Pocket Watch Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣬⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣵⡾⠋⠁⠀⠀⠉⠛⢟⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠈⣇⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢷⣄⠀⠀⡀⠀⠀⠀⠠⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⠀⠀⠀⠠⠄⣿⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣶⣶⡞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠁⠀⠀⠉⠉⠉⠙⠛⠹⠷⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢲⠂⠀⠀⠀⠀⠀⠀⠀⢨⡛⢿⣶⣄
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠰⣈⢣⠀⠀⠀⠀⠀⢃⣸⠀⠀⠀⠀⠀⡰⠂⠀⠀⠈⠀⡙⢿⣷⡀
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡷⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠉⠆⠻⣿⣄
⠀⠠⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⠶⠹⣿⡆
⠀⠂⠀⠀⠀⠀⠈⠉⠙⠒⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⡿⠛⠁⠀⠀⠀⢹⣿⡀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⣿⣧
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿
⡇⠀⠀⠠⢠⡔⠒⣋⡅⠀⠀⠀⠀⠆⠀⢤⣤⢦⣞⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⢤⣴⡆⠀⢸⢸⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡎⣿⡿
⠀⢆⠀⠀⠀⠀⢤⠶⠑⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⣦⠄⠀⣸⢹⣿⠃
⠀⠘⣆⠀⠀⠀⠈⢫⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠋⢀⣰⣣⣿⠏
⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡕⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⢀⠞⣱⣿⠏
⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⢾⠏⢰⠃⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠀⠈⠳⠄⠀⢀⡰⣫⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠙⠢⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡄⣷⠀⠀⠀⠀⠀⠈⠀⣤⠴⣫⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⡢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠄⣒⣩⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⣒⣦⠤⢤⣀⣦⣴⣶⣶⢶⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣒⢢
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠬⢿⡋
⠀⠀⠀⠀⠀⢸⡿⣥⣄⠀⠠⢤⡀⠀⠀⠀⠀⢠⠞⠉⠀⠨⠀⠊⡃
⠀⠀⠀⠀⠀⢸⢰⣯⠈⡱⢶⣌⡸⠇⠀⠀⠀⣿⠀⠈⢲⣀⣠⠄⠐
⠀⠀⠀⠀⠀⣿⢸⡾⠀⠐⠚⠀⡓⠐⣆⠀⠀⣿⡀⢀⠀⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⡟⠈⢿⣶⣧⣖⣉⣀⣴⡏⠀⠀⠈⠻⣦⣌⣀⣠⡴⠀⠀⣠⠔⠂⢂⠂⠀⣷⣦⡇
⠀⠀⠀⢀⡞⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⡜⣁⠂⢀⠈⠐⠃⢱⡌⢧
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⢳⡄⠀⠀⣤⡀⠰⡇⡅⠀⠐⠓⠠⢠⣈⡇⢸⡆
⠀⠀⠀⠈⠳⢤⣄⣤⠤⢚⣉⣀⣀⣤⣄⣠⡤⠶⠋⠀⠀⠀⠻⡿⣶⣿⣄⠂⡀⢠⡐⢦⡼⠃⡞⠀⡴⠛⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⣷⣿⡓⠶⠶⠖⠋⠀⠈⠳⠒⠃⠀⡖
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢚⣚⡒⠲⠶⠄⠲⠖⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠓⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⡾⠦⠼

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠚⠉⠉⠉⠛⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢀⣰⡦⢦⣠⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⠹⢿⠟⠋⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢐⠶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⢴⣧⣤⣥⣴⣤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢻⣭⠷⠒⠛⠚⠋⠙⠉⢛⡉⠛⠛⠾⢶⣭⣙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⡁⠶⠛⣀⣬⠔⠒⠂⠀⠈⠉⢀⠈⠉⠙⠛⠓⠚⠧⢍⡁⠀⢀⡁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡠⠎⠁⡨⠖⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣁⠰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣰⠟⢀⠐⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠑⢌⠙⠛⡛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⢈⡴⠃⠀⠀⠀⠀⠀⢰⠀⠆⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⢆⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⢳⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⢠⠂⠀⠂⠀⢄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠔⠀⢳⡁⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠓⣰⠏⠀⠀⠀⠠⠏⡔⠁⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢷⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡓⢻⠀⠐⠂⠘⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣾⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠤⠀⢻⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣶⣤⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠃⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⢹⡏
⠀⠀⠀⠀⠀⠀⢀⠘⡄⢹⡀⠀⠀⠀⠀⢀⠀⢀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠘⠛⠛⢺⠃
⠀⠀⠀⠀⠀⠀⠀⢧⢱⡄⢳⡀⢀⡀⠀⢘⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠲⠆⠰⠃⡘⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢆⢳⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠁⣤⠓⣄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⢀⠐⡀⠟⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠿⣈⠑⠆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠰⠋⠀⠁⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡙⢤⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠔⣁⣦⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⣤⠑⠂⢤⣀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⣠⠄⠒⠉⠤⠄⢋⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢈⣁⣉⣙⡒⠒⠖⠶⠶⠞⣟⢛⣏⠹⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣶⡶⠿⠾⠿⠶⣶⣄⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⢀⠖⠋⣙⣿⣯⡉⠑⢆⠀⠀⢀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠿⠀⢠⣆⠀⣀⣿⣿⣿⣧⢀⣿⡆⠀⡀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⢦⠀⢿⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠁⢀⡿⠋⠉⠉⢿⣿⣿⡀⠔⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⢸⣿⣿⣄⣴⣥⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇⠀⠀⠀⢘⠛⣛⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠙⠛⢭⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢾⠗⠛⠓⢻⣿⣿⠦⠤⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠚⠉⠁⠀⠀⢀⣀⣀⣀⣀⣈⣁⣀⣀⠀⠀⠀⠀⠀⠀⠠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⣀⣤⣴⠶⠟⠛⠛⠉⠉⠉⠉⠉⠁⠁⠉⠙⠛⠱⠶⣆⡤⠀⠀⠈⠹⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⣠⣴⠞⠋⠁⠀⠀⡀⠀⠆⠀⠤⠀⠰⠆⠀⠆⠀⠰⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡴⠟⠉⠀⣠⡄⠒⠄⠀⠀⠀⠀⠐⢿⡀⠀⢸⣷⣷⠀⠀⠀⠀⠀⠡⠖⢠⣄⠀⠈⠓⢀⠀⠈⠋⠓⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡴⠋⠀⠀⠰⠀⠀⠑⢾⡄⠀⠀⠀⠀⠀⠘⣷⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⢀⣤⠉⠀⣄⠄⠀⠀⠦⡠⡀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⣴⠁⠀⢀⡴⠋⠀⠀⠀⠂⠀⠛⢷⣄⠀⢻⣄⠀⠀⠀⠀⠀⢹⣇⣻⣿⡏⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠗⠀⠀⠁⠘⢢⠰⣎
⠀⠀⠀⠀⢀⡞⠁⢀⣤⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠷⣤⣻⣆⠀⠀⠀⠚⠒⠛⠛⠛⠓⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠑⡘⢧
⠀⠀⠀⠀⣾⠁⠀⢺⠁⠀⣀⠑⢀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠀⠀⠙⢈⢣⠠
⠀⠀⠀⣼⠃⠀⣄⠂⠀⠀⠛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⣄⠛⠁⠀⠀⠙⡆⠀⢣
⠀⠀⢰⡏⠀⢐⠃⠀⠀⠊⠀⠉⠉⠛⠛⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣽⠟⠋⠉⠀⠑⢠⠀⠀⠘⡀⠘⡆
⠀⠀⡘⠁⡀⠟⠀⢀⠓⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠣⠀⢿
⠀⠀⠉⠀⡇⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠈⢀⢇⠸⡄
⠀⠀⠁⠀⠈⠀⠀⡇⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠒⠀⠀⠜⡌⠀⡇
⠀⢰⡀⢸⢐⠀⠀⣧⠀⣀⣠⣶⠶⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⠀⣶⠀⠀⡜⡇⢀⡇
⠀⢸⡇⠸⠐⠀⠀⠁⠀⣿⣭⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⣠⣀⣤⠴⠖⠛⠉⠁⠉⠉⠉⠉⠛⠛⠷⠶⣤⣤⣀⣀⣀⣀⡀⠘⠿⠿⠿⠿⠶⠿⠀⠀⠀⠀⢻⠃⠈⡇
⠀⠸⡃⠀⡇⠀⠀⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠔⠛⠛⠋⠀⠀⡠⡖⠢⠋⠉⠉⠙⠖⠢⣄⠀⠀⠀⠀⠈⠙⠙⣿⠿⠷⠦⠄⣀⠀⠀⠀⢀⠀⠀⠀⢸⡆⢸⠃
⠀⠀⣯⠀⢳⠀⠀⠘⠁⠀⠀⠀⠀⢀⣤⣴⣦⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠚⢆⠀⠀⠀⠀⠀⠀⣸⣶⣤⣀⠀⠀⠈⠐⡊⠃⠀⢐⡟⡱⡘
⠀⠀⢹⣄⠘⣄⠀⠀⠛⠀⢠⣴⢾⣿⠿⣿⡿⠇⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢀⣴⢿⣟⡿⣿⣿⣶⠄⠀⠉⠀⠀⣼⠙⣴⡇
⠀⠀⠈⣿⣧⠱⡀⠀⠀⠐⠀⢿⣯⡷⠟⢉⣴⠞⠁⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠙⠻⣿⣿⡷⣯⡟⣀⠉⠀⠀⣸⠗⣶⡘
⠀⠀⠀⠘⣿⢇⠱⡄⡀⠀⠿⠊⠋⠀⣰⠟⠁⠀⠀⠀⣰⣦⡏⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠀⠛⠁⠀⢠⡏⢈⣷⠃
⠀⠀⠀⠀⠘⢟⢧⠹⣄⠀⠀⠰⠂⠙⠃⠀⠀⠀⢀⣼⢻⡟⢁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡈⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⣛⣴⣯⠃
⠀⠀⠀⠀⠀⠀⠛⠷⣈⢇⡠⠀⠀⠃⠀⡀⠀⣠⡾⣱⠏⠀⣸⡷⢤⡀⠀⠀⠀⠀⠈⠃⠀⠀⢀⡤⠇⠀⠈⠻⣦⡀⠀⠀⢀⡀⠈⠁⠀⢀⡶⣻⣟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⠑⢎⠀⠀⠈⠀⠠⠈⠻⠏⠀⢰⡿⠀⠀⠐⠛⠶⢀⣀⣀⣐⠦⠙⠋⠀⠀⠀⠀⡀⠈⠛⠀⠦⠀⠁⠀⣀⡼⢋⣵⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡄⠀⠀⠀⠀⠀⠀⠻⡂⢀⠙⠃⠀⠀⠀⠀⠀⢸⣟⠀⠹⣧⠀⠀⠀⠀⠀⠀⡁⡰⠗⠀⠀⠀⣀⡴⢋⡔⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢶⣀⠀⢥⣤⣀⠀⠀⠉⠀⠐⠋⠠⠶⠀⢠⡈⣉⣄⠀⣉⠀⠰⠄⠘⠓⠀⠁⠀⣀⣠⣴⣞⣣⣖⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣙⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣯⣿⣟⣻⣿⡿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣯⢾⣵⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠺⣿⣾⣣⣤⠒⠒⠌⣛⢄⡒⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠁⢀⣿⡿⢏⠟⣢⡍⠉⢳⠋⠀⠦⡈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡿⡾⣦⢄⠀⠙⢋⣤⣬⣤⣀⠟⠀⠻⣏⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⣿⠋⢻⣫⠈⠓⣢⠟⠉⣼⣷⠟⢶⡠⠾⠚⡣⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⠀⣿⣛⠺⣿⢀⡤⠈⡦⢴⣤⣿⠀⠀⢿⡀⣠⠔⣍⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⡏⠀⣿⣿⣶⠈⠀⠀⠀⠰⡀⠀⠉⠀⠀⢸⡇⡀⠀⣧⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠅⠀⠸⣿⣯⣦⣙⣠⡞⠁⢠⡁⠲⠦⠴⠋⣁⠈⢀⣻⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠟⠀⠀⠀⠹⣿⣿⡗⠿⡢⣄⡺⠋⠀⠰⠶⠀⠙⣠⡾⠝⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠞⠀⠀⠀⠀⠀⠈⢿⣿⣗⣻⣏⣽⡛⣲⣲⣖⣶⣾⣽⣧⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣷⣿⣽⣟⣺⣿⣦⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⡶⢷⡼⠷⢶⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣞⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⣴⣄⣷⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⠿⣗⣴⣶⣮⡬⠻⠛⠉⢀⣀⢀⣀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣰⣿⣿⠿⠻⠟⠻⠖⠿⠶⠿⠿⣿⣷⣾⣿⢿⣿⠞⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠻⠛⠁⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢠⡶⠈⠀⠐⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣇⡀⠀⡀⣀⣀⣤⣶⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⠻⠏⠟⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣤⠤⠰⠤⢤⣔⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋⠀⠀⠀⠀⠀⠈⠻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⠴⠒⢲⡖⠲⢤⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠀⣇⣤⣀⣆⣧⣴⣿⡇⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⡆⢙⡿⣿⠿⣿⣯⡝⡁⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⡇⠙⠀⢸⣷⣹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣬⣤⣭⡯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠧⠤⠤⠽⠧⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠺⠋⠉⣁⠐⠀⢐⣛⣛⣛⠃⠀⠀⠉⠙⠂⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠋⠀⠀⣀⠤⢚⣒⡩⠭⠥⠤⠬⢭⣙⡓⠦⢄⡀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠠⢀⢴⣾⠶⠛⡁⠀⠀⠀⠰⢲⠀⠀⠀⠈⠑⢶⣍⠂⢄⠀⢨⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡶⠂⣡⠎⠁⠀⠙⣷⡀⠀⣇⠺⠯⠀⠀⠀⢀⠎⠀⠈⠳⣄⡷⣅⣸⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⢡⡾⢁⠀⠀⠀⠀⠈⠁⠀⢻⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⢦⠘⡿⣿⡞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⢀⢊⡟⠀⠉⠙⠲⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠈⣇⢿⢹⣾⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⡶⢦⣄⠀⠀⠀⠀⠀⠀⢠⡞⢲⡄⠀⠀⠀⠀⠀⠀⡤⠤⠤⠄⡇⡇⢹⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⡇⡀⠈⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡸⡄⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⡸⢀⠃⣷⡞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣍⢳⡑⡘⢓⠝⠋⠀⠀⠀⠀⠀⠀⢻⣎⠀⠀⠀⠀⠀⠈⠻⢉⠓⣰⣣⠏⣰⡿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠄⠳⣔⢄⠀⠀⠀⡴⡷⠀⠀⠀⠈⠇⠀⠀⠀⣄⠀⠀⠀⢀⡜⣡⢏⣼⣿⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣢⡈⠳⣕⢄⡘⢫⠅⠀⠀⠀⠈⣦⠀⠀⠀⠙⠦⣀⡴⢫⠖⢁⣽⣟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣦⣈⠓⢬⣑⠢⢤⣄⠀⣀⣉⣀⠡⠤⠐⣉⠥⣊⣴⣶⢟⣩⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣍⠳⣦⣄⣉⡑⠂⠁⠉⢉⣉⣲⣬⣇⣤⣿⠿⣛⡵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠭⣿⣛⣛⡻⠿⠿⠿⣛⣛⣯⠽⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣖⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⡟⢶⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣾⣤⣍⢿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿
⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠹⣄⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⢹⡷⣮⡛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁⠈⢻⣮⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡐⣒⣥⣿⣿⣿⣗⣀⣠⣽⡆⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣵⠾⢋⠉⠀⠤⢶⠀⠀⣉⠛⢿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣑⠪⣢⠀⠀⠈⠉⠀⣰⠇⠀⠀⣈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠠⢦⠳⢹⠢⣀⠀⠀⢰⠃⡀⠐⡖⠉⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⢤⣀⠆⠀⠀⠛⢷⣴⢃⠰⠃⠀⠀⡤⣀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠉⠉⠀⠆⠀⡦⠈⠛⠀⡤⠀⠄⠀⠉⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⢖⠆⠃⢀⠢⡄⠀⠂⠀⡤⠀⠀⠰⠣⢀⣼⣿⠃
⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠶⠶⠿⣿⣷⡀⠀⡠⠂⠀⠀⠆⠀⠀⢖⣀⠀⣀⣾⣿⠷⠖⣛⣋⣹⣿⡷
⠀⠀⠀⢾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣷⣮⣀⣀⠈⠋⠀⣀⣠⣴⣾⣿⠟⡁⠀⠀⠉⠉⠉⠉⠉⠉⠉⢻⣦
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⠿⠿⣿⡿⠿⠿⠛⠛⠋⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠉⠉⠉⠛⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣰⣿⣿⣿⣿⣿⡆⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣥⣈⡉⢩⣝⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠓⣒⣠⣭⣤⣷⣲⣭⣭⣦⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⣶⡶⠟⠛⠉⠉⠀⣬⡴⡆⠉⠉⠙⠛⠷⣾⡙⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣢⣾⠿⣏⣱⡤⠀⠠⠀⠀⣀⢤⡅⡄⠐⠀⠀⠀⢠⠏⠙⠶⣌⠙⣷⡄
⠀⠀⠀⠀⠀⠀⢀⢌⣴⡟⠁⠀⠈⠁⡤⢶⡀⠀⠀⢸⡆⡇⡇⠀⠀⠀⣠⠄⠐⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠠⢻⣿⢋⡀⠀⠀⠀⠙⠳⣄⣳⡄⠀⠒⠙⠓⠃⢀⠆⣰⠃⠀⠀⠀⠀⠄⡠⠖⠹⣿⣄
⠀⠀⠀⠀⠀⢄⣾⠧⣬⠡⢠⠄⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⢘⡟⠆⠀⠀⠀⢀⡠⢖⡄⠐⠟⠁⢻⣿⡄
⠀⠀⠀⠀⣌⣿⡏⠀⢈⠀⠛⠛⢓⡲⠀⠀⠀⠀⠀⠀⠀⠒⠷⡆⠀⠀⠀⠈⠫⠚⠁⠀⠀⠄⠀⠀⢿⣷
⠀⠀⠀⠀⠋⢻⠃⠀⠀⢀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⡿⢻⡙⣙⠄⠸⠚⠛⣹⠀⠀⠀⠀⠀⠀⠀⢾⠷⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣗⣛⢸⣿⡇
⠀⠀⠀⠀⢡⡿⡇⠀⠀⠈⠉⠉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⢷⡀⡀⠀⠉⠉⠉⠉⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⢸⣷⣧⠀⠀⡀⢤⣶⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣾⡦⣄⠀⠀⠀⠀⠀⡿⡟
⠀⠀⠀⠀⠀⢯⢿⣦⡶⣆⠈⠋⣡⠞⠁⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⡷⠋⣠⠀⠀⣼⣽⠃
⠀⠀⠀⠀⠀⠈⢿⣿⢖⠛⠀⠀⠁⠀⣠⢫⢯⡇⠀⠠⡄⣄⠀⠀⢲⣄⠀⠀⠀⠈⠀⠘⠷⢉⡴⣽⠃
⠀⠀⠀⠀⠀⠀⠈⠻⡿⣷⣄⠀⠀⡀⠉⠳⢸⠅⠀⢀⡇⢻⡀⠀⠀⣈⠆⡀⠂⠀⠀⡠⣠⣎⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⣿⣷⣼⢁⡖⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⢠⠐⣇⠀⢀⡠⣞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣳⢵⣤⣄⡀⢀⢘⡐⣏⢀⡀⢀⡀⣓⡬⣖⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⠿⢽⣿⣷⣶⣺⣿⠽⠷⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠓⢶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⠋⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⡰⠀⠈⣿⣯⣷⣄⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣿⣷⣾⣿⣿⣿⡟⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢸⠋⠏⠙⣿⣿⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣂⣃⣀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢙⣻⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠁⠈⠁⠉⠉⠉⠐⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁⠀⢀⣠⠄⠀⠀⠀⡀⠀⠀⠀⠄⣀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠻⣶⣄⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⡄⣠⠎⠁⠐⣴⡀⠀⠀⢰⣾⠀⠀⠀⠠⠂⠀⠈⠙⢿⣦⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠞⠘⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠀⠈⢻⣿⣦⡌⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠈⠐⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢺⡵⠛⠁⠀⢻⣿⣿⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡇⢠⣤⣀⡆⠀⠀⠀⠀⠀⠀⣾⣻⡏⠀⠀⠀⠀⠀⠠⣦⣴⣦⠀⣿⡟⣧⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣇⠀⠀⣀⣴⣤⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⢠⣦⣄⣀⠀⣰⣿⣿⠇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡽⣦⡘⣫⠞⠁⠀⢀⡀⠀⠁⢸⠇⠀⠐⠀⠀⠀⠀⠉⠛⠋⣰⡿⠻⡋⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣿⣟⢥⣄⠀⠀⢀⡾⠇⠀⠰⠸⠗⠂⠈⠁⠰⡄⠀⢀⢀⣴⢟⡵⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⢿⣿⣿⣷⣄⡈⠀⠀⠐⠀⡀⡀⠀⠐⠃⠀⣈⣠⣶⠿⣭⠞⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣿⣿⣮⣝⣆⠂⠂⠄⢤⣬⣤⣤⣶⡿⢟⣫⣵⠞⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣶⣦⣤⣤⣶⣶⣾⣿⡯⠅⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⢐⡿⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⡋⠍⠀⣒⠒⠈⠡⢑⡲⠆⡀⠀⠀⣿⢣⡐⢄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡋⠘⣭⢦⡀⠀⠸⡆⠀⣱⡶⠀⠐⢈⢢⡰⣏⣷⣽⣯⣀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡕⣠⣀⠈⠓⠉⠀⠀⠄⠀⠈⠁⠀⣼⣦⠱⡑⣽⡈⠹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡯⠚⢐⣻⡿⠁⠀⠀⠀⢠⣷⠀⠀⠀⠀⠙⠋⠁⠳⢨⣷⠀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⡦⡀⠀⠀⣼⣏⠀⣀⣤⠀⠀⠀⠀⠀⣹⣝⡀⠀⠀⠀⠀⠤⠤⢄⡏⣿⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣞⠢⡀⢿⣹⡄⣛⡭⠀⠀⠀⠀⠀⠉⠉⠙⠭⣠⡙⠂⠀⠀⢰⠇⢸⠀⠀⢸⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⢿⣿⣧⠙⢾⢿⣧⠁⣀⠴⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⠯⠗⡼⠈⡿⠀⠀⢸⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢻⣿⣿⡌⢻⡿⣧⡀⠞⠁⠀⣀⠀⠀⢀⡀⠀⣴⣷⣄⢀⡜⠕⣾⠃⠀⣤⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠹⣿⣿⣦⠙⣿⢝⡲⣀⠊⠇⠀⢸⣿⣿⠀⠈⣋⠵⡫⣪⡾⠁⢀⣄⡿⠃⠀⠀⠀⢀⡴⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡘⢿⣹⣷⣜⠟⠷⣶⣅⣲⢶⠶⣖⣒⣁⣩⣵⡶⠟⠁⠀⠀⣌⡿⠀⠀⠀⠀⣶⡾⠃⠈⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⢙⣿⣿⣯⣆⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⢙⢷⣤⣀⠠⣤⡭⠀⠀⠀⠐⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠛⠛⠉⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠉⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣔⣭⣯⡽⠿⠞⠛⠲⢿⣶⣶⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣾⠋
⠀⠀⠀⠀⠀⢰⣾⠏⠀⠀⠀⢀⢤⣦⣤⣄⠀⠙⠓⠻⠿⠿⣷⣤⣴⠶⣤⣦⣤⠄⣤⣀⣄⣠⣄⡠⣤⣤⣤⡤⢦⣴⣶⣯⡿⠛⠋
⠀⠀⠀⠀⠀⢻⣏⣄⠀⣠⣀⣸⡦⡄⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠙⠛⠙⠛⠛⠓⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠯⠿⣿⣿⣿⡿⠿⣟⡤⢤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠐⢦⣈⣉⣉⣩⣭⣭⣁⠲⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣠⣷⠾⠛⠛⠉⠉⠉⠉⠉⠙⠛⠿⣷⣦⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠙⣅⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠰⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⡈⢦⡀⠀⢀⣿⠁⠀⣹⣽⣿⡿⡇⡀⢀⠔⢡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣼⣏⣀⣿⣤⣴⡿⠿⠿⣿⣃⣠⣽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣶⣶⣶⢲⣖⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣉⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⠹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢴⣤⣄⣤⣤⠤⣬⡀⠀⣿⣷⣿⡶⢤⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⢈⡙⠿⠛⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠭⠛⣻⠷⣯⣝⡛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠉⠁⢀⡀⠤⠘⠒⠒⠠⠉⠉⠉⠉⠩⠕⠒⢒⡠⠤⣀⡉⠒⠯⣙⠷⣦⣵⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠪⠁⠀⢀⡠⡔⠊⠓⠀⠀⠀⠀⠀⠀⠀⠠⣦⢴⠀⠀⠀⠀⠀⠉⠑⠛⡤⣀⠉⢋⣘⢿⣷⣦⣠⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠙⠁⡠⠒⠓⠁⢀⣐⢦⡀⠀⠀⢀⠀⡄⠠⠄⢠⡄⠀⠀⢠⠀⡀⠀⠀⠀⣠⠉⠫⢶⣅⠻⣿⣯⡻⣿⣦
⠀⠀⠀⠀⣠⠏⠀⠀⢀⡴⠊⠂⠀⠀⠀⠈⢠⡄⠐⠂⠈⠀⠀⠀⣤⠤⣤⠀⠀⠀⠀⠁⠘⠀⣤⠉⠀⠀⠀⠙⢷⣌⠻⣿⣾⢿⣧
⠀⠀⠀⡰⣁⠃⠀⣴⠋⠀⠁⠀⠀⠀⡀⠒⠀⣠⣴⡆⠀⠀⠀⠀⢸⡄⡟⠀⠀⠀⠀⠀⢀⡤⠀⠀⠂⡀⠀⠀⠀⠙⢷⡔⠹⣧⣻⣧⡄
⠀⠀⡼⠑⠁⠀⡜⠁⢀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠻⣝⣄⠀⠀⠀⠒⠚⠛⠀⠀⢠⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠾⣷⢻⣏⠆
⠀⣼⠑⠀⠀⣾⠁⠠⡬⡍⢀⡈⠀⡀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⠈⣠⠀⠚⠃⠘⣧⡰⢫⢿⣏
⢰⡟⠀⠀⡸⡅⠀⠀⠀⠀⡌⠁⠼⠷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢀⣠⢖⡻⠆⠀⠀⠀⠀⠀⢸⣷⢫⣞⣿⣤
⢸⠃⠀⢨⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢹⠗⡄⠀⠀⠀⠀⠀⠘⠓⠉⠀⠀⠀⠀⠒⠀⠀⠀⣿⡞⢹⣿⣧
⣾⠁⠀⢸⡀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢹⣇⢿⣿⣿
⡏⠀⠀⢸⠂⠐⣚⡁⣤⠀⢹⡿⣿⣟⠛⠿⠶⠶⡷⢦⣤⣤⣤⣤⣤⣲⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣖⣶⠀⢀⡀⠠⣀⠸⣿⢰⣿⣿
⡗⡤⠀⢸⡁⠀⠉⠁⠀⠀⠘⠁⠀⠙⠁⠀⠀⠈⠓⠂⠀⠉⠙⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠚⠻⠃⠀⠀⠙⠉⢀⣿⢨⣿⣿
⢷⠇⠀⢸⡁⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣜⣿⣿
⢻⠁⠂⠈⣤⠀⠀⠀⠀⣁⠀⢶⣲⡽⢟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⣀⠀⠀⠀⠤⠀⠀⠀⣸⡇⣿⣿⣿
⠈⣇⠀⠀⢡⠆⠀⢀⣀⠁⡤⠈⢯⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⣌⣕⡿⠀⠀⠀⠀⠀⢀⣿⣹⣟⣿⣿
⠀⢹⡆⠀⠀⢞⡄⠉⠵⠀⠠⠄⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⠃⡈⠷⠀⣼⢏⣿⣿⣿⡇
⠀⠀⢻⡄⢠⠈⠜⡄⠀⠀⠀⠠⠆⠀⠀⢀⡴⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢁⣾⠃⢾⣿⣿⡏
⠀⠀⠈⢿⣤⣢⡈⠞⠤⠀⠀⠀⠈⠁⡄⠀⠙⢾⠃⠀⠀⠀⠀⠀⢸⢰⡄⠀⠀⠀⠀⠀⢛⢦⠀⠀⠀⠠⠄⠀⠀⠀⣠⡾⣱⣾⣿⣿⠋
⠀⠀⠀⠀⠻⣷⣵⣄⠢⡠⣄⠀⠀⢠⠄⡘⠃⣀⠀⠀⠀⠀⠀⠀⣸⡊⣀⠀⠀⠀⠀⠀⠈⠀⢤⡀⠁⠀⠀⠀⢀⣼⢏⢔⣿⣷⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣾⣦⣈⠊⠳⡤⠘⠵⠃⠀⠀⠐⠃⠠⡆⠀⣀⠈⣀⠁⠀⠀⠀⠀⡄⠈⠂⠨⣄⡂⠀⣠⣶⢟⢕⣵⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣈⠂⢙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠁⢀⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣤⠞⠋⣀⣴⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣕⡠⣎⠶⣭⠛⣦⢶⣀⣤⣀⣀⣈⣉⣂⣀⣀⣠⣤⣴⡶⢞⡛⣍⢄⣲⣿⣿⣿⠫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢿⢿⣿⣶⣦⡄⢋⡉⠶⠛⣛⣋⣉⣉⡉⠛⣓⣢⣬⣿⣮⣿⣿⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⣿⠿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⡿⠿⣿⡿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢈⣵⣶⣶⡶⢖⡶⠦⣴⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣶⣞⡿⠯⠽⠙⠏⠩⢉⠛⠓⠒⠦⠤⣀⡀⠀⠀⠀⢻⣦⣌⡿⢼⣿⡇⣾⡇⢺⠉⣽⣶⣝⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⣿⣿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⢉⠓⠒⠲⠤⣄⣀⠉⠓⠦⣄⣀⠿⡻⢦⠀⡇⠉⠻⣿⣟⣼⣡⣿⢹⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣿⡷⠚⠉⡀⠀⠀⢀⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠈⠻⣄⢨⣮⣷⣿⣾⣿⢋⣛⠿⠿⠇⢈⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢱⡿⠋⠀⠀⠀⠀⠲⣦⣄⠙⢶⣄⠀⠀⠀⠈⠉⠀⠀⠀⠄⠤⠶⠀⠀⠀⠑⢄⢸⣿⣿⣿⠟⠻⠿⠾⢯⣿⣿⣿⡥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠃⣿⠁⠀⠀⠦⡤⡤⠠⠀⠁⠀⠀⠹⢯⣶⣄⡀⠀⣀⣰⣶⡶⠒⠀⠀⣀⡀⠀⠀⢺⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡁⡇⠀⠈⠀⠀⠐⠒⠁⠀⠀⠀⠀⠠⢪⣿⣿⣿⡿⡯⠁⠈⠁⠀⠀⠉⠀⠀⠀⠀⠈⣿⡇⣿⣏⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⣇⠹⡄⠀⢀⡤⠒⠀⠀⠀⠂⠀⠠⠜⠓⠨⢭⠍⠚⠁⠀⠀⠀⠀⠠⠀⠴⡆⠀⠀⢀⡿⢱⣿⠹⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣶⢱⠐⠆⠹⣦⡈⠂⠀⣁⠀⠀⠀⢠⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⣠⠞⣡⣿⠧⠘⡞⡷
⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠘⠅⣈⠻⢦⣄⡈⠐⠤⣀⢸⠀⠀⠀⢀⡄⠀⠀⠐⣆⠲⡄⠀⠀⠂⠛⢁⡠⠔⢊⣥⡾⠛⣁⠈⡼⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡝⣄⠳⣄⠀⠁⠀⠉⠛⠷⣦⣤⣉⠑⠐⠒⠴⠦⠤⠤⠤⠭⠦⠓⠖⠒⢃⣉⣥⡶⠞⠋⠁⠤⠜⣠⠞⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠳⣌⠳⢤⡀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⣶⣶⣤⣤⣶⣶⠶⠾⠟⠛⠉⠥⢠⢰⠲⢈⡠⢞⣡⠞⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠙⠦⣍⣗⡦⣄⣀⡀⠀⠀⠀⠀⡄⠠⢠⠖⠀⣄⡤⡀⠲⠶⠕⠦⢇⣀⣥⣞⣯⡶⠟⢡⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠙⠛⠶⣿⣭⣝⣓⣒⣲⣶⣶⠤⠤⠤⠤⣶⣶⣶⣶⣾⣿⣿⡿⠿⢛⠉⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣩⡤⠶⣒⣵⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣶⣤⣭⣭⣁⣀⣀⣐⣒⣒⣂⣖⣚⣋⣭⣵⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠃⢫⣿⠙⢮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣉⣋⣡⣤⣤⣈⣈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣫⠶⠛⠋⠉⠉⣀⡀⠉⠉⠛⠷⣦⣌⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣵⠟⠁⠀⢶⡀⠀⠀⢿⠇⠀⠀⣠⠂⠀⠙⢷⣄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠹⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡞⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠹⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠈⠉⠀⠉⠉⠉⠀⢾⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⣀⡤⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠈⠉⠊⠀⠀⡠⠀⠀⢀⠀⠀⠘⠄⠀⠈⠙⠟⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⢀⡞⠓⡀⠀⠈⠀⠀⠀⠑⢄⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣾⣿⡷⣤⣀
⠀⠀⠀⣴⡿⢛⣯⣤⠿⠟⢳⡄⠀⠀⣀⣀⣀⣤⣀⣀⣀⡀
⠀⠀⠀⠉⢿⣾⣿⣿⣴⠛⣾⣧⠶⠟⠟⢻⠿⠿⠟⠺⠿⠿⢿⣶⣤⣀
⠀⠀⠀⠸⣾⡅⠀⠈⣭⣾⡟⠁⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⢀⠍⠛⠿⣦⣄
⠀⠀⠀⠀⢻⣷⣄⣀⡾⠿⢠⣆⡄⠀⠀⣠⢶⡄⠐⣮⠃⠀⠀⠺⡶⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠙⠓⣾⣀⣰⣿⣿⡇⠀⠀⠈⠋⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⢴⢤⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⣿⣷⡇⠁⢮⡢⠄⠀⠀⣀⠔⠱⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⢿⣿⢻⡀⠀⠁⡀⠀⠀⠀⠀⠀⢘⣤⡀⠀⠀⠀⠀⠀⠰⢄⠠⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⢿⣆⢣⡠⢾⡬⠆⠀⠀⠀⠀⠈⠻⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⢻⢷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠈⣿⣧⠣⡀⠁⠀⠀⠀⠀⠀⢀⡄⠀⠈⠄⠀⠀⠀⠀⢰⢄⠀⠈⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡔⠘⣿⢷⡝⢆⠀⣖⢦⠀⠀⠀⡏⠀⠀⠀⠀⠶⠀⠐⠀⠀⠀⠀⠅⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⠈⣻⣟⣮⣙⢤⡁⠀⠀⣠⣅⠀⠀⠀⡀⡀⠀⠠⣠⠀⠀⢠⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⠻⢿⣿⣷⣝⣶⣄⣉⡁⠀⠀⠘⠡⠀⠀⠀⠁⢐⣰⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣿⣿⣿⣿⣷⣿⣿⣶⣶⣤⣤⣤⣤⣴⣶⣿⠿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣙⠛⠏⠛⠿⠿⣿⣿⣿⡿⠛⢋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣤⣤⣬⣭⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡮⠟⠒⠚⠓⠒⠒⠶⢶⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⠁⠀⣴⡒⣒⣒⣲⣶⡆⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣦⣀⠌⢿⠟⣿⣿⡿⠤⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⢷⡿⣷⣖⡻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠋⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣐⡶⠤⣽⣿⣿⣿⣿⡦⠖⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⠝⠚⣁⣤⠴⠖⠒⠒⡛⠒⠒⠲⠦⣤⣈⠙⠫⣶⣄
⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⣡⠴⢋⠁⠀⠀⠀⠀⠤⠄⡄⠀⠀⠀⠀⢉⠛⢦⣄⠙⢷⣦
⠀⠀⠀⠀⠀⢀⢮⠎⣠⠞⠁⠀⠀⡆⢰⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣄⠙⣕⡄
⠀⠀⠀⠀⢠⣳⠃⡼⠁⠀⠀⠀⠀⠁⠈⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠈⢿⣆
⠀⠀⠀⢀⢯⠇⡼⠁⠁⢲⠊⡆⠀⠀⠀⠀⠐⠱⠛⠛⠓⠛⠃⠀⠀⠀⠀⠀⠺⡰⠈⠀⢳⠘⣿⡆
⠀⠀⠀⣼⡿⢰⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⡇⢹⣷
⠀⠀⠀⣯⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⠸⣿⡀
⠀⠀⠀⡿⣿⣿⠀⠙⡘⠀⠀⠀⢀⠀⢀⣀⣤⠤⠾⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠐⢸⢠⣿⡇
⠀⠀⠀⣇⣿⣿⠀⠀⠀⠀⠠⠔⠣⠝⠉⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⠃
⠀⠀⠀⢸⣻⣿⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠈⠳⢄⡀⠀⠀⣤⠀⠀⢠⣿⣿⡿
⠀⠀⠀⠀⢫⢿⣷⡀⠄⠎⠑⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠚⢄⠒⠛⠠⢄⢾⣿⣿⠁
⠀⠀⠀⠀⠀⢫⢿⣷⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠿⠃⠀⢀⠀⢠⡄⠀⠀⠑⠄⡠⣳⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠱⣽⣿⣷⣄⠀⠀⡰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚⡀⠀⣠⣾⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣿⣓⠢⢀⡀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⣀⣵⣾⣿⣿⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣬⣅⣐⠒⠀⠀⠀⠒⣂⣻⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣤⣤⣭⣥⣾⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠛⠉⠉⠁⠈⠉⠉⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣤⣾⣷⡾⣷⣦⡄⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⢀⣸⣿⣿⣿⣿⣿⣿⢧⣀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣽⣿⣿⣿⣵⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⢿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠛⣋⣥⣤⠶⠶⠶⠶⠶⠶⢦⣤⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣉⣤⠖⠛⠉⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⣠⡾⠋⠀⠀⠃⠀⠀⠀⠀⠀⣶⠀⡰⠀⠀⠈⠐⠠⠔⠀⠈⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣾⣿⠟⢁⡾⠋⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠠⠄⠀⠀⠀⠀⡇⠀⡱⠆⠀⠈⠻⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣾⣿⡟⢠⡟⠀⣄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠊⠀⠀⠀⠄⢀⠘⣿⣿⣿⣿⡆
⠀⠀⠀⣾⣿⡟⢠⡟⠀⠀⠈⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⣴⡞⠁⠀⠐⠀⡖⠈⢃⠀⠘⣿⣿⣿⣿⡄
⠀⠀⢸⣿⣿⠁⣾⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠏⠀⠀⠀⠀⠰⠆⠀⠀⠄⠀⢸⣿⣿⣿⡇
⠀⠀⣼⣿⡿⢠⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⠀⠀⣿⣿⣿⣿
⠀⠀⣿⣿⣧⢸⡇⠀⠶⠀⠦⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄⠀⣿⣿⣿⣿
⠀⠀⢻⣿⣧⠸⡇⠀⢸⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⣿⣿⣿
⠀⠀⠸⣿⣷⡀⣿⠀⠀⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡤⢲⡶⠻⢿⡉⠛⠳⣄⠀⠀⠀⡄⠀⠀⠄⠀⢰⣿⣿⣏⡟
⠀⠀⠀⢿⣿⣧⣸⣇⠀⠈⣀⢀⠳⡀⠀⠀⠀⠀⣾⡁⠀⠀⣀⠀⠀⣹⣄⠀⠀⠉⠂⠀⡇⠀⠄⠀⢀⣾⣿⣿⣽⠃
⠀⠀⠀⠈⣿⣿⣿⣿⣆⠈⠁⢌⠀⠀⠀⠀⣀⣸⠀⠀⠀⢠⡄⠀⠀⠀⢸⣀⠀⠀⠀⠀⠁⠘⠛⢀⣾⣿⣿⣷⠏
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⡀⠀⠁⠀⠀⠀⡠⠑⣤⠀⠀⠀⠀⠀⠀⣀⣘⠀⡄⠀⠀⠀⠁⠀⣠⣿⣿⣿⣻⠏
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠁⠀⠘⠀⡄⢠⡄⠀⠠⠀⠀⠀⠠⣈⠀⢀⣠⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠈⢨⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠙⢿⣿⣿⣿⣿⣯⣅⣀⠀⠀⠉⠀⠀⠉⠉⠉⠙⠿⠯⠅⠌⠉⠭⢭⣭⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠗
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣼⣂⣀⣐⣂⣀⣀⣐⣀⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣯⣭⣽⣗⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣀⣤⣤⣤⣤⣄⣄⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣩⡿⠟⠛⠛⠛⠛⢿⣯⡛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢰⢁⡏⠀⠂⠀⠀⠀⠀⠀⣠⠔⠀⠀⠙⡆⢡
⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⠰⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠒⣦⡎⠁⣴⣲⠀⠀⣽⠘⣯⡇
⠀⠀⠀⠀⠀⠀⣼⣿⡦⢟⡿⣿⣿⣾⣷⣶⣿⣯⢟⡻⣼⡿⡇⠀⠀⠀⠀⠀⢠⢸⡄⠀⠀⠀⢀⠀⠀⢀⡀⠈⠀⠀⠀⡾⢸⠛⠃
⠀⠀⠀⠀⠀⢠⡗⠋⣪⠗⠋⠁⠀⠀⠀⠀⠀⠉⠑⠪⣗⠝⢿⡀⠀⠀⠀⠀⠈⢎⢷⡄⠀⠀⠈⠁⠈⠉⠉⠀⠀⢀⣾⢇⣿⠇
⠀⠀⠀⠀⣠⠋⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠳⣖⣦⠀⠀⠀⠈⢯⣿⣦⣄⡀⠀⠀⠀⠀⣠⣴⣿⣷⠋⠈
⠀⠀⠀⢠⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⢹⡿⠂⠀⠀⠀⠘⣿⢻⠿⢿⣿⣿⣿⡿⠿⠟⢻⡏
⠀⠀⠀⡞⢀⡏⠀⠀⠘⠲⠤⣀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣷⣤⡄⠀⠀⠀⠻⠼⠀⠀⠀⠀⠀⠀⠀⢠⠼⠁
⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⣀⣀⣉⠻⣷⡄⠀⠀⣏⣹⠀⠀⠀⢸⠀⣿⣷⡇
⠀⠀⠀⢧⢸⡇⠀⠀⠀⣾⣿⣿⣿⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡿⠛⠃⠀⠀⠀⣴⢲⠀⠀⠀⠀⠀⠀⠀⠐⢲⡀
⠀⠀⠀⠘⡌⣿⡄⠀⠀⠻⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠐⠀⣰⡿⣰⢷⠄⠀⠀⠀⢠⣿⡼⣶⣾⣷⣿⢿⣿⣶⡦⣾⣇
⠀⠀⠀⠀⠙⣜⢿⣄⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡱⠿⠏⠀⠀⠀⢀⡞⢡⠞⠉⠀⠀⠀⠀⠀⠉⠛⢆⠹⡄
⠀⠀⠀⠀⠀⠘⡦⣟⢿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣠⣴⡿⣫⣾⠁⠀⠀⠀⠀⢀⠎⡴⠁⠀⠄⠂⢁⠀⠀⠈⠂⠀⠀⠳⡘⡆
⠀⠀⠀⠀⠀⠀⢻⣿⠗⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣷⡇⠀⠀⠀⠀⠀⠸⢰⠁⠀⠈⠀⠀⠈⡄⠀⠀⠀⠈⠀⠀⢣⢸⣤⡄
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿⣿⠰⡿⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠻⠃⠐⠐⠀⠂⠀⢸⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠊⠁⠀⠀⠀⠀⠀⠀⠸⡸⣆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡟⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡻⣦⡀⠉⠂⠀⠀⠀⠐⠀⠀⣠⡾⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣤⣄⣀⣀⣤⣴⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣽⣟⣛⣻⡯⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⠉⠙⠛⠛⠛⠛⠉⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠉⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠒⠉⠀⠀⠀⢦⠾⠃⠀⠉⠁⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣴⡀⠀⣀⣀⢀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠻⠋⡏⡏⡏⠍⠋⢀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣤⣤⣤⣤⣤⠤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣂⣀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣟⣚⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠻⠛⠛⠛⠿⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠁⠀⠀⠀⠀⢀⠰⠂⠀⠐⠄⠀⠰⠖⠄⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⣏⣸⡃⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠇⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡀⠀⠂⣶⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡄⠠⠀⡠⠀⠀⠀⢡
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠐⠀⠀⠀⠛⠑⠊⠀⠀⠀⠄⢀⡤⢸⢁⠠⡀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⣥
⠀⠀⠀⠀⢸⣿⠀⡠⢄⠀⠄⠺⢸⠀⠀⠀⠀⠠⠖⢡⠆⣤⣞⣻⣆⠀⣱⣤⡀⠀⠀⠀⠀⠈⢤⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣿⠀⠁⢀⠀⠀⠀⠀⠐⠒⠚⠛⠙⠀⠂⢀⠀⠈⠉⠀⠸⠷⡽⡧⡀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⢰⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠛⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠃⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠹⣿⡄⠆⠀⠠⠀⠀⣼⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠌⣯⠀⡀⠠⠘⠂⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢻⣷⡀⢂⠀⠤⠀⠈⠀⠀⠀⠤⠄⠀⠀⠀⠰⡆⠀⠀⠀⠀⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠐⡀⠀⠀⠀⠀⠀⢀⡎⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⡈⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠢⣄⡀⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠀⡀⠤⠚⠁⣠⡴⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠈⠉⠒⠒⠂⠘⠧⠒⠐⠒⠈⠁⣀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠴⠴⠤⠤⠴⠶⠶⠟⠛⠉⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢤⣶⣤⣤⣼⣦⣤⣤⣤⣤
⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡆⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣹⠀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠿⠶⠶⠶⠤⠶⠶⠶⠶⠶⠶⠶⠶⠿
⠈⢅⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⡄
⠀⠀⠑⠢⠤⠤⠤⠆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠉⢉⣀⠀⠀⠀⠀⠀⠀⢀⡴⢿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⠀⢀⡀⠀⠀⠀⠀⣀⣈⣀⣼⠁⠀⠀⠀⠀⢀⡤⠒⠉⢸⡀⠈⠙⢆
⠀⠀⠀⠀⠀⣇⢠⢄⡠⠀⠘⠀⠀⠈⠦⡄⠀⠀⠈⡇⠀⠀⠉⠀⠀⠀⠀⠀⠜⠁⠀⠀⠘⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠉⢠⠋⢰⣄⠀⢀⡀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠘⠁⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⢺⠐⠀⠈⠓⠋⠀⠐⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⢀⣀⣔⠇
⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠈⠀⢀⠀⠀⠀⠀⠀⠈⠚⠶⢾⢿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠑⠀⠀⣀⡀⠀⠀⠀⠀⠀⣆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄
⢠⣠⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⠃⠈⠉⠳⡄⠀⠀⢠⣿⠋⠀⠀⠀⣀⣤⣬⣤⣾⣜⣂⣐⣒⣢⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠘⣆⢀⣾⡏⠀⠀⠀⠀⠈⠥⢤⣤⣤⣤⣤⣤⣤⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢹⣾⠋⠀⠀⠀⠀⠉⡉⠡⠉⠉⠁⠀⠉⠉⠙⠉
⠀⠀⠀⠀⣀⠄⢂⠄⠀⠀⠀⠀⠀⠀⢴⡈⣿⣷⣄⣠⠾⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂
⠀⠀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⡠⠉⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠁⠈⠁
⠀⢈⠀⠀⠀⠈⠀⡂⠀⠀⠀⠀⡜⠀⠀⢴⠀⠐⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣀⣂⣀⠂
⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⠀⠀⢦⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸⠀⢃
⢠⠆⣶⣔⡐⠚⠒⠐⡆⠀⠀⠀⠁⠌⣀⣤⠶⠗⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⢈⣵⣶⣶⡶⢒⡶⠦⣴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣞⡻⠯⢩⠩⠍⠭⠉⠛⠛⠒⠶⠤⣄⡀⠀⠀⠀⢻⣶⣬⡿⢼⣷⣇⣼⡇⢺⠉⣽⣶⣌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⢉⠋⠓⠒⠦⢄⣀⠉⠛⠢⣄⣀⠿⡛⢦⡀⡇⠈⠻⣿⣿⣾⣡⡿⢹⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢪⣿⡷⠛⠁⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠉⠒⢄⡈⠙⢆⢨⣾⣷⣿⣾⣿⢋⣛⣻⣟⡃⣀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⢱⡿⠋⠀⠀⠀⠀⠳⣦⢄⠙⢶⣄⡀⠀⠀⠈⠁⠀⠀⠀⠄⠴⠖⠀⠀⠀⠙⢆⢸⣿⣿⣿⠛⠻⠿⠿⠯⣿⣿⣯⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢇⣿⠁⠀⠀⠦⢤⠤⠤⠀⠀⠀⠀⠹⢯⣿⣄⣀⡀⣀⣴⢶⡾⠋⠀⠀⣀⡀⠀⠀⢹⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡀⣇⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠨⣿⣿⣿⡿⣯⠁⠈⠁⠀⠉⠁⠀⠀⠀⠀⠈⣿⡇⣿⣏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣇⠹⡄⠀⢀⡖⠒⠀⠀⠐⠂⠀⡲⠌⠁⠐⠶⠖⠛⠁⠀⠀⠀⠀⠂⠐⠲⡆⠀⠀⢀⡿⢰⣿⠹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢤⢱⠀⢀⠙⣦⡀⠀⠄⣀⠀⠀⠀⢠⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⢦⣀⠀⠀⠀⠀⣠⠞⣱⡿⢧⠘⡌⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⢣⡘⢀⢈⠛⢶⣤⣀⠑⠢⢀⣰⠀⠀⠀⢀⡜⠀⠀⠐⣦⠒⡆⠀⠀⠐⢋⡁⠤⠒⣋⣥⡾⠋⡅⢈⡜⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡙⢆⠱⣄⠈⠀⠀⠈⠛⠿⣶⣤⣈⡁⠒⠒⠠⠧⠤⠤⠤⠮⠦⠛⠒⠂⣉⣡⣤⡶⠟⠋⠀⠠⠞⣠⠎⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠳⢬⡓⢤⣀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠶⠶⢶⣶⣶⣶⠶⠾⠿⠛⠋⠉⠰⢀⡴⠓⢈⡴⢚⣡⠞⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⡙⠲⢬⣕⡲⠤⣀⡀⠀⠀⠀⠀⠄⠰⢠⣖⠀⣤⡔⡀⠺⠢⠘⠶⢃⣠⣴⣚⣽⡾⠋⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⠀⠉⠙⠷⢿⣭⣍⣙⡓⠒⢶⡶⠶⢶⡶⠶⢶⡶⣶⣶⣾⣿⣿⠿⠟⣋⠁⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⠀⠀⠈⠉⠙⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣡⡴⢖⣫⣵⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⣶⣭⣭⣭⣄⣀⣀⣒⣒⣂⣛⣹⣭⣭⣶⣾⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠈⠁





⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡟⣉⣿⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣂⠭⠉⠉⠩⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢸⡐⣲⣙⣹⣗⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣉⡙⣉⡭⠷⢽⠿⣆⣀⠀⠀⠀⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣥⠀⠀⠈⠛⣿⣉⣷⣯⡿⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠻⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢓⣬⣿⡐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠄⣂⠈⠩⢭⠁⣒⠀⠀⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢔⡠⠂⠁⠀⠀⠀⣎⠁⠀⡌⠰⢅⠢⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⢢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠗⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⠌⠃⠀⠀⠁⠀⠀⡀⠴⠞⠋⠈⠁⠠⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⣄⡀⠠⠤⠤⠤⠴⣾⠛⠐⠀⠀⠀⠀⢘⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠄⢃⠘⠀⠀⠀⠀⣀⠀⠙⣇⠀⠀⠀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⡌⡇⢸⡇⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⣯⢀⠁⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡕⢌⠪⣁⠀⢲⠆⠀⣠⡄⠀⠙⢇⢀⡴⡡⡁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡒⢆⠤⠀⡙⠃⠠⠈⣁⣈⠊⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣁⡉⠀⣀⠀⠨⢝⠒⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠾⠿⠿⢿⡿⣿⣿⣿⣉⡉⡉⣉⠒⡒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠍⡉⢉⢁⢀⡐⠒⠒⠂⣀⣀⡤⠐⠀⡈⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠂⠐⠀⠐⠊⠁




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⢾⡤⣒⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡞⠸⢺⠀⠀⡆⢑⡀⠀⢀⠔⠀⠀⡠⠦⡁⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠼⠅⠤⠬⠅⢀⣃⠀⠀⠰⠁⠀⢀⠌⠀⠀⠈⠄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠠⠄⠀⡀⠀⠀⠀⠀⠉⠛⠤⡀⠠⠂⠀⠀⠀⠀⠈⡀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠔⠂⠀⠈⠀⠀⠒⠤⢀⠀⠀⠁⠀⠀⡀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⢀⣀⠀⠀⠈⢄⠀⠀⠀⠀⠀⡆⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠾⢹⣆⠀⠀⠈⠂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠡⠀⠀⠀⡟⠢⠀⠀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠉⠀⠀⠐⠀⠤⢀⡀⠀⡠⠀⡀⠀⠈⠷⠆⠀⢃⠀⠀⠈⠁⠀⠀⠀⢃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠅⠀⢐⠀⠀⠈⡄⠀⠀⠈⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠇⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⡐⢁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣜⠁⡰⡆⠘⠀⠀⠀⠈⠆⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠰⢾⡀⢠⠀⠀⠀⠻⠤⠄⢇⠀⡀⠀⠀⢀⠆⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⠀⠀⠀⠐⠁⠀⠀⣀⢠⡁⠀⠀⡅⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠉⠐⠀⠀⠉⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡋⠀⠀⠀⠀⠀⠀⠈⠀⠀⣇⠀⠐⠀⢠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⡈⠁⠂⠀⠀⠤⠒⠁⠀⠀⣀⡴⠀⠀⠀⠀⠀⣻⡤⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠠⠄⣀⠀⠀⠀⡛⣽⠂⣤⠤⡤⢄⣿⣇⠀⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠀⡅⢹⢌⠀⢰⡀⢀⢹⠛⡰⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠐⠂⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠔⠁⠀⠀⠀⠀⠀⡋⢧⣀⠗⠁⣀⠃⠺⡶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠫⠁⢢⠔⡁⡘⠁⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢡⠹⡆⠁⠀⠜⢉⢜⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠨⠅⢒⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⠳⡞⡋⢩⠴⠗⡺⡺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠠⠖⠈⠀⢀⣀⠠⠄⠈⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⣠⣴⠶⠞⠛⠛⠛⠛⠛⠛⠶⢶⣤⣀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⡾⠋⢉⣠⣴⠶⠟⠛⢛⠛⠛⠷⢶⣤⣀⠙⠻⣦⣄⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣴⠟⢁⣤⠾⠋⣅⠀⠀⠀⠀⣿⡅⠀⠀⠀⢀⡍⠻⢦⣄⠙⢷⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⣠⡟⠁⠀⠀⠹⠇⠀⠀⠀⢿⠇⠀⠀⠠⠿⠁⣀⡀⠙⣦⡀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣼⠏⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡌⢿⡄⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣸⠏⠀⠈⠙⠃⠲⣦⣀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠛⠉⠀⠈⢿⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣿⠰⠶⠶⠶⠆⠀⠀⠀⠀⠈⢹⣏⣿⠁⠀⠀⠀⠀⠰⠶⠶⠶⠶⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢹⡆⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣾⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢻⣄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⣾⠃⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠹⣦⡀⠀⠀⣰⡆⠀⠀⠀⣾⡆⠀⠀⠐⣶⡀⠀⠀⣠⡾⠁⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣦⡈⠻⢶⣄⡋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣃⣴⠾⠋⣠⡾⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠛⢶⣄⡉⠛⠳⠶⣤⣤⣬⣤⣤⡶⠶⠛⠋⣁⣴⠞⠋⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠉⠛⠻⠶⣦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠉⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⡩⠕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⢀⠤⠂⠁⢀⡠⠔⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠂⠁⣀⠤⠒⠁⢀⠠⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⡔⠈⢀⠠⠐⠉⠀⡠⣴⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢹⣎⣀⡀⢄⣒⣥⣮⠶⠦⠤⠽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡁⠉⡺⠽⠃⣀⡤⠄⠀⠲⠤⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⡼⠃⣠⠊⠀⠁⠀⠀⠆⠀⠀⠀⣀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⢠⡅⠀⢠⠀⠀⢸⠀⠀⠀⠈⠉⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠑⠒⠿⠀⠀⠀⠀⣀⠄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⢌⠢⢄⣤⣀⣀⡀⠦⠔⠊⣠⠊⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣞⠢⠤⠤⣤⠤⠔⣒⠩⠕⠚⠉⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡔⠅⠂⠁⠀⢀⣀⠤⠒⠈⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠣⣤⠤⠒⠈⠁⢀⠀⠄⠒⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠦⡔⠂⠉⠀⡀⠤⠒⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⡖⠈⠀⠀⢀⡠⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⣁⣈⡩⠥⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣤⣴⣤⣤⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⡿⠞⠛⠉⠉⠉⠉⠙⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⢀⢀⣀⣀⣀⣀⢀⡀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⢰⣿⣮⣽⣯⣿⣧⣿⣿⠀⠀⢔⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠛⠉⠉⠉⠛⠙⠫⢿⣷⣷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣴⣤⣤⣤⣷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣻⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠠⠤⠠⠘⠒⠛⠒⠻⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠉⣁⠤⣤⣒⣶⣶⣼⣼⣤⡭⣤⣶⣄⣢⣤⣞⣣⠄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣂⣴⣶⣧⡶⠿⠛⠋⠉⠉⠀⢠⣆⣠⢲⡄⠈⠉⠉⠛⠻⠿⣿⣦⡌⠑⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡡⢞⡭⠟⣭⠁⠀⠀⠀⠀⢀⠀⠠⠀⠉⠌⠈⠄⠀⡀⠀⠀⠀⠀⡀⡽⠿⢶⣀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢊⣴⣿⠟⠋⢻⣤⡴⠞⠀⠀⠈⠀⠀⠀⢲⡆⠒⡗⢰⡆⠀⠀⠈⠀⠐⠀⡿⠋⠀⠀⠙⠳⣄⢀⡙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡠⢊⡷⠁⠀⠀⠀⡅⠀⣡⠰⣆⠀⠀⠀⠀⠀⣿⠀⡇⢸⡇⠀⠀⠀⠀⢀⡶⠂⠐⠀⡀⠀⠀⠈⢢⡹⣯⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⣾⣷⠏⠀⠀⢀⠀⠂⠠⠾⢤⡆⠈⢧⡀⠀⠀⣠⠇⠷⠷⠸⠇⠀⢀⠁⢀⡞⠁⠀⠀⠀⠀⠄⠀⠀⠀⣹⡜⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⣽⠃⣔⣦⠀⠄⠀⠀⠀⠀⠀⢙⢳⠾⠛⠀⠀⠀⠀⠀⠀⠀⣀⣰⠇⠐⠻⠀⠀⠀⠀⠀⠀⢀⡈⠐⠚⣉⢄⡀⢿⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠢⣰⣽⠷⠤⣲⠀⠂⠼⠄⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡍⠐⠀⠀⠀⠀⠀⢀⣠⠴⢋⣵⡈⠘⠓⠉⠀⠘⣧⢿⡄
⠀⠀⠀⠀⠀⠀⡈⢢⣧⠏⠀⠀⠁⠀⠸⠛⠛⠷⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢲⣤⣄⠀⠀⠀⠀⠀⠈⢻⡵⠞⠉⠀⠀⠀⡄⠀⠀⠐⠸⣿⣷
⠀⠀⠀⠀⠀⠀⢃⣹⣽⠀⠀⠀⠈⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠔⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡇
⠀⠀⠀⠀⠀⢘⠀⡈⡟⠀⢀⡀⠁⢠⡀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠰⢸⣟⡷
⠀⠀⠀⠀⠀⢸⠀⠃⣏⠙⣀⢃⠀⢰⠶⠛⠛⢙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣯⣭⣭⣭⣭⠀⠈⠏⢛⡃⢸⣟⡷
⠀⠀⠀⠀⠀⠸⠀⣤⣿⠀⠉⠁⠀⢲⠖⠒⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⢏⡘⠳⣄⠀⠀⠀⠀⠐⠟⠛⠛⠓⠛⠀⠈⠛⠉⠁⢸⣉⡿
⠀⠀⠀⠀⠀⠀⡴⢸⢸⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠩⢤⣑⣄⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡯⢽⠇
⠀⠀⠀⠀⠀⠀⢰⡼⡏⣧⠀⠀⠈⡀⠠⣔⣫⠵⣺⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣑⠦⣄⠀⠀⢀⠁⠀⠀⢀⢠⠳⣿
⠀⠀⠀⠀⠀⠀⠈⡴⢻⡹⣆⢠⢤⡄⠄⠩⠞⠋⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣽⡺⣽⣦⡝⠃⢀⠀⠀⠀⢀⡎⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣥⠱⣹⡟⢉⣶⡀⠄⠀⢶⠋⠀⠀⢀⡼⣳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠶⠟⠀⢀⡛⡠⠀⢀⡞⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡦⢳⡟⣎⠉⠀⠀⠂⠀⠀⠀⣠⠞⡴⢁⡾⠀⠀⠀⢲⠂⣦⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠝⠠⣠⠟⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⣮⣧⡀⠀⠀⠀⠀⠀⠉⠺⢥⢀⡇⠀⠀⠀⢸⠀⢹⡄⠀⠀⠀⠠⠙⣦⠄⠀⠤⠀⠀⠀⠀⡀⢀⡤⢉⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⣍⢢⡀⠀⠾⠓⣀⠀⠀⠈⡁⠀⠀⠀⠾⠠⠀⠷⠀⠀⠀⠈⠀⠆⣨⠀⠀⠀⠀⡀⢈⡴⢏⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢘⢷⣾⣿⠇⢠⣅⠁⠀⠀⠀⠈⠀⠀⣀⠂⢀⠀⠀⠀⠁⠀⢴⡊⠹⡄⠀⠀⣠⡴⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣝⡳⢂⢤⢂⠤⢄⣀⠀⠀⠀⠁⠚⣍⠀⠀⠀⠀⣀⠀⠛⣂⣥⠖⣟⣧⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣭⣛⣛⠶⠖⠺⠠⣭⣤⣉⣩⣭⡍⠒⠶⣂⣻⣭⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⠶⠶⠿⠶⠶⠞⠛⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢒⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠤⡄⣤⠄⡤⢤⡀⡤⢤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠄⠻⠤⠏⠿⠀⠻⠭⠁⠇⠸⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⣀⣀⠀⣀⣀⢀⡀⢀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣨⡇⣓⣲⠸⣇⣸⢸⡇⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢐⡢⣀⢄⢴⠐⢀⣴⠀⠀⢢⣀⠤⢤⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⡀⢀⠀⠀⢀⡀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠁⠀⠀⠀⠄⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠈⠁⠀⠀⠉⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠐⠁⠀⠘⠘⠒⠃⠁⠃⠀⠓⠐⠚⠒⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠋


⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠢⠤⠤⠤⠤⠤⢤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⣤⣾⠟⣩⣟⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⢀⡰⢯⣀⣴⡿⣛⣵⣿⣿⣟⣛⣿⣯⣻⠿⠛⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⢀⡄⠀⢀⣼⡿⠛⠉⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠈⠓⠒⠛⡏⢹⡦⣤⣧⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣯⣭⣭⣭⣭⣽⣟⡻⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⢿⢿⣿⡿⢿⣿⣿⣿⣿⣎⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠤⣓⠈⠉⢘⠸⢿⣿⣦⣽⣿⠛⢿⡻⣧⡹⣿⣷⣴⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡔⡵⠊⠀⠀⠀⠀⠈⠢⣽⣥⢬⣻⡄⠀⠈⠙⠙⢜⠻⣿⣿⣾⣿⣧⣶⣿⠀⢀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡾⠁⠀⠀⠀⢀⠀⠀⠀⢹⣿⠶⠟⠁⠀⠀⠀⠀⠀⠁⠢⢌⣙⠻⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠙⢠⡀⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠐⣲⠶⠤⡵⢤⢸⡇⣤⣤⣤⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠈⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠭⠊⢸⡇⠀⣶⣶⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠟⣶⣤⣤⣔⡺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠸⡇⠀⠉⠉⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠋⠉⢚⡇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⡅⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠤⠠⠤⠀⢂⣩⡆⡤⠤⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣵⣞⣿⣿⣿⠶⣌⢣⡈⢲⡘⣆⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡾⣽⣿⣿⡿⣟⣿⣞⣧⢵⡀⣁⣨⡶⠾⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣨⠴⠐⣗⣿⢿⣷⣁⣷⣞⣿⢸⣞⣷⣽⡧⠆⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⢏⠂⢇⢻⡽⣿⣿⣻⣟⡷⣏⣾⣿⡟⠉⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠈⢎⢆⠈⢣⡙⢿⣿⣽⣯⣷⣿⣿⣫⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⣼⡶⣟⣩⠤⠴⠿⢶⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⣏⡒⣁⣠⣤⡶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉