Spruce Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣼⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⣿⣥⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣴⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣸⣷⣿⣿⣿⣿⣛⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⢭⣟⡛⠿⢿⣿⣿⣦⢤⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣆⣤⣘⣯⣿⣭⣍⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⢩⢾⣿⣿⣿⣿⣿⣿⣿⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣀⡤⢶⣿⣿⣿⣿⣿⣿⣯⡹⠿⠷⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣯⣶⣼⣿⣿⡿⠨⣿⣿⣿⣷⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠸⣿⣿⣿⣷⣾⣿⣶⣎⠈⢁⣠⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠾⠿⢋⣙⣟⣿⣿⣿⣿⣿⡿⠻⣿⢋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣽⣷⣦⣴⣼⣿⣿⣿⣿⣟⡛⢿⣶⣤⡂⠘⠋⠁⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡆⡌⠙⠿⡶⢦⠰⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠛⣫⣴⣿⡿⠋⢙⡿⣿⣿⣿⣿⣿⣆⣴⣀⣠⣤⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⠿⢻⡒⣦⣸⡏⢁⣿⣿⣿⣿⣿⣯⣍⡛⡉⢉⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⣉⣥⣼⣿⣿⣿⣻⣶⣿⣿⣿⣿⣿⣭⠉⠙⣰⣿⣏⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⡿⣿⠿⢿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡛⠄⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣧⣾⡽⢿⣿⣿⡿⣿⣿⣿⣶⣒⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣻⣿⣿⣿⣿⣟⢻⣿⣷⣔⡊⠻⢿⣶⣾⣙⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⡿⣿⣿⣿⣃⠺⣿⣿⣿⣿⣾⡀⠀⠙⠿⠳⣂⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⣈⣴⣾⣿⣿⣿⣷⣶⣧⣶⣾⣿⣵⣿⣷⡀⠶⠚⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠷⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⡟⢿⣿⣉⣻⣿⣣⣷⣖⣐⣿⣯⠌⠛⠙⠿⢿⢿⣿⣿⣿⣭⣽⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⢁⣸⡿⢿⣿⣿⢿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢻⣿⣷⣿⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣿⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣌⣹⣿⣿⣿⣿⣿⣿⣖⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢉⣙⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⡿⣿⣯⣿⣡⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣈⠛⡛⠛⣿⠿⣿⠿⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠿⢷⣿⣿⠿⠿⢟⠉⠉⢉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣷⣿⣿⣿⣿⣶⣾⣥⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣤⣤⣤⣤⣬⣿⡿⣧⣤⣤⣀⡀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⣿⣷⣿⣿⣿⣏⣽⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⣤⣤⣤⣤⣤⣿⣾⣿⣿⣿⣿⣿⣿⣟⣛⠁⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠟⠛⠉⠈⢹⣿⠿⢿⣿⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣴⣶⣿⢿⣿⣷⣾⣧⣄⣀⣀⢀⣀⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠋⣹⡤⠘⣿⡀⠉⠛⢹⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣤⣤⣿⣷⣶⣶⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⣾⣿⣿⣿⣿⡿⠟⠿⠿⣿⣿⠟⠀⠈⠻⢿⣿⣿⣷⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠛⠟⠉⠉⠀⠀⠀⠀⣠⣿⠀⡀⠀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⡾⠛⠿⣿⠾⢿⣿⣍⡀⣀⣀⡀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠻⠿⠛⠛⠋⣁⣤⣶⣿⣦⣀⡉⠛⠿⠻⢿⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⣴⣶⣾⠟⢉⣴⣿⣧⣀⠈⠙⠻⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠠⢾⣿⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⣴⣿⣯⣴⣶⡾⠛⢻⣿⣿⣿⠿⡿⣾⠗⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡵⠾⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢛⣉⣁⣤⠾⣿⠀⠹⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢃⣻⠓⣀⡀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣤⢶⣿⣿⠏⠀⢐⣿⠗⠀⠘⠟⢻⣿⣶⣶⡶⣶⣦⣴⡶⠀⠀⠀⢳⣾⣿⣿⡿⣻⣿⣿⣶⣿⣿⣋⣀⣘⣯⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠟⠟⠋⠺⠋⢀⣤⡶⢩⣿⠓⠦⡀⠀⠀⠀⠈⠛⢷⣦⣤⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡟⠿⠿⠿⡿⣿⣋⣿⣿⠟⣿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠛⠉⠀⠘⣿⡃⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣾⣿⣿⣿⣿⣿⡟⠶⣄⣀⠀⠈⠉⠙⠰⠀⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣏⠙⣿⣯⣿⣿⣿⣿⣧⣴⡦⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣯⣽⣵⡶⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠾⢿⣿⣿⣷⣸⣿⣿⣿⣾⠟⠟⡉⢿⣿⡿⢿⠠⣿⠋⣿⣷⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢯⣿⡿⣿⣽⠀⠀⢹⣿⣿⡟⠚⠛⠁⠀⢻⠟⠙⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣧⣾⣟⣷⣿⠘⠃⠀⠀⠀⠛⢠⣿⡟⠳⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⢿⣿⢿⡟⠻⠃⠀⠀⠀⠀⠀⢠⠿⠸⣿⣷⣾⣇⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡏⢻⣾⣿⡁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠚⡹⣿⣭⡦⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡿⢻⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡂
⠀⠀⠀⠀⠀⠀⢀⣽⣿⣶⠦⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⣐⣿⣿⠶⠂
⠀⠀⠀⠀⠀⠠⠬⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⢨⠽⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣭⡄⠀⠀⠀⠀⠀⢽⣿⣿⣯⣤⡄
⠀⠀⠀⠀⠀⠒⠾⢿⣿⠶⠯⠀⠀⠀⠀⠀⠐⠖⣟⣿⣿⣦⡤⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⠦⠄⠀⠀⢀⣀⣹⣿⣿⣧⣀⢀⡀
⠀⠀⠀⠀⠀⠚⢛⣿⣿⣿⡗⠂⠀⠀⠀⠀⠈⢛⣿⣿⡿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡗⠂⠀⠀⠀⠀⢩⣿⣿⣿⣟⡛⠋
⠀⠀⠀⠀⠀⠀⠉⠹⡿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠐⢻⡟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠇⠀⠀⠀⠀⠀⠠⡴⠾⣿⣭⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢾⣥⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⢀⣿⣯⡀⠀⠀⠀⠀⠀⢠⣿⣿⡉⠀⠀⠀⠀⠀⢐⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⣀⡀⠀⠀⠀⠀⠀⣿⣯
⠀⠀⠀⠀⠀⣘⣿⣿⣆⠀⠀⠀⠀⠀⠠⣽⣯⣤⠀⠀⠀⠀⠀⢬⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣫⣿⣯⡉⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⢠⣾⣿⣿⡷⠄⠀⠀⠀⢠⣿⣿⣷⣄⣀⠀⠀⠀⠀⢠⣿⣟⣛⠁⠀⠀⠀⠀⠀⠴⢾⣿⣿⡒⠀⠀⠀⠀⠀⢨⣿⣿
⠀⠀⠀⠀⣩⣽⣿⣟⣛⡑⠂⠀⠐⠞⣻⣿⣿⣏⣁⠀⠀⠀⠀⣘⣿⣿⠷⠂⠀⠀⠀⢀⣀⣾⣿⣿⣾⠷⠆⠀⠀⠀⠀⣠⣿⣿⠖
⠀⠀⢀⣤⣙⣿⣿⣿⣟⢛⠂⠀⠀⠠⠿⣿⣷⣅⣀⡀⠀⠀⠀⣀⣺⣿⣖⠂⠀⠀⠀⠀⠉⢁⣴⣿⣿⣭⣀⣀⡀⠀⠀⢶⣿⣿⣛⠉
⠀⠀⠀⠈⣭⣿⣿⣿⣿⣭⡀⠀⠰⠒⣾⣿⣿⣭⣽⠉⠀⠀⠐⢶⣻⣿⡟⠛⠂⠀⠀⠤⠴⠞⣻⣿⣿⣧⡉⠉⠁⠀⠀⠼⣿⣯⡍⠁
⠀⠀⠀⠀⠰⠚⢹⡇⠀⠀⠀⠂⠒⠛⢛⣿⣿⣷⠶⠤⠄⠀⢈⣛⣿⣿⣍⣉⣉⡀⠀⠀⢠⣤⠶⣿⡷⠶⠶⠶⠠⠀⠀⠴⠿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠁⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋



⡿⠿⠿⠿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣩⣿⡏⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣚⣻⣟⣛⣯⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⣟⣿⣛⣿⣍⡙⠓⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⢼⣿⣧⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⣿⣿⣿⣿⣍⡉⠓⠀⠀⠀⠀⠀⠀⢽⣿⣭⣷⣄
⠀⠀⠀⠀⠀⠀⢐⣾⣿⣯⣄⡀⠀⠀⠀⠐⠿⠗⣲⠶⡯⠄⠼⠿⡿⠿⡻⢿⡒⠶⣤⠀⢠⡾⣿⣶⣎⣿⢶⣄⡀
⠀⠀⠀⠀⠐⣿⢿⣷⣮⠻⢬⣅⡀⠀⠀⠠⡶⣛⢨⣤⡶⠁⣠⣴⣦⣿⣛⠛⠆⠀⠀⠀⠠⠶⣿⢿⣿⣿⣿⣧⣀
⠀⠀⠀⢲⣶⢞⣻⣟⣿⣿⣿⣥⣄⣙⠛⢻⣿⣿⣾⡿⣶⣦⣼⡈⣭⣷⣀⣀⡀⣤⣄⣴⢶⣿⠿⣲⣿⣹⣿⡯⠿⠏
⠀⠀⢀⣴⣶⣯⡿⢻⣿⣽⣷⡭⠽⡟⠁⢀⣠⣴⣾⣿⣯⣿⢿⣿⣿⣿⣿⡿⠷⠦⢩⣿⣿⣷⣿⠇⣭⣴⣿⣿⣷⠶⠄
⠀⠀⠉⣻⣿⣷⣾⢿⣿⣼⣿⣿⣷⣶⣼⣿⣿⣿⡿⠿⣿⠿⢿⣧⣭⣭⣿⣿⣿⠶⢯⣽⣿⣿⡷⣚⣏⣉⢷⣬⣽⣷⡶⢦⡄
⠀⠐⠋⡽⢿⣿⣿⣿⣭⠛⢿⣮⣽⣿⡿⢿⣿⣿⣾⠿⣃⣴⣾⣿⣿⣿⣿⣛⠻⢷⣤⣶⣛⣉⡐⠻⣿⣿⣷⣿⣷⣶⣥⣤⡤
⠀⠖⣾⡿⠿⣯⡖⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡏⠉⠡⣤⣙⣻⣿⣿⣿⣿⣛⡿⢂⣶⣦⣶⣮⣿⣶⣬⣉⡙
⣰⣿⣿⣿⣿⣿⣿⠛⡿⢯⣼⣭⣽⣿⣿⣿⣿⣿⣍⣤⣄⣤⢀⣴⡦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠧⠄
⠀⠚⣟⣿⣿⣿⣧⣾⣿⣦⣻⣿⣿⣿⣾⣿⣿⣿⢿⣿⣰⣿⣽⣿⣿⣴⣿⡿⣿⡟⣋⣽⣿⠛⠛⣛⣿⣽⣻⣿⠺⣟⠻⠟⠒
⠀⠉⠉⠵⠛⢹⠿⠟⣿⢻⠟⠿⠉⠉⠀⠈⠉⠀⠸⠋⠻⠏⢹⡏⠉⠁⠉⠛⠀⠀⠁⠋⠹⠟⠉⠟⣿⢿⡍⠛
⣠⣤⣠⣤⣀⣄⣤⣤⣿⣄⣀⣤⣤⣤⣤⣤⣠⣠⣀⣀⣠⣄⣼⣇⣤⣀⣀⣤⣤⣤⣤⣄⣠⣀⣤⣠⣿⣤⣤⣄⣠⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣏⣡⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⣿⣿⣺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣼⣿⣿⣿⣿⣿⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠒⠒⣿⡿⣿⢛⣿⣿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢉⣋⣽⣿⣾⣟⣻⣿⣿⣏⣩⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠻⢿⣿⣿⣿⣿⣯⣿⣿⣭⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠷⠶⣾⠻⢿⣿⣿⣾⣿⡟⢛⣄⣀⣀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣾⣿⣿⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡽⣽⣾⣿⣷⣯⣰⣿⣧⣬⣤⣤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣴⣶⣰⣿⣿⡿⣿⣿⢿⣿⣭⣬⣙⠡⣴⣶⣶⡶⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠿⠟⢁⣾⣿⣿⣾⣿⣿⣾⣿⣾⣿⣿⣗⢯⡉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⡿⣿⢉⣬⣶⣿⣿⣭⡉⣿⠿⢿⣿⣷⣿⣿⣷⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⢏⣐⣛⢯⣟⣵⣶⣿⣿⣿⣶⣿⣶⣤⣤⣌⣉⣛⡛⠛⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⢿⡟⣿⣦⣾⡟⣿⣿⣅⣩⣉⡛⠛⠛⠫⣿⣿⠿⡿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡉⠀⠠⣷⣿⣿⣿⡿⠿⣿⠿⣿⡿⣟⡻⣦⡄⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣿⡿⠋⠙⠋⠀⢀⣿⠀⠀⠀⠸⠿⢾⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⠋⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⣠⣾⠃⣤⡴⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠶⢾⣿⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⢠⣿⣶⡿⠿⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⢿⣿⣿⣧⣤⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⢀⣽⣿⣤⣭⣿⣿⡿⠿⠿⠛⣳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖⣻⣿⣿⡿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣦⣄⠀⠀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣧⣶⣶⣶⣶⣾⣷⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣉⠛⡿⢿⡿⣿⣿⣿⣿⣷⡦⠄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⣤⣀⣠⣄⢀⣴⣿⣻⡇⣀⠀⠈⠛⢛⡿⢿⣶⣄⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣿⣿⣿⣶⣷⠾⠛⣿⣿⣀⣶⣤⠈⠡⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡙⢀⣼⣦⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠁⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢯⣤⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⣿⡿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣻⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠘⠋⠁⢚⣿⣥⣿⡿⣿⣿⣿⣿⣟⢛⠿⣷⣦⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠙⠟⢿⡆⠘⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠉⣀⠀⣾⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⢿⣶⠟⢿⣶⣿⣿⢛⣼⣿⣇⠀⢸⣿⠿⠿⠿⣽⣏⠀⠲⠦⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠋⠀⠀⡈⠉⣴⣿⣿⣿⣧⣶⣼⣿⣦⣄⣴⠀⠈⠁⠀⠀⠀⠀⠤⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⠛⣭⣿⢻⣿⣿⣿⢿⣷⣦⠀⠀⢐⠄⣲⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠛⠉⠀⢀⣭⣵⣶⣾⣿⣿⣁⣾⣿⣿⣧⠄⠛⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⢶⣀⡤⠄⠀⠀⠐⣈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠁⠀⠶⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣤⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣷⣤⡉⠙⢿⣿⣷⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡀⠀⠉⠙⠻⣿⣿⣀⣬⠷⢀⣀⣀
⠀⠀⠀⠀⠀⠠⠠⣾⢿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣾⣿⡿⢿⠋⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠟⠁⠾⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠟⠁⣠⣴⣤⣶⡾⠋⠀⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⡗⢀⡄⢀⣀⣄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋⠁⠀⠀⣀⠀⢾⠇⢀⣿⣿⣿⣿⣿⣿⣿⣾⠹⠟⠿⣿⡿⠾⠟⢳⠾⡧⠄
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣟⣭⡿⠟⠀⢠⡄⠉⢻⠀⢻⡇⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡈⠁⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢠⣼⠛⢉⣀⣴⣶⣾⣿⡿⢿⡿⢋⣤⣬⣿⣿⣿⣿⣿⣟⣿⠛⠛⠛⠛⠛⠉⣩⣄⣼⣿⣿⠟⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣴⣾⣏⣠⣴⣾⣿⣿⣧⣾⣏⡁⢸⣷⣾⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣶⣤⡀⠐⣀⣤⣿⣿⣿⣁⠐⣷⠆
⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⢿⠏⢻⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠷⡀⠀⠉
⠀⠀⠀⠈⠁⠘⠁⠘⠋⠀⠀⠀⠈⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄⣀⢀⣀⣀⣀⣀⣠⣴
⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⡆⠉⠘⢿⣿⣿⣿⣝⡛⢿⣿⣿⣿⣿⣿⣩⣿⡛⣿⠛⣿⠋⠁
⠀⠀⠀⠀⠀⠘⠻⡿⠛⢿⢿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⠈⠹⣿⣿⣿⡆⠈⣉⠻⠿⠿⠿⣿⡿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣷⣎⣻⣿⣿⣿⣿⣿⣟⣿⡶⠟⣿⣿⣿⣿⣷⣤⠄⠈⠛⠻⢿⣿⣿⣀⣤⡀
⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⠑⣿⣿⣿⣿⣿⣿⣿⡇⣸⣶⡄⢀⡀⡉⢉⡿⠛⢦⣤⠤
⠀⠀⠐⠾⣿⣿⡿⣿⠿⢿⠿⠿⠿⠿⠛⣻⣿⣿⣿⣿⣿⣿⣆⡀⠙⠿⠿⠿⢿⣿⣿⣿⣷⣧⣼⡟⠟⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⢷⡞⠻⠶⠚⠶⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠉⣹⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠛⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣤⡀⠀⠀⠀⠀⣴
⣀⣀⣠⣴⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣼⣅⠀⠀⠘⣿⣿⣿⣧⡙⠛⠛⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡉⡉⠙⢂⣤⣼⡿
⠉⠉⠋⠉⣿⡿⠿⠟⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣁⣀⡀⠀⠀⠀⠙⠿⠿⣿⡿⠿⠿⣿⡿⠿⠿⠿⠟⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡛⣻⣿⣿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠉⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢥⠉⠉⠙⠻⣿⢿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⠀⠛⠀⠒⠂⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠀⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢨⣷⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣧⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⠖⣶⣾⣿⣿⡟⢋⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣀⣰⣿⣽⣿⡯⣿⡌⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣯⣽⣿⣿⣿⣤⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣾⣿⣿⣿⣿⣿⣿⣽⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡶⠖⢺⣶⣤⣏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⢿⡻⣿⣷⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢛⠛⡿⣿⣿⣏⢛⣻⣿⣿⣿⣿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣿⣿⣿⣷⣿⣿⣥⣾⣿⡿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠉⠂⠈⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣶⠀⣼⣿⣆⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣽⣿⣿⣿⣿⡿⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⡄⢹⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⡿⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢿⣾⣿⣿⣿⣿⣿⣿⣷⣎⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣡⣶⣶⣾⣦⣶⣶⣴⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣶⣤⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡿⠿⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⣨⣿⣃⣀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣛⣿⡿⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣤⣶⡀⠀⠛⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣽⣦⣼⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⡄⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢣⣴⢋⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣶⣄⣠⣦⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠻⠿⣿⣿⠞⢿⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠛⠛⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⠿⢿⣟⣿⠛⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣏⣤⡶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣴⣿⣶⣮⣵⣾⣷⣟⣤⣤⣶⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⢶⠎⠉⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣥⡿⠿⣿⣿⣿⣿⣿⣿⠿⣇⡙⠳⡀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠍⢿⣿⣛⡻⢻⣿⣿⣿⣿⣿⣻⣯⣉⡏⢩⡿⠛⠛⢤⣿⣿⣿⠋⠠⣔⠻⢤⣉⢧⣤⠅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⡅⠈⠩⢼⣏⣽⣧⠽⣫⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⢀⠨⠇⠀⠙⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠸⠟⢹⠖⠿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⣴⣿⡀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣈⡿⠈⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⡷⠚⢻⣿⣧⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢀⣠⣿⣿⡿⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⢿⣿⣿⣿⣤⣤⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣿⣶⣦⣽⣿⣿⣿⡟⢛⡛⢁⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣀⡀⠀⢀⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣇⣤⣤⣤⣶⣶⣶⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠗⢰⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣀⡀⠀⢀⡀⠀⣾⣇⠘⣇⠀⠉⠙⠿⣿⣿⣿⣷⠈⡙⠀⡀⣠⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣹⣷⡛⣿⣶⣿⡿⢿⣿⣇⢀⣀⡀⠈⢥⣼⡛⠋⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⢙⣏⣉⣀⣿⣿⣿⣿⣿⣷⣶⣾⣟⣧⣀⡶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠦⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠛⢣⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠾⢿⠟⢏⣠⣶⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠙⢿⣷⣾⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠈⠉⠁⠛⠃⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣁⣴⣦⠀⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣏⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠿⠿⠟⢿⡟⠙⠻⣿⡿⣋⣵⣿⣿⣇⠀⣸⣿⡉⠙⠛⠛⠻⣄⠘⠋⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾⠄⠀⠀⠀⠀⠀⠂⠀⠒⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⣸⣏⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠀⠲⠿⠛⠛⠛⠁⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠹⠝⠧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⠿⢛⣷⣤⡁⠀⣤⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣀⠀⣠⡀⠀⠘⠟⠑⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⢀⠉⠻⣿⣿⣿⡏⣀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣻⣿⣿⣿⣿⣿⠿⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠈⠙⢿⣿⣿⣤⡄⢛⣦⣠⣤⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠘⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢰⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠛⠋⠀⠿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⠃⢀⣠⣶⣴⣿⡿⠃⠀⠀⠉⣾⠿⣿⣿⣿⣿⣿⣿⣷⢠⣤⠀⢀⣤⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⡿⠛⠉⠁⠀⠀⢈⠀⢾⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⡙⠿⠿⣿⣿⡃⠿⠟⠻⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣶⣷⣾⣿⣯⣿⡿⠋⠀⣄⠀⠃⣄⠀⣻⡇⢀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠁⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠻⠏⢉⣀⣼⣶⣿⣿⣷⣿⣾⢋⣐⢿⣿⣿⣿⣿⣿⣿⡛⠛⠿⠻⠿⠻⠛⢻⣀⣠⣾⣧⣿⠟⠋⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡿⢋⣴⣾⣿⣿⣯⣼⣿⡉⠀⣹⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡄⠀⠆⣀⣽⣿⣿⣟⢉⣶⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡿⠻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⡏⠉⠰⠟
⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠛⠿⠃⠀⠀⠐⠛⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠈⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⣿⣿⣬⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡾⣷⣶⢿⣿⡟⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠙⢻⣿⣿⣷⣶⠛⠛⠿⣿⣿⣿⣿⣿⣾⣍⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠙⠿⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣷⣿⣴⠀⢹⠿⣿⣾⣷⣶⣆⣀⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⢷⣾⣿⣿⣿⣿⣿⣿⣾⣇⣠⣈⠙⠛⠻⠿⣿⣷⣄⠀⠀⣀⠴
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⡶⣶⡄⠛⠋⠁⠻⣎⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠻⠋⠉⠉⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢉⣽⣭⣝⣻⣿⣿⣿⣿⣿⣷⣌⣤⣄⡀⣤⣀⠃⢀⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⠉⠃⠈⠙⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⣿⠏⠀⠀⣀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢀⡀⠀⣸⣿⡟
⠀⠀⠀⣤⣴⣶⣾⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣶⣀⣀⣨⣿⣿⣿⣿⡤⠈⠉⠁⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣤⣄⣠⣾⡿⠛
⠀⠀⠀⠀⠈⠁⠰⠿⠛⠛⠛⠀⢀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⡀⠀⠙⠛⠻⠿⠟⠛⠛⢿⠟⠋⠛⠛⠛⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⠟⠛⢻⠿⠿⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠟⠉⠈⠙⠿⠿⣟⣿⣿⣼⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠘⠉⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣀⠐⠆⢀⣀⣐⡢⠤⣄⠀⡀⣀⣠⣤⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣉⠓⢰⠆⠻⣮⣽⣶⡚⣙⠿⡙⣷⠵⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠿⣷⣴⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠒⠀⢉⣱⣆⣤⣯⣵⡾⣿⡿⠿⠈⠀⢀⠄⠂⢀⠎
⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠠⢄⡐⣬⠧⣷⠀⠢⠀⠀⣌⡰⠦⢤⣄⣀⣤⣤⡖⣦⣿⣷⣯⠿⣃⠎⡯⠰⠀⠀⡀⠀⠂
⠀⠀⠉⢭⣬⣵⣾⣷⣮⣭⡭⢅⣤⣤⢬⣤⣤⢤⣉⣩⣝⡶⢤⣯⣭⢯⢻⠿⢿⠿⠷⠂⣰⡟⢿⠉⠀⠀⠇⢸⣗⣢⣄⠠⠄
⠀⠀⠄⠒⠘⣼⠯⠋⣩⠐⡉⠈⠹⠁⠈⣅⢢⣿⣿⣿⠟⠓⠖⠉⠀⡟⡧⢠⠀⠀⢐⠼⡏⣯⠨⠃⠀⠀⠀⠤⢔⣑⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠐⣃⣻⠙⣽⠏⠉⠀⠀⠔⠀⠀⠱⡏⢀⠰⠀⠁⠀⢶⠈⠀⠀⠀⠀⢀⠠⡈⠉⠰⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⡂⣠⠿⠫⠓⠃⠀⠀⠀⠀⠂⠀⠀⢨⡅⠀⠣⠈⠀⠀⢸⡆⠀⠀⠀⠀⠀⠠⠠⣄⣩⠿⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣎⠛⢏⠂⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⣸⠁⠀⠀⠈⢀⡀⢺⡇⠀⠀⠀⠀⠀⢁⡄⠠⡀⠛⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠅⠁⠀⠏⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⢠⡏⠀⠀⠀⠀⠀⠀⣻⡅⠀⠀⠀⠀⠀⠀⢁⣐⡉⡭⡗⠾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⣱⣼⠃⠀⠀⡌⠀⠀⠀⢼⡃⠀⠀⠀⠀⠀⠀⠈⠀⠤⢐⢀⡙⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣁⣾⡏⠀⠀⠀⠀⠀⢠⡵⢾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⠭⢚⣩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣩⡟⠀⠀⠀⠀⢀⡀⠀⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢍⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⢀⡿⠁⠀⠀⠀⠀⠐⠁⠄⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢁⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡺⠇⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⣦⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⢿⣴⡗⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠛⢺⢋⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠟⣿⠷⠟⠛⢠⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣨⣀⣤⡾⠋⠳⠾⠛⠾⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡿⠋⠱⡀⢲⣶⣆⣄⡀⣈⣀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡀⣐⣁⣀⣠⣠⣨⣾⠋⠹⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠿⠛⠋⠙⢦⡀⣄⡀⠀⠀⠀⠀⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⡀⠀⢀⡀⠀⣈⣿⠞⣻⠿⣶⣴⣄⣶⠤⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⠤⠶⠋⠙⠛⠉⢀⣴⠋⠐⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣐⣀⣈⠀⠀⠀⣠⣴⣶⠇⣠⠾⣿⡛⣁⠀⠀⠀⠈⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⠶⢾⠿⠋⠛⠂⠀⠀⢘⢿⢿⣿⣦⡄⣤⣦⡀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠀⠀⠀⠀⠀⠀⣠⢿⣧⡀⠀⠉⠛⠛⠃⠉⠙⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠉⠀⠀⢀⡄⢠⣴⠧⣤⠶⣏⡀⠉⠋⠃⠤⠀⠀⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣁⣀⣠⣤⠶⣴⣦⣾⠷⠟⠃⠀⠀⠀⠻⢷⣷⣤⢀⣀⡀⠀⠀⠈⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠅⠉⠀⠀⠀⠀⡀⣤⠀⣠⠞⠁⠙⣿⣯⠿⠶⣄⡀⣀⡈⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⠀⠀⣴⣴⠴⣿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣻⠋⠛⠛⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⠶⢦⣤⡴⠾⠋⠉⠀⠈⠙⠶⠶⠶⢬⣧⣶⣤⣤⣦⣀⣨⣷⣷⣿⣷⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠛⠈⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡉⣹⡅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣮⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣿⣥⣄⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢑⣾⣷⣦⡼⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠓⢲⣿⣿⣿⣿⣴⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⣤⣼⣿⣷⣿⣿⣉⡔⢁⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢮⣍⣿⣿⣹⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣶⣾⣾⣛⢻⢿⠿⣿⣿⡷⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⣉⣻⣿⣿⣿⣿⣿⣿⡤⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣿⣿⣿⠿⢿⢿⣿⣿⣥⡔⣡⣴⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣹⣾⣿⣿⣿⣿⣿⣿⣿⣏⣴⣯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣀⣄⣨⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣹⣾⣿⣷⣿⣷⣽⣿⣿⢿⣻⠏⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣡⡶⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣠⣄⠒⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢤⣄⣩⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣭⣠⣾⡗⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣙⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠭⢄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡉⠙⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣶⡶⡚⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠑⠻⠿⠛⠟⠿⣿⣿⢿⡿⣿⣿⢿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣶⣾⣷⢿⣿⣿⣷⠶⠶⡤⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⠦⠀⠀⠀⠉⠑⠻⠟⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣾⡽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡿⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡽⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣟⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⣻⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣽⣿⠓⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣻⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡾⠏⠹⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣿⣿⣠⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡟⠀⣀⢝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡼⠋⠉⣿⡗⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡉⠀⣼⡟⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣡⣤⠞⠟⠿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣹⣥⡾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠟⠙⢛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⢁⣠⣾⣷⡬⠙⠃⠀⠀⠀⠀⠀⠀⠈⢻⡟⣠⠿⡷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣇⣠⣤⣞⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⠏⠑⢻⡿⢿⣄⣄⡄⠀⠀⠀⠐⠀⠰⣿⣿⣿⡦⠱⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠶⠋⠿⣧⡄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣿⣿⣤⣴⣮⠙⢶⣭⡉⠃⠀⠀⠀⡀⢀⡴⠋⡼⢟⣿⠫⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⣿⠻⠻⣤⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠛⠙⠛⠂⠈⠟⠀⠀⠀⠀⠀⠀⢈⣵⡶⠶⣿⣿⣇⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠉⠼⢷⣶⣄⣀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣀⣙⣻⣿⠙⢿⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣼⠟⠉⡋⠓⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣿⣿⣿⢿⣿⣻⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⢶⣿⠟⠋⠀⠈⢃⠳⢶⣦⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣀⣯⢸⠟⡀⣿⣷⣙⠣⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⢾⣿⡀⠀⢠⣰⡟⠗⠤⠙⠛⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢟⣽⣻⣿⡇⢹⡿⣿⣕⡂⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣦⡟⠃⠴⡟⡟⢷⣷⣤⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢛⣻⣿⣻⡿⣀⣿⣌⡻⢿⣅⠐
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⠟⠉⠀⠀⣠⣾⡿⣌⠻⠛⠛⠛⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠁⢹⣿⣿⠁⠙⢿⠏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠻⠿⡷⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣯⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢫⣽⣷⣼⣿⣿⣿⣿⣿⣿⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣿⣾⣿⣿⣿⣿⣿⣯⣽⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡶⠶⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢸⣿⣿⣿⣿⣿⡇⢀⣿⣾⣿⣿⣿⣿⣦⣌⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣛⣿⣿⣿⣿⣿⣿⡺⣿⣿⠟⣿⣿⡙⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠛⠻⠀⣿⡇⠀⠈⠙⠻⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⣂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢁⡿⠄⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣹⢸⡟⣇⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡍⠰⠀⠀⠀⠀⠀⠴⣠⠄⡧⣠⠀⠀⠀⠀⣰⢻⡇⣿⢸⡇⢹⡄⠀⠀⠀⠐⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣬⠭⠵⣫⡴⣿⡂⠀⠀⣠⠇⡾⢸⣿⢸⣿⠈⢷⡀⠀⠀⠐⠀⠁⠀⠖⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠥⠞⠑⠃⠀⠀⠉⠈⠁⠉⠉⠈⠉⠀⠈⠁
⠀⠀⠀⢰
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠸
⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠃⠐⢩⢔⠀⠀⠀⠀⠀⠚⠥⠀⠀⠀⠀⠀⠀⢠⢋⡂⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡔⠃⢒⡀⠀⠀⠀⠀⡈⠉⠭⠂⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠐⠠⠠
⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠃⠀⡈⠀⠰⠣⠀⠀⡀⠭⠭⠭⠙⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠋⠉⠌⠄⡠⠀⠀⢑⣒⣒⢒⣒⣲⠄⠀⠀⠍⠀⠀⠀⠀⡄⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠌⠌⠀⠀⠀⠀⠀⠀⠸⠡⠤⠬⡭⠥⠤⠄⠀⠐⠦⠀⢀⠀⠀⠀⠀⠀⠀⠁⣀⡐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣨⣿⠋⣥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣿⣿⣿⣷⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡈⣻⣿⡟⠛⠫⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⢿⡏⢙⣧⣀⣴⠛⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡀⢀⣿⠟⢿⡟⠛⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⡿⢿⣿⣾⣿⡿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣏⠀⠀⣿⣄⣼⣇⠀⣀⡟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⢹⣿⡿⣿⡿⠛⠻⣿⣿⠿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⣤⣼⣷⣴⣿⣇⠀⣀⣿⣧⣤⣾⣭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⠛⣿⣿⠛⠛⢻⣿⠟⠿⣿⣧⣽⣿⡏⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣴⣿⣿⣄⣀⣸⣿⣤⣤⣿⡟⠉⠹⣿⡿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⠛⢿⣿⡿⢻⣿⣿⣿⣧⣤⣶⠿⠿⢿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣼⣷⣤⣼⣿⣿⣿⣿⣧⣀⣿⣿⣏⡀⠀⣼⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠋⢻⣿⢉⣻⡏⠀⠈⢻⣿⣿⠋⢹⣿⣿⣾⣿⠟⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⡿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣤⣾⣿⣦⣶⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣍⣀⣸⣿⠁⠀⢹⣿⠛⠛⣿⣿⣥⣿⡟⠁⠉⢿⣏⠁⠹⣟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⣿⣿⣿⣿⣦⣴⡿⢻⣶⣾⣿⠋⢹⣿⣧⣄⣠⣿⣿⣿⣿⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⣛⣿⣿⠿⢿⣶⣾⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠁⠉⢫⠝⠛⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⠀⠀⠄⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⠀⠤⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁

⣿⢿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⣋⣴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣾⣿⣿⣿⡿⠋⣁⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢟⣩⣶⣿⠟⣉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣫⣾⣿⠞⣫⠿⣫⣴⡿⢛⣡⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣉⣴⣿⣿⡿⢟⣭⣶⡿⠋⣀⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢉⣴⣾⣿⣿⣿⡿⢞⡿⠟⣩⣴⣿⠿⠋⣀⣴⣶⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠾⢛⣽⣾⠿⢛⣥⢞⣫⣶⣿⠿⢋⣡⣶⡿⠿⠿⠿⡿⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣤⣾⣿⡿⣿⣿⣿⣵⣾⠿⣋⣥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⣋⣵⣾⠟⣫⣿⣿⣵⡾⠛⠉⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⢉⣴⡾⠟⣩⣴⣿⣿⠿⠛⠁⣀⡴⠞⢋⣡⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⢁⣤⡾⠛⣉⣴⣾⣿⠿⠋⢁⣠⡶⠟⣉⣤⣾⡿⠟⣁⣤⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢁⣴⣾⣿⠿⠋⣁⣴⠾⢛⣡⡴⢛⣽⢞⣫⣶⣿⣿⣿⣿⢛⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⣤⣾⣿⠿⢋⣡⣶⠟⣋⣥⠾⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⡛⠛⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣋⣥⡾⠟⣫⡴⠞⣉⣴⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣵⡾⢛⣭⠶⠛⣡⣴⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⡿⣟⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣛⣵⠞⢋⣠⣶⣿⣿⣿⣿⣿⢟⣫⣵⣾⣿⣿⣿⣿⣿⢟⣫⣵⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⢉⣠⣶⣿⣿⣿⣿⣿⢟⣭⣶⣿⣿⣿⣿⣿⡿⢛⣩⣶⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⠟⣋⣵⣾⣿⣿⣿⠿⣛⣭⣾⣿⠿⢛⣥⢞⣭⠶⣿⣅
⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⡿⢛⣩⣴⣿⣿⣿⣿⠟⣫⣵⣾⣿⠟⢋⣡⣾⣿⣿⣿⣿⣿⡿⠛⠿⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⠿⣋⣥⣶⣿⣿⣿⡿⢟⣫⣶⣿⡿⠟⢋⣤⣾⣿⣿⣿⣿⣿⣿⠿⠋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣴⣾⣿⣿⣿⡿⣛⣽⣾⣿⡿⠛⣉⣴⣾⣿⣿⣿⣿⣿⣿⡿⣛⣥⣾⣿⣿⣿⣯⡀
⠀⠀⠀⢀⣠⡶⣛⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⣿⣿⣿⡿⣻⣵⣾⣿⠿⢋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢋⣤⠀⣠⡄
⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⢋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣾⣯⣵⡾⣋⣤⡶
⣸⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⠿⠛⣁⣤⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣵⣾⣿⣿⠟⣫⣿⣿⣿⣿⣻⡷⠻⣆⣠
⠉⠛⠉⠛⠁⠉⠁⠀⠀⠘⠋⢩⣽⣿⣿⣿⡿⠟⢋⣡⣴⣿⣿⣿⣿⣿⣿⠿⢛⣩⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣛⣠⣾⠟⣉⣴⣾⣿⣿⣿⢛⡿⠛⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠉⠀⠘⢋⡽⢿⣿⡿⠿⠛⢋⣡⣶⣿⣿⣿⠟⠉⠉⠋⠙⠛⠉⠃⠺⠏⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⣿⣿⠿⣿⠟⠁⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣡⣞⣥⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⡵⢋⣤⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠞⠋⣼⣷⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⡀⣿⣿⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⡿⣿⣿⣿⣟⡳⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⣯⣿⣿⣿⣿⣋⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣶⣶⣿⣿⣿⣿⣿⠿⠛⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠛⠻⣿⡿⠻⢿⣿⣅⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⠿⡀⣴⣿⣿⣿⣿⡟⢿⣿⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣰⣆⣡⣾⣿⣿⣿⣿⣿⣿⡟⠦⠙⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣿⣿⣿⣿⣿⣿⣧⣽⣿⡛⢿⡿⣷⣶⣶⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢩⣍⡉⠉⢠⣷⣬⣾⣿⣾⣿⣤⣦⣿⣿⣿⣯⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣽⢿⢷⣈⣤⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣾⣿⣿⢿⠿⡟⢷⣾⢿⣿⣿⣿⢿⣿⣷⣛⠿⢿⣾⣅⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⢟⡀⢀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣜⠛⠉⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⡏⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣝⣿⣿⣶⣿⣯⣽⣿⣿⣿⣿⠟⢿⣿⣏⣽⣿⣬⣛⣻⣿⡿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣟⣻⣿⠏⠛⠻⠇⠙⠃
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⠿⠻⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⡟⠫⠈⠁⣿⣿⣿⣿⣶⣿⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⣿⣷⣤⣼⣾⣿⣿⡿⠋⣻⣿⣿⣿⣿⣇⣰⠀⢀⣿⣿⣿⣽⠙⠿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⣿⡻⣿⣿⠿⢿⣿⠏⠹⣿⣿⣿⣏⠛⠻⣿⡷⠉⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠙⠋⠀⠀⠉⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⠀⠀⢠⠀⡄⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠀⠁⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⣱⠎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢤⣿⣷⡶⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠞⠛⢁⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣶⣾⢹⡅⣠⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⡿⣧⣾⣷⣤⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣄⡋⣀⡿⠿⠛⢠⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⣁⣅⣠⠄⢾⠿⠾⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏⠈⢻⣄⣘⣷⠈⠑⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠠⣤⠟⠁⡈⣠⡴⠋⠉⡾⠆⡷⠂⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢂⣾⣿⠋⡪⣴⣀⢱⡤⠶⢂⣤⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣄⠴⠲⠾⠿⢃⢠⣄⣼⠛⠋⡀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⢠⡶⢠⣀⣈⣉⠀⠴⠶⡅⠀⣀⡤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠘⡻⠊⣸⡿⠃⠀⠘⠋⠀⠀⡈⠁⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀⣤⡂⠀⠈⠀⢸⡿⢁⠠⣀⠖⠀⠀⠀⠈⠓⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠐⣿⣾⠋⠀⠉⠀⢠⠀⠀⠈⠰⠄⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣄⠀⢀⠀⠄⢻⣿⣶⡀⠀⡰⢿⠀⢀⢀⠄⠂⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠀⠈⠁⠀⠀⡰⠃⠀⠀⢀⣧⡀⠀⠀⠦⠈⡀⠰⠊⠀⠀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠉⠒⠥⠰⠚⠃⠐⠒⠀⠚⠛⠟⢉⣠⠤⠊⡑⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠂⠐⠂⠀⠂⠠⣤⣦⠔⠀⠀⠹⠷⡰⠚⠓⠋⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⣤⣄⣀⠆⠚⢸⣿⠏⠀⠀⠀⣶⡆⠀⢈⡀⠀⠀⠒⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠄⣨⡼⠏⠀⠀⡸⢡⠀⣀⣠⠁⠀⠀⠀⠀⠘⢆⠀⢀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠁⣿⣿⣿⡇⠀⢠⡈⠀⢀⠀⠈⠡⠀⠈⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⠝⣿⠁⠐⠈⠁⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠆⠠⠤⣀⣀⣀⡤⠖⠚⠉⠑⠢⠤⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣉⠴⠒⠓⠂⠀⠠⢤⡤⠤⠒⢊⣉⡁⠒⠠⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣡⠴⠚⠉⠉⠐⠂⠤⠤⠖⠊⠉⠁⠉⠙⠒⠲⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠊⠀⠀⠈⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢻⠙⠢⢤⣀⣀⣠⠤⠶⣦⣄⣀⡈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣦⣠⣤⣧⠴⠒⠋⠙⠲⢄⡀⠀⠉⢻⣿⣿⣷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⣀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣿⣿⣧⠀⠈⠳⣄⠀⢀⣀⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⢱⣿⡿⠃⠈⢧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⡆⠀⣀⠼⢻⡉⠀⠉⠳⣄⠀⢀
⠀⠀⠀⠈⠁⠀⠀⠀⣼⣿⠀⠁⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡿⢋⣹⣿⠉⠀⠀⢸⡇⠀⠀⠀⠈⠳⣼⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢷⣀⡀⠄⢿⠀⠀⣿⠀⠀⠀⢸⣇⠀⠀⢾⣷⠀⢨⠗⢄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⣇⠀⣠⠄⠀⠀⣀⡾⠓⠁⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢹⠀⠀⠀⠀⠙⠳⣦⣈⣋⣠⠏⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠙⠋⠀⣀⠴⠚⠁⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⠀⠉⠀⠈⣇⠀⣀⢀⢀⡀⡈⢻⣿⣟⠀⠀⠀⠀⠀⠱
⠤⠀⠀⠀⠀⣺⡟⠛⣿⠀⣀⡶⠛⠉⠀⠈⠛⠒⠢⣤⡞⠋⠁⠀⠀⠀⠈⠙⢆⠀⠀⠈⢠⡤⠤⠤⣤⣤⠬⣿⣿⣉⣁⡀⠀⠀⢰
⠀⠀⠀⠀⢀⣿⠀⢀⣿⡟⠉⠉⠙⠒⠦⣄⠀⠀⢀⣿⠀⠀⠀⠰⠖⠲⡄⠀⠈⡆⠀⠀⣾⠀⢰⣾⡿⢿⣿⣿⡏⠀⠀⢹⠀⢠⠏
⠀⠀⠀⢠⠞⣧⠖⠉⢸⡇⠀⠀⠀⠀⠀⠈⠳⣄⠈⢿⡀⠀⠀⠀⠀⢀⡇⠀⢀⡇⠀⢰⡇⠀⠘⣏⠀⠀⢻⣿⠃⠀⠀⣸⠀⡞
⠀⠀⢀⣸⣿⡇⢺⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠓⠦⠤⠔⠋⠀⢀⡾⠀⠀⣼⠁⠀⠀⢻⡀⠀⢸⡟⠀⠀⠀⡇⡜
⢀⡴⠋⠀⠹⣷⣈⠛⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠲⢤⣀⣀⣀⡤⠶⠋⢀⠀⠀⠙⠢⡀⠀⠈⠁⠀⣾⠁⠀⠀⢀⡿
⢸⠀⠀⠀⠀⢹⣿⣿⣷⣿⠀⠒⣀⣈⣀⡀⠤⠤⠶⠶⠒⠒⠒⠓⠂⠈⠉⠉⢙⡒⠦⣵⡀⢹⠀⠀⠀⡼⠃⠀⠀⠀⠘⠁
⢸⠀⠘⠉⣁⣠⣿⣿⣿⡟⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣖⣒⣞⠙⠀⠀⠀⠙⠾⠀⢠⠟⠁
⢸⠀⢀⡟⢡⣾⡿⢿⣿⡇⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠉⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⣀⡀
⢸⠀⡼⠀⠘⣿⠀⠀⣿⠃⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠂⠀⠤⢤⣤⣤⣤⣤⡤⠤⠤⠒⠋⠟⠁
⠘⣸⠇⠀⠀⢻⡆⠀⣿⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟
⠀⣿⠀⠀⠀⠈⢷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿
⠀⠟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣋⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠠⠀⣀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⡄⡀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠀⢈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡋⣳⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠰⡦⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢈⣟⠛⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⣤⡄⠀⡀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡏⢹⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡷⠁⠤⠀⠀⠀⢰⣿⠎⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡶⣤⣤⣴⣤⡾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⣼⣋⣻⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡤⠉⣗⡆⠀⠀⠈⠉⠉⠀⠀⢤⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡶⢠⡾⠿⣷⣀⡀⠀⠀⠀⠀⢞⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠛⠛⠉⠛⢷⡤⡄⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⢦⣴⣄⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠏⠀⣽⠿⢿⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⡧⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡤⢸⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣖⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⣀⡀⣀⡤⣤⣴⣲⠖⠻⣾⠿⢯⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠭⠗⣾⣽⣶⣿⠽⠛⠓⠋⠉⢹⣯⣿⡆⠀⠀⠙⠛⠋⠀⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⣥⣆⣴⢞⣁⣻⣭⣽⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣀⣈⠳⣤⣶⣌⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⣩⡿⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠉⠛⣽⣶⣖⣦⣠⢤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⢿⠇⠀⠀⠀⠘⣿⣭⡏⠀⢈⣿⣻⡷⠛⠻⣽⣶⣟⠦⢴⣲⠤⣖⠶⠾⡿⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢲⣾⣵⣧⡶⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⠀⠘⣯⣭⠇⠀⠀⠀⠀⠙⣦⣴⣾⣷⠚⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡤⣀⣴⣺⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢟⣶⣶⣖⣦⣤⢲⣤⣴⣢⣤⣖⣦⠴⣲⠶⠾⣽⡿⣷⠛⠉⠛⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠗⢲⠿⣿⣪⣿⣾⠇⠉⠀⠨⣿⣙⡧⠀⠀⠀⠀⠀⠻⣶⠿⠀⠀⠀⠀⠐⢿⡾⢿⡖⠽⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣯⣿⢿⣲⣤⣠⢤⡙⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠉⠀⠋⠀⣽⡯⣿⠊⠉⠓⠛⠛⢯⡿⣾⡽⠶⢾⡷⠶⢏⣶⣶⡭⠖⠺⠽⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣊⢥⡶⠃⠀⠀⢀⡴⣤⢈⡟⣻⠀⣠⡄⢠⠿⣸⣯⣿⡁⣠⣄⢰⡄⣴⣯⣬⣧⡀⠀⠀⠙⢶⠬⣳⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠰⠞⠒⢏⡤⠞⠹⠋⠱⠊⠷⠛⠋⠁⠈⡇⠀⠀⠀⢸⠋⠁⠈⠛⠙⠞⠻⠏⠻⠏⠲⢄⡟⠚⠳⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠤⠬⢆⠀⠀⠀⠀⠀⠑⣀⡂⠁⠀⠀⠀⠐⠀⠆⠐⠂⠀⠀⢰⠑⠆⠖⣿⡇⠀⠀⠀⡊⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⡸⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢸⠀⡀⡀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠠⠤⠄⣤⣥⣀⡠⠀⠀⠠⡤⠄⠡⢄⠀⠀⠀⢀⡜⣆⣞⡅⠀⠀⢘⣀⡁⢢⡇⣛⠀⠀⠀⣇⢂⣲⣦⡄
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⡀⠀⣠⡀
⠀⠀⠀⠀⠄⠒⠢⣠⠔⢢⠀⠀⠀⢐⠀⠂⠁⠀⠀⢠⠌⢐⣀⠀⠢⡀⠀⠀⠂⠀⢪⣦⣀⡄⠀⠀⠑⢊⣈⡛⡀
⠀⠀⠀⠀⠈⠡⠁⡘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠈⠀⠚⠁⠀⠀⢀⠁⠸⡍⠙⠃⠀⠀⠀⠈⠂
⠀⠀⠀⢀⡤⠄⢠⣇⠀⠀⠀⠀⢠⡦⣒⢶⡦⠀⠀⠀⣴⣴⣰⣤⡄⠀⠀⣄⡤⠀⣄⡅⠀⠀⠀⠀⣀⡄⠀⢬⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠀⣦⣠⡆⣤⠶⣦⢠⣶⡆⠲⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠽⠃⠟⠹⠇⠻⠦⠟⠰⠯⠟⠀⠿

⠀⠀⠀⠀⢀⠂⠀⠀⠂⠀⠀⠀⠀⢈⠀⡑⠄⠀⠀⠀⠀⢠⢀⡕⠄⠀⠀⠀⠐⣄⢀⡵⡀⠀⠀⠀⠐⣳⣴⠢
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡄⠧⠴⠃
⠀⠀⠀⠀⠠⢤⣄⣤⠤⠀⠀⠀⢘⢭⣆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣠⡄⠀⠀⠀⡅⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠈⠉⠈⠁⠂⠀⠀⠀⠉⠋⠉⠉⠃⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢰⠊⠀⠀⠂⠀⠀⠠⠀⠀⠈⠂⠀⠀⠀⣷⡄⠄⢠⡾⠀⠀⡐⠁⠀⢱⠀⠀⠀⠀⠀⡐⠁⢀⠁
⠀⠀⠀⠀⣰⢰⢄⠈⠀⠀⠀⠀⣁⠇⠀⠰⣎⠆⠀⠀⠈⠀⣀⠀⠁⠀⠀⠳⠈⠡⡌⡄⠠⡀⠀⠀⡆⡙⠚⣁
⠀⠀⠀⠀⠱⣩⠠⡀⠐⡀⠀⠀⠰⢂⣀⡀⡈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡞⠀⢛⠣⡿⠭⠅⠀⠀⡊⠁⠀⠉
⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠁⠉⠁⠁⠀⠀⠉⠈⠀⠉⠁

⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡖⠋⠛⢶⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢻⡄⣰⠏⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢠⣤⣤⡤⠶⠄⣤⣤⠀⠀⠀⢠⣄⢠⣤⡄⠀⠀⣤⡄
⠀⠀⠀⠀⢠⣤⣤⣤⣽⣷⣦⣄⣿⣇⣤⣤⣶⣞⣛⡉⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⡀⣿⣿⠀⠀⢀⣿⣿⢸⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣟⠉⠉⠉⢉⣽⠛⣿⢿⡛⠛⠛⠛⠛⠛⣿⡃⠀⠀⠀⠀⢸⣿⠋⠉⠉⠁⣿⣟⠀⠀⣸⢻⣿⢸⣿⡇⠀⠀⣿⣟
⠀⠀⠀⠀⣿⣿⣉⣀⣴⠟⠁⢸⣿⠀⠹⣦⡀⠀⠀⠀⣿⠁⡾⠋⠙⣷⢸⣿⡇⠀⠀⠀⣿⣿⠀⢰⡏⢸⣿⢸⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⣿⡏⠉⠉⠀⠀⠀⢸⣿⠀⠀⠈⠻⣦⣀⠀⣿⠀⠛⢂⣰⠟⢸⣿⡇⠀⠀⠀⢿⣿⣠⡟⠀⢸⣿⠈⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠉⠛⣿⠖⠛⠋⠁⠀⠘⠟⠃⠀⠀⠀⠈⠛⠋⠀⠀⠘⠛⠁⠛⠛⠛⠛⠙⠛⠛⠛⠃
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢢⣹⠉⣙
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣤⡿⠉⢳⡀⠀⠀⠀⠀⠀⢰⣿⠀⣇⠀⠀⣸⢿⠉⠛⠀⠀⠀⠀⣤⡀
⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⢰⣿⢃⠀⠘⡇⠀⠀⠀⠀⠀⢸⣿⠀⠈⢙⣋⣁⠋⠁⠐⣿⡆⠀⠀⣿⣿⡄⠀⣠
⠀⠀⢀⡾⡋⠙⢷⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡯⣿⠀⣸⠁⠀⠀⢠⡖⢢⣸⣿⡀⢠⣿⡇⢸⣴⣿⠀⢿⣧⠀⢠⠇⢹⣿⡾⠁
⠀⠀⣾⢷⡇⠀⠀⡇⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣿⡇⡟⡰⣃⡀⠀⠀⣿⠀⠀⡿⣿⡇⢸⣿⡇⠘⢸⣿⡀⠀⡟⠛⠋⠀⣠⢿⣷⡀
⠀⠀⣿⢸⠃⠀⢀⠇⠀⠀⣿⡇⠀⡠⠶⠦⡀⠀⣿⡷⠊⠀⢩⡅⠀⢀⣿⡇⠚⢱⢿⣷⠀⣿⣇⠀⣼⢿⣧⢠⡇⠀⠀⢰⠋⠈⢿⣧
⠀⠘⣿⡿⣶⡦⡼⠤⣤⣤⣿⠧⠄⢧⡀⣀⡹⣆⢹⣿⡀⠀⢻⣿⢠⡏⣿⣧⠀⣼⠈⣿⡄⢸⡿⡶⠏⠈⠿⠾⠁⠀⠀⣿⠀⠀⢸⣿
⠀⠀⣿⣇⠀⡼⣱⢻⣷⢉⡏⣿⣇⠁⠙⠶⠷⣿⠛⣿⣷⡀⠘⢿⡿⠀⠘⢿⣶⡟⠀⠈⢿⣄⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠸⣿⡞⢰⠏⠸⣿⢸⣿⠻⣿⡄⠀⠀⢠⡿⠀⣌⠿⣷⡶⠢⢄⠠⡦⢀⡤⠶⣤⠐⣶⡞⢲⡦⢀⡤⠶⢦⠒⣶⠖⠸⢷⣶⠾⠷
⠀⠀⣷⢻⣿⣼⠀⢸⣿⡼⣿⢸⡟⠿⣿⣿⠿⠃⠀⣿⣿⣿⠻⠿⠾⢯⣿⡟⠀⢀⣿⠇⣿⡇⢸⣿⡟⠀⠀⣿⠇⣿⡇⠀⢸⣿
⠀⢀⣿⠇⢻⣿⡇⠀⣿⣧⠇⢸⡇⠀⠀⠀⠀⠀⠀⣿⡟⣿⣧⠀⠀⠘⣿⢁⣠⡾⠋⠀⣿⡇⢸⣿⠁⣀⡾⠋⠀⣿⡇⠀⢸⣿
⠀⢸⣿⣤⣤⡙⠿⠀⡘⢿⣦⣼⠇⠀⠀⠀⠀⠀⠀⣿⠇⡈⠻⣷⠀⠀⣿⠉⠁⠀⠀⠀⣿⡇⠸⣿⠿⣅⣀⠀⠀⣿⡇⠀⠸⣿
⠀⠈⠉⠉⠉⠙⠛⠛⠛⠓⠉⠹⠾⠿⠿⠿⢷⣶⣶⣿⠀⠳⠶⠟⠀⠀⠿⠀⠀⠀⠀⠠⠿⠧⠘⠿⠀⠀⠈⠁⠠⠿⠧⠀⠀⠿

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⣰⣣⡄⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠘⣣⠒⠀⠀⠀⠀⢾⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⣴⣶
⠀⠀⠀⢠⡯⠏⠁⡀⠀⠀⠸⢿⡿⠇⠀⠀⠀⠠⠰⠀⠀⠀⠀⠴⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⣾⣿⣿⣧⡀⠀⠀⠀⣷⣿⣆
⠀⠀⠀⠚⠉⠙⠛⠛⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠘⠉⠉⠉⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⢀⣼⣿⣧⠀⠀⠀⢀⠡⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⢾⣿⣿⡂⠀⠀⠀⢀⣽⣿⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⣿⣿⡄
⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⠈⠐⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠰⣿⣿⣿⡦⠀⠀⠀⣠⣾⣿⣧⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⣿⣿⣿⡷
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⠙⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⠶⣳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣞⣿⡖⢀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠉⢳⢷⣖⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣋⠹⣿⣿⡟⣬⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⡏⢹⡟⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢫⠟⠺⢯⢃⡔⠘⠿⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⣽⡠⣿⣧⠈⢛⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⣣⠶⡴⠃⠈⠱⠒⣤⡀⢀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠶⢻⣏⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⢈⡍⠈⢨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠋⢠⣿⡿⢎⠨⠛⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠠⡿⠗⠀⣉⣴⠁⣀⡀⣠⠈⣆⡀⠀⠀⣀⢠⠖⠋⠉⣵⡾⢏⡽⢿⣴⣗
⠀⠀⠀⠀⣀⠠⠀⠐⢡⣮⣭⣭⡥⣶⣤⣤⣍⢄⣬⣿⣦⣼⣿⣿⠇⠐⣋⣥⣴⠂⠀⣾⣿⢞⣶⣷⣢⣄⡤⠄
⠀⠀⠀⠀⠙⠛⣶⣾⠋⣼⣿⣿⢁⣨⣿⣿⣿⣧⡀⠙⠛⠿⠟⠁⢀⣾⣿⣿⣿⣷⠀⣿⣿⠈⠱⣿⣏⠁
⠀⠀⣀⣤⢶⣿⣿⡏⠀⣿⣼⡟⠘⠛⠛⢿⣿⣿⣇⢀⣠⠤⣀⠄⢻⣿⣿⠿⠿⠛⠁⢻⣿⢷⡦⣿⣿⣷⣦⣤⣤
⠀⠀⠙⠻⢦⣽⡷⣧⠀⢹⣯⣷⠀⠀⠀⠈⠉⢁⣿⢸⡯⠀⠘⣷⠸⠃⠀⠀⠀⠀⠀⣾⣿⣿⡀⢸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠉⠿⣿⣦⣾⣄⢿⡀⠀⠀⠀⢰⣿⢏⡼⠣⣄⠀⠻⣧⢄⡀⠀⠀⠀⠀⣿⣿⣿⢡⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣬⣧⣀⣀⣠⣾⣿⣿⣿⣽⣤⣾⡛⠻⣯⡓⢤⡀⢀⣘⣷⣿⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⢿⣿⣅⣈⣁⣤⣼⣷⣟⣠⣼⣿⡶⣦⣬⣭⣷⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⡀⠘⢿⠙⢿⣿⣿⣶⣿⣻⠿⠉⠿⢠⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣼⡟⣿⣿⢿⣿⣿⣤⡀⠀⠀⢨⣽⣿⡿⠀⠀⠀⢀⣡⣼⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⠏⣼⣿⣼⣇⣿⣿⣿⣿⠙⢿⣧⡀⢺⣿⣉⣴⠀⣀⣴⣿⣿⣿⣿⣿⢻⣿⣿⡇⢰⡄
⠀⠀⠀⠀⣴⠋⢐⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⣿⡛⠚⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⠀⢹⡀
⠀⠀⠀⣼⢃⣼⠟⣈⣿⣿⣿⣿⣿⣿⣿⣷⣸⠗⠇⣤⣤⣴⣿⠟⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⢿⣷⣦⡁
⠀⠀⢀⣼⣿⣵⣿⠛⠒⠻⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⡏⣿⡌⠫⣿⢻⣧⣄
⠀⣰⣿⢟⣋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⡁⠉⠙⠛⠛⠓⠛⢋⡽⠛⠻⣿⣯⣠⠏⠙⢿⣠⡄⠠⣀⠉⠉⠐
⠻⠇⠀⠀⠉⠀⠀⠠⠄⣀⠀⢀⠀⠀⠀⠀⠀⠁⣤⡀⠀⠀⢠⠼⠋⠀⠀⠀⠈⠹⣿⡄⣀⡈⠻⠛⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠲⣶⠖⠀⠀⠀⠀⠀⠀⠀⠈⠡⠖⠀⠀⠀⠈

⠀⠀⠀⣊⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠰⣶⣶⠆⠀⠀⠀⠀⠀⣀⣀⠀⣤⠀⠀⣤⢀⣀⡀⠀⠀⠀⠀⢠⠦⣀⣀
⠀⢠⣶⣟⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⢈⠉⢉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠘⠻⢿⡞⠉⠙⣷⡿⠟⠁⠀⠀⠀⠀⠈⡿⠋⠉⣹⣧
⠀⢿⠋⢻⣿⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠘⠀⢤⡄⠘⠀⠀⠀⠀⠀⠀⠀⢸⣇⡤⠖⠋⣼
⠀⠈⠳⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠊⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠃⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣏⠃
⠀⠀⢀⣤⠀⣮⠷⠉⠁⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣾⣿⡎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⣠⣶⠆⠀⠀⠀⠀⠠⠚⠿⣿⣿⣻
⢤⡜⣯⠻⠀⠉⠂⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿⣟⠕⠁⠀⠀⠀⠀⠀⠸⠿⡿⠿⣿⠿⡿⠟⠀⠀⠀⠀⠀⠐⠄⣀⠀⠈⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉


⠀⠀⠀⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⢀⣜⣛⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣧⣄⠀⠀⠀⠀⠀⠀⡴⠻⠓⠒⠺⠗⣄⠀⠀⠀⠀⠀⠀⠠⣿⣿⣯⠀⠀⠀⠀⠀⠀⠐⢛⣩⣥⣶
⠀⢈⣍⣋⣩⡄⠀⠀⠀⠀⠀⠀⠀⣸⣟⡻⢝⣻⡇⠀⠀⠀⠀⠀⣷⣶⡖⣶⢲⣶⣿⠀⠀⠀⠀⠀⠀⣆⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆
⠀⠈⠁⣉⡁⢘⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣧⡿⠃⠀⠀⠀⠀⠀⣿⣿⣡⣿⣢⣿⡟⠀⠀⠀⠀⠀⠀⠸⣦⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡧
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⡿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣄⠈⢷⣜⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢫⣿⣾⠁⢳⣄⠻⡷⣝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣱⣿⣿⡟⢲⡀⠻⣧⡈⢮⡳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢃⣼⣻⣿⡟⣇⠀⠹⣦⡈⢯⡢⣙⢦⡑⢽⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⡽⢋⣴⡟⣱⣿⠟⣴⡏⢷⣄⠈⠻⣦⡙⢮⡓⢭⣢⣌⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠖⢋⣴⣿⢋⣼⣿⢋⣾⠳⡇⠀⠹⣷⢄⠙⢿⡳⣽⣦⡈⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠵⠚⣩⠞⣡⣾⠟⣡⣿⠃⢠⡟⢦⡀⠈⠳⡙⢦⣙⢦⣉⠻⢶⣄⡀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⢾⡿⣫⡾⡿⠃⣠⢿⣦⡀⠻⣦⡀⠙⢦⡈⠓⢬⡳⢤⡈⠛⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⣱⣟⡴⣫⠞⢁⣼⠟⢸⡏⠻⣦⡈⠻⣷⣄⡙⠦⣀⠈⠑⠻⢷⣤⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⡴⠃⣴⣿⠋⣰⢻⠷⣄⠙⢿⣷⣌⠻⣝⠲⣬⡳⢤⡀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⡴⠋⣠⣾⠟⢡⣾⠏⣸⠧⣜⢷⣄⡙⠻⣟⢮⣝⣦⣍⠓⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢀⡴⣋⡴⣚⡿⢁⡴⣫⢏⡼⢻⠀⠈⠳⣝⢿⡦⣌⠙⠮⣙⠻⢿⣶⣤⣉⡙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⣡⠖⢋⡴⢋⡜⣡⠞⠁⢸⠀⠀⠀⠈⠓⢿⣮⣝⠲⠮⣽⣶⣄⡉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣡⠖⢋⡴⢋⡾⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡈⠉⠙⠛⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠿⠚⠉⢀⡴⢋⡴⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣫⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡄
⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣟⠦
⠀⠀⠀⠀⣸⣯⣿⣧⠀⠀⠀⠀⠀⠀⢴⣶⣾⣶⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠐⠂⢁⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣿⣟⣆⡀
⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣶⣷⣶⣷⣶⣿⣿⡆⠀⠀⠀⠀⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⠛⠄
⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣬⣟⣛⣛⣛⣫⣭⣾⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣰⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣤⣿⣾⣿⣿⣿⣿⣇⡀
⠀⠀⠈⠉⠉⠹⠿⠉⠛⠃⠀⠀⠀⠉⠈⠛⠋⠿⠋⠈⠉⠈⠁⠀⠀⠈⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠏⠉⠉⠀⠀⠀⠀⠈⠉⠈⠉⠹⠟⠛⠿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡟⣻⠀⠀⣤⢀⣠⣤⣄⠀⠀⠀⠈⠛⢻⡟⢛⣃⣤⣤⣄⢸⡇⠀⠀⣿⠆⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣀⣤⣿⢸⣏⣠⣄⠀⠀⠀⠀⠀⢸⡇⢸⣁⣤⣤⡿⢸⡇⠀⢀⣿⠀⣿⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠉⠉⣿⢸⡟⠉⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⢿⣤⡀⠸⣿⣀⣼⣿⡀⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠀⠀⠉⠈⠛⠛⠙⠀⠀⠀⠀⠀⠈⠃⠘⠁⠀⠙⠁⠀⠙⠛⠋⠘⠃⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⢰⡞⠛⢲⡄⣶⢠⡶⠚⠻⣶⢐⡃⣿⠀⠀⠀⠀⠀⠀⣰⠶⠛⢷⡄⢸⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠙⢷⢸⣷⡶⠟⠃⣿⢸⣶⣶⠟⠋⢸⡇⢸⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⡟⣸⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⠟⢸⡇⠀⠀⠀⣿⢸⡇⠙⢷⠆⢸⡇⢸⠀⠀⠀⠀⠀⠘⢷⣤⣴⠿⠁⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠷⢀⡀⠀⢀⡀⣴⠾⠛⠿⣦⢀⠀⠀⣘⡛⢻⡿⣿⠀⠀⣀⠀⠀⢠⣿⣧⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⡁⣀⣼⡇⣿⣤⣶⡾⠋⣴⠀⣿⡉⠁⢸⡇⣿⣷⣼⣿⠀⠀⡾⢹⣿⣇⠀⣾⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⢸⡟⠋⣿⡇⣿⡛⢿⣄⠀⣿⢠⡌⠉⢳⢸⡇⣿⠻⠟⣿⡀⣸⠛⠛⢿⣿⢠⡌⠉⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠘⠃⠀⠙⠃⠙⠃⠈⠛⠁⠙⠈⠛⠛⠋⠘⠃⠋⠀⠀⠛⠃⠃⠀⠀⠘⠛⠊⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⡴⠦⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡴⠶⢶⣄⢿⡆⠀⢀⡾⢡⡶⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠦⣤⡀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠁⠀⢈⣿⠸⣿⣀⣾⠃⢸⣧⡴⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣄⣠⠇⠀⠀⠀⠀⣿⣤⣦⡌⢷⣄⣠⣾⠃⠀⢻⣿⠇⠀⢸⣇⣀⣀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠰⠀⠀⢠⡄⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠠⠋⠁⠀⠀⠀⠀⠞⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠰⠆⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠉⣶⠶⠁⠀⠀⢀⠾⣿⠣⡀⠀⠀⠀⢀⣾⡄⠀⠀⠀⣹⡅⠀⠀⢩⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⣹⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡼⣿⢷⡈⠀⠀⢀⣾⣿⣿⡀⠀⢈⠼⢌⠀⠐⢛⣿⡟⠀⠀⠀⣼⣧⠀⠀⠀⠉⣹⣿⣏⣉⡀
⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⢈⡴⣿⣧⡙⠂⠀⣾⣿⣿⣿⣷⠀⡨⢘⠢⡁⢠⣾⣿⣿⡆⠀⢠⡿⢼⡄⠀⠀⢙⣿⣿⣏⣉⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢿⢦⠑⠆⣸⣿⣿⣿⣿⣿⣧⠠⠞⠦⠀⠈⣸⣿⣆⠀⠀⣾⡿⢹⣷⠀⠲⠟⣻⣿⣿⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠋⠀⢸⠀⠑⠀⠟⠿⠿⠿⠻⠟⠛⠂⢸⠀⠀⠼⠿⠿⠿⠇⣸⣿⣧⣽⣿⡆⠠⡾⠿⣿⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣞⠭⢈⡭⠭⠅⠢⠤⣄⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠦⠍⠉⠭⠕⠒⠀⠀⡀⠀⡎⠀⠰⢆⠀⠉⠻⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢩⠀⠞⠁⠀⠈⢈⠅⠐⠂⠀⠀⢀⠀⠀⠤⠀⢈⠀⠀⠀⠈⢅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡠⠂⢖⠀⠰⠂⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠃⠀⠘⠀⢨⠂⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡏⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡚⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢃⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡀⠀⠀⢀⣴⠄⢠⣿⡄⠀⢀⡀⠀⠀⣹⣿⣄⢸⣿⡄⠀⢰⡄⠀⠀⣾⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠀⠀⣸⣿⣧⣼⣿⣷⠄⣿⣷⡀⢀⣿⣿⣯⢿⣿⣟⡀⣾⣧⡀⣰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢦⡠⢽⣿⣿⣿⣿⣿⣦⣿⣿⣆⢴⣿⣿⣿⣽⣿⡿⠄⣿⣿⣟⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣭⣩⣴⣧⣤⠼⠿⣿⣻⠿⠿⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣯⣿⣛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣷⣾⣯⣽⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣷⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣽⣛⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣷⣯⣿⣻⣿⠿⠿⠿⠿⠿⢿⣿⣛⣂⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠙⠛⠀⠀⠀⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠒⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣻⣿⣛⡟⠿⠿⠿⠿⢿⢷⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣸⠀⠀⡀⣾⡖⢛⣛⡓⣚⣒⢿⣿⣿⣿⣿⣿⣿⣿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠸⠁⠀⠀⠘⢹⡇⢸⣿⣿⣿⣿⣿⡏⠀⠈⢉⡋⢹⣿⢐
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣈⠃⠀⠱⡀⠀⠀⠀⠀⠀⠆⠀⣼⡇⢸⣿⣿⣿⣿⣿⣿⡶⠿⠾⣷⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⣴⠒⣄⠀⠀⢸⣧⣱⡀⠀⡇⠀⠀⠀⢠⠀⢀⠀⢿⡇⢨⣿⣿⣯⣽⣿⡏⠀⡀⠀⠈⠉⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⣿⣿⠇⠀⡇⠀⠀⠰⡟⠀⠈⠁⣿⡇⢸⣿⣿⣿⣿⣿⣖⣀⡀⡀⢠⠀⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠰⠀⡈⠉⠀⢀⠃⠀⠀⢈⡇⠸⠀⠀⣽⡇⣸⣯⣿⣯⣽⠹⣿⡿⢿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠄⡀⠀⠀⠀⠀⠀⠸⣶⣿⠇⠀⠰⠁⣔⠀⠀⠘⡆⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣏⡏⠀⡀⢙⠁⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠈⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡌⠙⠀⠘⠱⠠⡀⠆⣿⡇⢸⣿⡿⣿⣿⢓⡧⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⢠⣀⣀⠘⠯⣄⠀⠀⠈⠐⠒⠒⠂⠁⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢸⠆⠶⠓⠶⣶⣶⣲⣒⣚⣓⣒⣠⣼⣭⣥⣭⣭⣄⣀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡨⣯⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉
⠀⠤⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠑⠤⠴⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠂⠠⠀⠀⠀⠠⠤⠾⠂⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠂⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠂⡰⠁⢠⣀⡀⠀⢠⣂⡰⠀⠈
⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢿⣿⠃⠀⠸⣿⠇⡂
⠀⠠⢤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠉⠀⣀⣴⣀⣀
⠀⠀⠀⠀⠓⠢⠤⠔⢦⣄⣤⣤⣄⡀⢀⣀⣀⣀⢀⣀⡠⠤⠤⠤⠀⠓⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⣳⣤⣀⣀⣠⣼⡩⢤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣶⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⣁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠭⢽⣿⣛⣿⣿⣿⣿⠷⠶⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣠⠖⠒⠒⠦⣴⠋⢳⣀⣀⣤
⠀⠀⠀⠀⠀⡏⠉⠉⣿⡄⠀⠘⢦⡀⣴⠛⠓⢦⢸⠁⠀⣤⠉⢻⠀⠘⠋⠀⡽⢧⠀⠉⣀⡬⠇
⠀⠀⠀⠀⠀⢻⠀⠀⠈⠁⠀⠀⠈⡇⡏⠀⠆⠈⢿⡄⠀⢀⣠⠾⡇⠀⢰⠊⠁⣼⠀⡞⠁
⠀⠀⠀⠀⠀⠈⣇⠀⠀⣤⡄⠀⠀⢷⡇⢠⠶⡄⢘⣧⣤⣼⣤⣀⡙⢚⡭⠤⢤⣨⠟⢧⡀⣀⣤⣄⡤⠤⢤⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⡀⠀⢹⠻⣤⣤⣼⣉⠉⢠⠼⠟⠚⢻⡇⠀⣄⠙⣾⠀⢀⠀⢿⢦⡀⠙⠁⣠⣿⡀⠀⠤⣞⠀⠀⠀⢠⡟⠉⠙⣇
⠀⠀⠀⢀⡤⢦⡀⠓⢚⡯⠤⣄⣿⠉⠙⡇⠘⢲⡄⢰⢿⡇⠀⠿⠃⣿⠀⣈⡀⠈⣇⣷⠀⡏⠁⣏⠉⠃⠀⢈⡇⣤⠶⣼⡇⠀⠀⣿⣠⣄⡀
⣾⠛⠉⣿⡀⠀⠛⣶⠏⠀⣤⡄⢻⡀⠀⠷⠶⡞⠃⠘⢻⣧⣤⡤⠞⠳⠤⠏⠹⠴⠞⠛⠚⠃⠀⠙⠲⠤⠴⠚⢸⡇⠀⠈⠃⠀⠀⠟⠁⠀⣿
⢹⡄⠀⠈⠁⠀⠀⢸⣆⠀⠹⠃⢸⣇⣀⣤⠴⠟⠛⠋⠉⠀⠀⠀⣴⠛⠶⣄⠀⣠⠖⠛⣦⠀⠀⠀⢠⡴⠶⠶⠶⠛⠒⡂⠈⠀⠈⠉⠒⢛⠛⠛⠛
⠀⢿⡀⠀⢶⣆⠀⠈⣿⠲⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣏⣀⣀⡭⠉⢅⣀⣀⣻⣤⣤⡀⢸⡇⠀⠂⠀⠀⠊⢆⠀⠀⠀⠀⠄⠁⠀⠀⡀
⠀⠈⣧⣀⣸⠟⠖⠒⢋⣤⣀⡴⣆⢀⣄⡀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣧⠈⡗⠀⠀⠀⠀⠠⠚
⠀⠀⠈⠉⠁⠀⡴⠦⣾⠀⣿⠁⣿⠋⣸⣃⠀⠀⠀⠀⢺⠥⠭⠬⠤⠤⢬⠀⣄⠀⠇⠒⠒⠒⠒⣿⠀⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⢠⣷⣄⠘⣇⢸⢠⠏⡰⢋⣽⣃⣀⣠⣤⠸⡇⠀⠀⠀⠀⢲⠀⠉⢀⢸⣄⠀⠀⠀⣿⠀⣿⠀⠄⠁⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⢀⣤⣬⡷⠾⠷⠾⠛⠈⠉⠋⠉⠉⠉⠁⠀⢸⠀⣧⠀⠀⠀⠀⠁⠀⠀⠀⠙⠃⠀⠀⠀⣿⠀⢻⠂⠀⡀⠈⠀⠀⠄⠀⠀⠰⠂⠀⢀
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣿⠀⢸⡄⠂⠀⡠⠀⠀⠀⠀⠀⠸⢀⠐⠁
⠀⠀⠀⠸⡗⠂⠈⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⠀⡀⢒⠀⠀⠘⠁⠀⠠
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠈⠀⢸⠀⠀⢀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⡀⠀⠀⣿⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⡇⠀⠈⣇⣀⣊⣀⣀⠀⢀⡀⢀⣈⢀⣀⡐⠁⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠋⠁⠉⠁⠀⠙⠛⠷⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⡾⠛⠋⠉⠉⠀⠉⠙⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⡀⠀⠀⢸⡇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢸⡇⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣇⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⣤⣀⣀⠀⠀⡀⠀⠀⣸⣇⠀⡀⠀⠀⠀⣀⣀⣠⡴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠉⠉⠛⠛⠉⠙⠋⠉⠛⠛⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄
⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⢀⡴⠚⠻⣿⣆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⡠⠶⠂⠈⠉⢹⣿⡿⠀⣰⠏⠀⠀⠀⣿⣿⠀⢀⠴⠋⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣰⠟⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⣿⣿⣄⠸⠇
⠀⠈⠁⠀⠀⠀⠀⢸⣿⡇⣴⠃⠀⠀⠀⠀⣿⣿⣠⠋⠀⠀⠀⣸⣿⡇⠀⠀⢀⣤⣤⣸⣧⣸⡃⢀⣠⣤⡿⢷⣾⠒⢾⣿⡇⠀⣿⣿⡀⣠⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠁⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⠟⠀⢀⡿⠛⠀⣿⣿⠀⢸⠁⠀⣼⣿⠇⣼⠛⠿⠿⠋⠀⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⢸⣿⡿⠀⠀⢀⣿⣿⣇⢀⡜⠁⠀⢀⣿⡏⢠⡏⠀⠀⢿⣿⣦⠋⠀⠀⠀⢀⡟⠀⣿⣿⡇
⠀⢀⣤⣤⣄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⡜⠉⠛⠛⠋⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠘⠛⠉⢀⣴⡆⠀⣸⠀⢀⣿⡿⠁
⣴⣿⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠶⠋⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠈⠳⠟⠛⠁
⣿⣿⠃⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣤⠾⠋⠁
⣿⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠛⢿⣿⣿⠛⠛⠛⠛⠛⠋⠁
⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣠⣤⡀
⠁⢀⣴⠞⠛⣿⣷⣄⠀⣿⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⣴⣦⢠⣿⣿⡏⢹⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣀⡾⠋⣿⣿⣿⡄
⣶⠋⠀⠀⣰⣿⣿⡟⠀⠈⣿⠿⠤⠶⣶⣶⣶⡆⠀⠀⡈⠁⠘⣿⣿⣷⣾⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣾⣿⣷⣼⡆⢹⣿⣿⣿⡇⠀⢻⣿⣿⡇
⠀⠀⢀⣼⣿⣿⠟⠁⣠⡾⠋⠀⠀⣴⣿⣿⠏⠀⢠⣾⣿⣷⠀⠘⣿⣿⣿⣤⡀⠀⠀⢠⣾⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠇⠈⣿⣿⣿⠀⠀⢸⣿⣿⣷
⠀⠀⣼⣿⣿⣏⣠⡾⠋⠀⠀⠀⣼⣿⣿⠏⢀⣰⠿⣿⣿⣿⠀⢀⣿⠋⠻⢿⣿⣿⣿⣇⢸⣿⣿⣧⠀⠀⠀⣰⡿⣿⣿⠟⠀⠀⠛⠋⠁⠀⠀⠀⠛⠛⠋
⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⢸⣿⣿⣯⣤⠾⠁⠐⣿⣿⣿⢀⣾⠇⠀⣠⡾⠛⢿⣿⣿⣾⣿⣿⣿⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠻⣿⣿⠿⠃⠀⠰⣿⠀⣠⣾⣿⣿⠃⢻⣿⣿⡆⢀⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠈⢿⣿⣿⡿⠃
⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄
⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣶⣦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣿⣏⠀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡈⢿⣿⣿⣶⣤⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⣷⣽⣿⣯⣴⢛⢀⡀⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣴⡾⠿⣿⣿⣗⠉⠉⠛⠛⠉⢩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣍⣯⠀⢀⢽⣿⡿⠦⠄⣁⣀⠀⠛⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⡄⠽⢻⣿⡷⣾⠟⠑⢰⣼⣿⣛⣤⡶⠯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠓⠓⢓⡋⠰⢿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⣠⣄⠐⠏⣿⣿⡅⠀⠙⣿⣍⢁⣁⣈⣀⣤⢶⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠒⢿⡿⠿⢷⣶⣽⡳⢦⠾⠿⢏⣿⣿⣭⣻⠍⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢂⣀⣩⣿⠀⠀⢰⣟⣿⣿⣿⣿⣷⣿⡛⠙⠻⠏⠈⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠛⠿⠿⠲⣿⣭⣿⣿⣿⢿⣝⣿⣟⣶⡴⠾⣻⠿⢷⠶⡦
⠀⠀⠀⠀⠀⠀⠰⢽⣦⣶⣶⣾⣴⣶⡿⠟⢿⣿⢀⣟⣶⣿⣿⣿⠁⠀⠀⡸⣦⠴
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡤⡀⣉⡐⣤⣥⡼⣟⣯⣿⣏⣳⣮⣿⣷⣀⣈⣽⣧⣶⣯⣭⣀
⠀⠀⠀⠀⠙⠗⣶⣦⣄⣉⡉⢁⣭⣍⣛⣷⣿⣿⣿⣬⣋⠻⡟⣿⣯⣹⣿⡷⣶⣤⣬⣍⠙⠓
⠀⠀⠀⠀⠈⠀⠀⣈⠹⠙⢙⣿⢿⣿⠋⠉⠉⢿⣿⣷⣿⣟⣧⣸⣽⣿⠿⢿⣞⣂⣉⣉⡀
⠀⠀⠀⠀⢀⣠⣤⡤⠶⠚⠋⢀⣽⣿⠀⢠⢄⣹⣿⣿⣿⣿⣯⣀⣼⡁⣀⠀⣿⣿⠿⢿⣢⣦⣤⡀
⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⣶⣿⣍⣿⡿⣛⣿⠻⣿⡿⡏⣿⣏⠿⣼⡿⢶⠾⠻⡷⠄⡀⠈⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠙⠋⠉⠀⣉⣽⠿⠛⠁⣰⠟⠈⣷⡜⢿⣆⠀⠛⢷⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⢹⡧⠀⠈⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠊⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⣈⣏⣹⣋⣏⣫⣙⣏⣙⣉⣋⣟⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣿⣿⣯⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣱⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣻⢯⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣟⡬⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠌⡀
⠀⠀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠲⠿⣿⠂
⠀⠀⠀⠀⠀⢠⠷⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⢻⡟⢚⠓⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡉⢖⣤⣛⡄
⠀⠀⠀⠀⠠⣌⡐⠂⠄⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣰⣶⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠽⣃⢤⠨⣟⣂
⠀⠀⠀⢀⠒⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⣯⣿⣷⣾⠇⣀⠀⠀⠀⠀⠀⠀⠀⠲⢶⠺⠇⢘⠃⠙⡴⠖
⠀⠀⠀⡀⠑⠂⠄⠄⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢩⣟⣙⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠓⣎⣑⠋⡉⠐⠼⠗⣚
⠀⠀⠀⠃⠐⠀⠒⠒⠂⠀⠚⠁⠄⠀⠀⠀⠀⠀⢶⡖⣿⣟⡑⣿⣹⣆⣿⣏⣁⠄⠀⠀⠀⠀⢩⣎⡝⣿⠏⡽⡤⠘⢘⠥⡠⠄
⠀⠀⠁⠀⠀⠶⠀⡀⠁⠈⠉⠀⠀⠀⠀⠀⠀⣄⢀⢩⣽⣿⠿⢿⡿⣿⣿⣿⢃⡀⢀⠀⠀⠀⡑⡀⠀⡦⢰⣆⠀⢋⣴⣧
⠀⣌⠃⠄⠤⠀⠄⠀⠀⠂⠀⠁⠀⠡⠀⠀⠀⢀⠙⣫⣾⣯⣼⣿⣗⠛⣿⣟⡿⣟⠃⠀⢀⡺⢿⡓⢒⡂⣠⡄⢤⣤⡀⢩⣤⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠂⠘⠐⠂⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣧⢼⣿⠿⣿⣾⣦⠾⠗⠛⠀⠀⠉⠛⠁⠁⠷⠟⠃⠈⠈⠑⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠓⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢸⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣷⠛⣩⣍⣻⣿⣿⠇⢺⡿⠿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠿⡄⠙⠋⢸⣿⠋⠀⣬⠰⣾⣟⠀⠘⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⢿⣿⠛⠉⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘
⢈⣠⠀⠀⠀⠀⠈⠉⠁⠀⠉⠸⠿⠟⠀⡜⢻⣿⠐⠃⢸⣿⣿⣿⣿⣿⣾⣧⠀⢀⠹⠿⠿⠿⢿⣿⣿⣿⣿⡟⡋⠉
⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠷⠐⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣦⡄⠀⠘⣿⣿⣿⣽⣿⣶⣶
⣿⣼⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⣀⣴⣿⣿⡿⠿⢿⣿⣿
⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠂⠙⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣀⣼⣿⣿
⣿⣾⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠀⠀⠀⠀⠀⡇⢙⠛⣿⣿⣿⠏⢀⢤⡀⠀⠤⡄⠀⠀⠀⠀⠈⢿⡿⠋⠉⠛⢿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠗⠁⠀⠈⠻⠏⠀⢸⡿⠁⠀⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣿
⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿
⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠐⠈⠀⠀⠀⠀⠀⠒⠐⠠⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉

⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡍⠠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠠⠄⠀⠀⠀⠀⠀⠰⢽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠠⠫⢝⢔⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠎⠃⠂⠀⠀⠀⢤⣭⠦
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⢦⣤⠶⠂⠀⠀⠀⠈
⠀⠀⣾⣿⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡶⠞⠂
⠀⢸⣿⣿⣇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⡶⠞
⢀⣿⣿⣿⣿⡄⠀⠐⠐⠀⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠀⠀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⣀⣐⡂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣈⣛⣁⠀⠀⠀⠠⢈⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣙⣟⣁⡤⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⢁⢁⠁⠉⠄⠄⠀⠀⠀⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠐⠐⠐⠈⠀⠀⠀⠀⢈⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢨⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⢀⡴⠖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣕
⢸⠀⠿⣷⡀⣀⠀⠀⠀⠀⠀⠂⠀⢀⠀⡀⠀⠠⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣦⡀⠀⠀⠀⠀⢰⣶⡆⢰⣶⢰⣶⡖
⠀⢀⣔⡛⣿⠋⠀⠀⠀⠀⠀⠱⠀⠠⡀⠀⠠⠀⠀⠀⠀⠀⠈⣛⣿⣿⣯⡄⠀⠀⠀⠀⠀⠸⣿⣧⣾⣿⠇⠀⠀⠀⠀⠀⠉⠉⣰⣶⠉⠉⠁
⠀⠙⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆
⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣦⠄⠀⠀⠀⠀⢀⣠⠖⠦⣄⣀
⠀⣾⠿⠿⠿⢷⡄⠀⠀⠀⠀⠀⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡟⣗⠀⠀⠀⠀⠈⡍⠀⠀⠀⠀⢩⡍
⠴⢿⠐⠀⠐⢸⠷⠀⠀⠀⠀⠈⠳⣀⠀⠈⣳⣤⡤⠀⠀⠀⠘⠛⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⣰⡏⣸⡇⣿⠀⠀⠀⠀⢰⢧⣴⣶⣦⣶⡜⣇
⠀⠈⠳⠅⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠛⠀⠿⠀⠀⠀⠀⠈⠈⠛⠛⠛⠛⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⠀⡀
⠀⠀⢰⡆⠀⠀⠃⠀⠀⠀⠀⠀⣻⣛⣭⣥⠀⠀⠀⠀⠀⠀⣰⣿⣿⣹⣿⣆⠀⠀⠀⠀⠀⠀⠶⠄⠀⣻⡆⠀⠉⠁⠀⠀⢀⡴⢞⣻⣷⣤⡄
⠀⢀⣼⣷⣴⡖⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠐⠦⠀⠀⠠⣫⢾⣛⣻⡿⢿
⠀⢀⣍⣭⣡⣀⠀⠀⠀⠀⠀⠀⢹⡟⠿⣿⡆⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁