Crab Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠁⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠶⠀⠀⢨⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢡⠀⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⠁⠀⡀⠀⠀⠀⠈⠉⠀⠀⠈⠑⠀⠀⠀⠀⠀⠙⠒⠀⢻⠂⠀⠸⢠⡀
⠀⠀⠀⠀⠀⡒⠠⠀⠈⡍⠹⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣹⡏⠀⠠⠖⢠⠇
⠀⠀⠀⠘⠀⠘⣆⡠⢀⠑⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⢀⡔⠀⢀
⠀⠀⠀⠐⠂⠀⠈⠢⢤⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠋⠠⢀⠉
⠀⠀⠀⠀⠀⣀⠀⢀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⣂⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠈⠀⠤⠵⠆⠀⠴⠶⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣵⣖⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⠔⠚⠋⢱⣄⣀⠀⠀⠀⠀⣀⣠⣤⢾⡑⠀⠀⠉⠉⠛⠓⠦⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊⠀⠀⠀⡶⠛⠉⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠙⠓⠞⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⡉⡛⢿⣙⣠⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣠⠶⠛⠉⠀⠙⢀⣁⣒⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣿⠀⢠⠾⠋⠨⠛⣤⠀⠀⠀⠁⣸⠛⢻⢿⢿⣎⢥⢴⣶⣶⣦⣤⣀⠈⠛⢿⣿⢛⡟⠂⠔⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢰⣿⣉⣴⣿⠀⠀⢀⣤⠛⣷⠀⢻⡀⠛⣶⣿⣫⣬⠘⢾⡌⠉⠀⠀⠈⠙⢻⠒⣤⣽⣿⣿⡆⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⣿⡇⢿⣿⣿⣤⠴⣫⣀⣶⣼⠻⢮⠇⢈⣽⣿⣿⣷⡀⣨⡷⡀⠀⠀⠀⠓⢀⢤⡟⠈⠻⣿⣿⡄⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡬⣿⣿⠇⣄⣽⣿⣿⣿⢆⣈⣰⣦⠙⣿⣿⣿⠗⠎⠀⢨⣿⣧⡤⠀⠐⠮⡿⣴⠃⠈⠿⡧⠀⢀⡾⢘⠇
⠀⡤⠀⠀⠀⠀⢹⣧⡘⠷⢶⣾⣿⣿⣿⣧⣶⣿⠛⢀⣴⠟⠛⢿⣿⣄⣴⣿⣿⣿⡿⠀⠦⠀⠈⢫⠙⡋⠀⡰⢂⣾⢣⠈
⠀⢳⣾⣦⣤⣄⠀⠈⠻⡖⢶⣿⣿⣿⣿⣟⠛⠧⠸⠟⠁⡄⢠⣿⣿⠛⠙⣿⢿⣟⠛⢷⡀⠀⠀⠀⠀⠀⠀⣠⠾⠡⠎⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠹⣿⣿⣿⡷⠤⢠⣦⣀⣿⣿⣿⣿⣿⣞⠀⠀⠀⠀⠀⢸⣿⠘⠀⣾⢻⣼⡿⠀⠈⠀⠀⠀⠀⠁⢠⣄⠘⢂⣠⡔⠒⢈⣩⠄⠀⠀⠀⠁
⠀⠀⠀⠈⠛⠾⠿⣶⣤⣼⣿⠻⣶⣿⣛⠙⠇⢗⡤⠀⠀⠀⠛⢠⡄⠀⢸⠂⠙⡿⢶⡀⠀⠀⠀⢈⣡⢶⢿⡟⡋⠉⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⡟⠻⠿⠿⣿⣿⣦⡋⠁⠁⠀⠀⡀⣸⡇⠀⠾⠀⠀⠀⠁⠈⣀⣴⡾⠯⠄⡍⣌
⠀⠀⠀⠀⢠⠴⢋⣩⣤⡞⢡⣴⣦⣤⣄⣹⣿⣿⣄⣀⣠⠤⠉⠀⠀⠀⠄⢀⣀⣀⣠⣞⣋⣀⣴⡖⠚⠓⠛⢶⣌⠒⣄⡀
⠀⠀⠀⣴⠟⠚⠋⠁⠀⠀⣠⠰⠙⠉⠉⠛⢛⣏⣯⣻⠽⣿⣿⢿⣭⣿⣽⢿⣿⣾⣿⡀⠉⣩⣉⣛⣷⢆⠀⠀⠈⠓⠪⣱⣄
⠀⠀⠀⡷⠀⠀⠀⢀⣤⠾⠋⠛⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠓⠌⠉⠉⠛⢧⠱⠄⠀⠀⠀⠀⢬⣃
⠀⠀⠀⠀⠀⢀⢤⡿⠉⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡉⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⠿⠟⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⢈⠉⠙⣳⣶⡤⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠰⢿⣶⠶⠂⠀⠀⠀⠈⠓⠦⣄⡉⢣⡀⡤⠋⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠑⢐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡦⠊⠀⠀⠀⠀⠀⢀⡀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠶⠏⠀⠀⠀⠀⠀⠂⠀⢠⠄⠃⠘⠈⢳⣬⡆⠀⠀⠀⠀⠀⠀⡄⠈⠉⠁⠻⣧
⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⢠⣶⡆⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⣿⡧⠠⣄⡀⠁⢠⢶⠆⠀⠀⠀⣠⡇⢀
⠀⠀⠀⠀⢻⡄⠈⢆⡀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠄⠈⡷⢀⣼⣿⠀⠀⣠⡾⠏⠀⡞
⠀⠀⠀⠀⠀⠡⣄⠀⠈⠀⠐⠯⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠛⠉⠉⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠤⣤⣀⡈⠩⢷⣄⣀⡀⣦⣄⣀⣦⣀⣤⣾⡿⠏⢀⣀⣐⡦⠀⠀⠋
⠀⠀⣠⣤⣤⣄⠀⣐⡀⠠⢧⠤⠤⠤⠄⢾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⣤⠤⠄⢠⡬⠁⢐⠂⠀⢠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⡠⠴⡂⢀⣀⠀⠗⠁⠀⠀⠈⠁⠀⠲⠀⣀⣀⢁⠶⠴⠆⠀⠲⠄
⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠼⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠦⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠋⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠈⢻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠃⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠉⢩⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⣿⣿⣿⣟⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢘⣿⣿⣿⡟⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⢿⣿⣧⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⠿⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⣷⣶⣶⣶⢞⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢶⣶⣶⣶⣿⡿⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⣄⣀⣉⣉⣭⣶⡿⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠻⣷⣮⣭⣉⣁⣀⣠⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠿⠿⣫⣴⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣬⡻⠿⢿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢛⣿⡿⠋⠁⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠈⠻⣿⣟⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠟



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡎⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠈⡆⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠼⠤⠚⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⠢⠼⠤⠼⡄
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡜⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠘⡄⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⢰⠁⠀⢀⠞⠀⠀⠀⠀⢶⠆⠀⣀⣀⣀⡀⠀⢶⠆⠀⠀⠀⠘⢆⠀⠀⢱⠀⠀⠀⠀⠀⣏⡇
⠀⠀⠀⠀⢻⡉⢢⡀⠀⠀⣏⢉⡶⠯⣄⠀⢀⡠⠔⡊⠉⠉⠀⠀⠀⠈⠉⠉⠒⠤⣀⠀⢀⡬⠷⣎⢉⡇⠀⠀⣠⠊⡹⠃
⠀⠀⠀⠀⠀⠙⢄⡱⢄⡀⠈⠫⣀⡁⢊⠗⠩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⠀⣁⡨⠋⠀⣀⠴⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣹⠒⠒⠢⠽⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠅⠒⠒⢺⡡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣓⣒⣒⣛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣓⣒⣒⣋⣉⣉⣀⡀
⠀⠀⠀⠀⠀⢀⠴⢺⡥⠼⠦⠤⠤⠤⣤⡤⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⡤⠤⠤⠤⠾⠤⣽⠢⢄
⠀⠀⠀⠀⠀⣷⠞⠁⠀⣀⠴⣋⣉⣉⣁⣠⠤⢜⣲⣄⣀⠀⠀⠀⠀⠀⢄⣂⣴⣛⡤⢤⣀⣉⣉⣉⡳⢄⡀⠀⠙⢶⡇
⠀⠀⠀⠀⠀⢿⠀⠀⢰⢧⠞⠁⠀⠀⡶⢿⡭⠥⠬⠷⠚⠋⠉⠉⠉⠉⠛⠲⠯⠤⠬⣭⢷⡄⠀⠀⠑⢦⢷⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠘⠇⠀⣼⢸⠀⠀⠀⠀⢱⠔⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠓⢴⠁⠀⠀⠀⢸⢸⡄⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣢⣄⠀⠀⠀⠑⠮⠤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠬⠖⠁⠀⠀⢀⣤⣪⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠱⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠐⣇⢀⡎⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣄⣠⣸⣶⠞⡵
⠀⠀⠀⠀⢠⠃⠀⠈⠙⠓⣅⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠈⠀⠫⠇
⠀⠀⠀⢀⡇⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢈⣰
⠀⠀⠄⢸⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣺⣻⠿⠓⠐⠻⠚⠻⢟⣻⡀⠀⠀⠀⠀⠀⠹⠇⠀⢄⣘⣿
⠀⢠⠀⢿⣶⠔⢀⡛⠟⠁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢠⡇⠀⠐⠀⣬⡇⠀⠀⢰
⠀⢸⠆⢸⡇⠀⠀⠀⡴⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢡⠀⠸⡅⠀⠀⠀⢰⠀⠀⠀⠈
⠀⠘⡄⢻⡅⠀⠀⠉⡇⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡄⣷⠐⠀⢤⡞⠀⠀⠰⡞
⡇⠀⠘⣼⢿⣄⡀⢀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣴⣟⠀⠀⠀⣰⠃
⢧⡀⠀⠘⢜⢿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣭⠎⠀⢤⡴⠃
⠈⢇⠀⠀⠈⠢⡙⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⡁⠈⣠⠞
⠀⠈⢳⡴⠤⠀⠉⠻⢶⣶⣾⣷⢴⣶⡆⣄⡀⠀⣢⠀⣴⡤⢦⡀⠀⠀⡀⢀⣠⡂⣼⠖⢲⣮⠴⠋
⠀⠀⠀⠙⠒⠒⠒⠒⠛⠓⠶⠾⣿⣿⣿⣧⣦⡟⠁⠀⢻⠇⠀⠑⣰⣾⣿⢻⣷⠞⠛⠛⠋⣡⠀⠀⠀⠀⣠⣤⠎
⠀⠀⠀⠀⠀⠀⠀⣠⣧⣬⣄⣀⣀⣬⣿⣿⣿⡄⣀⣁⣈⣁⠀⣠⣾⡿⣳⣿⡛⠉⠉⠉⣛⡍⠛⠒⠛⠋⠁
⠀⠀⠀⠀⣰⣦⡴⠋⠀⣠⣄⠈⠉⣉⣙⣻⣿⣻⢿⣿⣿⡿⢿⣿⣻⣽⣿⠛⠋⠉⣙⣿⠛⠷⡀
⠀⠀⠀⢐⣨⡟⠀⢀⡞⢹⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠛⠉⠉⠉⠻⣆⠀⠈⣶⠆
⠀⠀⠐⣿⡋⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢶⠀⠹⣄⡀
⠀⠀⠀⠈⠳⡀⠀⠈⣇⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠙⠀⠀⠘⠿⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢚⣳⠶⠂⠀⠀⠀⠀⠐⠶⣟⡓⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⢀⡴⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⢀⡴⠋⢀⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠙⢦⡀⠀⠀⠈⠳⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢻⡁⠀⠀⠀⢀⡞⠀⣠⠟⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⣄⠀⢳⡀⠀⠀⠀⢀⠟⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠁⠀⠀⠘⠷⠞⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠳⠾⠃⠀⠀⠈⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢯⡖⠒⢦⡀⠀⠀⠀⠀⢀⡴⠒⢲⡽⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀
⠀⠀⠀⠀⠀⠀⡿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢸⠀⢀⣼⠃⠀⠀⠀⠀⠘⣧⡀⠀⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠈⠒⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⢸⡆⣸⠃⠀⠀⠀⠀⠀⠀⠘⣇⢰⡇⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠐⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾⠉⠁⠀⠀⠀⠀⣀⣀⣷⡼⠤⠶⠶⠶⠶⠶⠶⠦⠯⣾⣀⣀⠀⠀⠀⠀⠈⠉⣷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⠀⠀⡽⣄⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⣠⠏⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠈⢻⠏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⡟⠁⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠓⠒⠦⣤⣀
⠀⠀⠀⠀⣠⠞⢉⡴⠷⠶⢶⣶⣶⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣶⣶⡶⠶⠾⢦⡉⠳⣄
⠀⠀⢀⡞⢁⡴⠋⣀⡴⠚⠉⠁⣀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⠈⠉⠓⢦⣀⠙⢦⡈⢳⡀
⠀⠀⣿⣹⠋⢀⡾⢋⡾⠓⠛⣩⡽⠋⠉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠉⠙⢯⣍⠛⠒⢷⡙⢷⡀⠙⣏⣻
⠀⠀⢿⠏⢠⠟⢀⡞⠁⢠⠞⣁⣠⢴⡾⠋⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠙⢷⡦⣄⣈⠳⡄⠈⢳⡄⢻⡄⠹⡿
⠀⠀⠀⠀⡾⣴⠏⠀⣴⠋⢠⡏⢠⡞⣥⠖⠋⠈⠳⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⠞⠁⠙⠲⣬⠳⡄⢹⡄⠙⣦⠀⠹⣦⢷
⠀⠀⠀⠀⢷⣿⠀⡼⣃⡴⠋⢠⡏⢀⡟⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⢻⡀⢹⡄⠙⢦⡘⢧⠀⣿⡾
⠀⠀⠀⠀⠈⠃⠀⣧⣸⠀⠀⡾⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⢷⠀⠀⣇⣼⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠟⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⡟⠟⢻⣷⣿⠃⠀⠀⣀⣀⣀⣀⣤⣤⣤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡉⠉⠉⠉⠁⠀⠀⠀⠺⠋⠉⠀⠀⠀⠀⣴⣶⣶⣶⠞⠁⠀⠙⠻⣋⣍⠁⢸⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣿⠓⠶⠂⠀⠀⠀⠀⠔⠀⠀⣠⣿⢀⡄⠀⣰⠟⠛⠉⢄⠀⠀⠀⠀⠁⠀⠶⠦⢷⡄⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠯⠽⠿⠿⢭⣟⣿⣿⣿⣿⢻⣷⣤⣤⣤⣤⣤⣊⣀⣴⣿⠿⣷⡿⠓⠉⢀⣀⣠⡴⠿⠤⠤⠤⢄⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⣔⣾⣁⠇⠀⠀⠀⠀⢀⣾⣿⣿⠿⢣⠿⠟⠈⠓⠂⣩⠇⣀⣀⣴⣇⣤⣠⣦⣠⠾⠋⠉⠁⠐⠒⠒⠛⠓⢺⣿
⠀⠀⠀⠀⢠⡟⢁⣿⡏⠀⠀⠀⠀⠀⢈⡿⠛⢹⣿⣷⣾⡻⢋⡽⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠈⠀⠸⣿⠁⠀⠀⠀⠀⣠⣿⡄⢰⣺⣿⣿⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣰⣿⠛⣧⣸⠛⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠃⠀⠈⣻⡀⠀⡟⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠟⢆⠘⢦⡙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄⠀⠁⠒⠚⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣉⣙⢛⣟⣋⡿⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢼⣏⠀⠀⠀⠀⢀⣠⣾⣾⣿⣿⣶⡴⣖⣠⣴⣾⢧⣍⣩⣭⣿⡿⣿⣿⣦⣄⡀⠀⠈⠳⣦
⠀⠀⠀⣠⡼⢿⡆⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣝⢿⣷⣿⣿⣿⡿⠉⣹⣿⡟⣻⣿⣿⣿⣿⣷⡤⡔⣾⢤⡀
⠀⠀⠀⢹⣧⢞⢿⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⢿⣿⡞⣿⣿⣾⣿⣼⡅⣼⡟
⠀⠀⠀⠀⣽⣧⣃⡹⣿⣿⣿⣼⣿⣾⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣽⣿⣿⣇⣴⣯
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣟⣿⣞⠁
⠀⠀⠀⠀⢀⣀⣤⣤⣼⣯⣿⡧⣭⡲⣝⡻⣿⣷⡙⢟⣿⣟⡛⣣⣿⣿⡿⣋⢻⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⣴⣿⣿⡿⠻⠿⠛⠁⠀⠻⠿⢾⢶⣾⢿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣽⠿⠟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠟
⠀⠀⠰⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠤⡀⠀⠀⣖⣚⣻⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣰⣿⡿⣿⣿⣿⠟⠁⢀⣀⣀⣀⣀⠀⢀⠄⠀⠙⠿⣿⣯⣷⣷⡄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢿⣿⣳⣭⣥⢀⣤⣶⣾⣿⣿⣯⣿⣿⣿⣾⣦⣀⣤⣴⣶⡿⡿⠃⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡹⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣠⣶⠿⠋
⠀⢀⡴⠾⠿⠿⠒⠾⠷⠶⣭⣟⣷⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣟⣻⣥⣷⣶⠾⠗⠿⠷⠶⢦⡄
⠀⠈⠀⠀⠀⣀⣤⣤⣴⣶⠴⣦⣭⣽⣟⣛⡿⣿⣿⣻⣼⣿⣏⣿⣿⣿⣿⣯⣾⣿⣿⣿⡿⠶⠶⣦⣤⣄⡀⠀⠀⠙
⠀⠀⠀⠀⢸⠋⠉⠀⠀⣀⣤⢰⣶⣦⣿⣯⣥⣅⠾⠟⣿⡿⣿⡟⠩⢶⣿⣿⣿⡿⢿⣠⣴⣤⣀⠀⠙⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡿⠷⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⠿⣿⣿⣇⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣾⠉⡧⢀⡴⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⣤⡇⠀⡿⢻⠃⠀⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢠⢃⡞⠁⣧⠀⡿⣿⠀⣰⠏⢿⡏⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡶⠦⠤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⠉⠀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠿⠾⠷⣯⣼⠃⠀⣿⢦⣤⣤⡽⢦
⠀⠀⠀⠀⠀⠀⢀⣴⣋⣽⠦⠶⠚⠛⠲⢶⡏⠳⣄⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣧⢀⡞⠉⣷⣀⠙⢳⣄⣧
⠀⠀⠀⠀⣀⣤⡿⠭⣶⠶⠶⠦⠤⢤⣀⠀⢳⡀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⡏⢀⣰⢁⠈⠳⣟⠉⢻
⠀⠀⣠⠾⣇⣀⣀⣠⠼⠲⠶⠶⠶⢶⡏⠛⢦⡙⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡿⠋⠉⠉⠉⢻⣿⣄
⣠⢎⡴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⢀⡞⠀⠙⣿
⠿⠋⠀⠀⠀⠀⠀⣀⣤⢤⡶⠒⠒⠶⠶⠶⠮⠿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡈⠓⡾⠳⠶⠶⣶⠋⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡴⠋⠁⣠⠜⠓⠒⠒⣶⣶⣶⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢜⣭⣿⣿⣤⡠⣄⣉⡿⠁⠀⠀⢠⡟⠲⠶⠒⢺⡏
⠀⠀⣀⡴⠚⢓⡶⠋⠁⣠⡴⠚⠋⠉⣉⣉⣭⠏⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣽⣿⣥⣼⢿⣿⡿⠃⣷⡼⠋⠀⠀⠀⠀⡟⠀⠀⠀⠀⣸⠃
⠀⣴⠁⣠⡾⠋⠀⠀⣰⠋⠉⡟⠉⠉⠉⠀⣸⠷⣴⠋⠀⡴⠀⢀⠀⢀⠀⠀⡀⢠⡿⣿⣿⠟⢹⡧⣄⣠⡴⠋⠀⢀⣠⠴⠒⡻⠛⢤⣀⠀⣰⠏
⠀⡟⢹⡇⠀⠀⠀⢠⡇⢀⡼⠀⠀⠀⠀⢰⠃⠀⠈⠻⢾⣥⣴⣏⣀⣸⡀⣀⣇⣈⣳⣤⣀⣠⣾⣷⠶⢿⡷⣀⠴⣫⡤⠖⣾⠇⠀⠀⢩⠟⠁
⠀⡇⢸⡅⠀⠀⠀⢸⠛⠉⡇⠀⠀⠀⠀⢸⠀⠀⢀⣀⣼⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⠟⠀⠀⠴⠟⠋⠁⢀⡾⠃⠀⠀⣠⠏
⠀⠹⣜⡇⠀⠀⠀⠘⣆⢰⡇⠀⠀⠀⠀⠘⡟⠋⠉⠀⠈⢳⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣛⣠⠤⠖⠋⠁
⠀⠀⠘⠧⠀⠀⠀⠀⠘⣏⠙⢆⠀⠀⠀⠀⢿⡀⠀⠀⢀⡼⠉⠉⠉⠛⠲⠦⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣙⣦⣀⠀⠀⠛⠒⢾⠉⠀⠀⠀⠀⠀⠀⠴⣶⣦⡤⣶⠾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⠤⣤⣄⣀⣀⣀⣀⣠⡤⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⡆⠀⢀⡤⡀
⠀⠀⠀⢀⠞⠳⣄⠀⢰⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⡠⠖⠂⠉⠐⠲⢄⣠⠖⢉⣀⡀⠉⠓⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⡴⠋⠀⢱
⠀⠀⠀⢸⠀⠀⠈⠣⣸⠀⠀⠀⠈⢆⠀⠀⠀⠀⡘⠀⢀⣾⣿⣿⣦⢀⠃⢰⣿⡿⣿⣆⠀⠈⡆⠀⠀⠀⠀⡰⠁⠀⠀⠀⠸⠊⠀⠀⠀⡸
⠀⠀⠀⠘⡄⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⠀⠘⣿⣧⣸⣿⠀⣆⢸⣿⣧⣼⡿⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠳⢄⡙⠻⠟⣋⠔⠉⠲⢝⡛⣛⡡⠔⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⣀⠀⠈⠣⣀⠀⠀⠀⠀⠀⢀⣈⠤⠏⠈⠒⠒⠒⠋⠀⠑⠒⠂⠤⢄⡀⠀⠀⡠⠃⠀⢀⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠈⠑⠦⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠀⠀⠀⠀⠀⢎⠀⠀⠀⢀⡤⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣈⠙⠲⠤⣀⡏⠀⠀⠀⠀⠀⢀⣀⢤⡤⡴⢶⠒⡏⢩⣈⡖⣯⠃⠀⠀⠀⠀⠀⠈⠦⠔⠊⣁⠤⢦⠀⠙⢄
⠀⠀⠀⠀⠀⢠⠎⠀⢠⠊⠀⠉⢲⣤⣄⠀⠀⠀⠀⠀⠀⠈⠻⡖⠧⢶⠴⡶⢺⠈⣇⡷⠁⠀⠀⠀⠀⠀⠀⢀⣤⠶⢯⡀⠀⠀⢣⡀⠈⢣
⠀⠀⠀⠀⢠⠃⠀⡰⠃⠀⢀⡔⠁⣠⣉⡛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠬⢦⣥⠴⠗⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⡀⠱⡄⠀⠀⢱⡀⣀⠇
⠀⠀⠀⠀⠈⠂⠜⠁⠀⢀⠎⠀⡸⠁⠀⢩⠵⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢧⠀⠀⠀⢣⠀⠘⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⡴⠁⠀⠀⡏⠀⡆⠐⠒⠒⠒⠂⠤⠤⠤⠄⠀⠤⠤⠤⠔⠒⠈⠉⠉⠉⡇⠈⡀⠀⠀⠀⠧⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠞⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⠳⡍⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠔⠋⡠⠶⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠕⠶⢄⠉⠢⡈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠞⡰⠚⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⢆⠳⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠓⠂⠀⠐⢖⠋⠁⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠈⠙⡳⠂⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⣀⡠⠒⠜⠳⠞⠡⠐⢄⣀⣠⠛
⠀⠀⠀⠀⠀⠢⠀⠀⠂⠉⠙⠋⠢⠤⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⣀⠤⠔⠙⠋⠉⠐⠀⠀⠔
⠀⠀⠀⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⢀
⠀⠀⠉⠇⠀⠀⠀⠙⠢⢀⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⡀⠔⠋⠀⠀⠀⠘⠉
⠀⠀⠀⣠⠦⠀⠀⠀⣀⡎⠁⠀⠀⠀⠀⢀⡠⠐⠒⢦⡀⠀⠀⠀⠀⠀⢀⡴⠒⠂⢄⠀⠀⠀⠀⠈⢱⣀⠀⠀⠀⠴⣄
⠀⠀⠀⠈⠁⠐⠠⢰⡅⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⢨⡆⠄⠀⠀⠁
⠀⠀⠀⢀⣀⣀⣠⠔⠀⠀⠢⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⠀⠢⢄⣀⣀⡀
⠀⠀⠀⠉⠛⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠉
⠀⠀⠑⠀⠀⠀⠠⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃⠄⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣨⡓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⢚⣅⠀⠀⠀⢀⠔⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠂⠈⠉⠉⠉⠁⠀⠐⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠀⠉⠀⡄⠀⠀⠀⢀⠀⡀
⠀⠀⠀⢨⣠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢉⡝⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠉⡀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠈⠉⠉⣓⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠉⢩⡝⢤⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣰⢪⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠷⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢠⡺⡀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠑⠄⠐⡀⠔⠻⠀⠙
⠀⠀⠀⠀⢡⢄⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢀⡶⠦⠀⠒⠀⠀⠀⠀⠉⠉⠁⠐⠂⠄⡀⠀⠀⠀⠀⠀⠰⠶⡞
⠀⠀⠀⠀⠇⠙⠗⠠⠬⠄⠀⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣎⠀⠀⠀⡠⠊
⠀⠀⠀⠀⢢⡤⠦⠀⠀⠀⠀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃⢀⣁⠤⠒⢒⡆
⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠠⠤⡶⠋
⠀⠀⠀⠀⠀⡤⠠⠤⠤⠤⠤⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠗⠒⠒⠚⣚⠆
⠀⠀⠀⠀⠀⠉⠲⣦⠶⠂⠀⢉⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⡒⠪⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⣉⣠⣀⠽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠈⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣏⣁⡼⠋⠀⠉⠂⠤⢀⢀⣀⡀⡀⠠⠄⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⡿⠿⠷⠦⠄⠀⠀⠙⠻⣿⡅⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠺⢴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠄⠐⠃⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡈⣻⣿⣷⣶⡶⠂⠀⠻⢿⣿⣿⠿⠃⠀⢀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⠃⣠⣆⡄⠑⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠪⡾⣷⣷⣸⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢾⣿⠏⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢄⠠⢄⣀⡀⠀⠈⠻⢿⣿⠁⠐⣀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⢀⡞⠁⠀⠀⠀⠀⡂⠉⡍⣿⡾⠉⠀⠁⢻⣿⠀⠲⠀⡄⢄⠀⠀⠀⢀⣿⡟⠀⢀⠆
⠀⠀⠀⠀⡇⠀⠀⢷⣾⣿⣾⠇⠀⡰⢠⠐⠁⠀⠀⣴⡅⠁⠀⠀⠀⠀⣿⡶⠀⠀⠀⠳⢔⣶⡲⣸⣿⠃⠀⢸⠆
⠀⠀⠀⠀⢸⡀⠀⠈⠛⢿⡛⣦⣤⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣿⠟⠁⠠⣴⠋
⠀⠀⠀⠀⡀⠙⠶⣆⣀⡀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠁⢠⣴⠟⠁⠀⡴⠁
⠀⠀⠀⠀⠙⢤⠀⠙⠻⠿⠷⣴⣶⣦⡀⣄⠀⠀⠠⣄⣄⠀⠀⠀⠀⠀⢠⣤⣴⣦⣤⡀⣠⠿⠟⠛⢡⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣤⡴⢶⣤⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠉⡿⠛⠿⠿⠿⠖⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⣀⣤⣶⢦⣴⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢠⠾⠷⠶⠄⠒⠲⣤⣤⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣆⣦⣴⡮⣤⠀⡀⠀⠀⠀⠐⠿⠲⠦⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣶⠶⢶⣉⣩⣽⣷⠶⠟⠛⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠛⠁⡠⣽⣋⣩⡦⠴⢲⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢠⣴⣾⠁⠙⣟⡀⠀⢀⡀⢐⢻⣙⣡⠔⠊⠁⠀⣠⡤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⣽⡂⠀⠀⠙⣿⣟⣉⣄⣷⠞⠋⠀⠀⠀⣠⣾⡟⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⠹⣝⡦⣶⡚⠋⠉⠉⠉⡀⠀⠀⠀⢠⣾⣿⢿⣵⡿⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⣰⣖⣁⣀⡀⠙⣷⣀⠐⣋⠴⠂⣠⡖⢯⣬⣿⣾⣿⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠛⠛⡉⠩⠍⠛⠋⠛⠛⠋⢉⡟⢿⡍⠀⣾⠟⣠⡞⠀⠀⠀⢨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠻⣿⠁⠀⠀⠀⠀⠀⠀⢀⡠⠌⢰⣶⣴⠟⠛⢳⣴⠉⣿⣿⡈⠀⠀⢰⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡽⠟⠀⠀⠉⠳⢤⠀⠀⠀⠀⠢⠤⣤⣀⣈⣱⣿⣦⡄⣾⠈⢧⡀⠘⣿⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣤⢚⣧⠖⠊⠛⠛⠈⠳⣦⠀⠀⠀⠈⣩⣷⣿⠿⢋⣠⠁⣶⣀⣙⣦⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣻⢿⣿⠛⢿⣿⣿⠑⠠⠀⠀⠀⠀⠀⣈⢷⡜⠧⣾⠿⢻⣆⡐⠿⣤⣿⣾⣿⡷⡶⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠁⠻⣿⡄⢿⣿⣅⠀⡀⣀⣤⠎⢀⡼⢲⡄⠰⢶⣶⠌⣙⣿⣿⣷⣬⣉⣉⡀⠄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⣼⣿⠄⠀⠙⢿⡆⠀⠩⣿⢸⣿⡿⢷⠛⠛⠛⠰⢿⣿⣯⣧⣶⠙⢿⣿⣿⣦⣌⠛⠿⣮⠛⠛⠦⠽⡛⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡜⣿⠧⠙⣇⣠⠀⠛⠋⢀⣀⡟⣿⣯⣷⣼⣿⣿⣦⣴⡄⢿⣿⡟⠿⠳⣆⡉⠉⣉⡙⠳⣦⡀⢧⡀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣯⠹⣿⡇⡈⠻⡀⢈⢿⠰⢿⣦⡨⠶⣾⣿⡿⡿⠉⠁⠁⠛⢾⣃⡜⠙⠛⠷⢦⣄⡻⢶⡙⠙⠳⢮⣥⣌⠻⡄⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢀⣠⡶⢒⣶⣾⣿⡗⠙⠳⣥⢠⣵⣘⢾⠿⠆⠋⠁⠀⠀⠛⠻⠧⠾⣄⣤⣀⠀⣿⡆⠀⠀⠀⠀⠀⠈⠓⠿⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠘⡌⠓⣹⣯⠉⠉⠛⣆⢀⠚⣷⠽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢰⣏⣀⠷⠏⣀⡴⢣⡇⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠄
⠀⠀⠈⢿⣿⣦⣤⣴⡴⡿⠃⡘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⠙⠛⠿⢿⣄⣀⣰⡟⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠻⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⠦⠶⣴⢀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⡄⢘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⣄⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆⣿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡼⠃⠀⠀⡸⠳⠛⢯⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡏⠀⠈⣿⡆⠀⠀⠀⡸⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠙⠿⠒⢀⡀⢀⠀⡀⢀⠠⠠⢤⢀⣀⣀⣀⠀⠀⠀⠏⠀⠀⢀⣿⡇⠀⠀⢀⣡⡇
⠀⠀⠀⠀⠀⢷⠃⠀⠀⣷⠀⠀⢀⡼⠄⢃⣈⠀⠀⠤⠤⠤⠶⠀⠴⠶⣿⣧⣭⣤⡳⠶⣷⣶⣤⣾⡿⠁⠀⠀⠈⢹
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠸⣤⣴⠛⠀⣰⠎⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠸⣿⡋⠻⣿⣷⣍⢻⣿⠟⠁⠀⠀⠀⢠⡞⠀⠀⠀⠀⡀
⠀⠸⡆⠀⠀⠈⣦⠶⠀⠀⠈⠙⠂⣴⠃⠀⠀⠀⠀⣿⠀⠀⠀⡆⠀⠀⢀⣿⡃⠀⠈⣿⣿⠛⡇⠀⠀⢀⣼⣷⡟⠀⠀⠀⢀⡾
⠀⠀⢳⡴⢄⠀⠈⢦⠈⢠⡤⠀⢠⡿⢆⣀⢀⡀⣀⣼⡷⣄⠀⡇⢀⣀⣼⣷⡁⠀⢀⣿⣿⡆⢿⣤⡎⣠⣿⠋⠀⠀⢀⣜⡽⠁
⠀⠀⠀⠑⢆⠐⠄⠀⠉⠃⠇⠀⠸⠁⠀⠈⠉⠀⡼⠉⠀⠀⠀⠇⠉⠉⠙⢿⡛⠛⠛⣿⣿⢇⣼⠿⠛⠋⠁⠀⢀⠔⣼⡏⠁
⠀⠀⠀⠀⠀⠳⢤⣹⡇⠐⢾⣐⡆⡆⠀⠀⠀⠀⠳⣄⠀⠀⠀⡆⠀⠀⠀⡸⠁⠀⢀⣿⣿⣾⣿⡄⣤⣴⠒⠒⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠂⡙⣄⠀⠀⠀⠀⠀⠛⠒⡄⡅⠀⠀⢾⣅⡀⢀⣾⣿⣿⠿⠿⠛⠋⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠊⠀⠉⣻⣮⡛⢶⣖⠀⠀⠀⢈⡅⠁⠀⠀⠀⠈⣹⣿⣿⣿⣧⠤⠤⣀
⠀⠀⠀⠀⠀⠀⣠⣅⡘⠉⠉⠉⠉⣀⡀⡬⣦⡙⢦⣄⣀⣺⡄⠆⠀⠀⣀⣤⣿⣿⡉⠛⠛⠻⠶⠾⣿⠶⡄
⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⢰⣁⠀⠀⠐⠋⠙⠿⠶⢒⣉⣁⣀⣰⣿⠿⠿⠟⠻⠿⣍⣐⣄⠀⠀⠘⣷⠛
⠀⠀⠀⠀⠀⠰⣞⡀⠀⠀⠀⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠇⠀⠀⠘⣧⡇
⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⢠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠟⠀⠀⣠⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠛⠋

⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠱⡄⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⢻⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⡇⠀⡜
⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⣷⠈⢯⠘⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠹⣄⠙⢶⣴⣿⣷⣄⡀⠀⠲⣄⠤⢤⡀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠑⢬⡙⠻⢭⣕⢲⡈⠑⠶⣦⣤⣀⠀⠀⠈⠁⠒⠖⠠⠤⠤⠀⠀⠀⣼⠀⠠⣤⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣬⣽⣒⡛⠳⠦⣭⣒⢦⣰⠟⣻⣅⠒⠂⠀⡀⠀⠀⠀⠀⠀⢀⠡⣦⡀⠀⠀⢁⡃⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣛⡛⠿⠷⣿⣷⣿⣞⢁⣖⠀⠙⠿⣷⣷⡾⢿⣿⣶⣿⣿⣿⣿⠘⣿⣶⣠⣄⡴⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢩⣭⣿⣿⣷⣾⣯⣿⣿⣇⠜⠢⣀⠈⠁⠛⠚⠛⢛⣿⣿⣿⠯⢸⣿⣿⣿⣿⣶⣦⣄⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡠⠖⢫⣄⣦⣬⣭⣭⢭⣦⢤⣬⣽⣶⣷⣶⣶⣴⡦⠶⣾⣿⢟⣀⣠⡾⠿⡋⢸⡏⠀⠉⢈⣥⠤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡾⡡⣪⠞⢋⣵⡶⠟⣛⣯⣽⣿⡿⠿⠛⠟⣛⣫⣭⠿⠟⠁⣩⠟⣫⣤⡴⠟⠶⣏⣀⣠⣎⠱⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠋⣥⣴⠟⠉⢀⡜⣿⠉⣴⣦⡶⣛⣿⠟⣻⡿⠊⠀⢀⡜⠁⡠⠞⠁⣀⣦⠴⢿⣿⣅⣿⠂⢀⡴⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⠕⣺⠅⠀⠀⢀⠌⠀⣿⠀⢇⢄⠟⣉⡴⠋⠁⠀⠀⢀⠟⢀⡞⢀⡴⠋⠀⣠⠖⠛⠛⢛⢿⣶⡎⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣨⠃⠘⠁⠀⠀⠀⠋⠀⠀⢧⠀⣼⡋⠀⠀⡇⠀⠀⠀⠀⠋⠀⠈⠀⠊⠀⠠⠊⣠⠴⠒⠚⢛⢷⡂⠁⢠⣤⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠁⠀⠀⠀⣿⡰⠟⠳⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠴⠛⠉⠛⠛⣇⣤⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠘⣿⠀⠀⠀⢹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠇⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣑⠀⠀⠘⢦⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣆⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣻⡿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣾⠟⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣾⣿⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⠆⠀⠀⠀⠸⠁⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⡼⠛⠰⣊⠉⢹⣄⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠰⡀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⢠⡇⡀⣿⣦⣤⣼⠿⠽⠤⠤⠴⠦⢤⣀⡀⠈⣆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠩⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢘⠉⠀⣿⣄⠀⣾⠀⠀⢀⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠐⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠆⠀⣷⡀⠘⣯⣤⣿⡖⠟⠤⠷⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣲⡤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡔⠈⠳⣤⣈⣿⡯⢉⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠉⠉⠄⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⣤⡀⢌⠙⣿⣇⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠺⣇⣠⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠨⡙⠶⣥⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢾⣻⣿⣧⣤⣴⣾⡿⠋⠀⠀⣀⡿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠁⠀⠈⠳⢿⣶⣤⣽⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⢈⡷⢐⣿⣟⣛⠛⠉⠁⠀⢮⠴⠛⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠀⠀⠀⠀⠀⠀⡈⠙⠛⣿⡽⠀⠰⠀⠀⠰⠂⡁⣷⣾⣿⡟⠙⠛⠶⠶⠶⠟⠛⠉⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠜⣶⠲⠶⠚⠛⠳⣅⠊⠀⣀⣢⣾⣿⣿⡟⠉⠙⠳⠶⠦⠤⠴⠴⠷⣦⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⡏⠀⠉⠙⠳⠶⢤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⠄⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠰⠋⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⡰⠟⠃⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




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

⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣤⣶⣤⣤⣤⣀⣀⡀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣯⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣀⣀⣤⣤⣤⣤⣤⣤⣄⣤⠤⣤⣐⣶⠟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢠⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⡐⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⣧⡀⠙⠻⠿⢿⣿⣷⣤⣄⠀⠐⠲⢦⣄⡀⠀⣀⣀⡀⠘⠁⣀⣉⠻⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢹⣿⣿⣿⣷⣤⣄⣠⣬⣿⣾⣿⣿⣿⣶⡟⠉⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣬⣧⣤⣄⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡴⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣽⣲⢬⣉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣬⣛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣠⣴⣾⣿⠿⢿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⠟⠛⢿⣮⣟⠻⠷⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣛⣡⣤⣀⣀⣀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠤⣾⣿⣿⠏⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣎⡾⠟⠉⠀⠀⢠⣶⣶⣾⣿⣿⣵⣾⠿⢻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣄⠉⠉⠿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠘⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠋⠁⠰⣠⡞⠁⠀⠈⠙⠛⠛⠋⠁⠀⠙⠛⠻⣿⣿⣿⣿⣟⠋⠙⢿⣿⣦⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠘⠧⠀⠀⠀⢸⣿⡯⠀⠀⠀⠀⢠⣞⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⡀⠀⠘⠿⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⠇⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠸⡿⠿⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠃⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡨⣀⣔⣶⢶⣿⡍⠿⠦⠀⢀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠱⢟⡽⢈⡹⡿⢟⣱⠶⠓⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⢀⠀⡀⠀⠋⠀⠀⢸⡏⢰⣋⣴⢾⠏⡀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠐⠁⠀⠀⠠⠀⠒⠇⠈⠀⠠⠀⠁⠀⢐⠁⠀⠊⣳⡼⠟⠉⠈⠰⡈⠁⠠⡀⠘⣷
⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⣀⡤⠞⣁⣤⡀⠀⠀⠀⠀⠄⠀⠈⠀⢽⡇
⠀⠀⡠⠂⡀⠀⠊⠀⢃⠀⢀⣀⠀⠀⠑⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢊⠡⠔⣈⡅⢠⡉⠠⠀⠀⠀⠈⢄⠀⠀⢸⡧⠄
⠀⠸⣠⠈⠀⠀⠀⠀⢸⣦⣀⠀⠁⠸⣄⢟⠀⠀⠀⠀⠀⠀⣀⣤⢶⢿⣿⠷⠒⠋⠉⠀⠀⠉⠲⢬⡆⠀⠀⠈⠄⠀⢠⡿⠀⠠⡀
⠀⠀⡌⠑⢄⡒⠛⠛⠛⢻⣿⣷⣶⣾⡿⠛⠳⣶⣶⢶⣖⣿⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢆⠀⠀⠈⡀⢸⡇⠀⠀⠀⢀
⠀⣰⠀⠀⠀⠙⣶⣴⣾⣾⡿⡮⠥⣬⣿⢶⡦⠈⠻⣿⣿⣿⠿⡻⢿⣿⣿⣷⣖⠦⣄⠀⠀⠀⠀⣸⠀⠀⠳⡄⠀⠁⣼⠃
⡇⡇⠀⢀⡽⠋⣩⡿⣿⡟⣒⡒⠿⣧⣹⣦⣽⢶⡄⠈⠻⣝⠳⣌⡓⠬⣙⢋⣻⢧⣼⠆⠀⠀⠀⠃⠀⠀⠀⠹⠄⢰⡟⠀⠀⠀⠀⠀⠀⠁
⢠⠁⠐⠢⠀⢾⡾⣿⣿⣦⡘⠛⠓⢦⣙⢍⠿⠜⠇⠀⠀⠈⠳⡌⠻⣆⠈⡆⢻⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⡞⠠⢸⣿⣿⣿⡟⠛⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⡆⠀⠀⢿⣸⣇⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⢀⠀⠀⢻⠹⣽⠌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣷⠀⡀⢸⣿⢹⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠋⢀⠀⠘⡤⢎⢶⡀⣌⠛⠶⢤⣤⣤⣀⡀⢀⣤⣀⣀⠀⡟⣿⠀⡤⠎⠈⡎⡆⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠑⠲⠤⣁⣁⠑⣏⣛⣃⣾⠿⢅⣁⣙⣻⣻⣿⠟⠀⡇⢻⠀⠇⠂⣀⣠⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣾⣿⢟⡛⠟⠻⠶⠶⠷⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠰⠁⠂

⠀⠀⠀⠀⠀⣮⠽⣆⠀⢀⣴⣟⡋⠉⠉⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠻⣄⣹⡄⠿⣧⣈⣰⡆⢀⠀⠠⣭⡴⡄⣠⢀⣀⡤⣠⣤⣄⣾⡦⠀⢀⣀⠤⣄
⠀⠀⢠⡾⠿⠶⣬⣁⠀⠀⠌⠉⡉⠉⠁⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⠁⠀⠊⣭⡀⢀⡀
⠀⠀⠀⠙⠳⠖⠛⠉⠈⠀⠐⠀⠙⠒⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣠⠞⠇⠈⡟⡩⢑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠁⠀⠀⠀⠀⢀⣄⣈⣠⠄⠀⠀⠀⠀⠀⠈⡰⠇⢀⣀⡞⠁⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠒⢀⡹⠷⠂⠀⠀⠀⠀⡴⠁⡠⠛⠋⠄⠊
⠀⠀⠀⣠⠤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠉⠀⠛⢉⠀⠈⠀⠀⠀⠐⢞⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⢀⢀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢊⡄⠁⡈⢲⡀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠛⠒⠒⠗⠀⠀⠠⠔⠋⠁⠵⠀⠁⠀⠧⠃⠐
⠀⠀⡄⠐⡇⠀⠀⣆⠀⠀⠘⢀⡀⠀⠀⠀⠻⠶⠖⠒⠁⢀⡶⠲⢄⠀⠀⠐⢼⡗⠒⡂⡴⡋⠀⠀⠠⠦⢀
⠀⠀⣀⠔⠀⡄⠐⡆⠮⠀⢘⡂⣈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⡸⠀⠀⠀⠈⠀⠀⠛⠁⠀⠂⡡⠀⠀⢰⠇
⠀⠀⠈⢤⣸⠦⢀⠀⠀⢰⡉⢾⡃⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠆⠶⠘⠁
⠀⠀⠀⠀⢺⠃⢸⠐⠀⠈⡧⠘⠣⠀⠀⠐⠉⠈⠛⠛⣳⠀⢀⣤⡶⣿⣿⣿⠖⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⢧⡤⢴⡟⠀⠀⠀⠀⠐⠖⠶⠛⠋⡁⠀⢿⣟⡿⠿⠛⠁⠀⠀⠀⠐⣻⣦⠴⠒⠛⣲⣦⠈
⠀⠀⠀⠀⠀⠀⡀⠀⡥⠀⡇⠀⠀⠀⠀⠀⢀⠠⠒⣹⠇⣠⣄⠀⣠⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⢹⠀⠀⠀⠀⢀⠥⡶⠂⠊⠀⠋⠈⢣⠘⣦⢀⠑⢦⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠠⡧⠼⠂⣀⠆⠀⠀⠀⠀⠀⠀⠀⠸⣀⣸⠄⠈⠙⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠈⠒⠂⠐⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⣀⡀⡀⠀⠀⢀⣲⣶⣲⣶⣶⣷⡒⠶⠤⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⣅⣤⣤⠶⠞⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠆
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡓⠂⠲⠒⠀⣂⣥⣤⣤⣬⣭⣭⣭⣥⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠩⢽⠧⡀
⠀⠀⠀⠀⠀⢠⠀⠈⠹⢿⣿⣿⣿⣿⣟⣉⠁⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠚⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢣⣢⡀⠀⠀⠈⠉⢿⣿⣿⣯⣢⣄⠀⢀⣉⣹⣶⣴⣾⣿⣿⣷⣴⠊⠈⠁⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠹⣅⢢⣤⣀⣀⠈⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣭⣐⠠⣉⡉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣠⣄⡀⢀⡀
⠀⠀⠀⠀⠀⢀⡤⣐⣾⣿⣍⠲⢮⣭⣉⡛⠛⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⢃⢀⣀⣀⣼⣿⡟⠛⠛⠻⠿⠼⣇⡀
⠀⠀⠀⠀⣀⣾⣾⡿⠁⠀⠉⠛⠶⣦⣬⣉⣳⣦⣾⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⡿⢾⣟⣩⣉⣁⣤⣶⣤⣄⣀⠀⠀⠈⠂
⠀⣀⢀⡼⠟⠛⠋⠀⠀⣀⣀⣤⣤⠤⠞⢉⣉⣽⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡵⢾⣿⡟⣿⣟⣛⣛⢻⣿⣿⡋⠛⠻⠿⢾⣆⢀
⠀⢽⡇⠀⠀⠀⠀⠀⣸⣿⣿⣶⣾⣿⠿⠟⠋⠁⠀⣠⠟⠋⠉⠛⠿⠿⠷⠶⠿⠛⠛⠿⡷⢿⣿⣍⣙⡿⠿⠿⠿⢿⠿⣶⡀⠀⠀⠉⠻⣥
⠀⠈⠛⠂⠀⠀⠀⠰⣻⣯⠁⠀⠀⠀⠀⢀⠄⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡖⠀⠀⠘⣎⣻⡄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠉⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣶⠁⠀⠀⠀⢠⣽⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠚⠟⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠈⠛⠷⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⣐⠄⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠤⠀⠀⠀⠀⠀⠄⢈⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠊⢠⡔⠉⠀⠀⠀⠀⠀⠀⠈⢻⣽⣯⡉⠀⠎⠀⢀⠀⠀⠀⠀⠀⠶⠤⣀⡋⢀⡄⠀⠀⠀⠀⠀⠀⠤⣄⠒⠀⣱⠂
⠀⠀⠀⢈⠥⠒⠒⠦⠿⣶⠶⠀⣀⣀⡠⢔⠴⠯⡀⠑⠂⠴⠤⠔⠁⠀⠀⠀⠀⠀⠀⡠⠤⠨⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣦⡀
⠀⠀⡴⠉⠁⢠⠈⡀⠀⠇⠀⠁⡉⠉⠁⠨⢠⠂⠈⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠔⠁⠑⠒⠀⣄⠀⠀⠀⠀⠀⠀⢀⠰⠦⠈⠛⢯⠂
⠀⠀⠂⠀⠀⠁⠀⡏⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠁⡀⠐⠀⣤⡤⢈⡁⠀⠀⠓⠀⠐⠋⠁⣀⠀⠈⡻⠉
⠀⠀⠀⠠⠁⠀⠀⢣⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠸⠋⠓⠒⠀⢐⡒⠴⠛⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⢔⠉⡐⠀⢈⡦⠒⡂⠀⠀⠀⢰⢆⡴⠂⢶⡍⠛⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠀⠘⠀⠈⠀⠠⠉⠠⠤⠐⠁⠀⠑⠂⠾⠤⢾⢈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⠄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠁
⠀⠀⠀⡀⠀⠀⣀⢠⠀⠱⣰⡦⠂⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠐⠠⠤⣀⣀
⠀⠀⠀⠄⠀⠈⢤⡈⢢⣐⠋⠀⠀⠀⠀⠀⠘⣆⠀⠀⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠚⠉
⠀⠈⠀⠀⠀⠀⡀⢁⣄⣻⠀⠀⠀⠀⠀⠀⠀⡷⠐⠐⠃⡇⡀⠀⠀⠀⠀⠀⠠⠜⢋⡁⠒⣳⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠳⠢⡀
⠀⠀⠀⠀⡀⠊⠀⠀⠈⠙⠄⠀⠀⠀⠀⢀⠼⠋⠁⡘⠈⠃⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠈⠀⠀⠀⠡⣤⠶⠤⠶⠶⣚⡂⠀⡄⡁⠙
⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠠⠯⠔⠂⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⡀⠁⠀⣀⣼⡐
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠦⠁⠀⣀⢎⣠⠟⠁⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣤⠀⡄⣤⠂⠀⢀⠔⠢⡄⣠⠒⠀⡴⠂⢀⣤⢠⣄⠀⡄⠀⢠⠀⣤⠀⣄⡔⠢⡄⡤⢤⢠⠀⡤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡟⠘⠇⣿⠁⠀⠸⣄⣠⠟⢣⣀⠠⣏⠀⠾⠳⠴⠉⠳⠇⠀⠈⠿⠉⠏⠸⣄⣠⠿⠻⠏⢬⠀⣇⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⡄⣀⣀⣀⠀⣄⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠁⠁⠀⠁⠀⠈⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢠⣄⡀⢤⡀⢤⡄⡄⢤⠀⢤⢀⣠⠀⡠⡄⠀⣧⠄⡀⠀⢴⣁⢸⠇⡟⢀⣦⢠⠤⠀⡇⠀⢠⠤⠀⣤⣿⠲⡆⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢀⡀⠸⠠⠤⠏⣧⠀⢣⠸⠗⠃⠰⠸⡆⠠⡽⠺⡇⠀⠀⠇⠀⠃⠸⠔⠻⠾⠃⠇⠻⡄⠸⠀⠀⠷⠄⠺⠀⣆⠿⠻⠄⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢀⡀⢸⠀⠀⠠⡤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠈⠁⠘⠋⠙⠀⠀⠋⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣴⢻⣀⣀⡀⠀⠀⠀⠀⠀⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢤⠈⠁⠉⠉⠛⠲⠦⠶⠶⠦⠰⠒⠂⠠⠤⠤⠤⠄⠐⠋⠀⠀⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⣌⠳⣤⣀⣰⠶⠦⠤⢤⡤⢀⣿⣀⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⣤⠴⠶⢺⣆⡀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠉⠳⠾⣁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣻⣤⣄⣉⣉⠲⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣄⣠⡴⠛⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠈⠉⠉⠉⠉⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠅⠀⠰⣿⠛⠛⠚⠛⠙⠢⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣴⡿⠶⠛⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢹⣆⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⣀⠀⠀⢀⣰⣿⠖⠒⢚⣛⠈⣻⠓⠞⠛⠋⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⢿⣍⡙⠛⠛⠛⠛⠋⠙⠳⠶⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⡶⡾⠀⠀⠀⠀⠀⠀⠉⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⡭⠔⠁
⠀⠀⠀⠀⠸⠒⠒⠀⠐⠀⠐⠀⠀⠀⠒⠀⠒⠂⠀⠐⠆⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠈⠁⠁⠁⠈⠁⠁⠀⠉⠉⠁⠈⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠈⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠂⠐⠀⠐⠀⠐⠒⠂⠐⠀⠒⠒⠀⠀⠀⠀⠁⠀⠙⠒⠀⠒⠒⠀⠐⠀⠀⠐⠃⠀⠒⠒⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⡄⡀⢤⠀⠠⣤⠀⠤⠤⢠⡄⠀⠤⠤⠀⢤⠀⠀⠄⠀⠤⠠⠄⠄⠀⠀⠤⠤⠄⠠
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠀⠈⠀⠐⠊⠀⠀⠐⠀⠰⠒⠐⠊⠀⠀⠃⠐⠀⠀⠀⠑⠂⠀⠀⠒⠂⠒⠀⠒⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠢⠀⠄⠀⢤⠤⠄⠤⠤⠀⠠⠠⠦⠤⠠⠤⡤⠄⠤⠤⠀⠀⢤⠴⠄⠴⠀⠠⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⣀⡀⢀⣀⠀⠠⢀⡀⠀⠀⠀⡀⠀⡀⢀⠀⠀⡤⠀⠀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣋⡀
⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠄⠀⠄⠀⠀⠀⠀⡠⠀⣒⡀⢒⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣁⢰⣿⠙⠋⠉⠉⠈⠁⠓⠀⣋⣁⣀⡀⠉⢀⣵⠉⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡤⣾⣿⣶⣧⠜⠛⠉⠉⠁⠀⠈⠉⠉⠛⠛⠿⣿⣦⣄⣈⣿⡿⣷⡀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠘⡷⡄⠀⠀⠀⠀⢀⡟⢻⣿⣿⣿⣿⠿⠋⠀⣀⣠⣴⠦⣤⣠⣤⣴⣧⣤⣀⡀⠈⠙⠻⢿⣧⣰⣿⣿⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢞⢢⡄⠀⠀⠀⢿⡼⢛⣧⣿⣤⣄⣴⣿⣿⠛⠛⣻⣿⡇⠘⠻⣿⣿⡿⣿⣷⣶⣿⣿⢻⣮⣿⠃⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⠦⣄⠀⠈⠑⢿⣿⢿⣿⡟⠁⢹⣿⣤⣧⣿⠟⣧⣤⣴⣿⠏⠀⢸⣿⣿⣿⣧⡿⠋⠀⣀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠼⣷⢤⣄⠀⠙⠻⢿⣇⠀⣼⣿⣿⣿⡇⢠⣿⣿⣿⣧⡀⣴⣾⣿⣿⡿⠋⢀⣠⣾⣽⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⣠⡭⣧⣌⠳⢦⣄⠀⢿⣿⣿⣿⣿⣿⣯⣙⣫⣽⣿⣿⣽⣿⣿⣿⡿⢃⣴⣿⣿⣿⣿⣿⡿⣿⣿⣷⣦⣤⣄⡀
⠀⠀⠀⣀⣠⣶⢿⣿⣿⡦⠐⠛⠉⠷⢯⣛⡻⣦⣍⠙⡞⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⢿⣿⣽⣿⣿⣿⣋⣀⡀⠉⠉⠛⠿⠿⠗⠿⣶⣄
⠀⠀⣼⡿⠛⠉⠉⠉⠁⠀⠀⣠⢴⣶⡿⣱⡧⣬⣝⠳⣦⣴⣟⣿⣿⣳⣦⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⡾⠻⣿⣏⣤⣄⣀⠀⠀⠀⠀⠀⠉⠳
⠀⠸⠋⠀⠀⠀⠀⠀⣠⣴⣾⣷⠿⠋⠀⣉⣩⡖⢤⣬⣭⣽⣿⡽⠋⠉⠉⠛⠉⠉⠉⠉⠉⠻⠿⣏⣉⣈⣻⣿⣿⣓⣤⣄⠈⠻⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠋⠁⠀⣠⣬⣵⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠈⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢠⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣝⣦⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⣀⡄⢶⠋⠁⠀⠀⠄⢰⣦⣼⣦⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣤⠾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⣼⠁⠀⠁⣸⣇⠀⣤⠀⡏⣠⣿⠉⠻⣖⡒⠗⠒⠒⠦⢄⡀⠙⢿⣴⣄⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣼⣏⠀⣠⠚⢁⣘⣦⣼⡆⠀⣿⣿⣿⡁⠘⣧⡀⠀⠀⠠⠀⠁⣸⠈⠻⣿⣇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⣿⡏⠁⣷⣾⣿⡇⠀⢁⡜⢻⣿⣿⡿⠙⠁⠱⣶⡀⠀⠘⢌⡷⡀⠄⠹⡿⡆⠀⢠⠘⠄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠙⣇⠸⡇⣀⣿⣿⣿⣿⣠⡶⠏⠀⣠⠟⢿⣷⡀⢀⣾⣿⣤⠀⠀⠀⠀⠈⠢⠀⠈⣡⠀⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠀⠙⢷⡤⢼⣿⣿⣿⣿⢟⣃⠠⠞⢁⠀⣸⣿⠃⠙⣿⢿⡟⠰⡄⠀⠀⠀⠀⠀⠀⣁⠞⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠩⡻⣷⣶⠄⠀⣇⡀⢿⣿⣿⣿⣞⡅⠀⠀⠈⠀⣿⡟⠀⣴⢟⣼⠇⠀⠁⠀⠀⠀⠂⢀⠀⠳⢀⡀⠄⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⣹⡿⢷⣼⣟⠏⠋⢱⡄⠀⠀⠀⠉⠀⠀⢘⠁⠋⠂⢄⣀⠀⠀⢐⣩⣴⣿⠒⡋⠡⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⡟⠿⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠗⠀⠸⠀⠀⠀⠋⠁⢀⠀⠉⢈⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣩⡥⠌⠧⣶⣦⣤⣌⣿⣿⣦⣀⡠⠤⢀⣀⡀⠀⣀⣀⣀⣴⣋⣁⣠⡀⠘⠛⠻⢶⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⠀⠀⣠⡒⠉⠉⠉⢉⣿⠧⠹⠾⠿⠻⠯⠽⠭⠿⢿⠿⣧⠀⠠⣬⣩⣗⠆⠀⠀⠉⠒⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢃⡑⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢊⣡⠞⠁⠀⠀⠀⠀⠀⠀⢨⣱⣍⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⣠⠴⢛⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡍⠳⡄⠉⠒⢄⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣈⠇⠀⠀⠹⡄⠀⠀⠀⠘⡿⡄
⠀⠀⠀⠀⠀⣾⡄⠀⠀⣿⢠⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣤⣤⢽⡄⠀⠀⠀⡇⢹
⠀⠀⠀⠀⢸⠹⡇⠀⠀⡇⠀⠈⢢⡀⠀⠀⠀⣤⡄⢀⡀⢀⡀⢤⣀⣀⣀⣰⡆⠀⠀⣠⠊⠀⠀⡰⠀⠀⠀⠀⣇⠘
⠀⠀⠀⠀⢸⠀⡇⠀⠀⢻⣆⠀⠀⢳⣀⠀⠔⠛⠁⠀⠀⠀⠀⠀⠀⠈⠁⠙⠓⠦⣼⣧⡀⠀⡴⢃⡠⠴⠒⠋⣙⠶
⠀⠀⠀⠀⢸⡄⣿⣀⣀⠈⢿⢷⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣏⡠⠤⠚⠋⠁
⠀⠀⠀⠀⠈⢧⣿⡈⠉⠙⠛⣷⠋⠀⠀⢠⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⣏⣀
⠀⠀⠀⠀⠀⠀⣈⣉⣹⣶⣶⢿⣐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣴⣿⣉⣉⣙⣓⣲⣤
⠀⠀⠀⠀⡐⢫⠥⠤⠤⢤⣤⣤⣼⣷⣮⣑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠒⠋⠛⠶⣄⠈⠹⣮⢳
⠀⠀⠀⡜⡠⠋⠀⢀⡠⠔⢚⣉⣀⣠⠾⠛⢿⣶⣿⣶⣶⣖⣒⣒⣢⡭⠴⠖⠻⠿⣿⣤⠌⠛⠷⣖⠲⡞⠳⡀⠘⣧⣧
⠀⠀⣸⠜⠁⠀⢀⡞⠀⠉⢩⠽⠋⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡰⢊⡷⢿⡀⣇⠀⠈⢻⡆
⠀⠀⠋⠀⠀⠀⣼⢀⠎⠀⢸⡄⢖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡞⠁⠈⣧⣿
⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠹⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠋⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠓⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⠛⠛⠻⠿⠿⡿⣣⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠈⠻⢶⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣼⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⡿⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢿⡃⠀⠲⢄⣀⣤⣄⣀⠴⠂⠀⢀⣤⢿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⣙⡳⣦⣌⡻⣶⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣭⡴⣛⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⣉⡍⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⣍⡉⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⣠⠖⠿⠿⠷⠝⠿⠿⣿⡿⠿⠟⠵⠿⠿⠗⢦⡈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⢀⣀⣤⠖⠂⠀⠒⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⡀⠸⠻⡍⠀⠀⠤⣶⠉⠀⠀⠀⠀⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠐⠞⠛⣶⢶⡀⠀⠈⢳⣄⠈⠻⣆⠀⠀⣩⠀⠀⢰⠏⠉⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⢀⠉⠀⠀⠀⠙⢟⣦⡀⣀⣿⣦⣠⣿⣆⣴⣯⣠⣴⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣈⣄
⠀⠀⠀⠄⠀⠀⠀⠾⢦⡀⣀⠿⣯⣾⡿⣿⣿⣿⣿⠟⢟⣛⣛⡻⠿⣿⢿⣿⢶⣶⣶⣤⣤⣴⣤⣤⣤⣀⣤⣿⣹⢿⡟⠉⢷
⠀⠀⠀⠀⠉⠒⠀⠀⠈⣟⢩⠛⠛⠂⠀⠀⠣⣿⣿⠀⠀⠁⠀⠟⠲⠀⣿⠀⠈⣿⠀⢿⡇⠉⠿⡏⠹⣿⠈⣿⡅⠩⡗⠒⠺⠄
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣯⡘⣤⣄⠀⠀⠀⡔⣿⣿⠀⠀⡂⠀⣦⠶⠀⣿⠀⢠⣿⠀⣼⡇⣠⣼⡇⣠⣿⢀⣿⡃⣐⡧⠤⢴⠂
⠀⠀⠀⠊⠀⠀⠀⢴⠞⠁⠉⣶⣟⠿⣶⣿⣿⣿⣿⣦⣾⣭⣭⣵⣶⣿⣾⣿⣿⠿⢷⠛⠛⠿⠟⠙⠛⠉⠛⣿⣻⣾⣧⣀⡴
⠀⠀⠀⠀⠀⠀⢀⠘⢷⠀⠀⠀⣠⣾⠟⠉⠉⣿⠟⠙⣿⠟⠻⣟⠙⠻⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠈⠃⠤⣦⣤⠾⠿⠃⠀⢀⡼⠋⢀⣴⠏⠀⠀⣸⠀⠀⠸⣄⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠁⢰⣴⡃⠀⠀⠒⠿⣀⠀⠀⠈⠀⡉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠈⠉⠳⠦⠀⢀⠤⠁⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣠⡀⠀⠐⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⣀⠀⠀⣀⠤⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⡘⠀⢀⠞⠳
⠀⠀⠀⠘⠀⠙⢦⡀⡇⠀⠀⠱⡀⠀⠀⠀⠀⡰⠉⢀⣴⣦⣄⠑⡎⢀⣴⣶⣤⠀⠈⢆⠀⠀⠀⠀⢠⠎⠀⠀⠀⣩⠔⠁⠀⠀⡇
⠀⠀⠀⢡⠀⠀⠀⠙⠃⠀⠀⠀⠘⡀⠀⠀⠀⡁⠀⣿⣿⠙⣿⡆⡇⢸⣿⡋⣻⡇⠀⢸⠀⠀⠀⠀⡈⠀⠀⠀⠀⠁⠀⠀⠀⡜
⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠱⣀⠘⢿⣿⠟⣡⠗⢌⡻⣿⠿⢁⡴⠃⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠙⠢⠄⣀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠁⣒⡲⠈⠧⠤⠤⠏⠉⠏⠠⠄⣀⠀⠀⠀⢀⠎⠀⢀⠤⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠙⠢⣄⣀⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠋⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠑⢤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⢎⠀⠀⠀⢀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⣈⠑⠢⠤⣀⠇⠀⠀⠀⠀⠀⣀⣠⡤⠤⢴⠒⡎⢋⣹⠼⡟⠀⠀⠀⠀⠀⠈⠦⠔⠊⣡⠤⡄⠈⠢⡀
⠀⠀⠀⠀⠀⡴⠁⢀⠜⠀⠉⣒⣦⣄⠀⠀⠀⠀⠀⠀⠙⢗⠷⠺⠔⡖⢻⠙⣠⠞⠀⠀⠀⠀⠀⠀⢠⡴⠖⢧⠀⠀⠈⢆⠀⠱⡀
⠀⠀⠀⠀⡜⠀⢠⠎⠀⢀⠔⠁⡤⢉⣃⠀⠀⠀⠀⠀⠀⠀⠙⠲⠧⠵⠜⠊⠁⠀⠀⠀⠀⠀⠀⣀⠤⠐⠲⡀⠱⡀⠀⠈⢆⣀⠅
⠀⠀⠀⠀⠈⠒⠁⠀⢀⠎⠀⡜⠀⠀⡰⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉⠱⠀⠀⠀⢱⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠜⠀⠀⢠⠁⢠⠉⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⢡⠀⢃⠀⠀⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉





⡶⡶⢶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⡶⢶⣶⢶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⣠⣴⡶⣾⡅⠻⠆⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠊⠑⢛⠷⣠⠻⣛⡵⠟⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡄⠈⠀⠀⠐⡏⢸⣶⡟⠟⠠⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠤⠈⠁⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠜⠋⠀⠀⠀⠃⠀⠐⠀⢸⡇
⠀⠀⡠⠀⠀⠄⠁⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡋⠅⡊⢉⠂⡀⠀⠀⠁⡀⠀⠈⣧⡀
⠀⢈⡀⠀⠀⠀⠀⣷⣄⠈⠁⢰⡸⡃⠀⠀⠀⠀⢀⣀⣴⣾⣷⠷⠒⠋⠁⠈⠓⠤⣦⠀⠀⠐⡀⠀⣿
⠀⢀⠍⠢⣐⠋⠛⠛⣿⣷⣶⣾⡟⠙⢶⣶⣶⣞⣿⣿⣯⣍⣀⠀⠀⠀⠀⠀⠀⠀⡜⠢⡀⠀⠀⠀⡿
⠀⡎⠀⢠⣬⣷⣶⣿⡟⢒⣲⠾⣟⠿⣀⠙⢿⡿⣟⠛⡛⠿⣿⣿⣕⢢⡀⠀⠀⢠⠁⠀⠙⡄⠀⢰⠇
⠂⠀⢀⠞⢡⣲⣿⣿⠁⣬⣉⠳⣾⢷⡟⣇⠀⠙⢮⡻⣦⡑⢢⠰⣿⢳⡇⠀⠀⠀⠀⠀⠀⠈⢠⡿
⠀⠀⠀⠀⡹⢋⢻⣿⣷⣴⡦⢽⡮⠈⠁⠀⠀⠀⠀⠑⣬⠱⡀⠀⢹⡈⡇⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠁⠀⡞⢟⡏⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡇⠀⠀⣿⢹⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠘⢀⠀⠱⡤⣱⡀⣈⠳⠦⣤⣤⣄⡀⣀⣀⣀⡀⡟⣿⠀⠴⠁⠏⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠒⠤⠀⢉⣯⣭⣰⣿⠧⣤⣭⣿⣿⡟⠁⡁⣿⢈⣀⣀⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡿⠿⠉⠉⠉⠛⢛⢿⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠄⠀⣤⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣦⣠⣠⠞⠀⠰⣀⣀⣤⠴⠲⠎⠀⠉⠁⠀⢸⡀⢀⠀⢸⡀⢀⡋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢁⣤⡾⣿⢿⣿⡿⣤⡞⠋⠁⠀⠀⠀⡀⠀⠀⠀⡀⢄⢳⣿⣦⡘⣿⡌⣿⡞⡏⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢠⣤⣿⣿⣿⠇⢰⣹⡞⡁⢁⢀⡀⠘⠀⠁⠸⣦⣿⣷⣿⣿⣷⣽⣿⠶⠿⠷⢿⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣀⡾⢿⣿⣿⠟⠁⠀⢀⠋⡔⢰⠾⠧⠠⣀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣷⣿⡟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⡾⢋⣴⣿⡟⠁⠀⠀⢀⢴⣶⣧⠬⣼⣾⣿⣼⣧⣠⣿⣿⡿⠿⣋⠱⣆⠀⣾⠉⢿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⣽⠟⣡⣾⡿⠋⠀⠤⠤⠤⢴⣾⣿⡿⠿⠿⠿⠿⣽⠷⣾⠉⠻⣇⠀⢸⣧⢸⠀⠙⠃⠐⠋
⠀⠀⠀⠀⠀⠀⣾⡿⢏⣴⡿⠋⠀⠀⠀⠀⠀⢀⠍⠁⠀⠀⠀⠀⠀⠀⣴⣶⣿⣇⢀⡟⠀⣸⠇⣾
⠀⠀⠀⠀⠀⠀⢻⡥⠟⠋⠀⠀⠀⢀⣀⡀⠀⠈⠀⣀⢀⡄⢠⡄⣤⣴⣾⣿⣿⡟⢈⡇⢠⡍⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⢛⢉⠛⢻⣿⣿⠏⠀⠀⠀⠀⠘⢿⡟⣿⡿⠃⡞⠁⡸⠁⠈
⠀⠀⠀⠀⠀⢀⣴⣬⣵⡶⢶⣾⣿⣿⣿⣿⡿⠛⠋⣀⣄⣤⣤⣒⠋⢸⠿⠋⡱⠟⠀⠀⠁
⠀⠀⢠⡆⢀⠚⣩⠠⠄⠐⠊⠛⠒⠛⠉⠉⠀⣠⣾⣿⣿⣿⢟⠓⢋⡼⠀⠈
⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⢙⡤⠔⠋
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠝⠑⠋⠉⠁
⠀⠀⠀⠀⠀⠈⠚⠹⠟⠿⠙⠻⠛⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣭⣉⡀⠀⠈⠉⠉⠐⠿⣿⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣧⣶⣦⣤⣤⣀⠀⠉⠉⢿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣷⣶⣬⣛⢿⡛⢽⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣾⣒⣺⠄⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣧⣻⣾⣿⣿⣿⣛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡷⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣳⣿⣶⣼⣾⡿⡄
⠀⠀⢀⠀⢀⣀⢀⠀⣀⠀⠀⠘⣿⣇⠀⠀⠰⢤⣀⠀⠀⠀⠀⡀⣀⡤⠂⠀⠀⠀⢀⠀⣤⣴⣿⣿⣻⣉⣿⣿⡿
⢀⠖⠛⠚⠛⠻⠷⠾⣿⣧⣷⣤⣫⣿⣆⣤⣤⣤⣾⣟⣽⣿⣿⣿⣷⣦⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⢾⠿⠦⡀
⠈⢠⢬⣿⣿⣑⣓⣶⣿⡹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠈
⣰⠛⠛⠉⠀⠈⠉⠉⣙⠻⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠿⠻⠷⠛⠻⠿⡥⢄⡀
⠇⠐⠂⠀⣠⣀⣮⠼⠿⣼⣵⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠤⢤⣱
⠀⠀⡴⠞⠁⢀⡀⠀⠀⢀⡤⢊⢹⣍⣭⣿⠿⠛⠿⠿⠟⠛⠿⠿⠿⠟⠻⣭⣽⣽⣯⣛⣛⡋⠉⠉⠉⠙⠾⢦⣀
⠀⢸⡠⠄⠋⠁⠀⡀⣰⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠿⣶⣀⢄⡲⢤⣀⠀⠙⢷
⠀⠀⠀⠀⠀⠠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠻⢿⡀⠀⠁⠂⠜
⠀⠀⠀⠀⠀⢸⠁⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢺
⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠄⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⡀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⢳⡆⢤⢀⡀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠀⠉⣦⠄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠊⠀⢀⠊⢁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠂⢀⠀⢠⡀⠔⠒⠀⠀⠀⠀⠀⠋⠄⠀⢐⠀⠠⠂⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡀⠤⠒⠀⡉⠀⠀⠀⠀⠈⠸⠃⠀⠀⠀⠀⢀⡀⠀⠂⠐⡔⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⢀⠀⠁⠡⠊⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡌⠆⠂⠤⢀⡀⠁⢱
⠀⠀⠀⠀⡤⠀⠐⠂⠀⡘⠀⠀⠆⠁⠠⠀⢀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠰⠀⠀⠀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⠒⠀⠀⠀⠀⠅⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠠⣷⡀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡠⠎⠀⠀⠀⢀⠨⣤⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⣠⡀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠚⢛⠀⠀⠀⠀⠀⠐⣢⡌⢉⡁⠘
⠀⠀⠀⠀⠀⠀⠘⠄⠄⢀⡄⠤⠀⢀⠠⠀⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⢐⠐⣾⠀⠀⠀⠀⢀⠞⠁⢍
⠀⠀⠀⠀⢀⠀⢃⠀⠌⠠⠀⠀⠀⢢⠀⢠⠇⠀⡼⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠈⠀⢈⣽⠀⠀⠀⢠⡞⠀⢠⡀⠐⠒⠐⠒⠁
⠀⠀⠀⠀⠈⢆⠀⠑⠂⠼⠀⠀⠀⠀⢋⡁⠀⠒⠁⠀⡠⠀⠀⠀⠀⠁⠀⠀⡐⠀⠀⢨⣧⠀⡀⣀⠆⠀⠐⠀⠀⠑⠆
⠀⠀⠀⠀⢀⡀⠁⠒⠀⠚⡄⠀⠀⠀⣁⠂⠐⠐⠂⠀⠀⠀⠀⠀⡀⠀⡴⠸⡁⠀⠀⠈⠘⠤⠒⠋⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠀⠈⠉⡠⠋⡄⠀⠘⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠳⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡎⡁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠲⢿⣒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣞⠉⠉⣡⠼⠟⠓⠀⠀⠀⠈⢳⣀⣠⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠈⠓⠾⣁⣀⣀⠀⠀⠻⢿⣛⡋⠉⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⢀⣠⣤⠤⠤⠶⠚⠋⠀⠀⠀⠀⠀⠉⠓⠲⣄⠀⢀⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢹⠀⠉⡽⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⡉⠉⣰⠃⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢺⡀⣰⡧⠖⠚⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠙⠒⠾⣇⢀⡟⠀⠈⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡏⣇⠀⠘⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⢀⡏⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢻⠙⣆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡞⢹⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠷⡄⠳⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡽⠃⡴⢷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⠓⢦⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣥⠖⢛⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢚⣒⣚⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣒⡚⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣯⡥⠽⠤⠬⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠯⠤⠼⠥⣭⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡇⠀⠀⡴⢿⣉⣉⣙⣷⣦⣤⣀⣀⣀⣠⣤⣖⣿⣉⣉⣹⠟⡄⠀⠀⣧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⢽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠵⠋⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣶⣞⣿⣩⣋⣐⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡲⠟⠙⠁⣠⣼⡿⠛⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠊⠉⠀⢀⢑⣤⠴⠚⠁⠀⠀⠀⠀⠀⣠⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⢀⠀⢊⣵⠟⠁⠀⠀⠀⠀⠀⢀⡴⣾⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢶⡁⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⣀⢀⣀⡠⠴⡊⢔⡻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢊⠔⠋⠙⠳⢄⡀⢠⡴⠋⠀⢀⣠⡴⠋⠀⠀⡠⢀⣼⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⠄⠀⠀⢄⠀⠀⠀⠙⠛⠒⠚⠋⠉⠀⠀⣰⣲⠿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣰⠇⠀⢀⠀⠄⠀⠀⠀⠄⠀⠀⢀⣴⡾⢿⣞⠉⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣏⡀⠂⠄⢀⠀⠀⠀⢂⣠⣼⠵⠋⠁⠀⢸⢻⠁⠀⠀⠀⠛⠉⡂⡿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⢦⣀⠀⠀⠀⠀⢚⡽⠛⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠫⠭⢀⣿⣠⡋⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠌⠙⢲⡖⠋⠁⠀⠀⢀⠀⠄⠠⠤⡸⠄⠔⠚⠁⠀⠀⠁⠺⠃⠐⠛⠋⠒⠥⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢂⠀⢰⡇⣀⠖⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠐⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣄⣀⡴⠦⠝⠓⡿⢦⠂⠐⠐⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⢗⡤⢻⡶⠶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡇⠀⠈⠙⠠⣄⣀⣷⠘⠷⢄⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⠀⠠⠊⡀⣸⡻⠿⠦⣬⡟⢦
⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠟⠦⣀⡀⠀⠀⠙⠿⣧⠰⡌⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣿⡖⠀⠀⣰⡥⠚⣧⣶⠲⢵⣸⠆
⠀⠀⠀⠀⠀⠀⣺⢁⣤⣏⡤⣎⠉⠁⠀⢀⠂⠀⠬⣷⡙⢌⡢⡉⢷⡀⢀⠂⠀⠀⡀⠈⡆⠀⠀⠀⠀⠙⣆⡠⠀⠀⠀⣽⢀⡀⡸⠋⠀⣠⣿⢿⡻⣦⣉⠻⣤
⠀⠀⠀⠀⠀⣾⣿⡬⠛⠁⢀⣸⢷⠂⠀⠀⠀⠐⠂⠠⢹⣦⡹⣈⣦⡻⣦⡘⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⢀⣟⣠⠟⢀⣨⡞⠃⣿⢸⠇⠀⢙⠷⠛⣇⠄
⠀⠀⠀⢀⡴⠿⠛⣶⡶⠛⠉⣀⠞⢳⣤⣤⣀⣀⣀⠂⣤⣈⣙⣿⣿⣿⢾⣿⣦⡠⠀⡀⠀⢀⠠⡀⢂⠀⡀⠀⠀⣁⢼⣁⠾⠛⠉⠰⠃⠀⠙⣶⠁⢠⡏⠀⠐⣜⣧
⠀⣠⡝⠉⣐⡤⠞⡋⠀⠀⢠⡟⢀⡿⢀⣆⠀⠀⠀⠀⢀⠀⢀⣩⣏⣉⢻⣟⣶⣿⣶⣶⣤⣤⡤⠤⠤⣐⣶⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⡄⣰⠃⠀⠈⠀⠀⠀⠈⢽
⠀⡝⡝⠋⠁⠀⠀⣇⠀⠀⣿⢀⣼⡁⣻⠸⡿⠒⠶⠶⠖⠚⠋⠉⠉⠉⠉⠉⠉⠙⠏⣿⣽⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡟⠃⠀⠀⠀⠀⠀⠀⠀⠸
⢸⡜⠀⠀⠀⠀⠀⠙⠀⠀⣹⠏⠈⡅⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢀⠇⣿⣴⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣸⠀⢯⣯⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠘⠘⣦⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠉⠙⠒

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡒⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡿⠛⠉⠀⠀⠀⠀⠀⠈⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠻⡦⣀⠀⠀⠀⠀⠀⠠⢦⣤⠊⠀⠀⠀⣠⣤⡦⣮⣤⣀⠀⠀⠈⢳⡶⠞⠀⠀⠀⠀⠀⢀⠔⡟
⠀⠀⠀⠳⣌⢳⡀⠀⠀⠀⠸⣰⡷⠚⠋⣈⡀⠉⢉⠂⠀⠋⢉⣿⠍⣷⣾⣧⡴⠀⠀⠀⢀⣼⣫⠜⠁
⠢⣀⠀⠀⠈⠫⣙⣲⣄⣀⣀⣸⠇⠀⠀⠈⠁⠆⢈⠁⠀⠀⠸⠝⠓⠚⠊⣟⣁⡀⣠⣒⣋⠝⠁⠀⠀⣠⠔
⠀⠈⠙⠶⣤⣄⡀⠉⡉⠓⠛⠟⢶⠄⠂⠒⠀⡊⢳⡩⠀⠀⠀⡲⠡⢒⣶⠾⠟⠓⢋⣉⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠓⠻⠷⠶⣶⣮⣅⣠⢅⣤⣤⡉⢠⣰⣏⣖⣼⣾⣿⡶⠿⠛⠓⠋⠉⠉
⠀⠀⠀⠀⢀⣤⣴⡶⠶⠛⠓⢿⣷⣶⣶⣿⣷⣦⣬⣁⣤⣬⣿⣿⣧⣶⣿⢿⡏⠛⠓⠛⠷⣶⣄⡀
⠀⠀⢀⠴⠋⠉⠀⠀⣠⣶⠿⠋⠙⠛⠛⠟⠋⠉⠉⠛⠋⠉⠉⠛⠛⠛⠋⠉⠙⢿⣶⡄⠀⠀⠈⠛⠦
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠠⠀⢀⡠⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠂

⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣴⡒⠖⢶⡤⣄⠀⣀⣀
⠀⢀⠀⠀⢂⠀⠀⠀⠑⣠⣤⠤⠤⠶⠻⣿⡟⠉⠁⠒⠉⠂⠈⠉⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠹⣦⡀
⠀⠈⢄⠀⠀⠑⢤⣀⠀⠈⠁⠴⢤⣀⣀⣀⡀⡀⠀⠠⠴⠒⠒⠀⠂⠄⢀⠀⠀⠀⡘⠀⠀⠀⠀⠈⣷⢤⡀
⠀⠀⠀⠑⠤⣀⠀⠀⠉⠙⠒⢒⣚⣻⠭⠭⠛⠛⠓⣢⠶⡦⣴⣁⡒⠤⡀⠀⠀⢰⡇⠀⠀⠠⡾⢀⡇⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡇⠏⠘⠛⠛⠙⠃⠐⡾⣇⡀⠀⠈⣠⠞⠀⠀⢨⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢦⡣⡣⡀⠀⠀⠀⠀⣼⣾⣿⣿⣿⠉⠀⠀⠀⠀⢈⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠛⠎⠢⠀⠀⠀⠀⠀⣙⢿⣿⡷⠤⠄⢒⡂⠁⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠾⣿⣧⣀⠀⠀⠀⢀⣄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢏⠀⠉⠐⠂⠤⠟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠀⠱⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⢭⣭⣓⣦⣄⡐⠉⠀⠁⠀⠀⠀⠢⢶⣦⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣄⣤⣭⣿⣯⡀⠀⠀⢀⣀⣤⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠘⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠪⠼⡀⠀⠀⠀⠀⣴⣶⣄⠀⠀⡃⠀⠉⠀⠀⠀⠘⣌⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠅⠀⠀⢀⣿⠀⠙⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⢠⠀⠀⠀⠀⠀⠣⠀⠀⠀⡼⠼⣷⡄⠈⡷⢦⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⣠⣤⣼⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠻⡄⣧⠀⠰⠤⢘⣿⠿⣅⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣠⣤⡀
⡟⠉⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⢸⣷⠶⢿
⠁⠀⠀⡾⡁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⣄⣠⣤⠀⠀⠐⠿⠷⠺⢆⠀⠀⠀⠀⠈⢳⠀⠈⠻⡄⠈
⠀⠀⠀⠔⠛⠀⡿⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⢆⡀⠀⠀⢤
⠀⠒⠀⠀⠀⠀⠀⠀⣤⣴⠿⠏⠈⠡⠁⠀⠀⠐⠦⣴⢶⣦⢤⣤⣀⣀⣠⡤⠤⠀⠀⠀⠹⠿⠛⠛⠇
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⣠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢜⢭⡻⢯⣤⣀⡀
⠀⠀⢱⣆⠐⠊⢁⡀⠀⠔⠀⠀⠀⡠⠀⠉⠢⠀⠀⠀⠀⠀⢀⡌⣇⠈⠛⠛⠿⠿⣿⣦⣄⢀⣠⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⡎⠀⠀⠀⠀⠀⠀⠈⢹⠋⠀⠀⠀⠀⠇
⢦⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠉⠀⠀⠀⠀⢆⠀⠀⠈⠀⣀⡤⠰⠶⣄
⡴⡞⢰⡀⢀⡠⠞⠁⣠⣤⣴⠒⠒⠞⠀⠀⠀⡁⠀⠀⠀⣴⣧⠈⠓⢆⡀⠀⠀⠈⣇⠀⡠⣄⠘⠉⠤⢤⡤
⠀⠇⠉⠉⠁⠀⠀⢸⡏⣵⠬⠉⣚⠋⠀⠀⠈⢰⡀⠀⠐⣓⡹⠄⠀⠀⠀⠀⠀⠀⠋⡴⣡⠈⠐⣇⡀⡰⠄
⠸⠁⠀⠀⠀⠀⠀⣸⣷⢿⣿⣿⣥⡰⡀⡀⠀⡄⢱⠀⠀⢱⠖⢛⡀⠀⠀⠀⠀⠀⢸⡛⠛⢶⡞⠀⢈⡧⢰
⠀⠀⠀⠀⠀⠀⠠⠏⢡⡎⢾⠈⢳⣭⣙⣋⣼⠁⠃⠀⠀⢸⡅⡄⠶⠀⠀⠀⠀⡴⠈⢉⣦⣰⣟⣀⠞⠉⠉
⢤⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸⣏⡟⢿⡏⣴⠀⠀⠀⠘⢧⣔⠞⠁⠀⠀⠘⠀⠥⠈⠈⠉⠉⠋⠙⠛⠛
⠉⠁⢀⣤⡶⡟⠓⢦⠀⠃⠀⠀⣸⣿⠀⠀⢿⠁⠀⠀⠀⠀⢸⠅⡠⢄
⠀⠀⢸⠁⠁⠀⣠⣐⠆⠀⠀⢠⢿⡟⠠⣄⡾⠀⠀⠀⠀⠀⠀⠣⠿⠗⠀⠀⠀⠀⠀⢀⠴⠒⠒⠠⠄⣀
⣀⣀⣨⣪⣄⣀⣀⣈⣀⣀⣀⣀⣚⣀⣀⣀⣀⣀⣀⣀⣒⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣍⣀⣲⣂⣀⣀⣀⣷
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢀⣀⣠⡤⢤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠲⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣾⠒⣿⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⠀⠀⠀⠀⠀⠀⡍⢨⡝⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠿⠀⠀⢸⣦⡀⡀⠀⠀⠳⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣹⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢸⡱⠊⠀⠀⠘⠠⡻⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⡄⢠⠀⠀⢀⠀⡄⠀⠰⡋⠘⢻⡆⠀⣸
⠀⠀⢤⡔⠚⠁⠀⠀⠙⠶⣎⡤⠀⠀⠀⠀⠀⠀⢠⠉⠃⢀⡰⠼⢠⣞⠉⡃⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⢸⠀⠀⠈⠠⡈⢠⣾⡇⠀⢸⡍⢋⣁⠔
⠀⠐⠊⢁⡀⠀⠠⠀⠀⢀⠈⠦⠀⠀⠀⠀⠀⠀⠈⢆⠲⡈⡄⠀⣀⠟⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢼⠀⠀⠐⠤⢼⢀⡼⣷⣀⣾⣄⢰⠅
⠀⠀⠀⠈⠉⠅⠈⠁⠀⠄⠈⠀⠀⠀⣴⠀⣦⠀⠀⠀⠀⠈⠂⠀⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠⣬⡏⠀⠁⣶⣄⠀⠀⠈⠻⠔⠋⠛⠻⠈⠆
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣀⠟⣀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠰⠃⠀⠀⠃⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⣰⠀⠀⠀⢀⣀⡷⣤⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠊⠀⢀⠁⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡍⠀⠀⠀⠀⢹⠰⡆⢠⣄⣤⣬⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣤⠄⡠⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠳⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠙⠒⠠⡀⠀⠀⠀⠀⠀⠀⢉⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄⡥⣀⣤⡀⢀⣄⣴⡟⢛⣿⡆
⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠀⡄⡀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⣙⡟⡆⣄⣨⠇
⠀⠀⠈⠙⠻⠁⠀⠠⠀⠀⠀⠀⠄⢸⡀⠀⣀⣤⠴⠤⠽⠒⠖⠺⢅⡤⣔⣁⠀⡠⠒⠉⢿⣴⠿⠟⠋⣀⡠⣤⣤⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠆⡀⠈⢘⣥⡔⠈⠸⠒⠒⠉
⠀⠀⣠⠔⠂⡉⠄⠀⠠⠃⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⡁⠀⠀⠀⠂⠀⠀⠀⣸⠇⠠⠊⠀⠚⣡⡄⠀⠀⢤⣄⡀
⠒⠋⠉⠁⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠚⡷⡀⠀⠀⠉⠀⠉⠉⠀⠀⠀⢰⡧⠄⠀⠀⢀⡠⣀⠁⡀⠈⠐⠢⠭⢶⣄
⠀⠀⢀⡔⠋⡁⠐⡠⢔⡉⠘⠅⢀⠀⠀⠚⢱⢿⣆⣀⣀⠀⠀⠀⠀⣀⣼⡾⠇⠂⠀⠀⢰⢄⠸⡀⠀⡙⠠⣄
⠀⠠⡾⠁⠀⢠⡦⠐⠂⠀⠀⠀⠀⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠈⠪⡑⣌⠂⠤⢱⡄
⠀⠸⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢻
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣼⣧
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣾⡇⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢧⢿⠟⢬⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⣸⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢸⠆⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢾⣥⣷⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠘⠛⢻⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣨⣿⡿⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠳⣶⣎⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢯⠁⣾⡷⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢙⣢⣄⣽⢀⡀⣀⢴⠒⣎⠏⢙⣫⠛⠂⢏⢿⡖⡻⡗⡶⠢⣤⣤⠼⢦⣿⣴⠀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠸⣿⣄⠀⠻⣌⣽⣿⣿⣤⣮⡷⠛⠛⠙⠿⣿⣵⠠⣶⣿⠽⠧⣤⠀⠉⠟⣳⣦⠏⠁⣴⢿⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠹⣧⡴⠀⢈⣯⣉⡟⣿⣿⡛⠁⠀⠀⠀⢈⡆⠀⡟⠃⠀⠀⣐⣿⣿⣆⠙⣣⣤⢶⡧⠈⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡷⠄⠀⠀⠈⣧⣿⣿⣛⣿⣾⠻⠻⢻⣦⣤⠀⠀⠀⢡⠠⠁⠀⢀⠛⢁⡿⠇⠀⢏⣘⡻⠋⠀⢀⣀⣴⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢧⡠⡄⡀⠈⣷⠶⠉⠀⠀⠀⠀⠐⠟⠿⣷⣢⣤⣤⣴⠞⠛⠛⠋⠀⠀⠀⣾⢧⢘⣿⣾⠏⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠻⠿⠻⢇⡀⠀⠈⠁⠠⡄⢀⠀⠀⢀⣥⣾⡆⠀⠀⡀⠴⠐⣉⣁⣉⣤⢞⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣶⣦⣼⠷⠾⠿⠛⠛⠛⠓⢶⣴⣷⠄⢹⡇⢈⣤⣢⠌⣀⣴⠋⠉⢉⣙⠐⠾⠒⠊⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⠛⠁⠀⡀⡀⠀⢤⣴⠾⢦⡬⠛⠋⠉⠛⠊⠓⠒⠉⠑⠚⠻⠷⠆⠆⠘⠏⠐⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⢀⣹⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢴⣆⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠊⢀⣼⣿⣛⣻⣋⣭⣭⠍⠀⠀⠀⠀⠀⠿⢶⣭⣙⠻⣻⡋⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⣞⣀⣴⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⣶⣌⣷⣤⡘⢆⠀⠀⠀⠀⠀⣜
⠀⠀⠀⠀⠀⢸⡆⠀⠀⣧⣄⠀⢠⡏⠉⣹⣿⠿⣋⣠⣴⡶⠖⠛⠟⠿⠟⠿⠿⠿⠶⠶⢦⣤⣀⠈⠻⣿⣿⡿⠚⢓⡄⠀⠀⢨⡜
⠀⠀⠀⠀⠀⠈⢧⢦⠀⣷⢸⡀⣿⣷⣿⡟⣁⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⣌⠛⣦⣠⣼⡿⢀⡄⣸⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠸⣏⢤⡘⣧⡳⠈⣿⡿⣧⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠗⣿⣿⡿⣱⢛⣶⠇⠀⢠⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣎⢳⡝⠿⣶⣠⠿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣷⡞⣻⣿⣮⡷⠛⢉⡠⢎⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣽⣓⠦⣭⣿⣿⣿⣿⣿⣦⣄⡀⢀⢀⢀⣤⠀⣠⣄⣠⡀⣠⣴⣾⣿⣿⣿⣿⢋⣭⠥⣄⣐⣠⣽⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢙⡛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠵⢿⣛⠛⣛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⣯⠼⠟⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠾⠭⣗⣦⣕⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠀⠀⣰⠚⣷⣷⣿⣭⣿⣿⡿⠿⠿⠿⣿⡿⡿⠿⣿⣷⣶⣶⣶⣷⣯⣀⡀⢠⣄⠈⠙⠻⢿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠁⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠙⠿⣿⣿⣷⡄⠀⠀⠀⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢀⡏⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⢽⡀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠠⡀⠉⠉⠉⠉⠉⠛⠛⠻⠶⠶⢶⣺⣿⠿⠟⠻⠿⠛⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣇⡀⠀⠈⠲⢶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣉⣈⣁⠀⠀⠀⠀⠀⠀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢹⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⠤⠵⠿⠿⢿⠟⠋⢨⣷
⠀⠀⠀⠀⠤⣄⠀⡀⠀⠀⠀⠀⠙⠟⡆⠀⠀⠀⠰⠀⠀⠀⣀⣀⢀⡀⠀⠀⠆⠀⠀⠀⣠⣴⣯⡀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠤⣤⡀⠀⠈⠻⣆⠀⣶⣶⣾⣷⣿⣿⣿⣿⣷⣾⣶⣤⣤⣤⠞⠋⣤⣿⠟⠋⣁⣀⣤⠄⠖⠂
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡀⠈⠳⢤⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣼⡿⡤⠾⠛⣁⠴⠚⠉⠁
⠀⠀⠠⠞⠛⠋⠀⠀⠀⠀⠈⠓⢤⡀⠉⠒⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠤⠖⠉⢀⣀⡶⠶⠶⠒⢶⣄⣀
⠀⠀⠀⠀⠀⠀⢠⡄⠠⠒⠛⠠⣤⣌⣑⠦⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣶⡾⠟⣋⣁⡤⣄⠄⠀⠀⠀⠀⠈
⠀⠀⠀⣠⠞⠁⠀⠀⢀⡴⠛⠉⠉⠐⠒⠦⠤⢾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣩⣯⠽⠟⠳⣤⡀⠉⠚⢆⣠⡀
⠀⠀⠰⠃⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣽⣿⣽⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠄⠦⠤⠴⠶⢴⣂⡀⠀⢀⡠⠤⠤⠤⠒⠀⢐⠒⠰⠆⠤⠄⠀⠀⡀⣀⡀⢀⣠⣤⣄⣀⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⣴⡄⠤⢴⣄⣤⣦⣍⣳⣮⣁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⢊⡴⠂⠙⡏⠰⠂⠀⠺⣷⣶⣮⣝⣲⣤⣀⣒⢁⣀⢤⣤⣠⣤⣴⣶⡿⠓⠒⠚⠛⠚⠓⠢⠤⠦⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⣰⣏⡀⠀⠀⠈⠲⠶⣶⣄⣤⣬⣙⣿⣝⣓⣿⣿⣿⣿⣿⣿⣿⣯⡁⢚⢄⣠⡷⠶⠤⠀⢤⡀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠁⠠⠀⢀⠀⠀⠑⠂⢀⣀⠈⠙⠛⠋⠛⠚⠛⠛⠉⠛⠛⠋⠉⠹⣠⠃⠀⠀⠀⠀⠀⠉⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣷⣧⢅⣨⠀⣌⠀⢀⣿⣉⠑⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠘⢿⣿⣿⣿⣿⣷⣶⣀⠌⢿⣿⣷⣷⣤⣆⡁⠀⠀⠀⠀⠀⠀⠉⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣧⠀⠈⠛⡛⠿⢿⣿⣷⣷⣦⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣶⣏⠀⢗⢀⡀⠀⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠉⡁⠀⠘⣄⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣾⣿⣶⣮⡶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠀⣤⠶⠤⣤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣥⡾⣋⡤⠚⠁⠀⠈⠛⠲⢬⣙⣻⣿⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⡀⠀⠀⢈⣼⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣤⣿⣆⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣴⣿⣉⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⡴⠛⠷⣾⡆⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣥⡽⠟⢳⣤⣀⡤⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣿⣿⣿⣦⠀⠋⠀⠀⣰⠏⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠘⢯⣤⣴⣿⣿⡟⠛⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣈⣙⣻⣅⠀⠀⠀⠚⠁⣀⣀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣂⠲⣦⣼⠿⠿⠿⠿⢿⣿⣿⣶⣶⢿⣿⣻⣿⣿⣿⠿⣿⣿⠏⢉⣤⡄⠀⠀⠴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠡⢄⣀⣀⣀⠉⠳⠦⢿⣿⣶⣦⣤⣄⣀⡉⠛⢡⣾⣿⣿⣿⣿⣿⣿⣯⣶⣾⡿⠅⠀⠀⠒⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠿⠿⣿⣿⣿⣿⣿⣦⡘⠛⠛⠟⠿⢟⣛⣽⣿⣿⠷⠂⣷⠤⠤⠴⠾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⢿⣿⡿⣿⠿⠛⠛⠛⠛⠛⠻⣿⣿⣛⠒⠒⠂⠤⣤⡀⠀⠘⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠖⠋⢠⣦⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣬⠉⠛⣻⡇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠀⠀⢿⡟⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢄⠀⠀⠀⠀⠀⠈⠐⠂⠬⢉⡉⠙⠒⠲⠶⢶⣤⣀⠐⠒⠈⠁⠀⠁⠙⠫⣟⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠄⣀⠀⠘⡇⠀⠀⠀⠀⢄⣸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢾⣿⣿⣾⠾⢿⣟⡡⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠳⢠⠆⢤⡀⠀⠀⢠⡤⠄⡐⣄⠀⠀⠀⣠⢄⠀⠠⡄⠀⠀⠀⣀⡴⡎⢫⣿⣿⣿⠏⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⡓⠒⠢⣄⡀⠀⠀⠘⢄⢸⡄⠀⢀⣠⣵⠶⠦⠚⠋⠙⠉⠓⠴⠖⣮⣤⣀⡴⢏⠃⣀⢿⠟⠋⣉⠠⣴⣖⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢁⠖⠄⠈⠃⠈⢠⠏⠀⠀⠈⠂⢀⠎⠀⠑⡀⠀⠁⠀⠀⠘⡏⠁⠀⢀⠩⠴⣎⠱⠐⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⢊⠁⠀⣰⠤⠁⠀⠀⠀⠀⢺⣆⠀⠀⠀⠐⡅⠀⠀⠀⢨⠀⠀⠀⠀⢠⡿⠄⠗⠁⠄⡊⢥⣖⠒⠐⣲⠶⢦⣄
⠀⠀⠀⠀⠀⢀⣠⡶⠿⠄⠒⠊⠀⠀⡀⠈⣀⢄⡀⠀⠐⠠⢄⣿⣦⠀⠀⠀⡜⠈⠉⠁⢣⠀⠀⠀⣰⣿⡤⠖⠂⠀⢁⡠⢄⡉⣀⡀⠈⠑⠒⠤⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣤⠄⠎⡀⠀⡰⠇⢠⡄⠀⠀⠀⠤⣺⢯⣧⣀⠀⠁⠀⠀⠀⠈⠀⠀⢰⣧⣿⡧⠄⠈⠀⢤⡄⠸⣓⠠⢈⠱⠤⣄⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⢠⠄⢂⠔⢋⡵⠈⠀⠉⠐⠒⠤⠤⠤⠛⠿⠛⠒⠒⠚⠒⠚⠒⠒⠚⠻⠿⠤⠤⠤⠐⠂⠈⠀⠁⠪⡑⠢⡑⠤⣀⢩⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⢀⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢷⡀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢡⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢤⡒⣫⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣀⣽⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⣾⣿⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠒⠤⡀⠀⠂⠀⠤⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⣿⠿⠃⢰⣃⡀⠤⠄⠒⠒⠒⠒⠶⠾⠤⢤⣁⡐⠬⠁⢠⠂⠀⠈⢢⠁
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢵⠄⠀⠀⠀⢡
⠀⠎⠀⠈⠐⠢⢄⡀⠀⠀⠀⠧⣄⣩⠗⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠒⠢⡀
⠀⠀⠈⠁⠒⠦⣄⠈⠲⠄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠋⠀⠈⠆⢰
⠀⠀⠀⠀⠀⠀⠀⠙⠎⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠿⠛⠻⢿⣿⣿⠟⠉⠁⠒⡶⢦⠀⠸⢸
⠀⠀⠀⠀⡤⠐⠒⠘⠦⠶⢤⣀⣼⡀⠀⠀⢀⣴⣿⣿⠁⣤⡉⣿⣿⣿⣐⠿⢂⣼⢟⡥⠤⣀⣀⡴⠁⢸⠀⠀⡜
⠀⠀⠀⠀⡀⠀⡀⠘⠃⣀⠀⠀⠀⣸⠃⣠⡿⠿⣿⣿⣦⣭⣵⠿⠿⢿⡛⠻⠝⠚⠉⠀⠀⠀⡠⠀⢠⠏⠀⠀⠁
⠀⠀⠀⠀⠰⠀⠆⠀⠀⠀⠩⠉⠩⠒⠋⠀⠈⠉⠒⠒⠒⠂⠉⠉⣉⠤⠔⠒⠚⠋⠓⠒⠒⡘⢧⠔⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠄⣢⡀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⣀⣀⣀⠀⠀⠸⡞
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⡙⠻⡿⠯⣵⣽⣶⠶⠿⠋⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠁⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸⡀⢸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⢸⠀⣸⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⠜⠀⠈⠃⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠋⠀⢘⠴⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠀⠂⠄⠀⣀⠀⠀⢠⠎⠀⠀⠈⠃⠀⣀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⠐⠏⠀⠀⠀⠀⠀⠀⢀⣀⣔⣻⡄⠈⣜⠀⠀⠀⠀⠀⠀⠈⠗⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠠⠀⠀⢐⠔⠹⠃⠿⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠊⠁⠀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃⠀⠀⠠⠤⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⢊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠈⣁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠊⠉⡄⠀⠀⠀⠀⠀⢀⡌⠉⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠁⠀⠀⠀⠀⠁⠨⠂⠀⠠⠀⠠⠆⠈⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠲⠀⠸⠤⠄⠤⠄⠀⣄⠀⠰⠣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢄⡀⠀⠀⠀⠀⢀⠄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠓⠀⠤⣤⡤⠄⢊⠀⠀⠀⠀⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠠⠠⠄⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠄⠀⠀⠀⠤⠽⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠐⠳⠄⠺⠤⠤⠤⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⣀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠉⠑⢄⠀⢠⠒⠉⠑⢆⠀⠠⠠⣶⡆⠀⠀⠀⠀⠠⡀
⠀⠀⠛⠑⠒⠈⠁⢀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠄⠀⢈⠀⠸⡀⠀⢁⡜⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡀⠄⠘⠤⣀⣀⡠⠊⠀⠀⠈⠉⠉⠀⠀⠀⢀⠀⠀⠀⠐⠀⠈⠀⠄⠑
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⣠⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠁
⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⠐⠦⠄
⠀⠀⠀⠐⠐⠁⠀⡀⠀⠀⣀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠆⠀⠃
⠀⠀⠀⢀⠀⠀⠘⠟⢄⠠⠛⠁⠀⠠⠀⠀⠀⠀⢀⠼⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠄
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈⠁⠈⣉⢿⡷⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⡃⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠶⠎⠛
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠑⠠⠂⠁⠀⠀⠀⠀⠈⢤⣀⣀⣄⣼⠗⠀⠀⠀⠀⣭⠑
⠀⠀⠀⠀⠀⠈⠛⠢⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠿⠸⡅⠁⠂⠈⢄⡀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠼⣆⣀⣀⣀⣀⣀⣀⣀⣀⡟⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠚⠣⡘⢄⠀⠀⠀⠀⠀⢀⡜⡠⠋⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣔⣉⣀⣀⣀⣀⣀⣙⣦⣗⣀⠀⠀⢐⣯⡚⢁⣀⡤⠔⡶⠃⠀⣀⠤⢒⣉⠉⢹⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣖⠚⠛⠦⣬⠽⠶⠤⣤⡉⠦⢠⣀⡀⠀⠀⠁⠀⠀⠉⠉⠉⢁⣠⣌⣉⣠⣤⣼⠄⠒⠛⠉⠉⠁⢨⠿⡇⢸
⠀⠀⠀⠀⠀⠀⣠⠊⠀⡸⠶⠤⡜⠁⠀⢠⠞⠁⠀⠀⠀⠀⣹⠋⠉⠁⠒⠢⢤⣀⣀⣺⣀⠀⠀⠀⠉⠉⡻⠯⡉⠉⠉⣹⠻⣄⠈⢢⡀
⠀⠀⠀⠀⢀⠞⠁⡠⠊⢠⠶⠖⢧⠀⠀⡏⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⡈⠉⠲⢌⠉⠉⠀⠉⠙⡁⠀⣿⣿⠃⠙⡄⢫⢳⡄⠑⣄
⠀⠀⠀⡰⠃⣠⠎⠀⢀⠇⢳⢴⠖⠉⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠈⠉⠑⠢⢕⢆⠀⠀⠀⡇⢀⡿⠁⠀⠀⢱⡀⢇⡏⣦⠈⠢⡀
⠀⠀⣞⣠⠞⠁⠀⠀⡜⠀⡎⢸⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠄⣀⣀⣀⣹⠧⡄⢠⢧⡜⠀⠀⠀⠀⠀⢇⠘⣧⣧⠱⡀⠙⡄
⠀⠀⡆⡽⠀⠀⠀⢠⠇⡜⠹⡙⢆⠀⠀⠀⠀⠀⠀⠘⡏⢖⠒⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⡠⠔⠊⠀⢸⣦⠃⠀⠀⠀⠀⠀⢸⢀⣱⠃⠀⠹⡍⡧
⠀⠀⢣⡇⠀⠀⠀⣎⣠⠃⠀⠙⢌⣢⡀⠀⠀⠀⠀⠀⠘⣜⡄⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⠟⠀⠀⠀⠀⠀⡠⠞⡏⢸⠀⠀⠀⣇⠇
⠀⠀⠈⢷⠀⠀⠀⢯⡘⡆⠀⠀⠀⠙⠻⠦⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠆⢠⠀⢀⡄⠀⣄⡄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⢴⣻⣷⣟⣟⣧⣾⡷⣿⠁⠀⣇⣀⣿⢋⣿⣿⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠈⠉⠁⠉⠁⠁⠉⠁⠉⠀⠀⠈⠉⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⡿⠿⠓⠀⠀⠢⠀⠔⠁⠐⠒⢘⡛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢀⣴⣿⣯⣼⣷⣦⠴⠒⠒⠂⠀⠉⠛⠓⠺⢿⣷⣤⣙⣿⢷⡄⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⣏⢻⣿⢿⠿⠋⢁⣠⣴⣶⣦⡤⣶⣾⣦⣤⣄⡈⢙⣻⡧⣾⣿⠀⠀⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢝⣦⡀⠀⠹⣋⣿⣿⣶⡾⢻⣿⢈⣽⣿⣇⠈⣻⣿⠛⢿⣿⣿⣟⣿⠟⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢬⣦⣀⡀⠙⠿⣿⡁⢸⣿⣿⣿⠃⣿⣿⣿⡁⣠⣽⣿⣿⠟⠁⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠄⣠⡬⣮⣙⠶⣄⡈⢿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⣿⣷⠶⣶⣶⣤⣤⣀
⠀⠀⣠⣴⣾⣿⡿⠗⠈⠁⢙⣻⢽⠳⣦⡙⠻⢿⣿⣿⡿⢻⠿⣿⣿⣿⣿⣿⣟⣻⣿⣾⣿⣿⣥⣤⡀⠈⠙⠛⠛⠛⠷⣄
⠀⣼⠛⠁⠀⠀⠀⣀⣤⣺⡿⠛⠾⣛⠓⣹⠿⣿⣿⡷⠿⠾⠾⠿⠿⠿⠛⠻⠿⠿⣿⢿⡟⠛⠉⢿⣾⣶⣶⣄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢠⣾⠿⠛⠉⢀⣐⣻⠟⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠈⠙⣿⣷⣄⠈⠉⠛⢿⡆
⠀⠀⠀⠀⠀⣾⠃⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣧⡀⠀⠈⠷
⠀⠀⠀⠀⠘⠇⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⣿⣷⣶⣶⣶⣶⣶⣾⣷⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠟⠋⢻⡅⠀⠈⣹⣟⣻⣶⣤⡀⠀⠘⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢀⣾⣏⣉⠄⠀⠀⠀⠀⠀⠹⣶⠾⠛⠉⠉⠉⠙⠻⢆⠀⠀⠀⠀⠉⠉⠩⠿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠂⢠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡀⠀⢀⣴⣿⠏⠙⢳⣄⡀⠀⠀⢀⣀⠀⣷⣶⣶⣤⣤⣠⣤⡄
⠀⠀⠀⠀⠀⠀⢳⠄⠀⠘⡇⠀⡈⢸⡇⠀⢀⣿⡿⠿⠿⠿⠛⠛⠭⠚⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢓⠀⠹⣜⣇⠀⣸⡏⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡔⠀⠈⢧⡀⡈⠻⣧⣽⣓⡿⢬⣷⠤⠥⠘⠃⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⢀⣻⣤⡴⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣯⣴⣽⣿⣿⠑⠀⠀⠀⠀⠀⠀⡠⠤⠈⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠠⣀⣠⣤⡴⣇⠀⠙⠻⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⠿⢷⢀⣾⠻⣿⠃
⠀⠀⠀⠀⢀⡼⠉⠀⠀⢀⡜⢳⣄⢀⡚⣯⢀⡀⠀⠀⢀⣤⠆⠀⣨⡟⠀⠀⢀⠒⠀⠂⠀⡀⠀⠀⠀⢀⣿⠒⠀⠉⠙⢤⡏
⠀⠀⠀⠀⠘⠀⠀⢀⡶⠋⠙⢦⡙⢻⡇⠉⠢⢽⠗⠞⠞⢉⡴⢛⣠⡼⠆⠂⠁⠀⠀⠀⢈⣑⠀⠀⢀⢼⣏⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢲⠋⠀⠀⠀⠀⠙⠺⡇⠀⠀⢿⠀⣀⡴⠋⢴⡿⠁⠀⠀⠀⠀⠀⠀⣄⣿⢙⠀⠀⢨⣾⣿⣶⡀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣠⡾⢛⠀⠀⣾⣿⠛⠀⠀⠀⠀⠀⣀⣿⢉⠉⢀⡴⠛⠋⠹⣿⣿⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠠⠀⠉⢺⠿⣿⣷⡠⡰⣶⣤⣴⡟⢣⢐⣒⠋⠁⠀⢀⣵⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⡞⠒⢦⣤⠈⣁⡸⢛⡏⢩⣗⠛⣛⠛⠻⢿⣿⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄⠈⡑⢬⠁⠙⣧⡀⠙⠲⠤⣄⡀⠀⠄⠀⠀⠀⠀⢠⣄⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣻⠇⠈⢓⡾⠈⠙⠲⢤⡁⢢⠍⠙⠛⠂⠛⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⣰⠏⠀⢀⣼⠇⠀⠀⠀⠀⠉⠛⠳⢦⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⢀⠄⠀⠉⠉⠁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⡀
⠠⠁⠀⠀⠀⠀⠀⣀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠲⣄⠀⠀⢀⡴⠊⠉⠓⢄⠀⠀⢀⠔⣡⣲⣆⠀⢠⠀⠁⠈⠀⢘
⠀⠈⢯⠇⣀⣀⠸⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠀⠂⠖⢈⡇⢠⣁⠁⠈⠛⠃⠀⠈⠀⠠⠀⠄⠌⠓⠀⠠
⠐⡀⠀⠀⠈⠉⠀⠀⠀⣠⠄⠒⠀⠀⠢⠄⡀⠀⢸⡀⠀⠀⠉⠀⠀⢀⡏⠀⠘⢦⣀⣀⣠⠞⠀⠀⡤⠀⠀⠀⠀⡀⠀⢠⠀⠠⡀⠀⠀⢀⠲⠄⠠⠐⢈
⠀⠀⠠⢀⠀⠀⠀⠀⠘⡁⠀⠁⠀⠁⠀⢄⡈⠄⠀⠑⢤⣀⡀⣀⡠⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢄⡀⠠⠊⠀⠄⠨⠠⠈⠁⠀⡤⣀⣋⣁
⠀⠀⠀⠀⠀⠑⢀⠀⠀⠂⢈⠂⠀⠂⠔⠈⠑⢠⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠘⠓⠛⠓⢃⠠⠈⠈⠀⠀⠀⠀⠈⠂⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡦⢉⠀⠀⠀⠐⠠⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠀⠳⠠⠊⠈⠀⠊⢥⡀⠀⠀⠀⣀⡀⠐⠃⠀⠐⠄⣀⡀⠀⠀⠀⠀⠂⠀⠤⢀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠈⠂⠀⢆⠀⠀⣀⡀⠀⣀⡀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠑⠄⠉⠁⠐⠉⠁⠔⠀⠀⠀⠀⠐⠀⠀⠖⠐⡄⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⢀⠀⠀⢀⠄⡀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⣦⠀⣾⡶⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠊⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⢨⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⢥⠀⠀⡬⠐⢠⣉
⠀⠀⠀⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠈⠉⠀⡀⠊⠀⠈⠀⠠⠀⢎⢣
⠀⠀⠀⠀⠓⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠈⠀⣀⡀⣶⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢠⠁⠐⠈⠃
⠀⠀⡠⠀⠐⠀⠀⠀⢿⡿⠀⠀⡘⢿⠇⠀⠀⢙⡂⢄⠀⠀⠀⠀⠀⣰⣿⠦⢀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡀⠊⢀⠠⢊⡘⠀⠀⠀⠀⢁⠂
⠀⠀⠈⠀⠊⡀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⡌⢋⠁⠀⠀⢀⠤⠜⠁⡽⢷⣦⣄⣁⣰⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⢀⠊⠱⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡁⠁⠀⢄⡀⠀⠀⠀⠀⠀⡀⠔⠢⡉⢎⠀⠀⠀⠀⠀⠀⠀⢀⡾⡻⣞⡅⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠃⠀⠀⠀⣰
⠀⠀⠀⠀⠑⠁⠀⠀⠀⡉⠀⠀⠈⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠘⠀⠇⠀⠂⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⢄⠀⠀⠐⠀⠰⡀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠀⠀⠀⣶⣶⠀⠀⠠⠔⠆⠀⠀⠀⠄⠀⠰⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠈⠁⠘⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠰
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣤⣄⠢⡈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠆⠀⠀⡀
⢆⠀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⠀⠀⠀⠀⢷⠟⣀⠀⡨⠛⠋⠀⠠⠀⠀⠁⠐⡄⠀⠀⠀⠀⠀⢒⣟⣴⠀⠀⠀⠀⠠⠔⠠⠄⠈⠆
⠀⡀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⠓⡆⢶⢴⡲⣏⠎⠀⡢⠀⠀⢈⠀⣞⠓⣀⡀⠁
⠀⡡⠂⠀⠀⠀⠀⠈⠙⠣⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠅⢠⡝⡊⠿⡅⠀⠁⠀⠈⢅⢀⠈⠀⡈⠉⠉⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠈⠉⠉⠛⠛⠛⠛⠛⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠲⠠⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡉⡅⠀⠀⠀⠀⠀⠀⠀⢠⡃⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⠂⠀⠀⠈⠉⠉⠈⠉⠹⠀⠰⠃⠤⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⡇⢸⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠢⢀
⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣀⣨⠇
⠀⠀⢀⠔⢡⡜⠤⠤⢄⣉⠐⠤⡶⣥⣀⣀⠀⠀⠀⠀⠀⠢⡱⢄⠀⠀⠀⢀⣀⣀⣠⣎⣤⠤⠤⠖⠒⢻⣏⠡⠄⠒⠒⠀⠀⢀⡤⠤⢄
⠀⡐⠁⢠⠁⢘⠖⢠⣤⡀⣉⡒⠬⢺⣆⠹⡍⢹⠉⠛⠛⠛⠋⠉⠋⣩⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠒⠒⠒⠛⠛⠛⢤⣀⡑⠢⣄⠑⠄
⠐⠀⡰⡏⠀⣄⠔⠁⢠⠓⢤⣀⡉⠉⠛⢆⠈⠲⠤⣤⣀⣠⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⢄⡀⠀⠀⠀⠠⠊⠀⠈⠑⠪⣢⣘
⣇⡰⠁⢣⣠⠏⠀⢠⠃⠀⠀⠀⢉⠝⢓⡺⢦⡀⠀⠢⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⣀⠠⠄⠚⠃⠀⢲⠛⠊⠉⠁⠒⠒⠻⣯
⠀⢡⠀⢠⠎⠀⣠⠃⠀⢀⠤⢶⡤⠒⠉⠀⠀⠙⠢⢤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⠤⢖⡫⠕⠂⠉⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠘
⠘⢬⠀⠘⣄⣴⠁⠀⠀⡇⠀⣄⠤⠤⡤⠤⠒⠒⠠⠤⠤⣉⠉⠉⠉⠉⠉⠉⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡇⢿⠀⠀⠀⠑⠢⡅⠀⠀⠠⢄⣀⣀⣀⡀⠀⠀⠈⠢⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠰⠖⠋⣹⠃⠐⠒⠒⠚⠉⠀⣸
⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠢⡀⠀⠈⠉⠒⠦⡀⢡⠎⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⠐⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠈⠢⠄⣀⠀⢀⢈⠇⠀⠀⢀⠔⠍⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⠤⠄⠀⢸⠀⠀⣰⠁⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢰⠃⠀⠀⢠⠔⠚⠉⠁⠀⠀⠀⢀⣀⣠⡤⠴⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠐⠲⠶⢄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⢀⣐⠀⠁⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠀⠀⠁⣀⠠⠤⠤⠤⠤⠀⠤⠤⠤⠄⢀⣀⠠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠍⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠴⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢰⡆⠉⠐⠒⠦⣄⠀⠀⠀⠀⠀⠀⣄⣴⣚⠋⠉⠁⠄⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠀⠈⠉⠩⠗⠓⠒⠒⠚⠛⠻⢈⠁⢀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⡦⠶⠂⠀⠀⠀⠀⠲⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠋⠀⠀⢀⣀⣀⡄⡀⠀⠀⠈⠳⣤⣤⡇⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠸⣌⠳⡄⠀⠀⠀⠀⡄⣿⡤⠶⠂⠀⠚⠛⠥⠉⠝⠒⡶⠶⣤⣸⣇⡀⠀⠀⠀⢀⠴⣃⠞
⠀⠀⢄⠀⠀⠈⠳⡛⠦⣄⠀⠀⠙⡏⠀⠐⠈⠓⡠⠘⠂⠀⠀⠼⠿⠤⠿⢿⠟⠀⠀⣠⠴⢚⠟⠁⠀⠀⣠⠄
⠀⠀⠀⠑⠦⣤⣀⠈⠉⠛⠻⠽⢿⢇⣀⠀⠤⠀⡀⢦⣴⡀⠀⠀⢐⢤⢄⣤⡿⠿⠜⠛⠉⠁⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠮⠴⢶⣤⣤⣶⣄⡀⠒⠠⢈⡓⢀⠠⠌⣥⣴⣾⣯⣶⡶⠶⠽⠛⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡦⠶⠶⠶⣶⣯⣭⣿⣿⣍⣙⡃⣈⣛⣽⣿⣯⣽⣿⣷⠦⠗⠲⠶⣦⣄⡀
⠀⠀⠀⠀⢀⡴⠋⠉⠁⢀⣠⣶⠟⠓⠛⠻⠿⠟⠙⠛⠛⠛⠛⠛⠻⠿⠿⠓⠛⠳⣶⣄⠀⠀⠉⠙⠦⡄
⠀⠀⠀⠀⠁⠀⠀⠀⢀⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣵⠀⠀⠀⠀⠀⠀⠀⠠⢾⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠴⠀⠀⠀⠀⠀⠀⠀⡇⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠄⠄⢠⡇⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠁⠒⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠀⠈⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⣄
⠀⠀⢀⠄⣰⢆⣀⣀⠀⠤⣠⣔⡁⠀⠀⠀⠀⠀⠡⡱⡀⠀⠀⠀⠀⠀⠀⣠⣁⣀⣀⠤⠤⢶⠒⡉⠁⠀⠀⠀⢀⣀⡀
⠀⡐⠁⡐⠈⡦⠤⣄⣉⣐⠢⢄⣯⠹⡛⠓⠒⠒⠒⠛⠚⠓⢻⠛⠉⠉⠉⠉⠁⠀⠀⠀⠠⠯⠀⠒⠒⠒⠶⢄⡉⠢⢄⠑⠄
⡐⠀⠜⠁⢀⡰⠋⢠⠳⢤⣈⡉⠛⢧⠈⠲⠤⢤⣀⡤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⢀⠀⠀⠀⠠⠊⠀⠉⠢⡣⣈
⢧⡌⠈⠦⡜⠀⢠⠃⠀⠀⢀⠍⢛⡿⠧⡀⠀⠒⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣁⠠⠄⠂⠉⠉⢲⠉⠉⠉⠉⠉⠛⢧
⠀⢁⠀⠾⠀⡰⠁⠀⡐⠂⠳⠊⠁⠀⠀⠈⠓⠢⠤⢤⣤⣤⣤⣤⠤⠤⠖⡚⠝⠂⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈
⠀⠒⠀⢰⢺⠁⠀⠀⢄⠰⠒⠈⠑⠈⠉⠉⠉⠁⠒⠠⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠇⢀⣀⣀⡠⠄⢀
⠀⠀⠀⠘⡜⡀⠀⠀⠀⠙⡄⠀⠀⠙⢖⠒⠒⠢⠤⣀⠈⢂⡠⠊⠀⠀⠀⠀⣀⠠⠤⠒⠂⠉⠉⠉⣀⠜⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠢⣀⠀⠈⠂⢄⠀⠀⠀⠑⡜⠀⠀⢀⣤⠂⠉⠀⠀⠀⠀⠀⠀⡀⠚⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠀⠁⠀⢰⠁⠀⡰⠋⠀⠀⠀⠀⠀⢀⡤⠔⠁⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠃⠀⠀⡠⠒⠋⠉⠀⠀⠀⣀⣀⣤⠤⠖⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣥⣤⣤⣤⣬⣿⣶⣶⣾⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⠴⠒⠚⠒⠶⣄⠀⠠⣞⣩⣭⣉⣉⠉⠓⣶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠋⠀⠀⢯⠀⠐⠛⠛⢛⣿⠀⠀⠙⠲⢤⣀⠈⠷⡜⠃⠀⠀⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⡄⠀⠀⠀⢀⡴⢿⣿⣀⣠⠄⠀⢸⡤⢒⡾⠛⠉⠁⠀⠀⠀⠀⠀⠈⠛⢦⡀⣀⠀⣀⣸⠿⣿⢷⡀⠀⠀⠀⠀⠀⠀⢀⡴⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡝⢦⠀⢀⣿⡄⢸⣯⣿⣄⣠⣴⡯⠞⢁⣖⠦⠷⠦⠶⠦⠾⣤⡴⢞⣆⠀⠙⠮⣿⣿⢿⡋⠀⠀⣟⣆⠀⠀⠀⢀⡴⣏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣷⣼⡟⣷⣿⡿⠗⠿⢿⣭⡶⠞⠉⠉⢴⠀⠀⠰⡆⠀⠖⠀⠈⠙⠳⣦⣤⡼⠟⠛⠣⠀⡰⢫⡟⢀⣤⢞⣭⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⢿⣿⣿⣷⣀⣴⣶⠋⣤⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠱⢤⣄⡀⣰⣿⣷⣿⠟⠋⣀⡼⠋
⠀⠀⠀⢀⣠⠤⠤⢤⣤⣤⡤⠤⢽⣶⣶⡟⠻⢿⣿⣿⡍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⢹⣿⡿⠟⠋⢿⣿⣫⣞⣉⣤⣀⣀⣀⣀⣀⡀
⠀⠀⣰⢋⡿⠶⠶⠾⠿⠳⠦⣤⣴⣾⣋⣹⡶⠶⢶⣾⣇⠉⠓⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠾⠟⠋⢉⡿⣤⣤⣤⣼⣟⣒⣀⣀⡽⠲⡄
⠀⠀⣿⡏⠀⠀⠀⣠⡤⠶⣶⡶⠚⢻⣿⡛⠛⠶⠶⣾⣿⣇⡀⡐⠦⠤⣀⠘⡧⠀⠀⣇⠀⢀⡤⠖⢁⣤⡞⠿⠿⠓⠒⣀⣭⠛⣟⡛⠷⠤⣤⣀⠀⠀⠀⠙⢧⣿
⠀⠀⢸⡇⠀⠀⡼⢁⣤⠴⠟⠛⠒⠛⠋⢙⡶⢶⣶⡶⠾⣿⣿⣯⣵⠦⣌⠁⢠⠀⠀⡄⠘⣁⡴⡾⠡⣤⡗⠶⣶⠾⢿⣶⣶⣛⡛⠓⠲⣄⡢⣌⠙⣦⠀⠀⠈⠃
⠀⠀⠈⠇⠀⠀⢧⡿⠀⠀⠀⣠⡞⠋⠙⡹⣦⣤⣿⣤⣀⣸⣿⣦⣽⠷⠿⢿⣢⡶⣶⣤⡼⠯⠷⣍⣍⣄⣠⣒⣼⣿⢾⡅⠀⠀⢩⠳⣆⠀⠙⠚⢾⡙⡆
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢰⣯⣧⣤⣾⣿⡿⠛⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠛⠿⣟⡵⣞⡄⠸⡆⠀⠀⠀⢧⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⡏⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣯⣀⢄⡇⠀⠀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠽⠛







⣀⡀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠔⠋⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⡀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠈⠀⢤⠀⣢⠠⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢐⡂⡆⢒⢢⣄⣀⠀⠀⢀⠔⡈⠐⠀⠘⠀⠀⢀⣴⠏⠑⠎⠉⠖⠓
⠀⠀⠀⠀⠠⠀⠉⠀⠤⠀⢀⠀⠐⡂⢱⠀⠀⠀⠀⠀⡀⠞⢿⣩⢝⡱⣣⣞⡴⡯⣯⢕⣷⣮⡄⠀⠀⢸⠀⠀⡮⠛⢄⠀⢡⢠⠀⢠⠆
⠀⠠⠏⠢⢀⡱⡀⠀⡀⢀⠀⢁⣈⡀⠌⠀⠀⠀⢀⠌⢰⣦⠈⣗⣩⢟⣳⣳⣯⣭⢽⣹⡟⠯⢁⠀⠀⢘⠄⠀⠳⣄⠀⠡⣌⣜⠀⠜
⠀⠀⠀⠈⠒⠞⣵⢃⠣⠘⡁⠂⢡⠀⠀⠀⠀⠀⠘⠽⠀⠀⠀⢹⣾⣿⣿⣾⢿⠭⠋⠁⠈⠐⠠⢁⣀⣠⠆⠀⠀⠀⠁⠂⠬⠥⠊
⠀⠀⠀⠀⢸⣠⠁⢸⠀⠁⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠖⠿⠛⠋
⠀⠀⠀⠀⠈⠁⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠙⢫⠥
⠀⠀⠀⠀⠀⢀⣤⠐⠖⠀⠐⠖⠀⢀⠀⠀⠀⠀⡀⡜⠡⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡼⣁⠁⠀⢸⢶⠁
⠀⠀⠀⠀⡼⡁⠀⠀⠑⠂⠀⣀⠀⠈⠓⢄⠀⠌⣀⣡⠷⡚⡀⠀⠀⠀⢀⣨⠛⡒⠤⢤⣡⡶⠢⢄⢣⠀⠀⠀⢈⡟⢠⡟⣦⣢
⠀⠀⠀⢰⠀⠀⠰⡟⣆⠀⠀⠀⠀⠠⠄⠀⠓⠀⢄⣀⠤⠃⢰⠀⠀⣠⣙⠆⢧⣤⠂⢨⢽⢃⡇⣼⡜⠀⠀⢠⠋⡀⠀⢿⢅⢨
⠀⠀⠀⠘⠀⠀⠀⢉⠁⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠎⠀⠀⠈⠢⠄⣦⣮⡶⠁⣬⣿⢫⠏⣰⡄⠀⠘⢄⢱⠀⢸⡟⠉
⠀⠀⠀⠀⠰⡖⠒⠉⠀⡠⡤⢖⠖⡲⡲⠲⢶⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⠣⣣⡮⠚⠁⠀⢰⠲⢈⠇⣼
⠀⠀⠀⠀⠀⠈⠐⠐⠯⠮⠰⠅⠾⠚⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠗⠚⠁⠀⠀⠀⠘⠦⠥⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⡀⠀⠀⠀⢀⠎⣀⠀⡦⠀⡃
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⠖⢂⠀⢀⣰⣤⣤⣀⡔⠉⡄⠔⣀⠀⠡⡂⠀⠀⠨⡀⠙⠀⠂⢔⢩⣴⡀
⠀⠀⠀⢃⠘⣢⠄⠐⣶⠀⠀⠀⠀⣴⡊⠀⠩⣥⠀⠒⠀⠐⠖⢒⣒⣻⣿⣾⣿⠤⠤⣀⠀⡴⠀⠀⠀⠈⠒⣀⠰⣞⠣⡙⢿⣦
⠀⠀⢀⠔⠲⢓⠄⠐⣇⠀⠀⠀⣌⠈⠋⠀⠀⠺⠀⠐⣊⣩⡭⢟⡻⠛⠁⠃⡅⠀⢄⠈⠠⠂⠀⠀⠀⠀⠈⠑⢄⠂⢹⣟⡿⣿⡷⣄
⠀⠀⠃⠄⠂⡀⣸⠂⠘⠀⠀⠀⠀⠐⠠⠀⣀⣘⡇⠩⠤⠐⠊⠁⠀⠀⠈⠁⢤⢘⠘⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣌⢮⡙⠊
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠓⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢀⠋⡀⠀⠀⠀⠀⢰⠀⢹⡀⡀⠀⠀⣈⡁⠠⠴⡲⣂⠕⢀⠄⠀⠀⠀⠀⠀⣀⠴⣅⠙⡦⣀⣄⢀⣈⣽⡷⠀⢀⣀⣐⣲⣶⠶⠀⠀⠀⠚⣡⣶⣶⣦⣇⣄
⠀⢀⢸⢰⡇⠀⠀⠀⠀⠸⣦⣸⡇⢱⠀⢲⡜⠁⠈⠈⠒⠖⠶⠦⠀⠐⠀⠀⠀⠀⠘⠄⠔⠈⠙⣷⠿⢛⠋⠁⢀⣴⣟⣫⡼⠭⠴⠤⡤⣀⠀⠀⠋⠉⠀⣀⣃⠘
⠀⢸⢸⣿⣿⠀⠀⣄⡀⠀⢻⣿⡇⡜⠀⠈⠿⠲⣦⠤⠄⢤⢠⣤⣤⡥⣤⣤⠀⠀⠀⠘⠀⠉⠛⠖⠂⠀⠀⠀⠘⠿⢯⣤⣴⣭⣭⡾⠞⠁⠀⠀⠀⠀⣒⣥⠚⠋
⠀⠈⢆⢻⣿⣠⠖⠲⠷⣦⣼⡟⡴⢃⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡘⢙⣛⣿⡀⠀⢰⣿⣟⢛⣳⠀⠀⠀⢀⡄⢖⡄⠀⠀⠀⠀⠀⠖⢋⣩⡤⢠⣤⣴⣦⣬⣍⣒⣂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣐⡬⣷⣆⠂
⠀⠀⠀⠄⠐⡘⢻⡀⢸⣟⡒⠀⠀⠀⠀⠀⡅⠠⣛⠢⣠⠀⠀⠐⠁⡴⣟⡿⡀⢘⠋⠤⠄⠈⢩⡥⠛⠛⠃⠀⠀⠀⠀⠀⢰⡷⠶⠾⠗⠒⠉⠀⠀⠉⠳⣦⢦
⠀⠀⠈⠂⠡⠊⣒⣓⣒⠑⢍⠒⠀⠀⠀⠀⠹⠂⠙⠊⠋⠀⠀⠘⠘⢟⣿⣷⣿⢾⣮⣵⣶⣾⠧⠀⠀⠈⠉⠀⠀⠀⠀⢸⡇⢦⡀⠀⣠⣤⣤⣀⡀⠠⠂⣸⠇⡔
⠀⠀⠀⠀⠀⠀⣒⢒⣒⠀⠀⠀⠀⡀⣀⣤⣠⣀⣀⡀⠀⠀⠀⠀⠙⠉⠐⠠⠍⢠⠿⠏⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣿⣾⣿⣿⣿⢿⣿⣾⣍⠅⢊⡀
⠀⠀⠀⠀⠀⠀⠐⡶⠂⠀⠀⠀⢨⠾⡉⠉⠙⠻⢿⣽⣟⣰⣆⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢿⢛⣫⣿⠄⠀⠐⠉⠈⠻⢿⣿⢿⣿⣿⣿⣟⠉⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠠⢻⢧⡀⠀⠀⠈⠛⠿⢶⣴⠶⠦⠾⠿⠿⢿⣶⣿⣽⣾⣥⣦⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠐⠈⠀⠔⠉⠉⠙⠛⠋⠉⠢⡀⠈⠢
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉
⣶⡾⣒⣷⣷⣾⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣥⣷⣶⣶⣶⣶⣦⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠐⠦⠰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠠⠀⠀⠈⠁⠂
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠁⠀⣛⠀⠩⠤⠐⠒⠃⣄⠀⠂⠈⠁
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠅⠀⠈⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠀⠡⠄
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⡁⠀⠀⠀⠂⠀⠀⠊⢢⠄⠀⠀⠤⠤⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠄⠐⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⣉⠤
⠀⠀⠀⠀⠀⠀⡀⠈⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⡀⠀⢧⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁⠀⠠⢐⠆⠐⠄⡀
⠀⠀⠀⠀⠠⡮⡉⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠄⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢴⣆⢨⠄
⠀⠀⠀⠀⡂⠀⠁⠐⠐⠃⠠⠈⡁⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠷⠼⠣⠄
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠋⠀⡘⠄⠀⠀⠀⠀⠀⢊⠂⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠀⠀⠅⢀⡀
⠀⠀⠀⢨⠆⠀⠄⠐⠔⢶⠀⡔⠁⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠂⡠⠁⠀⠀⣀⣀
⠀⠀⠆⠈⢢⢀⠀⢀⡠⢌⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠑⣀⠆⠀⠈⠀⠀⠀⠊⢀⠄⠒⠀⠈⠀⠐⠢⠀⠀⠀⢄⠀⡢⠆⠀⠀⠀⠀⠀⠀⢟⠄⠀⠀⠀⠀⡌⠀⣤⡀⠀⠀⠀⢀⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠁⡣⠀⠁⠀⢀⢀⠀⣉⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠒⠁⢀⣘⠇⠀⠀⠀⠀⠀⠀⠀⡸⡄⢡⠢⠆⠶⣤⡄⡇⠀⠀⠀⠀⠀⠀⠏⠖⢲⠘⠇⠀⢂⢱⡀⠋⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡃⡥⠋⢀⠀⣿⢃⠁⠰
⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠔⠻⢪⢰⡜⡐⡄⢺⡁⠏⠇⠤⢁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⡀⢩⡦⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡜⠁⡆⡀⢘⢂⠂⠈⠰⡀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠎⢀⢈⠀⣼⢿⠁⠀⠀⡄⢉⣀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠾⠫⢜⣃⣖⢲⠄⠀⠀⠀⠀⡝⢨⠑⠏⠄⣠⠂⠈⠀⠀⠀⠀⡀
⠀⠴⣅⣌⠀⠀⠈⢠⠟⠃⠀⠀⠛⠀⢰⠀⢀⢆⣠⡄⠀⠀⠀⠀⠀⠠⠠⠶⠩⢍⡉⠲⡀⡶⠃⠀⠀⢀⠀⠃⠸⡠⠀⢶⠁⡄⠶⠀⡀
⠀⠀⠈⠻⠷⠤⠖⢠⣖⡆⠀⠀⠃⠀⠀⢉⣴⠏⠨⠔⠒⠒⠀⠀⢶⣳⡨⠡⠑⢄⠈⣆⠆⠀⠀⠀⠀⠀⠀⠈⠄⢘⠃⠐⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠈⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⣢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⠀⠀⢀⢠⣥⣬⣿⣶⣶⠀⠀⠀⠀⠀⢠⣾⣆⠘⠀⠉⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣟⣷⣦⣴⣶⣿⣼⣿⣿⣿⢿⣏⡀⠀⣠⠞⣶⣾⣿⣿⣧⡄⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⡿⠟⠿⣿⢿⣻⣻⣿⣻⠟⠁⠉⠿⠛⠙⣿⡿⠻⣿⢀⠚⠀⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣧⣼⣶⣾⣿⣿⣿⠏⣥⣰⣆⠈⣆⣱⢀⣼⡴⣿⠇⡟⢀⣷⠁⣠⣆⣿⣿⣽⡙⠚⠫⠙⠛⠋⠛⠋⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠙⣿⣿⣿⣿⣿⡏⣾⢿⣿⣷⡆⣸⣿⣿⣿⡿⡟⣸⣧⣿⠷⠟⠟⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣴⡾⢏⣁⢠⣿⣿⡿⢻⣿⣿⡿⠴⣼⣿⢷⣿⢻⣿⣿⣿⠗⠛⠉⠈⠀⢀⣠⡶⡖⡿⣿⠋⣯⠁⠀⠀⠀⡀⣪⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⣉⣿⠟⣿⣻⣟⢽⢿⡟⠟⢿⣿⡗⣿⠛⢿⣿⢿⣿⣵⣿⣿⡿⠟⠉⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠆⡩⠂⡤⢐⣋⢷⣽⠃
⠀⠀⠀⠀⠀⠀⢠⣾⢡⣿⣿⣿⣇⣼⣾⣿⣙⠿⣿⡄⠁⠀⢈⣻⣷⣾⣾⡿⠿⠿⠿⠋⢀⣠⠄⠲⠞⠛⣻⢿⡿⠟⠻⠿⣿⣿⡿⣞⣿⠆⢀⡼⣯⣿⡙⠃
⠀⠀⠀⠀⠀⢠⣿⣿⣸⡅⠀⠘⣻⣏⠈⠙⠛⠛⠛⠻⠄⢱⣾⢻⡟⠉⠀⢀⠀⡠⠖⠋⠁⠀⠀⠀⠀⣀⡖⠋⠀⠀⠀⣠⡾⣯⣾⠟⢁⣞⣼⣹⣦⠈
⠀⠀⠀⠀⢼⣾⠉⢸⣿⣟⢄⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣌⠆⠀⢳⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣠⣾⢯⠿⠋⣡⣾⣿⣿⣿⣿⣷⠁
⠀⠀⠀⢸⣿⣹⠀⢠⣿⣿⣿⡸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢱⡄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⣔⡴⠟⠋⢉⣠⣾⡷⠋⠈⣿⣿⠟⠏⣿⡆
⠀⠀⠀⣼⣿⡏⠀⢸⣿⣿⣿⣷⢻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⢀⣤⡶⠛⣿⣿⠁⠀⢸⣿⡗⠀⠸⣿⡟
⠀⠀⠀⣿⣿⠁⠀⠈⢧⣷⠈⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠚⠋⠁⣀⠴⠖⠋⠀⠀⢠⣿⡇⠀⠀⣿⣿⠁⠀⠀⣼⡇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠻⡄⠀⢸⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⢰⣿⡟⠀⠀⠀⡿⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠏⠀⠀⠀⡴⠁
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠃

⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣶⢷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⡷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⡴⢫⡴⠯⡼⠃⡠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡄⢿⠹⣎⢳
⠀⠀⠀⠀⠀⠀⣼⡷⠟⠁⣟⣠⠎⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠩⡈⡇⠹⣅⣇
⠀⠀⠀⠀⠀⣼⣟⠋⠡⡐⢯⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⠼⣃⠐⣸⣿
⠀⠀⠀⠀⢠⣿⣏⡁⠂⠟⠠⣶⣿⡄⠀⠀⠈⠄⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⢿⣿⡗⠺⠅⠀⢴⣿
⠀⠀⠀⠀⠸⣻⡀⠕⠀⣤⣼⣿⣟⠁⠀⠀⠀⠈⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠻⣿⣷⡄⠀⠈⢻⣿
⠀⠀⠀⠀⠀⢿⣿⠾⠷⡿⠛⠉⠀⠀⠀⠀⠀⠀⢰⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⢷⣼⡿⠃
⠀⠀⠀⠀⠀⠈⢻⡧⠘⠻⣦⡄⠀⠀⠀⢀⠀⠀⠘⡆⣰⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢼⡟
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣿⣿⣿⣶⣠⡶⠛⢷⡄⢀⣿⣿⡀⢠⡿⠛⢶⣄⣾⣿⣿⣿⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⡾⣹⠿⣷⣤⡈⣿⡟⢻⠛⢛⡿⢁⣤⣾⢿⣏⢦⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠻⠿⣿⣿⣿⠆⠞⠀⠠⣽⣿⣿⠿⠛⢿⡅
⠀⠀⠀⢀⣴⡶⠤⠾⠿⣯⣥⣾⡦⠀⠀⠈⢻⣯⣞⡄⠀⣲⣿⡟⠁⠀⠀⣼⣷⣭⡿⠿⠧⠤⣶⣦⡀
⠀⠀⣴⡿⢋⣀⢠⣤⣦⡀⢬⣏⡙⠛⠷⣦⣼⠟⠻⢷⡟⠿⢿⣇⣴⠾⠛⢋⣽⡤⢠⣦⣤⡄⣈⡙⢷⣄
⠀⠈⠋⣀⣿⠟⠉⠁⠉⠛⢿⡷⢦⣵⣦⣹⢇⣾⡀⠈⠀⠀⢠⢹⣁⣴⣮⡶⢿⡟⠛⠉⠉⠉⠻⣿⣢⡙⠁
⠀⠰⠻⠟⠁⠀⠀⢀⣀⣤⣼⣧⣤⣄⣉⣻⠸⠛⢡⢸⠀⠀⠰⢹⣛⣉⣠⣤⣼⣦⣤⣀⡀⠀⠀⠈⠻⠝⠆
⠀⠀⠀⠀⠀⢀⣾⠿⠋⠉⣽⠉⠉⠉⠉⢻⠀⠀⠀⠘⠀⠀⠀⢸⡏⠉⠉⠉⢹⡏⠉⠛⠿⣷⡀
⠀⠀⠀⠀⣰⠿⠋⠀⢀⣤⣾⠿⠞⠛⠋⠻⣦⣶⣥⣤⣤⣤⣄⣼⠛⠛⠛⠷⢿⣷⣄⠀⠀⠙⠿⡄
⠀⠀⠀⠀⠁⠀⠀⢀⣾⠞⣿⠀⠀⠀⠀⠀⣿⣿⣟⡉⠉⢹⣿⡯⠀⠀⠀⠀⠀⡟⠿⣷⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣿⠀⠀⠀⠀⠀⣹⣿⡿⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡇⠀⠀⠀⠀⠀⢹⣿⡿⠛⠳⣾⣿⠃⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡿⠛⠲⣿⣿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⡿⠷⠶⣿⡟⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⣿⡷⠖⠶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣠⣿⣧⣄⣠⣿⣧⡀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡠⢪⡿⠛⣿⡄⢈⣿⠛⢿⡓⣄⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢀⣁⣼⣁⣀⣽⣷⣼⣧⣀⣸⣧⢈⠀⠀⠀⠀⠀⠈⢆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⣟⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠿⡋⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡠⠚⠁⠀⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠙⠂⡈⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⠔⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠈⠀⢠⡄⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡀⢀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠘⢷⣤⠀⠀⠀⣸⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⠀⠈⣿⠀⠀⢀⠠⠄⠂⠐⠈⠉⠁⠀⠀⠀⠈⠙⠘⠀⠂⠀⠀⠀⠙⠖⠉⠙⣿⠇⡄⢀⣿⢰⡀
⠀⠀⠀⠀⠀⠀⡼⠀⣈⠀⠈⡟⠛⣯⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⡉⠈⣻⡟⠀⠉⣤⠇⢨⡇
⠀⠀⠀⠀⢸⠀⠘⣆⠈⠀⠀⠳⡄⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃⠀⢠⡌⠠⢺
⠀⠀⠀⠀⢀⠀⠀⠘⢷⠂⠓⠦⣙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⢀⣴⠟⠠⢀⡼
⠀⠀⠀⠀⠈⡉⠀⡀⠈⠓⠶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢌⠿⠛⠁⠀⠃⡩
⠀⠀⠀⠀⠀⠐⢄⣐⡄⡀⠀⠀⠈⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⣙⠀⣒⣄⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠃⢄⣈⣓⣦⠐⢀⣱⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⡶⠊⠉⠉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣉⠁⣀⣭⣿⠾⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣐⡿⢏⠉⠙⠒⠶⠶⠬⢦⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡴⠗⠋⠁⠄⣀⣠⣼⠟⠶⣦⣀⣶⣤⣤⣴⣶⡾⠿⠛⠶⣦⣉⢒⡄⠀⠀⠀⠀⠈⠛⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠋⠀⠀⠀⠀⢹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠚⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡶⣶⣿⣿⣿⣿⣟⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠿⠛⢿⣿⣿⠿⠟⠛⠩⠴⠾⠛⠋⠉⠀⠀⠉⢉⣛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⢋⠉⠁⠀⠀⣤⣷⣿⣻⣧⣦⣶⣿⣿⣶⣦⣥⣽⣾⠶⠶⠞⠋⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⡿⠿⠿⢥⣀⣴⣾⣯⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⢤⣤⣠⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠸⢷⡶⡶⢿⡻⠿⠿⠟⠛⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠙⠻⣿⠂⡀⠀⠀⠀⠀⢀⣸⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠹⣼⡷⡤⣾⡵⣣⢿⣿⣆⡀⠀⠀⠀⠑⢦⡀⢀⣤⣄⣀⠀⢠⠖⠁⠀⠀⠈⢻⡇⠀⠀⠀⣀⣾⠋⠀⠀⣰⠇
⠀⠀⠀⠀⠰⣄⠀⠙⣗⡀⠈⠛⠛⠛⢴⡋⠀⢻⣿⣿⣦⣤⠴⠶⠖⣛⣋⣭⣭⣙⡛⠿⠶⣦⣤⠀⢀⡿⠉⠀⣀⣼⡿⠁⠀⢀⣼⠎
⠀⠀⠀⠀⠀⠙⢵⣀⡈⠙⢷⣂⣄⣀⠀⠙⠢⣾⣿⣎⡉⣠⠰⡎⣸⢻⣵⣿⡏⣿⢹⣿⣶⣶⡈⠳⢾⣏⢀⣬⡽⠉⠀⣠⣬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣥⣤⣤⣉⡓⠒⠐⠲⠾⠽⠿⣇⢸⢿⣧⣷⣸⣾⢿⡇⣿⣸⣿⡭⢸⢸⣷⣽⡿⠟⠋⠀⠴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣙⠒⢒⠖⠺⠿⠝⣿⣾⢾⣿⣿⢿⣿⣷⣡⣿⣿⣿⣿⣼⣾⣷⣷⣶⣾⣷⣖⣋⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡴⠓⠋⢁⡐⠶⣿⣷⣶⣶⣽⣟⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠛⣍⡇⣪⡭⠟⠛⠉⠉⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠟⠉⠀⠀⢀⡿⠙⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠛⠛⠛⠙⠛⢛⣲⣁⣒⣛⣚⣷⣄⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠻⣧⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃