠀⢹⣇⠀⢠⢿⣿⡇⠀⡜⠹⣿⣠⠏
⠀⠀⠀⠀⠁⡴⢻⣿⠀⠈⠓⠋⠀⠀⠿⠞⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠋⠀⠀⠀⠀⠉⠀⠁⠸⣿⡇⡼⠁
⠀⠀⠀⠀⡜⠀⢸⣿⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡈⠉
⠀⠀⠀⢸⠀⠀⣸⡏⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠑⣄⠀⠀⠀⠀⢀⠞⠁⣿⡇
⠀⠀⠀⠘⠢⠴⠋⠀⠀⠀⠀⣿⣿⡀⠀⢀⠖⠈⠑⢢⠀⡿⠀⠀⠀⠀⢸⠀⠀⠀⢠⠏⠀⢰⣿⡇
⠀⠀⠰⣇⠀⠀⠀⠀⢀⠤⠊⢸⣿⡇⠀⡏⢀⣠⡄⠀⡇⢧⣤⡦⠀⠀⢸⠴⣶⣄⡏⠀⠀⣾⣿⠁
⠀⠀⠀⠈⠒⠀⠒⠀⣡⢤⣄⠀⣿⣿⡠⠽⣾⣿⠀⢀⡧⣼⣿⠇⠠⠐⡏⠀⣿⡿⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣿⡦⢿⣿⡄⠀⣿⡏⠀⢸⠁⣿⣿⠀⠀⡼⠀⢠⣿⡇⠀⠀⣼⣿⠇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡴⣿⡇⢸⣿⠇⠀⣿⡇⢠⠏⠀⠹⣿⢀⡴⠁⠀⠘⠿⠃⠀⠀⣿⣿⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠙⠛⠁⢸⡿⠀⠀⠈⠓⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⣿⣧⠴⠶⠶⡞⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠹⢦⡀⣠⡾⡣⠤⠖⠀⠀⡀⠀⠙⠒⠒⠤⢤⣀⣠⡤⠶⠛⠋⠉⠹⣇⠀⡠⠊⠀⠀⠀⠀⡷
⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠶⠟⢉⠉⠙⠒⠂⠀⠘⠃⠈⠉⠀⠀⠀⠀⠠⠚⠁
⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠐⠒⠒⠚⠉⠉
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡏⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⣸⣿⡟⠀⢀⣠⣴⣾⣶⣄⠀⠀⣾⣿⡿⢿⣿⣷⡆⠀⣠⣾⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣤⣿⣿⡇⢠⣿⣿⠁⠙⣿⣿⡇⢠⣿⣿⠀⠀⣿⣿⠇⣾⣿⣃⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠟⣿⣿⡟⠉⢹⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠇⣸⣿⣿⠶⠟⠋⠀⢸⣿⣿⠋⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠘⣿⣿⣷⣼⠿⠋⠀⣿⣿⡇⠀⠀⣀⠀⢸⣿⣿⣦⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⢸⣿⣿⠄⠀⠈⠉⠉⠀⠀⠀⠀⣿⣿⡇⠀⡞⠸⠃⠀⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣀⠋⠁⣀⡀⠀⣠⡦⠀⣀⠀⠀⠟⠋⠁⢸⠃⠀⣠⡄⣠⣤⠀⣰⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠧⠔⢻⣀⣴⣧⡼⠊⢹⡥⠊⡇⠀⠀⠀⠰⠒⣾⠋⢹⣏⣵⡗⣫⢶⠋⣠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠟⠀⠀⠉⠀⠉⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢸⠀⠀⣶⣳⠀⢰⡟⠂⢲⡖⠂⢲⡟⠂⡞⠂⢰⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⡜⠀⠀⣿⠙⣷⢸⡟⠂⢸⡇⠀⢸⡇⢸⡟⠃⢸⠷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡀⠀⠛⠛⠁⠈⠉⠁⠈⠁⠀⠘⠁⠘⠛⠁⠘⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣩⠇⠀⠀⠀⣰⣶⣦⣀⣀⣀⣴⣞⣳⣦⣀⣤⣤⢀⣤⠶⢶⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠞⠋⠻⢦⣤⠶⠛⠳⣬⡽⠋⠉⠉⠷⣬⡽⠏⠁⠀⠿⠋⠀⠀⣯⡤⠖⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠈⠈⠀⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⡠⢄⣐⣀
⠀⠀⠀⠀⢸⡳⡘⣷⣭⣙⡉⣶⣔⢲⣿⣽⣰⣀⡀
⠀⠀⠀⠐⠥⡽⡻⢿⣿⡿⠒⣿⠏⢼⠞⠻⢣⣿⣿⡆
⠀⠀⠀⡰⢾⣧⣈⡀⣈⡷⢺⡟⣣⣿⣀⣡⣿⡿⠛⣷⣶⡄
⠀⠀⠀⠇⠀⠈⠀⣿⠟⢣⣞⢢⣷⣥⢞⣽⡿⣣⠞⠙⢒⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣅⢠⢤⣛⣽⣿⣾⠡⠞⣿⡿⣾⣿⣞⣧⡄⠠⠃⠀⠀⡜⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠁⡰⠁
⠀⠀⠀⠈⠉⠛⣻⣿⣿⣟⣤⣂⣿⡽⡷⢝⣿⣥⡤⠀⠀⠀⢰⠂⠀⡠⢠⢀⠄⡏⠀⠀⠀⣇⠀⠀⠀⡌⠀⡼⠀⠀⠠⢀⢀⡇⢠⠅
⠀⠀⠈⠉⢠⣤⡏⠹⣽⡿⣿⡍⣿⣼⡴⠉⠁⢲⠀⠀⢀⠂⠀⠑⢰⠃⠏⡀⠘⠀⠀⠀⠀⠈⠉⠀⠜⠀⢸⠁⠀⠀⠇⠁⠘⠀⠘
⠀⠀⠀⠈⠉⡙⠁⠀⠈⢛⡏⡹⠽⠋⠀⠀⠀⡁⠀⠀⠀⠂⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⡲⠋⠉⠉⠀⠨⡳⣶⠿⠥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠂⠀⡄⠀⠀⣠⢀
⠀⠒⠀⠂⠉⠙⠉⠀⠀⠀⠀⠀⠐⢼⠅⠀⠢⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠇⠀⠸⠀⠈⠰⠁⠎
⠀⠀⠀⢁⢀⡀⣇⡀⠀⠀⠀⠀⠙⡶⠂⠀⠀⣧⠎
⠀⠀⠀⢠⣘⠧⠋⠈⠑⠒⡾⡿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠀⠀⠀⠐⠀⢤⡄
⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⡇⢰⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠠⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠈⣿⠇⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢦⣤⣀⡀⠀⠀⠉⠙⠀⠙⠀⠚⠉⠁⢀⣀⣀⣤⡤⠶⠶⠛⠛⠉⠉⠉⠀⡀⠀⠀⣀⣄⡀⠀⠀⣈⠉⠉⠛⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⠛⠛⠒⠶⠶⠶⠒⠚⠛⠛⠋⠉⠁⠀⣤⡤⠄⠀⠀⠀⠘⢧⣼⠃⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⡇⠀⢠⡶⠛⢶⡀⠀⣻⣋⣿⠀⠀⣿⠶⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⠷⠶⠟⠀⠀⠻⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢹⡇⠀⠸⣇⣀⣼⠃⠀⢹⠋⠁⠀⠀⠿⠒⠂⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠳⠶⣤⣄⣀⣀⠀⠀⠈⠉⠁⢀⣀⣀⣠⣤⡤⠶⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⠄⠈⠋⠘⢿⣦⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⣿⡇⠀⠀⠼⠋⢀
⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⠛⠛⢛⡀⠀⠀⠶⢾⣿⡟⠛⢠⣿⣻⡇⣰⣟⣿⠀⣿⠁⠀⠀⣙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⢶⡄⠐⣄⠀⠐⠋⠀⠀⠀⠀⣸⣿⠃⠀⠸⣿⣏⡴⢻⣿⣡⠞⣿⣴⠃⠀⠈⠓⠀⠀⠀⢀⡔⠀⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠘⢿⡙⣦⡿⠀⡈⠳⢤⡀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⢀⡴⠋⣴⡶⠶⠾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⢄⠙⠛⣠⣾⡟⠦⢀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⣫⠴⣤⡈⠻⡦⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⢧⡙⠀⢈⣿⠦⣄⡉⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⠶⠞⣛⣉⠀⢾⡅⠀⢸⡟⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⣾⠃⠀⠀⣽⠟⠂⣤⣤⣬⢉⣉⣉⠉⠉⠉⣩⡤⠄⢠⡟⠉⠙⣷⠈⠛⠛⣋⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠰⠟⠀⢠⡿⠲⠆⢸⣧⣼⠇⠀⠀⠙⠳⢶⡌⠻⠦⠶⣋⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣌⣉⣛⠂⠘⠃⠘⠳⠀⠀⣘⣛⣩⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⢲⣄⣀⠤⠤⠤⠤⠤⣀⣀⣀⠀⡾⠛⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⣤⠶⣄⠀⠈⢹⡇⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡴⠚⢻⣀⣠⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡞⠁⣹⣤⠾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠑⠊⠙⠦⣄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⢣⣾⣿⣷⡄⠀⢈⡇⠀⣴⣿⣿⣆⠀⠸⡀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⣾⠁⢸⣿⣿⣿⠇⠀⣸⠁⠸⣿⣿⣿⡿⠀⠀⠻⡄⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣠⡴⠃⠈⢷⣀⣻⠿⠛⣛⣛⣛⣛⣛⣛⠛⠻⢤⣤⣀⡀⠙⣦⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢧⣠⠴⠛⣿⠁⠀⠘⠫⠭⠬⠤⠭⠛⠀⠀⠀⢙⡏⠙⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⡶⠶⠒⠛⠉⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⣀⣬⠷⣦⣄⣀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⣀⣤⡶⠚⠓⠶⣤⠀⠀⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡠⠞⠉⢡⡖⢤⡀⠀⢈⡱⣾⠁⠀⠀⣯⠈⠻⣍⠻⢶⣒⣶⠶⢶⠒⣪⠟⣡⠟⢃⠀⠀⠀⣠⣷⣎⡉⠁⣤⡄⠀⣠⡝⢦⡀
⠀⠀⠀⠀⢀⣾⡷⢦⡀⢿⣀⣸⠇⢠⠏⢹⡌⢳⡀⠀⡇⠀⠀⠈⠳⣼⡟⢳⣴⡶⢿⣥⠞⠁⠀⢸⣀⣠⠞⠁⢿⣀⡇⠸⣤⠟⢸⣁⣸⢸⡇
⠀⠀⠀⢀⡏⢻⣀⣸⠃⠀⣉⣁⠀⠘⠧⠜⠁⠀⢻⣤⠁⠀⠀⠀⠀⠈⠳⠼⣿⡤⠞⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⣸⠃
⠀⠀⠀⠀⣇⠀⠉⢡⠖⠋⠉⠉⠉⠛⠢⣄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⠖⠛⠉⠙⠓⣦⠀⠀⠀⡏
⠀⠀⠀⠀⠸⡄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⠀⠀⢸⡆⠀⢰⠃
⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⢸⡇⠀⠸
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢀⡤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠸⡇⠀⢸⠄
⠀⠀⠀⠀⠀⡟⢠⠏⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠞⢁⡴⠋
⠀⠀⠀⠀⢰⠃⢸⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡤⠶⠋
⠀⠀⠀⠀⠘⣀⠈⢣⣄⣀⣀⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠈⠲⢤⣄⣀⣀⣀⣀⣀⣀⣠⡤⠖⠉
⠀⠀⠀⠀⠀⠙⠢⣤⣄⣉⣁⣠⡼⠋⠒⠢⠤⠤⠤⠤⠤⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢉⣉⠉⢉⡉⠉⠀⡀⠀⠀⢠⠖⢦⠀⣦⠔⢲⠤
⠀⠀⠀⠀⠂⠐⢀⡤⠤⣌⠉⠀⣀⡀⠀⢀⣠⣄⠀⡀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⢠⣟⣈⡟⢸⡟⠃⠚⡿⠂⠀⢸⠗⠋⠀⢵⣴⠋
⠀⠀⠀⠀⠘⠀⡘⠀⠀⠈⠁⣼⣩⠇⠀⣼⣁⣨⠛⡇⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⢸⡏⠉⠀⢸⡇⠀⠀⣭⠀⠀⢸⡄⠀⣀⢸⠹⡆
⠀⠀⠀⠀⠈⠛⡟⠛⠀⠀⠀⡏⠀⠀⠀⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡶⠞⢋⡻⢸⡅⢠⡆⠀⣧⣀⣦⢻⣄⡾⠀⠳⠤⠏⠸⠀⠣
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢧⠀⣴⠀⢷⣀⡾⠀⢷⣀⣀⣀⠀⠀⠀⠀⣷⠖⠋⠁⠀⠙⠋⣀⠀⠀⠉⠁⡀⠈⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠙⠁⠀⣠⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⠀⢀⡀⠀⢹⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⣼⠁⠀⠈⠋⠀⣷⡜⠛⣧⢠⣹⡏⠈⣣⣷⡞⠋⠹⠀⢈⡇⠘⡇⠈⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠓⠖⠚⢳⡀⡟⠃⢀⡷⢸⡀⠃⢀⡍⢰⠀⠀⠘⠁⣠⣅⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣤⠞⠁⠳⡤⠞⠁⠈⠓⠒⠋⠁⠘⠂⠀⠀⠀⠛⠂⠘⠗⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⡄⠀⢀⡀⠀⢸⡄⠀⠀⣿⠀⠀⣰⠀⠰⠆⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠙⢆⠙⠁⠀⠈⠃⠀⠀⠛⠀⠀⠏⠀⠀⠀⢠⡟⠀⣀⠀⠀⣀⡄⠀⠚⠂
⠀⠀⠀⠀⠀⢤⡀⠰⠀⠀⠀⠈⠳⣄⠀⢠⡀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠉⢀⡴⠋⠀⠀⠀⣤⠇
⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠈⠀⠀⣠⠔⠊⠉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠘⠁⠀⠀⣠⠞⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⢸⣗⠺⢴⣤⡤⣤⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠞⠁⠀⠈⠁
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠋⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠸⠇⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⣀⡤⠖
⠀⠀⠀⠀⠉⠛⠲⢄⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠉⠁⠀⠀⠶⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡴⣠⠴⠊⣹⠂⠀⠀⠀⠀⢠⢋⠏⢀⢎⠇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⡤⠤⠶⠒⠛⠋⠉
⠀⠀⠐⠶⠤⣤⣀⠀⠀⢰⠃⠀⠀⠀⡸⠁⠀⣀⠴⠁⠀⠀⠤⠤⢴⠷⡾⢤⡾⡾⢤⣤⣄⣀⣀⡀⠀⠀⠀⠓
⠀⠀⠶⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣰⠳⠯⠟⠳⡄⠀⠀⠀⠀⢀⢏⠎⠀⣜⡜⠀⠀⠀⠀⠉⠉⠛⠻⠿⣶⣦⡄⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⡀⢿⠀⠀⢰⠃⠀⠀⠀⠀⡷⢀⡔⣻⢀⡾⠃⠀⣸⠋⠀⡠⢋⡇⠀⣺⢀⣠⠆⠀⠀⠉⠀⠀⣀⡀⠀⠀⠀⠀⠰
⠀⠘⠛⠉⠉⡉⠉⠀⠀⠈⠀⢠⠏⠀⠀⠀⠀⣰⢇⣊⠔⢁⡾⠁⠀⣴⠃⠀⣰⡡⠊⢀⡔⠉⢩⠏⠀⠀⠀⣰⠀⠀⠀⠉⠙⠓⠦⢤⣀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡴⠿⣟⣡⠔⢹⣇⡴⠋⣇⣠⠔⣯⣀⡴⠋⠀⠀⣏⣀⡤⠂⢀⡏⠀⣀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⢀⣠⡤⠴⠖⠀⠀⠀⠈⠓⠒⠛⠉⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⢀⡞⠀⠀⡀⠙⠲⢤⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠙⠲⣄
⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⣠⠆⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⢦⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠶⠀⢀⠀⠀⠀⠉⠓⠲⠤⢤⣤⣤⣤⣤⠤⠴⠒⠋⠁⠀⣄⠀⠀⠀⠀⠙⠢⡀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⡆⠀⠀⢠⠀⠀⠀⣄⠀⢀⠀⢠⡀⠀⠀⠀⠘⢧⡀⠀⠠⡆⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⡜⠀⠀⠀⣼⠀⠀⠀⢹⠀⠈⠀⠈⣧⠀⢴⠄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁⠀⠀⠀⢀⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠳⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣄⠴⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⡄⠀⣈⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣀⡀⠀⣿⠀⠙⠦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠑⢤⡏⠀⠀⠀⠀⠀⠀⠀⢀⣶⠛⠉⠉⣼⠋⠀⠀⠀⠉⢹⡿⠲⠤⣤⣤⡾⠃⡴⢢⠀⢠⡎⡆
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⠊⣰⡟⠉⣷⢸⡇⠀⠀⠀⠀⠀⢰⡇⣸⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⠀⡆⢿⣃⡴⢋⡸⢷⣀⣀⡴⠀⠀⣿⠁⣿⢠⣿⢰⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⡤⢞⣡⠞⠛⠒⠋⠁⠀⠉⣡⡤⢤⡀⣿⣸⠃⢸⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠀⢠⠆⠀⠀⡖⢤⢰⣿⠀⣸⠇⣿⡃⠀⣨⣿⡀⢀⣠⠎
⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⢸⠃⢹⡄⠀⡀⠙⣾⠞⠿⣎⣥⠞⠉⠓⠚⠋⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⣠⡟⠀⠀⠙⠒⠋⠘⠁⠀⠀⠀⢀⣠⡀⡠⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⣈⠉⠀⠀⣀⢤⣤⣀⠀⣴⠋⠈⠹⣯⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠸⠯⣄⣀⣼⡟⠊⠀⢹⡆⣿⡃⠀⠀⣿⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠞⠉⣿⠘⢧⡀⢀⡼⠟⠉⠓⠂⠚⠁⢀⡉⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⡀⠀⠹⠤⠞⠃⠀⠀⠉⠁⠀⣀⣠⠤⠒⠚⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠓⠦⣄⣀⣀⣤⡤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠙⠐⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⡀⢀⣀⣀⣀⣀⣀⠀⠀⢠⡴⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠁⠀⠀⠀⢨⠋⠀⠀⠀⣀⣤⡉⠉⠑⢾⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⡼⠀⣠⠖⠻⣁⣠⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⣷⠋⣈⣧⠴⠋⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⡟⢀⣉⠉⠑⢦⡀⠀⠀⣀⡀⠀⠸⡀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⡎⢰⣿⣿⣷⠀⠀⡇⢀⣾⣿⣿⡆⠀⢣⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡴⠻⡄⠸⣿⣿⣏⣀⣸⣄⣨⣿⣿⡿⠃⠀⠀⢳⡀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣟⠀⣀⡽⣶⠟⠁⣴⠶⠒⠒⠶⡶⠈⠉⠛⢷⠲⣤⣟⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⠀⢿⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⡾⠀⠀⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣤⣤⠤⠶⠚⠁⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⢀⣬⡷⣤⣄⡀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣠⣤⠖⠛⠶⣤⠀⠀⢀⣠⣄⣤⣤⡀
⠀⠀⠀⠀⠀⣠⠖⠋⢡⠖⢤⠀⢀⣉⢶⡉⠀⠀⡇⠈⠻⡉⠳⣖⡶⠶⠶⣒⡹⢋⡼⠛⡀⠀⠀⣠⣷⣎⡉⢠⣤⠀⣠⣌⢲⡀
⠀⠀⠀⠀⣼⡿⠲⡄⠻⣄⡼⠀⣼⠁⡇⠙⣆⠀⡇⠀⠀⠙⠲⣿⠹⣾⠞⢿⠴⠋⠀⠀⣇⡠⠊⠀⠳⡼⠇⠳⠞⠀⢧⡸⢸⡇
⠀⠀⠀⢸⠘⢧⠴⠃⣀⣤⣤⣄⣙⠒⠁⠀⠈⣶⠀⠀⠀⠀⠀⠈⠒⢻⠖⠋⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣸⠁
⠀⠀⠀⠘⡆⠀⢠⠋⠁⠀⠀⠀⠉⠓⣄⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣇⢀⡴⠋⠀⠀⠈⠹⡆⠀⠀⡇
⠀⠀⠀⠀⢹⡀⢈⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⡟⠀⢰⡇
⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⣀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⣧⠀⢠⡄
⠀⠀⠀⠀⢸⠇⡼⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⣠⠏⢀⡞⠁
⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⡡⠔⠋
⠀⠀⠀⠀⢇⠀⠳⣄⣀⣀⡼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠈⠲⢤⣀⣀⣀⣀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠈⠓⠤⢤⣈⣀⡤⠞⠑⠒⠤⠤⠤⠤⠴⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣉⣉⠉⣉⠉⠀⣄⠀⠀⣰⠒⡄⢲⠔⢒⠦
⠀⠀⠀⠈⡀⢀⡴⠶⢦⡀⢀⣄⠀⠀⡠⢤⣀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣅⡼⠁⡟⠉⠈⢛⠃⠀⣿⠘⠁⢸⣶⡋
⠀⠀⠀⠀⣀⣨⣁⡀⠀⠀⡿⠜⠁⢰⠧⠴⠋⡇⠀⠀⠀⠀⠀⠀⠃⢀⣀⣄⢸⠁⠀⠀⢇⠀⠀⣰⠀⣀⢸⡀⢠⡌⡇⡇
⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⡇⠀⡀⢸⠀⢠⡄⢇⠀⠀⠀⠀⠀⠀⣟⢋⣠⠎⠸⣤⡞⠀⠘⠦⠾⠘⠶⠋⠀⠙⠋⠀⠁⠈
⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠳⠴⠃⠈⠳⠞⠀⠘⠒⠒⠂⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⡆⠀⡆⠀⠂⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡴⠛⠛⠦⠀⣆⡴⢶⡀⠠⣤⠛⠆⣖⣠⠞⣦⠀⠷⠀⡷⠀⠆⠀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠣⠤⠔⢦⡀⡿⠄⠀⡇⡏⠻⠀⣘⢹⠁⠀⠰⠀⣘⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⡴⠃⢧⣠⠞⠀⠛⠦⠖⠃⠘⠀⠀⠀⠈⠿⠁⠯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠈⠁⠇⠀⢤⠀⠀⠢⠄⠀⠀⠀⠘⠀⠈⢹⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠉⠂⠀⠤⠀⠀⠠⠄⠀⡀⠠⡄
⠀⠀⠀⠀⠀⠀⢀⡁⠈⠀⠈⡠⠀⠀⠄⠀⠀⠀⠀⠋⠀⠃⠀⠀⢁⠤⠀⢠⠀⠀⠀⠀⣄⡀⠀⠀⢀⡀⠘⠀⢀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡠⢴⣆⠤⢤⠄⠀⡂⠀⠀⡴⠒⢦⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠲⠦⣄⡀⠀⠀⢀⡤⠲⠎⠁⠉⠀⠈⠁⠀⠛⠉⠉⠁⠀⠀⠀⠀⠈⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠙⣆⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡴⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢀⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡂⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠈⠙⠒⢦⡀⠀⠀⠀⢨⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠉⠓⠒⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠚⠉⠁⠀⠀⢠⠚⠉⠉⠤⣄⠀⠹⡄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠁⠀⠀⢀⣸⠀⢀⡇⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⢤⠀⠀⡏⠀⠀⡜⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡴⠒⠓⠒⠦⢄⡀⠀⠘⠒⠊⠁⢀⠜⠁⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠦⡠⠔⠈⠁⠀⠀⠈⠐⠢⡀⡎⠀⠀⠀⠀⠀⠀⠉⢓⡤⠴⠶⠚⠛⠒⠠⢄⡀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠎⠀⠀⡠⠤⡄⠀⡤⠦⡄⠈⠣⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠀⠀⠘⢇⠀⣸⠀⠱⠴⠃⠀⠀⠡⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⠒⠲⡌⠙⠁⠀⠀⠀⠀⠀⠀⠀⢃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠑⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⣀⣀⠤⠚⠁⠀⠀⠑⠦⣄⣀⣀⣠⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠷⠶⣦⣄⣾⠉⠛⣷⣄⣾⡛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⢀⣤⣤⣤⣄⡙⠛⠀⢀⣿⣟⣹⠇⢀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⣦⡴⠶⢶⣿⣶⣿⠿⠿⣿⣿⣿⠇⠀⣈⣉⣉⣉⣠⣾⣿⣅⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⢀⣴⣶⡌⠀⢀⣾⡿⠋⢀⣶⠆⢸⣿⡿⠀⢠⣿⣿⢿⣿⣿⡇⠈⣿⣧⠞⠉⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣾⣿⣿⠃⠀⣼⣿⠁⠀⣛⣉⣴⣿⣿⠃⠀⣾⣿⡿⠀⢹⣿⡇⢠⡿⢋⣀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡿⠃⠀⢰⣿⡇⠀⢸⣿⣿⣿⡟⠁⠀⢰⣿⣿⠃⢀⣿⣏⣴⣿⣛⣉⣉⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠈⢉⣠⠆⠀⣾⣿⣿⣄⡀⠙⠋⣁⣴⣿⠀⠸⠿⠋⣠⡾⠛⠛⢿⣿⠿⢛⡙⢳⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠟⣋⡍⠀⢠⣍⡉⠙⠻⡿⢋⠙⢿⣿⣿⣷⣶⣶⣾⠋⢠⣾⠇⣼⠋⢠⣿⢇⣼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣴⣿⣿⠃⢠⡟⠛⢿⣆⣰⣷⠘⠇⢸⣿⣿⠿⠿⣿⠇⠠⠿⣫⣾⠃⠀⢟⣡⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣾⣿⣿⠃⢀⣾⠁⢀⣿⡿⠋⣿⣧⠀⢼⠋⢠⣶⠂⡿⠀⣰⣾⣿⡟⠀⢰⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣿⡀⠛⠛⢁⣠⣿⡇⠀⣼⣿⠁⢰⣿⡏⢠⡆⢀⣭⣤⣾⠇⠀⣿⣿⣿⠃⠀⢼⣿⣿⡇⢠⣿⡇
⠀⠀⠀⠀⠀⢸⣏⠙⠻⠿⠿⣿⣿⣿⠀⠀⠿⢁⡀⠘⠋⢠⣾⡄⠘⠿⠿⢋⣤⠀⠻⠿⢃⣴⠀⠸⠿⠟⢀⣾⡿⠁
⠀⠀⠀⠀⠀⢈⡿⠷⠒⣲⠟⣩⣿⠿⣷⣤⣴⣿⠿⢶⣾⣿⣿⣿⠶⣶⣾⣿⣿⣷⣤⣴⣿⣿⣷⣦⣤⣶⡿⠿⣷⣄
⠀⠀⠀⠀⠀⣿⣤⣤⣾⡇⢠⣿⠀⠀⣿⣿⠏⢠⣶⣦⠘⣿⠃⢰⣶⣄⠹⡿⠀⠸⠟⣉⠀⢹⣿⣿⢦⣤⣤⣴⣿⡟
⠀⠀⠀⠀⠀⠈⠛⠛⠙⢿⣾⣿⣧⠀⠹⠛⠂⠈⠛⠿⠀⠛⠀⢀⣉⡋⢀⣶⠀⢠⣾⡟⠀⣼⡿⣿⡆⠹⣦⡈⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢉⣴⠀⢸⡏⠀⣾⣿⠆⣸⡇⠀⣿⣿⠃⣼⡇⠀⣾⡿⠀⣼⣿⠇⣸⣟⣠⣿⡿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠛⠛⣠⣾⣿⣄⣉⣡⣼⣿⣷⣄⣉⣡⣾⣿⣇⣰⣿⣧⡀⠛⢋⣴⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡿⠿⠋⠈⠛⠻⠟⠛⠁⠉⠛⠻⠟⠋⠉⠛⠿⠛⠛⠿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢡⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡥⠶⠦⠀⠀⠀⠀⠀⣰⡿⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⣿⡏⢀⣴⣲⢀⣴⢶⡄⣰⣿⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣾⡿⢠⣿⡷⢋⣾⣣⡟⢡⣿⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⡿⠁⣾⣃⣴⣿⠋⣡⡤⢸⣿⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣼⠟⠁⠀⠈⠉⠁⠈⠛⠉⠀⠈⠿⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠈⠧⠘⠋⠀⠀⢠⡆⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⠉⠉⢉⣹⡇⠀⠀⠰⠾⣻⡿⠛⠶⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⣾⢃⣤⣶⠿⠋⠀⢀⣴⣿⣶⡿⠁⣀⣰⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⡟⠿⠛⢛⣳⣤⢶⡿⠛⢹⣿⠃⠺⢿⣿⠏⠉⠁⣴⣿⡇⣠⣴⣆⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣠⡶⣻⡿⠁⠸⣧⡾⣿⡇⠀⢀⣿⡏⠀⠀⣼⡿⢋⣴⣿⣿⡟⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢼⣿⡾⠛⢀⣠⣤⣤⣀⠹⣧⣠⠼⣿⠀⢀⡴⢿⣴⡿⢫⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⣾⡿⠟⠛⠛⠛⠀⠀⠀⠀⠈⠓⠋⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣶⡶⠿⢿⣷⣆⣀⣴⡿⣆⢀⣴⣿⣀⠀⠀⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣠⠤⣲⣿⣿⢏⣿⠏⢠⡟⣾⡏⢣⣿⣤⣾⣿⣵⣿⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⣤⣾⣿⠟⠁⢸⣿⣠⡿⠹⣿⢀⣾⠃⢀⣿⡟⢸⣿⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣴⣾⡿⠿⠋⠀⠀⠀⠀⠉⠁⠀⠀⠉⠋⠁⠀⠈⠛⠀⠈⠿⣄⡤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⣠⡶⠶⣦⣄⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠈⠉⠻⢷⣿⠇⠀⢸⣿⡞⣿⡄⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢀⣶⣿⣿⣷⣶⣤⡈⠀⠀⢾⣿⣵⡿⠁⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⢷⠟⠛⢻⣿⣿⠿⠛⠛⠛⣿⣿⣿⠇⠀⢠⣤⣤⣠⣤⣶⡿⢿⣧⡀⠀⣠⡴⠶⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣴⣾⣷⠀⠀⢠⣿⡿⠁⠀⣴⡿⠀⣼⣿⡿⠀⢀⣿⣿⡿⠿⣿⣿⡇⠀⣿⣿⡞⠉⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣼⣿⣿⡿⠀⠀⣾⣿⠁⠀⢘⢋⣠⣾⣿⡿⠃⠀⣼⣿⣿⠇⠀⣿⣿⠇⢠⡿⢋⣀⣤⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠁⠀⢸⣿⣿⠀⠀⣿⣿⣿⣿⠟⠁⠀⢀⣿⣿⡿⠀⢰⣿⣏⣴⣿⣛⣋⣉⠉⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠙⠉⣠⠀⠀⣿⣿⣿⣄⠀⠙⠛⠛⢁⣴⣿⠀⠸⣿⡟⠁⣠⡿⠿⠿⣿⣿⣿⠟⠛⠳⣄⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠶⠟⠋⠀⢈⠛⠛⠻⢿⣿⡶⠶⢿⣿⣿⣿⣦⣤⣤⣤⣾⠋⢠⣶⡆⣸⠟⠁⣴⣿⢀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣴⣾⡿⠀⢀⡿⢿⣷⡄⠀⣿⠀⣷⠀⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⠏⣰⠏⠀⣼⠟⣡⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢠⣿⣿⣿⠃⠀⣾⠁⠀⣼⣷⣾⢿⣧⠉⠀⣿⡿⠋⣉⡉⢻⠇⠀⣉⣵⣾⡿⠀⢀⣥⣾⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⣿⡿⠃⢀⣾⡇⠀⢰⣿⡏⠀⣼⣿⠇⠀⠛⠀⠼⠟⢁⣾⠀⢰⣿⣿⣿⡇⠀⢸⣿⣿⣿⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⣠⡾⣿⣄⣈⣉⣀⣴⣿⣿⠀⠀⣿⡿⠁⢰⣿⡟⠀⣾⠀⢰⣶⣾⣿⠏⠀⢸⣿⣿⡟⠀⠀⢸⣿⣿⡟⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣄⠈⠛⠛⠛⣻⣿⣿⣿⠀⠘⠟⢡⣄⠀⠋⢀⣼⣿⡀⠘⠿⠛⣁⣴⡄⠈⠿⠋⣠⣶⡀⠘⠿⠋⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⣸⡿⠟⠛⣻⠟⢡⣾⠿⢿⣶⣤⣶⣿⠿⠿⣿⣿⣿⣿⡿⠶⢶⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣶⣤⣶⣿⠿⢻⣷⡄
⠀⠀⠀⠀⠀⢸⣯⣀⣴⣾⡏⠀⣿⡇⠀⢰⣿⣿⠏⢠⣶⣦⠈⢻⡟⠁⣴⣶⡄⠙⡿⠀⠀⠿⢋⡁⠀⢹⣿⡿⢦⣤⣤⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠻⠟⠻⣷⣶⣿⣷⡀⠈⠿⠿⠀⠈⠻⢿⠇⠸⠗⠀⠈⠛⠛⠀⣴⠀⠀⣰⣿⠇⠀⣾⣿⣿⡆⠙⣦⡉⠙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠟⢋⡅⠀⢰⡆⠀⣴⣶⡤⢀⣶⠀⢰⣿⣿⠇⣸⡟⠀⢰⣿⡏⠀⣼⣿⡆⢹⣿⠀⣹⣿⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢰⣿⠇⢀⣿⣇⠀⠻⠟⢁⣾⣿⡀⠘⠿⠋⣰⣿⡇⠀⣼⣿⡀⠰⣿⠟⢀⣾⣿⣾⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⣤⣶⣿⡿⠿⣿⣶⣾⣿⠿⠻⢿⣶⣶⣿⡿⠻⣷⣶⣿⣿⣷⣤⣤⣴⣿⡿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠈⠛⠛⠛⠉



⣿⢿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⢿⣿⣿

⠀⠀⠀⠀⠀⢀⣄
⠀⠀⣰⡞⠉⢀⡥⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠉⢠⡤⢲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀
⠀⠀⠛⢠⠟⢿⡁⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⠟⢿⠁⢻⠁⡀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢁⢁⣴⠂⣽⡟
⠀⢻⢰⡇⢊⣴⢠⡿⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⡇⢦⡶⢰⡏⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⠂⠿⠹⣏⠐⣻⠐⣀
⠀⢘⣋⣓⣈⣃⣘⣃⣻⣀⠀⠀⠀⠀⠀⠀⣠⠠⠜⣚⠃⢘⠃⢙⠚⡇⠀⡆⠀⠀⠀⠀⠀⣷⠀⡖⠸⢠⡤⢰⡟⣼⠃
⠀⣸⣧⣹⣸⣧⣾⣠⣸⣿⠀⠀⠀⠀⠀⢀⠙⣷⢼⡃⠳⡟⠘⣿⢻⠇⢘⠁⠀⠀⠀⠀⠀⠸⠇⠷⠀⠿⠀⠿⠕⣿
⠀⠀⠀⠠⠠⠠⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⢷⢶⡶⣖⠾⠒

⠀⠀⢀⣀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠄⠀⢀⣤
⠀⣴⡟⣀⢡⡾⠁⣼⡏⠁⠂⡄⠀⠀⠀⠀⠀⠀⣠⡴⠒⠂⢀⣀⠠⣴⡦⠀⠀⠀⠀⠀⠀⢺⡇⣴⢴⠃⣼⠃⢸⠷
⠀⠙⠲⢿⡈⣣⢈⢻⡀⣤⢡⡄⠀⠀⠀⠀⠀⠰⢿⠁⣶⢶⡿⠁⢼⡟⠠⠀⠀⠀⠀⠀⠀⢰⡆⣵⢠⢀⡍⣸⠇⡾
⠀⠀⠀⠘⣇⢿⠀⣿⢸⡇⡟⠀⠀⠀⠀⠀⠠⣄⢀⣬⢡⢀⣩⢀⣴⢂⣶⠂⠀⠀⠀⠀⠀⠘⡧⢿⠈⠿⠁⠿⢸⡇
⠀⠀⢷⣀⡖⢠⡶⢠⣶⣴⠁⠀⠀⠀⠀⠀⠀⢻⡌⣿⡈⠻⡏⢼⡏⣼⠇⠀⠀⠀⠀⠀⠀⢾⣌⣴⠃⣴⠱⣾⣶⠁⡾
⠀⠀⠈⠉⠁⠀⠁⠈⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠐⠀⠋⠙⠀⠉⠀⠋⠙⠀⠂
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠂⠀⠈⠑⠄⠀⠀⠀⠠⠈⠁⠐⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⠑⠀⠀⠀⠀⠀⠀⠈⣁⢉⠖⠀⠀⠀⠀⠀⠀⠀⢁⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⢂⠀⠀⡐⠁⠀⠈⠀⠠⡀⠀⢀⠜⠀⠐⠁⠀⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠢⢀⠄⠀⠄⡀⠑⢢⡀⡀⠀⡀⡀⢢⠘⡀⠁⢀⠐⡆⠀⠀⠀⠂⡠⢣⡀
⠀⠀⠀⠀⠀⠠⠓⢀⢘⠀⠀⠀⡋⠉⠁⢸⢁⠈⠈⣀⠀⠀⣂⢹⠈⠙⠁⠀⢸⢌⢁⠱⠈⠀⠈⡀⢠⠁⠄
⠀⠀⠀⠀⡰⠀⠄⠀⢀⠄⠀⠠⡁⠘⠂⠈⠓⢂⡰⠃⠄⠀⠃⠁⣸⠂⢄⢀⣘⣄⢨⠀⡠⠀⠀⠀⠀⢀⠈⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⣄⡀⠀⣀⠀⠀⠁⢀⠀⠀⠀⠀⡄⠀⠆
⠀⠀⠀⠈⠀⣀⢀⠀⠀⠢⢀⠀⢣⠀⢯⠀⠘⡅⡰⠁⠀⣆⢴⠊⠁⠀⡏⠀⠐⠀⢘⠀⢀⡀⠀⠀⠀⠐⡤⠀⠁
⠀⠀⠠⠋⠀⠈⠉⠄⠀⡓⠐⠒⠀⠀⠀⡴⠀⢀⠇⠀⠀⡖⠜⢤⠀⠀⡇⡠⣄⠀⢀⠀⢴⠠⠄⡀⠀⠠⠂⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠂⠐⠘⠁⠀⠚⠀⠂⠀⠀⠀⠚⠃⠀⠀⠐⠋⠀⠀⠀⠊⠊⡤⠑⠀⠁
⠀⠀⠀⠦⡀⠀⠔⠉⠀⠐⡁⠂⢉⢁⠐⣄⠔⢀⡈⠉⢢⠀⡐⢀⣉⠉⠢⡐⠉⠈⠢⡀⠀⢨⠖⠈⠀⠁⡀⡠⠊
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠀⠈⠑⠫⡁⠀⢸⠀⡀⠀⣷⠀⢸⠀⠂⠀⢳⠀⠀⠀⠈⠂⢸
⠀⠀⠀⠀⠆⠀⠑⣄⠀⠀⡎⠧⡀⠀⢀⠷⡀⠈⠦⠄⢠⠟⡀⠀⠧⠀⢀⠎⠀⠸⡀⢀⠀⢸⡀⠀⡠⠊⠀⡐
⠀⠀⠀⠀⠘⠁⠀⠈⠁⠘⠨⠀⠀⠐⠋⢀⠼⠲⠀⠒⠁⠀⠈⠀⠀⠐⡍⠀⠀⠐⠃⢀⢑⠊⢘⠀⠐⠀⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠠⡈⠁⠆⢀⠀⠀⢌⠰⠚⠐⠀⠀⠀⠀⠂⠠⡀⠈⠀⠀⠀⠐⢃⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⢁⠁⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡀⠀⠒⠀⠐⠔⠁⠀⠉⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠄⠀⠀⠀⠀⠀⠀⠐⢄⡐⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⢦⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠠⠀⠀⠄⠀⠀⡠⠆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⣲⣶⣒⣒⣖⣰⣖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠓⢦⡄⠀⠀⠀⠀⣠⡴⠖⠶⣤⡀
⠀⠀⢀⣀⣤⢄⡀⠀⠀⠀⠀⠐⣏⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠹⣆⠀⠀⣼⠋⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⢀⡴⠋⠀⠀⠀⠙⣦⠀⠀⠀⠀⠘⣦⡀⠛⠋⠳⣦⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢰⡿⢻⣾⠃⠀⠀⠀⢀⣾⠏⠀⣀⣀⡀⠀⠀⢀⡾⠁⣿⠀⢀⡀
⡌⠀⠀⠀⡀⠀⠀⠘⣧⠀⣠⣤⣄⣿⠁⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⡾⢋⣉⣹⠛⣷⣠⡞⠁⣴⡟⢠⠏⢹⡆
⡇⠀⠀⢰⡿⣤⣀⣴⡟⢰⡏⢣⣾⢛⡿⢿⡄⠈⠻⣆⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣠⡄⠀⣠⠀⠀⣠⣾⠋⣿⠀⣿⣋⣙⠛⣿⠋⢠⣾⠟⢠⡏⠀⣾⠇
⢳⡀⠀⣼⣧⠼⠛⠉⢉⣿⣧⠘⢷⠟⣻⡎⢷⣀⣠⡿⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠻⠾⢿⣤⣴⡿⠁⠀⠻⣦⣈⣩⣽⡟⠁⣰⡿⠃⢠⠏⠀⣼⡏
⠈⢷⡀⠹⣏⣻⡇⠀⠸⣏⠙⢷⣤⣴⡿⠃⠀⠙⣛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠏⠀⣼⡟⠀⣰⠏⠀⣰⡟
⠀⠈⢷⡀⠈⠉⠀⠀⢠⣿⠀⠀⠀⠀⣠⠴⢚⣭⢭⣭⣍⣙⢦⣀⣠⠴⣚⣋⣉⣉⣛⢦⡀⠀⠀⢀⣀⣄⣀⣄⡀⠀⠘⢧⣄⣸⣧⡞⠁⢀⣼⠟⠁
⠀⠀⠀⠙⠷⣶⣶⠾⠟⠁⠀⠀⠀⣴⡇⣴⡿⠚⠓⠒⢦⡉⣳⡟⢠⣾⠅⠒⠛⢦⣉⠳⣙⠶⢛⣭⠶⠶⠶⠦⣍⠳⡄⠀⠉⠉⠹⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⢙⠀⣰⣿⣛⢲⣿⡇⢸⠛⡇⠀⣶⣟⠲⡟⢳⠿⣤⣾⠋⠉⣁⣉⢳⣌⣷⠹⡆⠀⠀⠀⠘⠷⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢿⣖⣿⣌⣧⡙⣬⣋⠼⠙⡇⠸⣆⣳⣌⣮⣻⣧⡇⡆⠀⡇⢣⠀⣾⢿⡍⢻⠉⢻⡦⣿⣄
⠀⠀⠀⠀⠀⠀⢀⡴⢺⣝⣶⡶⣊⠁⢸⡷⣄⣉⣛⣤⣄⣤⣾⠖⢋⡥⠴⠤⠤⢬⡑⢿⡀⢻⡦⢷⣽⡶⠕⠋⠀⣾⠙⠻⣌⣉⣶⣤⡀
⠀⠀⠀⠀⠀⣴⠫⠷⣿⡭⢿⢰⡉⠀⢘⣧⠴⠒⠒⠛⠻⡿⢏⣰⡿⠋⢉⣉⡑⣦⡙⡌⢷⡀⢑⣦⠤⠽⠶⠤⣶⡏⠀⠸⣏⢻⡺⢿⣙⣷⡀
⠀⠀⠀⠀⠀⠘⢿⡉⠉⠀⠸⡆⢽⣰⠋⣴⣮⠭⠭⢭⣹⠇⢸⠉⡅⢠⠿⣯⡙⡏⠙⣷⣸⠏⣡⣖⣲⢿⣒⠲⢬⠳⡄⣴⢃⡞⠙⠿⣭⣩⡽
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠹⡾⢹⡾⢿⠁⢠⣶⠶⣽⣧⠘⡷⠽⣮⣳⡬⠖⠃⠀⡿⢻⡴⡟⠁⢀⣄⣌⣳⣌⣧⢹⣏⡾⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣧⠘⣧⡹⣄⢯⡻⢖⡼⠹⡆⠘⠦⣤⣭⣷⣦⣴⣾⡇⠸⡇⢧⠠⡟⢿⠎⣿⠈⣻⠀⣿⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⢬⡽⠶⢿⡆⠹⣏⠛⠺⢿⣉⠀⣀⣽⡷⣶⣤⣤⣤⣬⣿⣷⣿⡀⢻⠺⠷⣼⣗⠛⠁⢀⣿⡿⣿⣤⠶⠋
⠀⠀⠀⠀⣀⣠⣾⣀⣥⣾⠗⠀⠄⠻⣤⣈⡉⠛⠛⠻⠿⢿⣋⣴⡿⢿⡏⢯⡓⠉⢦⡈⢧⣀⠙⠒⠲⠿⢿⣾⡿⢞⣵⣿⠻⣦⣤⣤
⠀⠀⠀⠀⠉⠁⠀⠀⡰⠃⢀⣠⣶⣠⠼⣟⣻⣷⣿⢿⠻⣿⣯⠉⣷⣼⣏⣴⠹⣦⣾⡷⢸⢋⡛⢷⣶⡶⠶⠶⠾⣿⡏⠈⢹⡖⠛⠁
⠀⠀⠀⠀⠀⠀⠴⠚⠛⠂⠉⢻⡄⠀⠀⢻⡇⢹⣿⢮⣷⢿⠋⢆⠙⡇⢻⠀⣧⡿⢧⣤⠀⢸⣇⡼⠻⣴⡆⢸⡆⣿⠇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⣇⢸⠛⣎⠇⡏⠀⠈⣦⠃⠈⣦⡟⠁⠘⠉⣤⠋⠉⠀⠀⣹⣃⣾⡟⠁⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⣿⠋⢠⠟⠀⠙⢦⡼⠃⠀⠐⠻⡄⠀⠀⠀⠏⠀⠀⠀⠰⠛⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠹⡆⠀⣀⣠⣤⣤⣀⣽⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣼⣃⣀⡀⠀⠀⠀⠀⠀⢠⡶⣄
⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠉⠳⣦⠀⠀⠀⢻⡾⠋⠁⠀⠀⠉⠻⣆⠀⠀⠀⠀⣇⣰⠞⠉⠉⠛⢦⣀⠀⠀⣰⠏⣿⠀⠙⢷⡄⠀⠀⢀⡟⠀⠘⣷
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠹⣧⢠⡟⠀⡇⠀⠀⠀⢻⡄⠀⣾⠁⠀⢠⣿
⠀⠀⡿⠀⠀⠀⢀⣴⣶⣶⣤⣀⣠⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⢰⡇⠀⠀⠀⠘⣿⢰⡏⠀⠀⣸⡏
⠀⠈⣿⠀⠀⠀⢿⡏⠀⣀⣈⣛⣋⠁⠀⢸⡇⠀⠀⢰⡿⠿⡆⠀⠀⢸⣷⠀⢸⡇⠀⠀⢠⣶⣦⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿⣿⠁⠀⢀⣿⠃
⠀⠀⠙⢷⣄⣀⣈⣙⡛⠉⠉⠉⠉⠻⣦⠈⣷⠀⠀⠘⠷⠶⠃⠀⠀⢸⡿⠀⠘⣧⠀⠀⠀⠉⠁⠀⠀⢠⣿⠀⣼⠃⠀⢠⡄⠀⠸⠇⠀⠀⢸⡿
⠀⠀⠀⠀⣉⣿⣿⣿⣿⡷⠀⠀⠀⠀⣿⡇⠸⣧⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⢹⣆⠀⠀⠀⠀⠀⢀⣾⠏⢀⡿⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⡋⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⠁⠀⠘⢷⣄⣀⣀⣀⣴⣾⠿⣇⠀⠀⠀⡟⠷⣦⣤⣠⣴⣿⠋⠀⣸⠇⠀⢀⣿⣿⡀⠀⠀⠀⢰⣿
⠀⠀⠀⠈⠻⣦⣤⣄⣠⣤⣤⣤⣶⠿⠋⠀⠀⠀⠀⠉⠛⢻⡟⠉⠀⠀⠙⣆⠀⠀⣧⠀⠈⠉⠉⢹⠇⠀⠀⣿⣀⣠⣾⠟⠘⢷⣀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⡆⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠙⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣇⠀⣿⠀⠀⠀⢰⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢸⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣴⣶⡄⣾⣿⣿⣿⢀⣿⣿⣿⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⠁⣿⣿⣿⡏⣼⣿⣿⣿⢱⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠘⣿⡟⠋⠀⠘⠛⠉⢻⣿⣿⣿⣿⡧⠀⣿⣿⠇⠀⣿⣿⣿⢱⣿⣿⡿⢃⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⢹⣿⣠⣤⣤⡀⠀⢸⣿⣿⠀⠉⠀⠀⣿⣿⣴⣦⣿⣿⢇⣿⡏⠀⠀⣼⣿⡿⠁⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠙⢿⣿⡇⠀⢿⣿⣿⣿⡇⠀⠈⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⡟⣼⣿⣷⡆⢰⣿⡿⠁⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣉⣤⣄⡘⣿⣿⡉⠀⠀⠀⢻⣿⣿⡆⠀⠀⠙⠋⢹⣿⣿⢡⣿⡿⣿⢇⣿⡿⠁⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣼⣿⣿⣿⣿⡸⣿⣷⣶⣿⣶⠈⠻⢟⣀⣀⣠⣾⣿⣮⠙⠁⣾⣿⣄⠀⣼⣿⠁⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢿⣿⣿⣿⣿⡇⠹⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣷⣿⣷⣄⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣎⠙⠋⢻⣿⡇⠀⢈⣛⡋⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⣙⣋⡘⣿⣿⣿⡇⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣿⣿⢣⣾⣿⣿⣿⣦⠀⠀⠙⠿⣿⣿⡟⠁⠀⢰⣦⠸⣿⣿⣿⡌⠛⠛⠱⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢡⣿⣿⣿⣿⣿⣿⠀⢀⣤⣄⠈⠙⢃⣴⣦⡌⣿⣷⣹⣿⣿⣇⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣿⡛⠁⢠⣿⣿⣿⣷⠀⣾⣿⢿⣿⣸⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠻⣿⣷⠀⣿⣿⠉⣿⣿⠀⣿⡇⠀⣿⡇⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢸⣿⡇⠀⣾⣿⠀⣿⡇⠀⣿⡇⢸⣿⣷⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⣸⣿⡇⠀⣿⣿⠀⣿⣿⠀⣿⣧⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢸⣿⣿⠀⢻⣿⣦⣿⡟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠘⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢶⣦⣤⣀⡀⢰⡞⠻⢶⣄⢀⣴⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⣀⠈⠙⠻⢿⠇⠀⢸⣿⡟⣿⠆⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣸⣧⣀⣾⣿⣿⣿⣿⣶⣤⠀⠀⠺⠿⠾⠟⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⣉⠙⠟⠉⢉⣿⣿⠟⠋⣉⡉⢻⣿⣿⠇⠀⣰⣶⣶⣶⣶⣿⡟⠻⣷⡄⣠⡴⠟⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣠⣿⣿⡧⠀⠀⣾⣿⠁⠀⣼⠿⠁⣼⣿⡿⠀⢀⣿⣿⡏⠛⣿⣿⡇⠀⣿⡿⠋⠀⠀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢰⣿⣿⣿⠃⠀⣸⣿⠇⠀⢠⣤⣴⣾⣿⡿⠁⠀⣼⣿⣿⠃⠀⣿⣿⠁⣴⣟⣥⣴⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⣿⠿⠁⠀⢠⣿⣿⡀⠀⢻⣿⣿⡿⠟⣠⠀⢀⣿⣿⠏⠀⣼⣿⣵⣿⣯⣵⣶⣤⣀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣀⣴⡇⠀⣼⣿⣿⣷⣤⣀⣉⣁⣤⣾⣿⡄⠀⠻⠋⣠⡾⠛⢉⡉⢿⣿⠟⢉⣍⢹⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢛⣩⡥⠀⢠⣤⣄⡈⠙⢻⡟⢩⠉⢿⣿⣿⣿⣷⣶⣿⡟⠁⣼⣿⢃⡾⠁⣰⣿⠏⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢁⣴⣿⣿⠃⢀⡾⠙⠻⣿⣀⣼⣇⠸⠀⢸⣿⣿⠿⠿⣿⡟⠀⠸⠟⣡⣾⠁⠀⠟⣡⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⣿⣿⣿⠏⠀⣼⠇⠀⣸⣿⠟⢉⣿⣆⠀⣼⠏⢀⣴⠆⢸⠃⠀⣶⣿⣿⡏⠀⢰⣿⣿⣿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣇⠘⠿⠟⠁⣠⣾⡟⠀⢠⣿⡟⠀⣼⣿⠇⢠⡄⠀⣈⣡⣴⡿⠀⢸⣿⣿⣿⠁⠀⣿⣿⣿⡟⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠙⠻⢷⣶⣶⣿⣿⣿⡇⠀⣼⠟⠀⠀⠿⠏⢀⣾⠀⠸⣿⣿⠟⣡⡀⠸⣿⡿⢃⣄⠀⢹⣿⡿⠁⣰⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣷⣦⡤⣤⡶⢛⣿⣿⣧⣀⣀⣴⣿⣦⣤⣴⣿⣿⣷⣤⣤⣤⣾⣿⣷⣄⣀⣤⣾⣿⣦⣀⣀⣠⣾⣿⣿⣄
⠀⠀⠀⠀⠀⢰⡟⠁⣠⣶⠏⢀⣿⠋⠉⣽⣿⣿⠋⣉⣭⡉⢻⣿⠟⢉⣭⡉⠻⣿⠏⠙⣿⠟⠛⠛⢿⣿⣯⣛⣉⠉⣀⣼⣿⠆
⠀⠀⠀⠀⠀⠘⠿⣿⡿⣿⣦⣼⣿⡄⠀⢻⣿⡇⠀⢻⣿⡇⠈⣿⠀⠘⠿⠿⠀⢋⠀⠀⢁⣶⡇⠀⣸⣿⣷⡉⢯⡙⠛⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠿⢛⠀⠀⣤⠀⢠⣤⣈⡁⢠⡄⠀⣶⣶⡖⢀⣿⠀⢠⣿⡿⠀⣰⣿⠉⢻⣧⠀⣿⣶⣤⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣴⣿⠃⢠⣿⠀⠸⡿⠟⣠⣿⡄⠐⢿⠟⢁⣾⡏⠀⣼⣿⠃⢠⣿⡿⠀⣾⣷⣴⣿⡟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣉⣡⣴⣿⠿⣷⣶⣴⣾⣿⠿⢿⣶⣶⣶⣿⢿⣷⣤⣿⣿⣧⣀⣉⣤⣾⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁⠀⠈⠙⠉⠁⠙⠻⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⠀⠂⠀⢀⠀⢐⡙⢷⣀⡾⢩⡆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣧⡜⢛⠖⢻⢠⣶⡍⣡⢔⣞⣧⠠⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣞⣋⠲⣟⣹⡟⡻⠾⠾⢶⠹⠛⠻⠿⠷⣿⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣟⠛⠊⠀⠁⢰⢃⢰⠁⢸⠁⠀⠀⡀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣖⣾⡠⣀⣈⣫⣈⡁⣾⢦⢚⣖⠶⣩⢞⡁⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢾⣾⣿⣷⣯⡴⠬⠿⢒⠓⢛⠺⠾⠾⣧⣯⣴⣀⣀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⡆⠠⣤⠀⠀⣦⣦⠂⣾⠀⢸⡀⠸⣀⠀⠀⠀⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⢶⣶⣽⣀⠀⠉⠙⣤⠉⣠⣲⣿⣷⢧⣴⡤⡶⣸⠖⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠲⢛⣿⠟⠃⢨⡍⢠⢍⠃⣪⠿⠽⠿⠤⣟⣿⣟⠙⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢋⠀⠀⠨⠆⠹⠞⠸⣭⠃⣾⣞⠀⠀⠀⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢶⣴⢿⣛⣛⣉⠉⢲⠶⠤⢤⣤⣤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠽⢢⠏⣿⣷⣤⣶⣀⡜⠷⡖⠺⠛⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠂⠀⠀⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢿⣿⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠈⠉⠛⠆⠸⡇⠰⠛⠉⠁⠀⠀⣀⣠⣤⣤⠶⠶⠛⠛⠋⠉⠉⠉⠉⠁⢀⣀⠈⠉⠉⠉⠙⠛⠳⠶⡤
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠦⠤⠶⠶⠶⠶⠞⠛⠋⠉⢉⣀⣤⠀⠀⠀⠀⠰⣆⣼⠃⠀⢸⡏⠉⢿⡄⠀⣿⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣶⠀⠀⣤⠶⢦⡄⠀⢰⡶⢻⡆⠀⢸⣯⡤⠀⠀⠀⠀⠀⢹⡇⠀⠀⠸⢧⣤⡾⠁⠀⢻⣄⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⣿⠀⠀⣿⠀⢈⡿⠀⢸⣿⠛⠁⠀⢸⡧⠴⠀⠀⠀⣀⣀⣈⣡⣤⣤⣤⣤⣤⣤⣤⣤⣀⣈⣉⠁
⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠀⠉⠀⠀⠙⠛⠛⠁⠀⠀⠉⢀⣀⣀⣤⡴⠶⠖⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠺⠟⢹⣭⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⣠⡶
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢴⣶⡦⠌⠀⠀⢀⣠⣿⣷⣶⡦⢠⣶⣶⡄⣠⣶⣶⢀⣿⠀⠀⠀⠡⢴⣶⡦⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠈⠛⠁⢀⣠⡀⠀⠀⠀⠀⣴⠖⠀⠀⠈⠁⣸⣿⠀⠀⢿⣷⠟⣠⣿⡷⠋⣸⣿⢀⡄⠀⠳⣦⠀⠀⠀⠀⢀⠄⣠⡀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠠⣶⠿⣏⣳⡄⠘⢦⡀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⠈⠛⠛⠁⠙⠛⠛⠁⠛⠋⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣈⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⠏⢁⣴⣄⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢋⡀⠻⣯⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢴⡟⠳⡌⠁⢦⣄⠙⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⢡⡞⠉⠻⣷⠈⠛⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡙⠂⠀⢀⣾⠋⠙⠲⣤⣌⡉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠿⠛⠛⠉⣥⠶⢶⣦⠸⣷⣤⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡙⠁⠀⠀⣸⡏⠀⢰⣟⣛⠃⣴⡶⢶⡄⠀⠀⣾⣋⣁⠸⣷⡀⢀⡿⠂⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣙⠀⠀⠾⣯⣍⠀⣿⠛⢿⡁⠀⠀⣠⣭⡿⠃⠉⣉⣩⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣦⣤⣤⣭⣤⣬⣭⣤⣤⣤⡶⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠂⠀⠀⠀⠐⠀⠂⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠳⣤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠐⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣾⠀⠣⣈⠉⣧
⠀⠀⠀⠀⠘⠠⡞⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠉⡾⠉⠀⠈⠉⢸⡿⠤⢤⣀⣴⠏⢠⢠⠀⢠⢒⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⢀⣾⠋⣳⢸⡇⠀⠀⠀⠀⢠⡏⢸⠀⡿⢸⡇⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠨⢠⠘⣧⡴⣋⡼⠷⣀⡤⠊⠀⢸⡇⡾⢰⡇⣼
⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⡧⠚⢉⠉⠉⠀⠀⢀⡶⠒⣦⢸⣷⠃⢸⣷⠃⠀⢀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣱⠀⡏⠀⠀⠯⣰⢸⣇⡴⢋⡼⣇⣀⡼⠳⢤⠴⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⡟⠀⠻⣄⡰⠤⠟⠀⠙⠚⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠐⠟⠁⠀⢀⢀⠀⠀⣠⠔⠐⢤⡊⣷⠊⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢰⣟⡀⢀⣼⠗⠁⢹⡆⣿⠂⠀⢸⡇⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣿⠀⠀⢠⠖⢉⡇⢻⣄⠀⣰⠟⠙⠳⠀⠚⠀⢉⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣆⠀⠘⠴⠞⠁⠀⠈⠀⢀⣀⠤⠤⠒⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠩⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠠⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠎⠒⢘⡭⢰⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⠂⣀⠔⣶⡷
⠀⠀⠀⠀⠀⠀⢺⡇⣴⣦⡿⠁⣼⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⣶⣾⠏⢠⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠏⠙⢂⣠⠄⢲⣿⠇
⠀⠀⠀⠀⠀⢤⠀⣤⢉⠄⣛⠀⣴⢃⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢠⡌⡅⢈⡃⣰⡆⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢰⡷⣾⠏⢀⣿⢃⠄
⠀⠀⠀⠀⠀⢸⡆⣿⡀⢾⡏⢸⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢱⡿⢠⣿⢸⡏⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠚⡁⠙⠂⢀⣼⢀⣴
⠀⠀⠀⠀⠀⢠⡥⣬⡴⢶⡦⣦⠤⡼⣤⡄⠀⠀⠀⠀⠀⠀⢰⣇⠙⣨⡤⡁⣠⢍⣠⣥⣸⡃⢰⡏⠀⠀⠀⠀⠀⠀⢿⡄⣿⠀⢧⣾⠇⣼⡏⣼⠇
⠀⠀⠀⠀⠀⢼⣷⣬⣧⣿⣴⣷⣴⣴⣿⡄⠀⠀⠀⠀⠀⠀⡀⢹⡗⢿⡀⠙⢿⠈⢿⠏⣿⠀⣈⠀⠀⠀⠀⠀⠀⠀⠘⠗⠻⠆⠘⠗⠀⠛⢂⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠠⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠹⡗⣶⣺⣞⠿⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⣶⠋⠓⢠⡶⠂⣹⡿⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣸⡟⢠⣄⣴⠂⣽⠏⢠⣆⡀
⠀⠀⠀⠀⠀⢿⣇⣼⠆⢿⡃⠰⣿⢃⠄⠠⠉⠁⠀⠀⠀⠀⠀⠀⣰⣿⠋⣠⡀⣴⡟⠉⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⢈⡃⢿⡉⠓⠈⠟⢠⡬⢩⡄
⠀⠀⠀⠀⠀⣀⠈⠉⣶⢰⡇⢰⣼⠆⣾⢱⡟⠀⠀⠀⠀⠀⠀⠀⠘⠓⠰⠟⠙⠿⠥⠈⠻⠇⢂⠀⠀⠀⠀⠀⢀⡀⢸⡇⢸⠃⢣⣾⠃⣿⢃⡿⠁⢀
⠀⠀⠀⠀⠀⠀⣠⢠⠹⠌⠧⠘⠯⠸⠇⢾⠀⠀⠀⠀⠀⠀⠀⢲⡆⢰⡇⢸⢠⣶⠂⣼⡟⣰⡿⠁⠀⠀⠀⠀⠀⠀⢀⢻⠘⣃⠈⢓⡈⢛⠸⡇⢀⡄
⠀⠀⠀⠀⠀⠀⠻⣆⣾⠑⢰⡏⢲⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠘⣿⡸⣷⠄⠹⠯⠰⣿⠡⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣦⣸⠋⢰⡏⢸⣿⢿⠇⢸⠃
⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠈⠁⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⠈⠁⠀⠁⠀⠁⠘⠂⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠙⢲⠄⠒⠒⠀⠤⢤⡞⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⡌⣠⠔⢎⡹⠀⠀⡇⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠻⠤⢟⡁⠀⠀⠀⢱⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⢣⣾⣷⠀⡱⢠⣾⣷⠀⢧⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⡜⠙⣌⡿⢟⣶⣷⣞⡻⠯⣄⣈⣳⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠉⠸⣀⠈⠉⠉⠉⠀⢀⡼⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠙⢲⠒⠉⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⣀⠀⡨⢶⣄⣀⡀⠀⠘⠀⣀⣀⣤⠖⠣⢄⠀⣀⠠⠤⣀
⠀⠀⠀⠀⠀⢀⣴⡁⢘⢱⠀⡴⡿⡄⢸⠀⠙⢍⡿⣿⣻⣟⠕⠉⡆⡠⠚⣟⡄⣶⢠⢲⢳
⠀⠀⠀⠀⠀⡎⠧⢆⡨⠭⣄⡓⠃⠘⣾⠀⠀⠀⠑⢻⠗⠁⠀⠀⢹⠀⠀⣀⠀⣀⠀⠉⡜
⠀⠀⠀⠀⠀⢱⠀⡎⠀⠀⠀⠈⢦⢠⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢶⠊⠀⠀⠈⡆⠀⡇
⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⣀⠷⠊⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡇⢀⠇
⠀⠀⠀⠀⠀⢰⢡⠃⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣱⢔⡡⠊
⠀⠀⠀⠀⠀⠸⡘⠦⣀⡼⢄⡀⠀⠀⠀⠀⠀⣀⠜⠉⠢⢄⣀⣀⣀⣀⠤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣒⡒⠒⠁⠉⢉⡀⠉⠉⠉⠀⢀⠀⠀⠀⡔⡆⡦⠠⡦⠀⣾⠇⢸⡽
⠀⠀⠀⠀⠀⠀⣸⡀⠈⢸⠟⠀⡧⠋⡇⠀⠀⠀⠸⣀⡠⣸⠉⡀⡇⢀⣇⢀⢣⣀⢸⢣
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣠⠀⢇⠆⢣⣀⠀⠀⠀⠧⠚⠀⠒⠁⢈⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠂⢠⡠⢤⢠⡴⢢⣤⠔⡆⠘⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⢑⠼⡁⡸⠸⣁⠼⠹⠀⠃⣴⢠⣧