Branch symbol Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⣿⠏⠀⣀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢸⡿⠃⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⡇⣀⣾⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⢸⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⣿⣿⡇⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠃⢠⡞⢁⣴⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⡿⣡⡾⠛⠉⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⠁⣰⠯⠤⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⣾⠏⣐⣛⣥⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢛⡃⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣾⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣿⢠⡏⢠⡟⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⠉⠳⣄⠀⠀⢹⣼⣧⠏⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⠛⠶⣌⣧⠀⠀⣿⠃⠀⠀⠀⠀⠀⢠⡞⣡⡴⠛⠁⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢤⣬⠽⢧⡀⣿⠀⠀⠀⠀⠀⢠⣿⣞⣡⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⣠⠟⠋⣉⡤⠶⠚⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢶⡀⠀⠀⠀⣿⠀⠀⠀⣴⠋⣠⣾⡭⠶⠒⠛⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⣀⠀⠀⠀⠀⢷⠀⠀⠀⠹⡄⠀⠀⢹⡄⠀⣼⡷⠞⠙⠛⠒⠶⠦⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢤⣈⠙⠳⢦⣄⠈⢷⡀⠰⣄⢿⠀⠀⠸⡇⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠈⠙⠳⠦⣌⡛⢦⡙⢦⣙⣾⡇⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣀⣀⣙⠳⢿⣦⡈⠛⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⢦⡘⣇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⡴⠃⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⣠⠞⠉⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠉⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠹⣆⣿⠀⠀⠀⠀⠀⠀⠀⣠⣟⣤⢖⣋⣡⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠈⠛⠛⠶⢤⣈⠳⡄⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣠⡴⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣤⣄⣀⣉⠳⣽⡄⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⣛⣁⣀⣤⣤⣶⣚⣛⣛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢷⡄⠀⠀⠀⢀⡟⢀⡴⠟⠋⠉⠀⠀⠈⠙⠳⢤⣉⡉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⢉⣛⡲⢤⡀⠹⡆⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠈⠉⠳⣿⡀⢻⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠙⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠸⠿⢲⡏⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡝⣷⡀⣾⣵⠏⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡘⣷⡘⣷⣽⠋⢀⣠⡶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢷⡜⢷⣿⣟⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⣷⠀⣿⣿⠷⠞⠋⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣶⢇⣠⡶⠞⠛⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢟⣁⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⣴⣶⠂⢀⣴⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠀⣠⡴⠟⢉⣼⠃⣠⡾⠁⠀⠀⣀⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⡿⢀⡼⠋⠀⣠⡾⢁⣴⠏⠀⢀⡴⠟⢉⣡⠞⢁⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣼⢣⡟⢁⣤⠾⠋⣠⠟⠁⢀⣴⣏⣤⠶⠛⣁⣀⣀⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⢁⡾⢃⣿⣿⣿⣷⡶⠞⠛⠛⠛⠻⣿⣿⣟⡛⠻⢿⣭⣭⣉⣉⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⣀⣿⡿⠟⠋⠉⠀⠀⠻⣟⠛⠶⣤⡀⠀⠙⢷⣌⠙⠷⣄⠀⢨⣭⡍⠁
⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⣾⢱⡇⠀⣠⣴⠞⢋⣁⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠛⢦⡀⠀⠙⠷⣤⣈⢷⡌⠉⠁
⠀⠀⠀⠀⠀⢀⡾⢻⡇⠀⣿⣿⣶⣿⣿⡛⠛⠛⠉⠙⠛⠛⠳⠶⣤⣄⠀⠀⠉⠻⢶⣬⣻⣆⠀⠀⠈⠉⠛⠿
⠀⠀⠀⠀⠀⢸⣇⣿⣠⡶⠟⠉⠀⠀⠉⠛⠛⠶⠶⠶⠶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⣸⣿⠟⠿⣿⣟⣛⠛⠛⠳⣦⣄
⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉
⠀⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⢠⣾⣃⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⣀⠾⠛⠛⠷⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⣀⠔⢋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣾⡿⢃⡤⠪⢾⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⢀⣿⠗⠋⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡠⢋⠀⣦⡀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡰⣡⣿⠀⠹⣿⣶⣝⠻⢿⠟
⠀⠀⠀⠀⢠⣿⡟⠀⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠙⠻⣿⣄
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⡀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⠊⠀⠐⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠀⢱⡀⢠⠃⢰⠀⠸⠀⡠⠒⣡⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠱⡀⡄⠀⠀⠆⡠⠃⡐⢁⠔⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⠀⡾⠊⠀⠀⢱⢆⡞⡉⠬⠙⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠈⢉⠐⠢⢄⠱⡄⠀⠀⢀⡞⠙⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⠥⠤⠞⠓⢷⠀⢀⠊⠹⠯⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠂⠀⠀⢣⠑⠌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⣂⠀⠒⢠⣀⠀⠀⠀⠸⠀⠀⠀⠀⠑⠤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠤⠔⢊⡁⢀⡉⠶⢀⠀⠀⠀⢀⠠⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠔⡠⠀⠀⠀⠀⠀⡐⠁⡔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠚⡡⠜⠁⠀⠀⢨⠀⣐⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢅⡀⠀⠀⠀⠀⡦⠚⢋⡈⠀⠀⠀⠀⠀⢀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠀⠈⠉⠒⠤⡀⠀⢡⠀⢌⠢⡀⠀⡘⠀⡰⢁⠇⠀⠀⢀⡠⠊⠁⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡈⠒⠤⣈⠢⠀⠣⡈⢆⢱⠀⠁⢀⠀⠇⠇⠀⡴⠃⠀⢀⠎⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠵⠷⢄⠈⠲⡄⠰⠀⢨⡼⠈⢀⣜⡀⠄⣊⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡃⠇⣠⠶⠐⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠈⠑⢖⠂⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⢄⠉⠒⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠒⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄
⠀⠀⠹⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆
⠀⠀⠀⠹⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⢰⣿⣆
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣆⠀⠀⠈⢿⣿⣿⣿⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠧⠀⠀⠈⢻⣿⣿⠀⠀⢸⣿⣿⣿⣧
⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠢⣀⠀⠙⠏⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢠⣷⡄
⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠳⢄⢠⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⡿⠿⠷⠀⠠⠀⠙⣦⡀⠀⠀⠹⣿⣿⣿⠀⠀⣿⣿⣿⣿⡄⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠹⣿⡏⠀⠀⢿⣿⣿⣿⣧⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠙⢦⡀⠘⠁⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠑⢄⡆⠀⠀⠀⢿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠂⠻⣄⠀⠀⠘⣿⣿⡏⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⢢⡀⠀⠹⡿⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠑⡄⢠⡀⠀⠀⠸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⡀⠈⢸⠃⠀⠀⠀⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠺⣇⠀⠀⠀⠸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠈⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣄⠀⠀⠀⠘⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠏⠀⠀⠀⠀⣀⡴⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢡⠏⠀⠀⢀⡴⢚⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⠏⠀⣠⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡏⢠⡞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⡼⠟⢀⡟⣰⣫⠿⠋⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⣸⠃⢠⣮⠞⠋⣁⣀⡤⠴⣒⣻⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠇⠀⠀⠀⠀⠀⠀⠀⣰⣳⠃⣀⠀⢀⡏⢠⣿⣡⢖⡋⠉⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡾⠀⠀⠀⠀⠀⠀⠀⣰⠃⣯⣮⣼⣷⢸⣱⣿⠿⣛⣩⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢰⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⡿⣿⣿⢏⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠁⠀⡀⠀⠀⠀⢀⡏⣞⣠⠇⢨⣧⠏⠀⢀⣀⡤⠴⠖⣒⠚⠋⠉⣉⣩⠭⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠁⢸⢠⢋⣿⣷⡀⠀⣸⢸⢁⡞⢀⡾⣁⡤⢚⣩⠤⠖⠛⠉⣉⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⣾⣿⣿⣿⣿⡇⢀⡏⢀⡞⣠⣿⡾⠟⣋⣉⣤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⡏⢿⣿⣿⣿⡇⢸⢣⢎⡞⠛⣋⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢰⠇⠈⠻⣿⠟⢀⣿⣿⣋⣴⣟⣽⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡞⠀⠀⠀⡟⢀⡼⠛⠉⠀⠈⠻⠿⠿⠿⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣰⠃⠀⠀⣸⡵⠋⢀⣠⠤⠶⢒⣛⣫⠭⠭⠽⠿⠗⠒⠀⢀⣀⣀⣤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡏⠀⣀⣴⡯⠖⠋⠉⠀⠀⠀⠁⠀⠖⠚⣁⣠⠤⠖⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣾⣋⣁⣀⣀⣀⣀⣀⣠⡤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠠⢀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⠀⣦⡎⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⣄⠂⠸
⠀⠀⠀⠀⠀⠀⣱⢂⢈⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡙⠀⢱
⠀⠀⠀⠀⡄⢀⣿⢸⡆⡠⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⡅⣿⣸⡆⢀⡀
⠀⠀⠀⢰⡇⢸⡏⡌⣿⢇⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣿⠃⣼⡇⠘⣧
⠀⠀⠀⠈⢰⠀⠇⡇⠘⡿⠀⠀⣰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⢹⡏⢀⢻⠇⡸⠁
⠀⠀⠀⠀⠀⠣⡰⢷⠀⠠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⢘⠁⣰⠞⡠⠁
⠀⠀⠀⠀⠀⠠⣝⡈⡄⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠆⣚⡥
⠀⠀⠀⠀⠀⡨⣌⠳⣿⡄⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⣼⡼⠋⡌
⠀⠀⠀⠀⠀⢸⣷⠀⠈⠻⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡼⠋⠀⢰⡿
⠀⠀⠀⠀⠀⠀⢻⣜⠀⠀⠈⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⢐⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⢄⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⢀⠌⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣀⣀⠀⠢⡘⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠋⡠⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠈⠂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠂⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⣶⣤⣀⠀⣀⡀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡀⠀⢀⣠⣤⡦⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠥⠴⠔⠒⠓⠒⠀⠄⢀⠀⠀⠰⠶⠧⠦⠤⠭⠽⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⢠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡆⣿⣿⣿
⠀⠀⠀⠀⣴⣄⠀⠀⠻⣿⣴⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣷⣼⡿⠃⠀⢀⣴⡄
⠀⠀⠀⠀⣿⣿⣧⠀⠀⠈⡙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣉⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠘⢿⣿⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣼⣿⠟
⠀⢸⣷⣦⡀⠀⠈⢉⣙⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⣉⠉⠀⠀⣠⣶⣿
⠀⠘⢿⣿⣷⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣰⣿⣿⠟
⠀⠀⠀⠉⠻⠛⠛⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⠛⠻⠋⠁
⢿⣷⣶⡄⠀⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⣴⣶⣿
⠈⠻⢿⣿⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⠿⠋
⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠁
⢺⣿⣿⣶⣌⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣎⣴⣾⣿⣿
⠀⠙⠛⠿⠿⢟⠋⣠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡈⢛⠿⠿⠟⠛⠁
⠀⠀⠀⣀⣀⡈⢤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣧⠌⣀⣀⡀
⠀⠀⠻⣿⣿⣿⣾⣿⠋⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠈⢻⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠉⠉⠁⠈⠢⣸⣿⣿⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢸⣿⣿⡠⠊⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⠃⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⢻⣿⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠙⠢⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⠚⠁⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⢿⣿⣿⣷⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣯⣥⣤⣤⣤⣤⣭⣽⣶⣦⣤⣤⣤⣤⣤⣤⣶⣾⣭⣥⣤⣤⣤⣤⣭⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣡⣨⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣭⣭⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⣫⡞⠁⠀⣈⣙⡛⠛⣫⣤⡄⠀⠠⣴⡶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢫⣾⣿⠀⠀⣾⣯⣿⠏⠀⢙⡛⠁⢠⡀⠘⣿⣮⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠛⠁⠀⠀⠉⠀⣤⡶⣫⡿⠀⢀⣾⢿⡆⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⢀⡄⠀⠀⣰⣆⠀⢸⣿⣱⣿⡇⠀⠘⢿⡾⠃⢸⡶⣄⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣳⡏⣿⡀⠀⢿⣿⣷⠘⢿⡿⠟⠁⢠⣄⠀⠀⠀⣼⣿⢹⣷⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⡇⠀⣬⣉⠁⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠘⢿⣼⠏⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠀⠀⢷⣿⣷⠀⢀⠀⠀⠈⠛⠡⣾⣿⣦⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⡄⠀⢉⣽⣶⡞⢶⠁⢀⣴⡆⠀⠉⠁⠲⣴⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣘⣇⡀⠛⠻⠛⠁⠸⡆⢘⠛⢁⣠⠔⠁⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⠷⠉⠳⢲⣦⣄⣀⣧⣾⠞⣿⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⠃⠙⣿⠁⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠭⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠤⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡆⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉
⠀⠀⠀⠀⠀⠀⠃⣆⠄⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡐⠀⠀⢀⣀⡀
⠀⠀⠀⠲⣶⣄⢠⠉⡼⠟⢱⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢡⡀⠐⠛⠛⠁
⠀⠀⠀⢀⠀⣀⠰⡆⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠠⢿⠁
⠀⠀⠀⠈⠀⡵⠀⢩⠩⡤⢹⡿⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠶⠌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠃⠸⠃⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢿⠁⠏⠰⢤⡿⠏
⠀⠀⠀⠀⠀⢦⣴⣶⣤⣳⡀⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄⠀⠀⡀⠈⠀⡰⠃⡀⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠉⠣⡀⢻⡏⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣠⣾⠇⢀⠔⠑⠿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣤⡤⠌⠦⣄⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⣿⣟⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠒⠗⡀⠽⣄⡀⠀⠀⠀⠠⠶⠃⠀⡠⠶⠒⠋⠒⠾⠷⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠶⠦⢄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡠⠊⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⡇⠘⢀⣾⢂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢘⠀⢱⠀⠀⣧⣆⣼⠿⠁⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠟⠀⠀⠀⡇⠀⡇⠀⣻⠿⠧⠔⢊⣁
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢠⠉⠸⡀⠀⠀⢳⣀⡇⢠⡣⠔⠊⢉⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⡀⠀⠀⠀⠀⠸⡀⠀⢱⠀⠀⠈⣿⣡⠋⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⠢⣀⠀⠀⠀⢣⠀⡈⡇⠀⢀⣾⠿⠁⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡈⠓⢄⠀⠀⠳⣷⡇⢠⠞⠁⣀⠤⠔⠒⠀⢀⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⢤⡀⠳⡀⠀⠘⣷⢋⠔⠋⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⣀⡀⠑⠢⣍⡢⣵⠀⢰⣿⠛⣁⣀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠉⠒⢄⠀⠉⠛⢷⠏⠉⠁⢀⣀⡤⠤⠤⠶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⢕⣄⠀⡏⣀⠴⠊⡉⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠿⠷⠿⠶⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⣀⡠⢖⢀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠸⣯⠁⣼⣟⣛⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣠⡄⠀⢠⣦⡀⠀⣠⠖⡋⢸⠇⠀⠀⠈⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⣞⣹⠇⠀⢨⣟⡇⢀⡷⠭⠴⠋⠀⠀⠀⠀⣿⠀⠀⢀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢸⠉⠁⠀⠀⠀⢻⣀⡟⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡾⠛⠶⠞⠛⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠸⣿⢸⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣤⣀⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⠈⠓⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡙⣆⠀⠀⢻⡏⠀⢠⠖⠖⢒⠒⣺⠏⡴⢲⠞⠉⠀⠈⠻⣦⠀⠀⣼⠁⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣻⡏⠀⠀⠈⡇⢀⣿⣾⣛⣋⣤⠟⠀⣿⡼⠁⠀⠀⠀⠀⢸⣇⣼⡏⠀⠀⠀⠀⢀⣾⣿⣃⡀
⠀⠀⠀⠀⠀⠀⣴⣶⠖⠛⠲⢆⢸⠀⠀⠀⣰⠖⠋⠀⠀⢉⣉⠀⠀⠘⠋⡴⠟⠀⡀⠀⠀⠘⣿⣿⠀⠀⠀⢀⣴⣿⠋⠀⠀⠈⡟⣷⡀
⠀⠀⠀⠀⠀⢸⠋⠥⠃⠀⠀⠀⠻⣄⠀⢰⡇⠀⠀⢀⡾⢿⡒⠽⣆⠀⣴⠥⢮⣉⡝⠀⠀⠀⢸⢿⠀⢀⣴⡿⠟⣥⠀⠀⠀⠀⠳⣈⣙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⠀⠀⠀⠀⠀⠀⢹⡎⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣿⠰⢊⡵⠋⢀⡴⢻⡆⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⣾⠏⣿⠀⠀⠀⠀⣰⢇⡼⠋⢠⠀⣿⢁⣼⣥⣴⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠃⢀⣿⣋⡴⠃⠀⢀⣠⢔⣥⡾⣥⣾⣿⠀⣷⠞⢉⣩⡥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢧⠎⠉⣿⡄⠀⡴⢫⡶⠛⠉⢹⡏⡿⢸⣿⣯⣤⣟⡛
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣦⣛⣎⣀⠀⢻⣆⣀⣠⡤⣄⠀⠀⢸⠀⠀⠘⢿⡊⢠⡏⠀⠀⠀⠘⢧⣧⢾⠀⠀⣠⣼⣯⠽⠟⠛⣛⣡⣲⠂
⠀⠀⠀⠀⠀⠀⠀⣿⠖⠲⠤⠊⠁⠉⠙⢿⣿⣦⣉⠙⠛⣷⠀⢸⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⣹⣎⠴⠚⠙⠦⣤⣤⣤⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣌⠛⠉⠉⠱⣼⣆⠀⠀⢸⡇⠈⣇⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠘⢿⣧⠀⠀⣿⠀⠘⣄⢴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠘⡏⢧⡀⠸⡆⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣭⣛⠀⠉⠙⠓⢤⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠹⡇⠀⢀⡄⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠘⣃⣼⣭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠀⢀⣟⣀⡤⠤⢤⣀⢛⣋⣛⣳⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣸⡶⣫⠟⠁⠀⠀⠀⠉⠱⢌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣿⡼⠁⠀⠀⠀⠀⠀⠈⠒⠈⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠝⠊⠁⠹⠊⠀⠒⠂⠀⠀⠀⢀⡟⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠲⠔⠦⠶⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠗⠀⠀⠊⠙⠉⠁⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠀⠀⠀⠴⢊⡤⠄⠤⠴⠀⠀⠀⢀⣀⣀⡀⡰⡀⠈
⠈⠁⠀⠀⠈⠉⠋⠉⠀⠀⢀⠰⠒⠉⠉⠒⠒⠤⣀⡀⣀⡀⡀⠀⠴⠿⣷⡄⢀⣠⣴⡶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠉⠉⠀⠙⣅⡀⣠⠖⢗⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠁⢀⠛⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠚⢄⢠⠔⠤⠀⠊
⠀⠀⠀⠀⠀⣀⡴⢧⡶⠒⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠑⠀⠀⠀⠁
⠀⠀⠴⠂⠉⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖
⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⢀⣤⣄⠀⠀⠀⠀⠀⠐⠄⠀⠀⠒⠺⠷⣼⢵⣶⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠦⠈⠀⢀⣶⣆⠀⠀⠀⣁⠸⢆⠀⠀⢀⡦⡽⣷⣤⣄⠀⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⣗⠒⠖⠈⠛⠋⣤⣀⡀⢀⠀⠀⠑⢄⠀⠀⠀⠉⠖⠀⢉⠀⠶⠆⠀⠀⠠⡀⠀⠀⢼⡷⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⣰⢛⣛⣁⣬⣈⣳⣶⠶⠿⠦⠤⠶⠲⢴⠿⣿⠦⠴⠿⠶⢤⣽⣤⢤⣀⡀⢀⣴⠆
⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⠉⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠒⠒⠂⠛⢷⣌⠉⠉⠛⣦
⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⠂⢠⣤⣄⠘⠀⠀⠈⠾⠀⠀⠔⡆⠀⠀⠀⢀⣀⠰⡆⠀⠀⠀⢀⣀⣹⣶⣦⣾⠗⠢⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢛⠛⠁⠀⠐⢀⡂⠂⠒⠚⠒⠶⢦⡄⣘⠟⠗⠐⢃⡬⠛⠉⠁⢀⣠⡤⠶⠋⠙⠒⢦⣌⡂⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡰⠇⠀⠀⠀⠈⠁⠀⠰⢷⠄⠀⠋⠐⠊⠡⠄⠚⢩⣄⡤⠒⠈⣉⠋⠀⠀⠀⠀⠀⣀⣼⠿⠶⣌⡑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⢩⣥⡄⠀⠚⠢⠀⠀⠀⠀⠴⢾⠉⠀⠀⠀⠀⠉⠲⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠐⠿⠋⠰⣦⡄⠀⠁⠀⣦⡀⠛⠋⠀⠀⠀⠀⢀⡴⣿⠀⢰⣿⡇⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⣆⡙⣃⠀⣼⠟⠠⠂⢰⡉⠛⠀⠀⠀⠤⠀⠀⠀⣴⡤⣔⠾⠋⣱⡌⠳⢀⣥⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠀⠀⠉⠀⠀⠈⢤⠄⠀⠀⠀⠀⢀⠤⠔⠊⣻⠿⠁⠀⠀⠀⠀⠛⠸⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⢠⣿⠀⠈⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣤⣆⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⠀⠅


⠀⡄
⠀⠄
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⡀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠃⠀⢠⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠐⡀⠀⠀⠀⢠⠘⠀⠀⢸⠀⠀⢸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢤⣇⠀⠹⡄⠀⠀⡏⢘⢂⠀⠸⡀⢣⣼⠀⠐⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀⠀⢹⡀⠀⡇⠀⠀⡂⠀⠑⣼⣃⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢪⣇⠄⢸⡇⠀⠑⣄⠀⡅⢀⢜⡁⠤⠐⠒⠒⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠐⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠄⡟⠀⡸⠀⠀⠀⣸⣮⡞⢁⠋⠀⣀⣀⣀⣤⠔⠂⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⠀⠈⢧⠀⠀⠀⠀⠀⣠⠤⠤⠤⢬⣳⣄⢸⡧⣶⣵⣾⣿⡟⠛⠻⣍⠙⠍⣋⠁⠀⢀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⡇⠀⠀⢠⠎⠀⠀⠀⠀⣀⣬⣷⡧⠶⡯⣍⠉⠉⠀⠉⠛⢿⢽⣑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡀⠀⣿⠀⠀⡇⠀⣀⣿⣀⣰⢥⣿⡾⠿⠯⠿⣇⠀⢣⣨⠧⠤⣄⡀⢆⠀⠁⠨⠻⣤⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⢠⡟⣠⠞⠋⠉⠀⠉⠻⣯⡝⠁⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠉⢾⢢⡀⠀⠀⠈⠓⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⡟⠁⠀⠀⠀⣀⣤⡀⠈⢷⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠂⡇⠈⠒⠤⢄⣀⣀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣇⠀⠀⠀⢸⠁⢂⡇⠀⢸⠠⣤⣤⡀⠀⢹⡀⡀⠀⢀⡴⠢⡄⣰⠇⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡣⠁⠹⣆⠀⠀⠀⠛⠉⠀⣰⠏⠓⠯⠭⠤⠶⠋⠑⢬⣦⣜⣧⣿⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡕⣀⣤⣔⢚⠛⢶⡦⠴⢖⠊⠙⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡜⠋⠁⠀⠀⠉⠙⠦⣤⣕⠲⡤⣀⣀⣀⣭⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⠉⢐⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⣴⠋⢀⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣸⠃⠀⠉⢿⠞⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡷⠺⠏⠀⠀⠀⢀⠟⠀⠀⢀⢠⣧⠻⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡷⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣾⣿⠀⠀⠘⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣤⣶⠀⣼⡀⠀⡀⠸⠿⣟⠀⠀⠀⠘⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⣠⡶⣿⡿⠋⠀⠙⠁⠀⠈⠶⣄⠿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠟⠀⠀⠀⠀⠀⠀⡀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡆⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⠀⠆⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣤⣶⣵⠊⢿⣶⣄⣄⠀⣀⠀⢀⣠⣤⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⠀⠘⢷⡌⠉⠛⠛⠈⢿⡿⣿⡿⠙⠃⣩⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡜⠀⠀⠀⠙⣦⡀⠀⠀⣀⣽⠟⢛⣤⣈⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣀⠀⢀⡉⠉⢉⠹⠠⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢻⡇⢼⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣿⠇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣿⣿⠃⠀⣠⡴⠁⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠟⠀⠚⠻⠃⢰⡟⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠐⣾⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠙⠛⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠈⣡⠆⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡶⠶⠿⠿⠿⣿⢿⣿⣯⡴⠞⠁⣤⠀⠈⠫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠔⣸⣿⠀⠄⢠⠇⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⣼⠟⠁⠀⠐⠛⢋⣁⣤⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣠⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺


⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢇⣠⠀⠀⠀⢴⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠁⠀⢀⣔⣉⣉⣁⣄⣀⡤⠚⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⢀⣤⡴⠞⠉⠉⠀⠘⣄⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠛⠲⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣼⣟⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⡾⠁⠀⠀⠀⠀⠈⢿⣴⠟⣿⢢⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠳⡴⠶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢀⣾⣿⠉⠳⡄⠀⠀⠀⢀⡴⠋⣸⡏⢳⡄⠀⠀⣠⠶⠶⠞⠋⠀⢿⡑⠉⠲⣄⠀⠀⠀⢀⣼⠋⠀⠀⠀⢀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣦⣤⣴⠟⠀⣾⢧⣝⡦⠙⠳⢯⣁⣀⣀⠀⠀⠀⠈⣿⠂⣀⣈⡷⢾⣧⡾⠁⠀⠀⠀⠀⢺⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⢀⡴⣾⠉⠀⠀⠀⠀⠻⣄⡀⠉⠂⠀⠀⠀⠉⠉⠑⠄⠀⠀⠘⠛⠉⠁⠀⢾⡈⠛⠶⣤⣤⣤⠞⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⢀⣿⡆⠀⠀⠀⠀⢠⣜⣯⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡄⠀⠀⣸⠃⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⢸⣿⣧⠀⠀⠀⠀⠈⢿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⡀⢻⡄⣿⣇⠀⢠⣿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⠀⠀⡄⠘⣧⠈⠓⠦⣄⠀⣤⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⣿⡀⢹⣿⣿⣠⣯⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣷⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⣿⣧⠀⠀⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣏⢢⣄⣸⣿⡄⠙⢦⠀⠀⠀⢸⣿⡇⠀⠀⢠⣿⣿⣿⠀⠀⣾⣿⣷⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⡁⠀⠀⣾⣿⣿⠀⠀⣾⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣍⣻⠋⢲⡾⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⢢⠁⢉⠁
⠀⠀⠬⡕⡀⠀⠔⣱
⠀⠀⠠⢅⡂⢸⠀⠀⢀⠰⡀⠠⠕⡀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢺⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠇⠘⠎⠀⠌⠣⣀⠔⠈⠁⠂⡄⠠⠗⠀⢀⠀⠀⠀⢀⠃⠁⢢⡤
⠀⡴⠀⠁⠥⠁⠀⠘⡇⢀⢀⡀⠈⠁⢀⣀⠏⢂⠐⠀⠄⠁⠀⠠⠡
⠀⠈⡁⡞⠃⣰⣧⣾⠿⡋⠛⠷⣴⠞⠉⠉⠱⠄⠄⡠⠒⠂⠠⠀⢠⠉⣉⠀⠀⠀⠀⣠⣀
⠀⠀⠉⢣⣼⠏⠁⠀⠀⠀⢐⡍⢹⠀⠀⠰⣤⠓⢲⠃⠀⠀⣤⠲⡆⠈⠀⠀⠀⢰⠒⢌⣴⠂⡄⠀⠀⡀
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⢀⡈⠢⢛⠈⢴⢂⡴⠛⠛⠓⠶⡥⣤⢬⡀⢐⠰⡀⠈⠗⠈⠊⠉⢀⠈⠀⣘⠂
⠀⠀⠀⢀⣿⣷⣶⣶⣦⣴⣏⣀⡀⠈⢉⣠⣾⣥⡴⠶⠶⠶⠾⣤⣆⣈⣠⡴⠒⠋⣒⠂⠐⠀⣈⢈⣒
⣠⣤⣾⣿⣿⣋⣉⣉⡉⠉⠙⠛⠛⡻⠿⢯⣍⡀⠀⠀⠀⠀⠰⠂⠄⠀⠈⠉⢩⡫⠈⠑⠠⠍⡀⠀⠐⡀
⣿⠿⠟⠁⠀⠉⠉⠈⠉⠲⢤⠀⠈⢈⠀⡆⠀⠉⡓⡲⠤⠄⠀⠌⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠁
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠃⠄⠄⠊⠀⠀⠀⠈⠁⠀⠀⠒⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢡⡄⣴⡧⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⣦⠠⣀⣾⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠃⠘⢱⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⣇⣽⣿⣿⢴⣿⠀⠀⣄⡀⠀⠈⡀⠀⡄⠀⡀⢧⠶⣀⠀⠈⢿⡆⡀⠁⠀⠀⠀⠀⠀⢸⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⣿⠋⣉⣽⡿⢿⣿⣥⣼⠏⡐⠇⣈⠓⢤⠀⠉⠀⢀⡠⠝⠃⠀⠻⠷⣆⠈⣿⣧⠀⠀⡀⠀⠀⠀⢀⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠤⢹⣟⣿⠇⣡⣤⡟⣻⣴⠖⢙⣇⡀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⢹⣆⢸⠏⠈⣶⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⢠⠀⣘⣷⣷⣴⣨⢻⡿⢘⠉⢰⣤⣿⣿⢿⣤⣿⠟⠛⠻⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⡀⠀⠁⢀⡾⠀⠀⣏⠈⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⡐⢉⠋⠉⠛⠻⠌⣧⠘⠀⡙⠉⢉⠙⣾⠋⠀⠀⠀⠀⠸⡄⠀⠀⠀⣀⠀⣠⠟⠉⠉⠀⠀⠀⢈⠿⠟⣸⡿⠶⣶⣦⣠⡔
⠀⠀⠀⠀⡀⢠⡟⠁⢰⡶⠒⢻⣿⣇⡉⠷⢧⣠⣄⢀⣼⠛⣲⠒⠲⣄⠀⠀⠹⣦⣴⣾⣿⣾⣏⣀⣀⡀⠀⠀⠈⢀⠀⡴⠋⡢⠀⠉⠛⠉
⠀⠀⠀⠀⠈⢻⠁⠀⠘⠃⠢⠈⣿⣷⠔⢢⡾⠷⣤⡶⠁⡾⡇⠀⠀⠈⠳⣦⣼⣿⢻⡤⠂⠈⣿⣿⣿⡝⠻⢶⡛⠄⠋⠀⢀⠃⠀⠀⠀⠀⣠⠐⠂
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠾⣛⣳⡾⠉⠀⣿⡆⠛⣦⠀⢀⠀⠀⠀⠀⠈⢿⣷⡜⠓⠀⣠⡿⠷⡄⠀⠀⡀⢁⡖⠀⠠⣾⣷⣿⠂⠀⢀⠀⢄⡠
⠀⠀⠀⠀⠠⠛⠻⢷⠠⣄⣀⠈⢿⣿⣷⣈⣼⣿⡀⠀⠙⣀⡀⠀⢀⡀⠀⠀⢀⠟⠻⠿⡟⠉⠀⠀⠀⠠⣤⡿⠉⠠⣆⠀⠉⣉⠻⢦⡄⣠⣽⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⡾⠛⠛⠛⠙⠛⣷⡀⠈⠉⠀⠠⠾⡿⣿⠿⠋⣀⠄⠀⠀⠀⠀⠠⡆⠸⠿⠃⠄⠀⠛⠚⣷⡍⠁⠀⠹⣯⣅⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣽⣁⣤⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣶⣤⠀⠀⠀⠄⡶⠀⠀⠘⡿⠀⠲⡷⡝⠛⠇⠀⠸⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣀⠀⠉⠛⠿⣶⡀⠀⠀⠀⢠⣤⣶⣶⡶⠶⠶⠦⢄⡈⣿⡇⠀⠀⠀⢰⠀⠉⠰⣃⠀⠀⠀⠠⡀⠀⣤⡀⣀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣄⣿⡇⠀⠀⠀⡌⠉⣠⣤⣤⣤⣀⠀⠀⢠⡟⠀⠠⠆⠘⡖⢧⡄⠀⠉⠀⠀⠈⣤⠿⣆⠁⠙⣧⡉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣹⣿⡿⠻⢿⡇⠀⠀⣾⠃⣼⠟⣿⣿⣿⣿⣷⠀⠈⣿⡀⠀⠰⢦⣄⡈⠉⢿⣦⣄⣠⠄⠁⢀⡄⠀⢴⣿⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠁⠀⠀⠀⣼⠀⠀⠀⠄⠀⠉⠀⠻⠿⠿⠿⠋⠀⣴⣿⣿⠇⡤⠀⢼⡏⠀⠘⠋⠉⠛⡿⠗⠤⠖⠀⢀⣦⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⠁⠀⠀⢃⠀⠈⠀⠈⠁⠀⣄⡀⠀⣠⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡿⠛⢧⢠⣤⣽⡄⠀⠈⣿⡶⢶⡟⠉⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿⠀⠺⠦⢸⡗⠀⠀⠀⠀⠀⠀⣸⣿⠘⣿⡟⠁⠀⢀⡤⢳⣿⣿⠛⢻⡏⢀⠀⣠⣶⠶⣿⣟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢿⣤⣿⠃⣠⣴⣿⠁⣿⢿⣿⡀⡜⠀⣿⣿⣥⠀⣤⢻⠘⡏⠈⠢
⠀⠀⠀⠀⠀⠀⠠⠶⡀⠀⢀⡀⢻⠀⢠⣴⠞⠓⠂⠠⣀⡀⠀⠀⠀⠀⠀⠈⣿⠀⠹⣿⣷⣿⣏⡿⠀⢽⣿⣿⣿⠷⠺⢀⠻⣎⡛⠳⠴⠞⣁⡴
⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠲⠊⠹⣇⠀⠻⣿⣛⣉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠈⢷⣤⣿⣿⣿⠇⠻⢀⠈⠀⣿⠃⡀⠒⠔⠀⠈⠙⢿⣷⠞⠋⠞⠁
⠀⠀⠀⠀⠀⢣⠀⠀⢸⠀⠀⠀⠀⢹⣆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡿⠋⠁⠛⢁⡄⠀⣄⢉⡃⢠⣀⢠⡦⠘⠆⣀⡀⠦⠀⢙
⠀⠀⠀⠀⠀⣄⠈⠀⢀⡀⠀⠀⠀⠀⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡏⠸⠏⠀⠁⡀⠀⠀⡄⠀⠀⠀⢙⠉⢧⣀⠀⠀⠀⠀⡠⠆⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠸⣿⢹⣿⢣⣶⣤⣤⣶⣶⡿⠟⠛⠋⣹⡿⠻⣦⡄⡄⠀⠒⠀⠀⠀⠁⠀⠀⢀⢰⣄⠼⠋⠙⠁⠛⡿⠁⠠
⠀⠀⠀⠀⠀⠀⡴⠶⠄⠀⠨⡤⠀⠀⠻⣌⣳⣸⣿⢿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠜⡿⠃⣺⡄⠀⣀⠄⡠⠄⢀⣶⣭⡿⠿⣶⡇⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⣀⠃⠈⠀⠷⠈⠯⢻⣷⣿⣦⡀⠀⠀⠀⠀⠀⡼⢣⡄⣴⣶⣿⣿⣧⢸⡟⠀⠀⠈⠻⠋⠀⠀⣿⣷⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠹⠀⠀⣠⠶⡀⠈⠿⣿⠉⢻⡄⠀⠀⠀⢸⣷⣿⣇⠿⡿⠛⠉⢁⣾⣷⣀⡀⣠⣴⡀⠀⠠⢿⣿⡇⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠑⠶⣾⢿⣆⣼⠇⠀⠀⠀⠘⣿⡿⠈⠀⠀⠀⠴⣬⠛⠋⠉⠉⠸⠿⢄⠀⠀⠀⠈⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⣤⣴⢶⠞⠙⠂⢹⠟⠀⠀⠀⠀⠀⢿⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⢰⣤⣴⠾⠃⣠⣤⡄⣩
⠀⠀⠀⠀⠀⣀⣤⣶⡦⢀⠤⠿⡂⢸⣿⡁⠂⡀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠈⢷⡈⠙⠿⠐⠀⡄⠀⠀⠀⠘⣧⡀⠀⣸⣿⡿⢰⡆⢠⠆⠀⠀⠒
⠀⠀⠀⣠⣾⣏⣩⡟⠀⠀⣰⣿⣿⣿⣿⣷⣾⣧⠀⠀⡟⢳⡤⡀⠀⠀⠀⠀⠀⢳⡄⢠⡄⠀⠀⢠⣶⠀⢠⡿⠿⣿⣿⣏⠑⠀⠁⢀⣁⠐⣚⣡
⠀⢴⡾⢿⡿⠟⣿⣷⣾⣿⣿⠋⠛⠻⠿⣷⣽⣧⠹⠖⠀⠈⠣⠀⠀⢠⠀⠀⠀⢀⡷⠉⠀⠀⠀⠸⠃⢀⠀⠀⠐⢈⣿⠻⢤⣀⠘⠣⠅⠀⠈⠁
⠀⠀⠀⠀⢳⠀⣿⣣⠛⠹⠫⡇⣀⠒⠀⢨⠿⣿⠓⠆⠀⠀⠀⢰⡀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡴⣛⠀⠀⠀⠘⠛⠀⠀⢨⠁⠀⢰⢶⡆
⠀⠀⠀⠀⠀⠀⠹⣇⠀⣶⠀⠂⣜⠿⣶⣶⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠃⠀⠀⠙⠂⠀⠘⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢠⠙⠃⠄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢏⡆⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣩⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡜⠿⢣⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣩⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⣾⣷⣦⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⣠⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢻⣶⡻⣿⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣙⣛⣛⣻⣩⣟⣻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣽⣭⣽⣯⣿⣯⣯⣯⣭⣻⣿⣽⣿

⠉⠀⠀⠀⣀⣆⣿⣿⠃⡠⢀⣤⣾⡩⠴⢴⠊⠈⡱⠤⣈⣱⣄⢀⡾⢑⠤⠤⢦⣤⠤⠞⠁⠀⠓⠄
⣖⣛⣛⣭⣥⣼⣿⣿⣿⣿⡿⠿⣶⣶⣴⣇⣀⠀⠀⠀⣣⣠⣤⠟⠓⠶⣒⠒⠛⢄⠀⢀⡠⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣟⠉⠉⠉⠉⢩⡟⢉⣉⡹⡈⠉⢿⡿⢷⣾⡛⠹⣄⣠⠖⠛⠒⠛⠶⠖⠛⠛⠗⠒⠒⠛⠊⠓⠄
⠋⠙⢦⣏⠻⢷⣾⣶⣄⣾⣠⣴⠶⠚⣟⠛⠲⣤⠶⠒⠛⢿⣙⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢀⠠⠀⠀⠀⠂⠈
⠀⠔⠡⠈⠉⢉⣽⡿⠟⡟⠛⠻⣷⢶⣿⡀⠀⢀⣀⣄⣀⡠⢹⠓⠶⢦⡤⠦⢤⣴⣮⡥⠤⠬⠄⠄⠐⠒
⣤⣤⣴⠶⠟⠋⠁⢇⣸⠃⠀⡰⢩⠛⠚⣟⠛⢿⣅⣀⣤⣤⣤⣥⣀⡀⢹⠄⠀⠀⢀⠌⠑⢄⣀
⣿⣿⣧⠀⠜⠉⠀⠈⣟⠀⠀⠹⡌⠢⡀⠀⠱⡀⠙⢧⡄⠀⢳⠄⠙⠛⢾⠦⣼⡁⠀⠀⠀⢀⡀⢁⡠
⠈⠛⢿⣿⣤⣤⣀⡞⠸⠗⠦⠮⣧⡀⠀⠀⠀⠀⣀⣤⠇⠀⠯⣄⣀⠀⢸⡤⢄⡉⡑⠉⠀⠈⠁
⠀⡎⠀⢹⣿⣗⠪⠀⠀⠀⠀⠀⠈⡟⠐⠀⢠⠜⠱⣏⡀⠀⠀⠀⠈⠳⣄⡇
⠆⠀⢠⡞⠛⠻⠷⣤⣑⢀⡤⠴⢤⢤⡤⣶⡃⠀⠀⠀⠹⠉⠁⠀⠀⣠⠟⢱⠤⠤⠒
⣇⣀⠀⢳⠀⠀⠀⢈⡟⠛⠓⠶⠶⠶⣤⣀⡉⠀⠀⢀⠠⠠⠄⠀⢀⠓⢄⠈⠂⢀⠀⠀⠠⠄⠀⠀⠀⡀⡀
⠀⢹⡀⠺⠤⡀⠀⠈⣇⣀⠀⠀⠀⠀⠎⠻⣯⠝⠒⠦⠤⠔⣋⠉⠙⠀⠀⠀⠀⠈
⠀⠟⠀⠀⠀⠀⠂⠀⠀⠙⣦⡀⠠⠀⠀⠀⠘⢷⣤⣀⡘
⠀⠘⠀⠀⠀⠀⣠⠤⡤⠞⡃⠉⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣾⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠉⠉⠻⠋⠉⠉⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣬⣿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⣧⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠻⢿⣿⣿⣷⡀⠀⠀⣠⣿⣿⣿⠿⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠙⠻⣿⣿⣦⣾⣿⡿⠛⠁⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠆⠀⠀⠀⠀⣨⣿⣿⣿⣏⡀⠀⠀⠀⠀⠺⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⣴⣾⣿⡿⠋⠻⣿⣿⣦⣄⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣾⣿⣿⣿⠟⠀⠀⠀⠘⢿⣿⣿⣿⣶⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣤⣤⣾⣦⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠟⠿⠿⠿⠟⠋






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⣠⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⢤⡰⠶⡉⠶⡖⠃⠀⠀⠀⠀⠨⠈⡏⠀⠀⠀⠐⠶⠀⠀⠀⠚⠓⠒⠋⠁⠀⠀⠀⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⢀⣠⠀⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠲⢷⠶⠶⠤⠄⢸⣧⠀⠀⠋⠀⠀⢀⣐⣟⢿⡉⢻
⠀⠀⠀⠀⠀⠀⠈⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢖⡂⠀⠀⠀⠀⠀⠘⠧⠀⢳⠀⣤⠀⠀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠐⠏⠁⠀⠀⠈⠀⠀⠀⠀⠀⠸⢠⠟⣠⡾⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣛⠄⠀⠀⠀⢰⠋⠁⠆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠊⠁⠀⠰⠦⠀⠀⠀⠁⢀⠈⠁⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠐⠁⠀⢀⡖⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢴⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡅⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠄⠶⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠲⠔⠛⢓⠤
⠀⠀⠀⠀⠀⠀⠠⡀⠠⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡦⣤⣄⢀
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡔⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣹⠷⣶⣋⠈
⠀⠀⠀⠀⠀⠀⠁⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⡽⠄⠀⠀⠐⠀⠀⠰⠷⠃⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⢲⣀⡶⡀⠀⠀⣀⡀⠀⢿⡧⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣬⣲⢄⠀⠀⠀⠀⢠⣤⣤⣿⣠⠀⠀⠀⣒⣒⣿⣯⣡⡿⣶⠀⠀⠿⠏⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠰⠿⠭⠿⠛⠁⠀⠀⠐⠛⠙⠻⠉⠛⠃⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠘⣿⡩⢋⡵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢹⡔⢋⠔⡩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢘⡗⡡⢊⠔⣩⠛⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣟⡡⠀⠀⠀⠰⣯⢊⠔⡡⠚⡠⢊⠔⡩⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢹⡶⢁⠄⠀⠀⠙⣧⠊⡠⢊⠔⡡⢊⡴⢋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⠀⠀⠀⣿⡡⠂⠀⠀⠀⠘⣧⠔⡡⢊⡴⢋⠔⡡⢊⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠹⣏⠄⠀⠀⠀⢻⡔⣡⠀⠀⠀⣰⡧⢊⡔⣻⠃⡡⢊⠔⡡⠆⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢸⡖⡡⠀⠀⠀⢻⡤⠀⠀⠸⣏⠴⢋⠔⡿⣄⣀⠁⠈⡠⢊⠔⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⣏⠔⡡⠀⠀⠀⠛⠀⠀⠀⢿⠘⡡⢊⠔⣩⢹⣆⠀⠀⠡⠊⡴⢛⠖⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣾⡡⠊⡠⢊⠀⠀⣄⠀⠀⠀⢸⣆⠔⡡⠚⡠⢊⢿⡀⠀⠀⠁⠔⡡⢊⠔⣳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡀⠀⠀⠀⢹⡧⢊⠔⠁⠀⠀⣯⠔⡀⠀⠀⢻⣌⠠⢊⠔⡡⢚⡇⠀⠀⠀⠈⠔⣡⠞⡡⢛⣆
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢠⡟⡀⠀⠀⠀⢿⡡⠊⠀⠀⠀⢘⣯⠔⣡⠀⠀⠙⣶⣡⣮⡤⢊⢿⠀⠀⠀⠀⠘⡡⢊⠔⡁⠊⣧
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣾⠋⡀⠀⠀⠀⠈⣷⡁⠀⠀⠀⢸⡧⠎⡠⢊⠄⠀⠈⠉⠀⠻⣥⢺⡇⠀⠀⠀⠀⠐⡡⢊⡴⢋⠜⡆
⠀⠀⠀⠀⠀⣰⠁⠀⠀⠐⣷⢊⠔⡀⠀⠀⠀⠸⡇⠀⠀⠀⠈⣷⢊⠔⡡⢊⡤⠀⠀⠀⠀⠹⣯⠷⡄⠀⠀⠀⠀⡴⢋⠔⡡⢊⢽⡀
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢻⡥⢊⠴⣁⠄⠀⠀⠀⠀⠀⠀⠀⣸⡧⢊⡴⢋⠔⡀⠀⠀⠀⠀⢹⣊⠄⡡⢀⡀⢋⠔⡡⢊⠔⣁⠜⣧
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣼⠔⢡⠜⡡⢊⠄⠀⠀⠀⠀⠀⠀⢿⡴⢋⠔⡡⢊⠄⣠⠀⠀⠀⠈⣧⢊⡴⢋⠔⡡⢊⠔⢡⠞⡡⢊⠼⡄
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣿⠖⡡⢊⠔⡡⠊⠀⠀⠀⠀⠀⠀⠈⣷⡡⢊⠔⣡⠞⡁⠀⠀⠀⠀⢹⣋⠔⡡⢊⠔⣡⠞⡡⢊⠔⡡⠊⣵
⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠙⢎⠔⡡⠎⡠⢊⠀⠀⠀⠀⠀⠀⠀⢸⠔⣡⠞⠡⠊⠀⠀⠀⠀⠀⠀⠱⢊⠔⠡⠞⠁⠊⠀⠀⠈⠀⠊⠜⡇




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢢⣳⠀⠀⠀⡼⠁⠀⠀⢀⣠⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⡝⠀⢠⣞⣠⣤⣤⣼⠕⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⣀⡴⠛⠉⠀⠀⠀⠀⠉⠓⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠟⠉⢀⠤⠴⠒⠒⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣕⣡⠤⠶⣗⡒⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣚⠡⠐⠊⠉⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣩⠖⣋⡁⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⡡⠖⠉⠉⠉⠉⠩⣉⠃⠒⠀⠑⠀⠀⠀⣰⠟⠚⠉⠈⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣁⣐⣉⣀⣀⣀⠀⠄⠠⣤⠄⠉⢉⣁⣀⣤⡤⠎⢥⣭⣘⣲⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢀⣨⠤⠖⠒⠚⠛⠛⢾⡛⠉⠁⠀⠈⠛⠻⢥⡀⠀⢄⡀⠀⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⡠⠞⠉⠀⠀⠀⠀⢀⡀⠀⠀⠙⢦⠤⣄⣀⡀⠀⠀⢌⠓⠦⣈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⢀⡴⠋⠀⠀⠆⢀⢀⠀⣰⠞⣀⡀⠀⠀⠈⢷⠠⡀⠀⠀⠀⠀⠑⠤⣈⠑
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⠔⠉⠀⠀⠀⠀⢀⣾⡴⠾⠟⠳⠟⠉⠙⠢⠀⠀⢱⠘⡄
⠐⠒⠒⠒⠋⠉⠉⠀⠀⠀⠔⠁⠀⢀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠉⠑⠒⠂
⠀⠀⠀⢀⣀⡤⠤⠴⠆⠴⠶⠒⠶⠦⠭⠥⢤⣀⣠⣤⣄⣀⣀⡀⠀⣀⣀⣀⡀⣠⠖⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢀⠈⠀⠀⠀⠈⠉⠂⠀⠄⣒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⢄⡀⠀⠀⠀⠠⡀⠈⠑⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⡆⠀⠀⠀⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠘⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⠁⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⢒⡶⠛⢛⠛⠓⠒⠲⠦⣄⣀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⣰⠋⠀⣰⠋⠳⡀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⢀⡜⠁⠀⢰⠃⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⠸⡄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⣀⡴⠒
⠀⠀⠀⢀⡞⠉⠙⠲⠦⢤⣀⣞⡀⠀⣤⣀⠀⠈⢻⠋⠀⢀⣠⡄⠀⣤⣄⣠⠤⠀⠀⠀⠘⣆
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡼⠉⠉⠙⡇⠀⠙⠲⣼⡴⠚⠉⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⡆⠀⢀⣀⣤
⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢻⡀⠀⠀⢹⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉
⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠓⠒⢻⠓⠒⠋⠁⠀⠀⠀⠀⢀⣤⣀⡠⠤⠀⠀⢸⡄
⠀⠀⣿⠒⠒⠒⠒⠒⠒⣿⠒⠒⠒⠒⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠒⠒⠂
⠀⠀⢹⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⢤⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣄⠀⢸⠁
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠚⠉⠀⠙⠒⠒⠋⠀⠉⠓⠒⠋⠁⠈⠓⡟
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢳⣀⣀⣀⣤⠤⠤⠤⢼⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⡸⠁
⠀⠀⠀⠀⠱⣄⣠⠤⠖⠚⠉⢯⠀⠀⠀⠀⠀⠀⢸⠖⠋⠙⠲⠶⠚⠉⠓⠶⠶⠋⠉⠲⡾⠁
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠳⣄⠀⠀⠀⢸⣤⠴⠛⠦⣤⣤⠞⠓⢤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠈⠣⡀⠀⢸⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠚⠒⠒⠚⠋⠉

⡆⢢⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⡔
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠂⡆⢸⠀⡜⡄⡮⢅⠀⠀⠨⠀⠀⠪⡀⢹⠀⡅⡄⡎⠈⡂⡧⠁⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡙⣾⠃⠀⢀⣤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡅⠀⢰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠂⠀⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀⢸⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⡇⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣇⢸⣿⣿⣆⠀⠀⢀⡄⣰⢇⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⣿⣿⣿⡀⠀⢸⣧⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⡌⠻⣿⡿⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⡄⣀⠀⠀⣰⣿⡆⠀⠀⠀⠀⡇⠀⢘⡕⠁⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⡇⠀⠌⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠈⢻⣿⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡀⠈⠂⠻⠀⠀⠀⠀⠀⣧⠋⣠⣴⣾⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡄⠱⡄⠀⠀⠀⠀⡏⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠙⠛⠿⠿⢄⠑⠀⠀⠀⢰⠁⠀⢀⣤⠌⠛⠻⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠁⢠⠀⠀⡜⠀⡧⠬⠍⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠃⠀⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⢄⠀⢰⠀⢀⠾⠿⠿⠿⢿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢿⣿⣿⡎⣿⡿⢻⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⣾⡟⢿⡎⠻⣧⠈⠻⡈⠙⣎⠱⢆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣿⠀⢸⡇⠈⣿⡄⠙⣧⡀⢹⣦⠘⡷⢾⣧
⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⢿⠀⢸⣷⡀⢹⡷⠀⠘⠿⣤⡏⢻⣧⠈⠉⣴
⠀⠀⠀⠀⠀⠀⣸⡀⣾⡄⠻⠇⢀⠏⠠⣾⠀⠘⣷⡀⢹⣧⠈⢿⡀⢸⣯
⠀⠀⠀⠀⠀⠀⠛⣷⡌⢻⣷⠀⢻⣦⠀⢻⣇⠀⢻⣧⠈⣿⡄⢸⣿⣄⣿⡇
⠀⠀⠀⠀⠀⠀⢠⠈⢷⠀⣿⡄⠘⡟⢣⡀⢿⣆⣼⠁⣶⡟⢃⣾⠃⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠘⣀⠀⢶⣿⠃⣀⠀⠈⢡⣤⠙⣿⠀⣼⠇⠈⣿⠀⢹⠃⣸
⠀⠀⠀⠀⠀⠀⠀⢻⠗⢸⣿⡄⠘⢿⡆⠀⣿⡆⠙⣀⣿⡆⠀⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠉⢿⣷⠄⢁⣶⡉⢷⠀⣿⠋⢁⣀⠃⢸⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢾⣦⠴⣿⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠄⢣⣄⠙⢿⣧⠀⢰⣏⠀⢸⡿⠀⡈⢁⣘⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡟⢁⣾⠇⣴⠋⢘⡟⢹⡿⢣⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣄⡈⠛⠷⣄⡙⢷⠀⣿⠀⠘⢇⣸⡷⠾⠋⠉⠁⠀⠀⠀⢀⡹⠏⠀⠀⠀⠀⠀⠀⡀⠙⢿⣧⠈⠀⣾⠋⠀⠾⠇⠈⠁⢸⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣶⣄⣈⣿⣿⣷⣀⣤⣰⣿⠛⠓⠂⠀⠀⠀⣀⡀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡏⠀⣰⠿⣷⡆⠀⣾⠇⢀⡾⣆⣼
⠀⠀⠀⠀⠀⠀⣤⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⠟⠿⣷⡖⠒⠋⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡸⢿⡇⠘⣧⣤⡟⠀⣿⠀⢸⣿⣤⡈⢀⡿⠃
⠀⠀⠀⢴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠿⠛⣇⠙⣿⣿⡟⠀⢄⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⡇⠈⡇⢸⡏⢻⠇⢠⣶⣀⠇⠈⡏⠀⢘⣁⣀
⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⣻⠟⠉⡹⠋⢀⣾⠀⢿⠀⢻⣿⢹⣧⠀⠉⠀⠀⠑⠆⠀⠀⠀⠀⠀⢀⠀⠀⢸⣷⣄⣡⡜⠁⠈⣀⠶⠈⡿⠀⣠⣁⣰⡟⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⡎⠁⢀⠘⣿⠀⠀⠀⠀⠐⣷⠙⢡⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢼⠀⢶⠈⠛⠈⢿⡇⠀⣾⡟⠀⡀⠁⣠⠟⢉⡉⣠⡈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠇⠀⢠⡌⠀⢸⠀⠀⠀⣄⠀⢸⣶⠀⠙⠦⡀⠀⠀⡆⠀⠀⠀⠀⠈⣤⠀⣄⠘⡇⢸⣧⠈⢻⠀⢠⠿⠿⠁⢠⣾⠗⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠃⠀⠀⠘⠀⠀⠀⠋⠀⠈⢻⡄⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠉⣤⠉⡄⢠⣾⡿⠀⣼⡟⠁⠀⠃⣠⣾⣥⣴⣤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢀⡴⠋⠀⠀⠀⠀⠀⠻⣤⠟⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⡇⢠⡟⠁⣠⣿⠏⠋⠀⣠⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠶⠎⣻⣿⣷⣮⣤⡞⠋⢀⣀⡰⠾⠛⠉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⡁⠾⣿⡟⢻⡿⣿⠏⣉⣀⣀⣀⡀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⢀⣤⠂⠀⣤⣿⡇⠈⢰⠀⠲⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⠀⠀⠀⠘⠛⠘⠛⠀⠀⠀⠀⠀⣦⠀⠀⢠⡀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠁⠀⠘⢁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠓⣀⠁⠀⠀⠀⠈⢣⣀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠁⣀⠉⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡀⠀⠀⠀⠀⠀⠰⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠰⠀⠸
⠀⠀⠤⠀⠠⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢀⡘
⠀⠏⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠈⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠂⡐⠃
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣄⠁
⠀⠇⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠛⠋⠁⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠇⡀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠃⠀⠀⠀⠀⢀⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠶⠄⣀
⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠉⡄⠀⢰⡆⠀⢀⠴⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡄⢠⡄⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠁⡄⠀⠁⣀⠚⠀⠀⠀⣠⠐⠒⠀⠈⠁⠀⠀⠀⠀⠀⣐⠁⠸⠇⠀⢀⠀⠀⠉⡆⠀⠀⠀⢀⡀⠒⠂⠀⠀⠁⠀⠀⠀⢶⡆
⠀⠀⠀⠀⠀⠈⠃⣄⠀⠀⠀⠀⠰⡆⢸⡟⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠀⢰⡄⠀⠘⠀⠀⠀⠀⣄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠤⠄⠀⢠⣾⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡇⠀⠇⠸⠇⠀⠀⢰⠀⠀⠀⡟⠁⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠰⢿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⡇⠀⡄⠀⠸⠀⠀⠀⡀⠀⣸⠃⠀⢀⡰⠎⠉⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⣀⠴⠖⠈⠉⣀⠀⠀⠀⠈⢹⠿⣷⣶⠂⠀⠀⠐⠶⠂⠉⠀⠀⠀⠀⡇⠀⡇⠀⠀⠈⣤⠀⢻⣀⣧⡀⠒⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⡠⠊⠁⠀⠀⢀⠚⠁⠀⠀⠀⠀⢸⡄⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠈⢱⣼⣿⣇⠀⠀⠀⠀⠀⢠⣤⠒⠊⠁
⠀⠀⡴⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⣠⣾⣿⠛⣄⠀⠛⠻⠿⠂
⠀⡦⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠁⠀⡁⠀⢀⣾⠏⠀⠿⠀⠈⠃⡀⠀⠀⠘⢦
⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠁⠀⠁⢠⣾⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⡀⠀⠀⠀⢰⡆⠀⠀⠀⢻
⠿⡄⠀⠀⠀⠀⠀⠀⠀⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣀⠀⠀⡄⠀⣼⣿⠇⠀⠀⠀⠀⠿⠀⠀⠀⠈⠁⠀⠀⠀⢸
⠀⠘⠛⠠⠤⠤⠄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣀⠀⣧⠀⣿⡏⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠈⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣠⣿⠆⠉⠇⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠶⠆⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⣀⣀⡏
⣾⣷⣶⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣾⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶
⣿⣿⣿⣿⣿⠛⠋⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠐⠛⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣀⠀⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⣇⠀⡀⠈⢹⠀⠀⠀⠀⠀⠀⠈⢀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠀⠉⠖⣁⠂⢸⠀⠀⠀⠀⠀⠘⠄⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⣈⠁⠒⢚⣧⡔⠃⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡶
⠀⠈⠁⠲⣜⣫⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧
⠀⠀⠀⠀⠈⠁⠉⢉⡷⠂⣤⡄⠒⠒⠈⠁⠀⠀⠉⠳⣦⣄⣀⣤⣤⣤⣴⠶⠿⢷⣤⣀⣀⠀⠀⢰⡄⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⢀⠉⣠⠖⢰⡆⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠀⠀⠀⠀⠠⠶⠖⠉⠉⠙⠳⠤⣴⣇⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠠⠾⣤⣀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠿⠛⠛⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠒⠒⠒⢉⣥⣒⣤⣄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠀⠀⠀⡠⠞⠀⠀⡏⠉⠛⣿⣶⣤⣀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡦⠀⠀⢠⡞⠁⠀⠀⠀⡄⠀⠀⠁⠀⠉⠛⠻⠿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⢶⣶⣴⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠀⠀⠆⠁⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⢀⡿⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠜⠀⠀⣀⡠⠤⠎
⠀⣤⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠦⠔⠋⠻⠈⠁
⠀⠈⢻⣦⡀⠹⣧⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠙⢿⣦⣽⣷⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠀⢸⠋⠙⠿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣧⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣿⣿⣧⣾⣷⡆⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣽⠇⢸⣆⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣇⠌⣷⡀⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⠿⠿⠿⠛⡿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠉⣿⣀⡾⠃⣠⠿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⣼⣿⣿⡿⠇
⠀⠀⣤⣤⣤⣤⣴⣶⣾⣿⣿⠿⠋⠀⠀⠀⢠⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠙⣿⠁⣼⡏⠀⠙⠃⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣤⣽⣧⣹⣿⣯⣤⣶⣾⡀⢀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⠃⣿⠟⠁⣠⣤⣄⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣾⡏⠰⣾⣿⣿⡿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢿⣿⣿⣿⣷⠹⣷⣀⣠⣼⡿⠶⠿⣿⣻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡧⢾⣿⣿⣆⠙⠿⠛⠿⠆⢹⣿⠋⠀⡹⢶⣦⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⣋⠛⠛⠋⠀⠀⠀⠀⢀⣾⡏⠀⠀⣼⣿⣿⣿⣿⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠉⠙⢷⣄⡐⣆⠀⠀⢸⣿⡀⢠⣴⣶⣿⣿⣿⣿⡆⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣧⠀⢠⣿⡇⠀⠉⠿⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⡿⡿⠃⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠉⠓⢲⠖⠦
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⡄⠛⠀⠀⠀⠀⠰⡤⢦⡄⠀⠀⠀⠀⣴⡀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣷⣼⣯⣤⣿⣾⣿⣦⣄⣤⣀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣴⣿⡿⠿⠿⠖⠛⠛⠓⠂
⠀⠀⠀⠀⣀⣠⣶⣶⣾⣿⡿⠛⠛⢿⣿⠉⠉⠛⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⢀⣀⡤⠤⣘⣳⠶⠛⠋⠉
⠀⠀⠀⢀⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠴⠶⢶⣿⣿⣷⣶⠶⠶⠶⠿⢿⣥⣶⣾⣭⣁⣀⣀⣀
⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠉⠁⠀⠤⠤⠤⣤⣤⣾⣿⣿⣿⣶⣤⣤⣄⣀⣀⠀⠀⠉⠉⠉⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠿⠿⣿⣿⣿⣶⣦⣈⠛⠛⠿⣿⣷⣶⣶⣶⣤⣤⣀⣀⣀
⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣏⣿⣿⣷⣶⣤⣌⣛⣠⣌⣙⣛⣫⣭⣭⣙⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣷⢾⣣⣼⣯⣹⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⡀⠀⢀⡀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠸⠀⠀⢤⠀⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡄⠀⠀⠀⢇⠀⠸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⢆⠀⡇⡆⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠢⣄⠀⠀⠀⠈⠣⡷⠁⠀⠀⢀⡴⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠐⣄⠈⠳⡀⠀⠀⠀⡇⠀⠀⡰⠋⢀⠎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠘⡄⠈⢦⡀⠹⡀⠀⠀⡇⠀⡜⠀⡠⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠈⠲⠤⣙⣦⡇⠀⠀⡇⢰⣡⣚⣀⠴⠊⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢤⡀⠀⠀⠀⠀⠀⠈⠓⢴⠗⠋⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⠈⠳⡄⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⣀⣀⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠈⢦⠀⠈⡆⠀⠀⠀⢀⠇⠀⢀⡤⠒⠉⢁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠱⣄⢸⠀⠀⠀⡞⠀⡴⠉⢀⡠⠔⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢄⠀⡜⢀⣸⣤⣚⣉⣀⡠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣶⠶⠖⠀⠀⠸⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠴⠋⠉⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⢀⣼⡆
⠀⠀⠀⠀⠀⠀⠰⣶⡟⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⣰⣿⡁⠠⠀⠀⠀⠀⠀⠀⢸⡁⠁
⠀⠀⢀⣀⣀⡀⠰⣿⣷⣀⡀⠠⣤⣤⠔⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠
⠀⠀⡏⣙⣿⣹⣿⣻⣧⣼⣷⠀⠁⠀⢀⡔⢶⣳⢤⡀⢠⣔⡆⢢⡄⠀⢸⡏⣠⠶⣶⠶⣄⠀⢀⠴⢶⡶⢦⠀⠛⠶⠆
⠀⠀⠙⠟⠛⠛⠛⠿⠛⠻⣿⡀⠀⠀⠘⣷⣾⣿⣾⠃⢠⣼⣿⣿⡟⠀⠈⠁⢻⣤⣿⣷⡿⠀⠸⣦⣼⣷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡠⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠐
⠀⠀⠀⠀⠀⢀⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢐⣿⠿⠋
⠀⠀⠀⠀⢀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠂
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢀⠴⢾⡶⢦⠀⠀⠀⡴⢶⣷⢢⡄⠀⠀⢀⡔⠶⣴⢦⡀⢠⣜⣖⢲⡄⠀⡾⠀⢠⠲⢮⡖⢦
⠀⠀⠀⠀⠀⠀⠘⣦⣾⣷⣾⠀⠀⠀⢧⣶⣿⣾⠇⠀⠀⠘⣷⣶⣿⣾⠇⢰⣴⣿⣿⠟⠀⠀⠀⠸⣶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈
⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⡀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⣷⠀⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠙⠀⢋⡀⠂⣼⡇⠀⠀⣠⡀⠀⠀⠀⡀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠗⠂⠂⠙⠶⡟⠁⢠⣾⡟⢸⣦⣰⡾⠃⣀⠀⠰⡿⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⠔⣀⠿⠋⣷⠀⠻⠿⠷⠒⣿⣇⠐⠀⣼⠏⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠉⠛⢉⣀⠈⠀⠀⢿⣁⣠⣤⣄⠀⠈⠙⢀⢰⡁⠄⢛⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⢸⡆⠀⠾⠛⠿⠟⠠⠀⠀⠉⠉⠉⠉⠉⡀⠀⠠⠘⣧⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠸⠇⠀⣾⡆⠀⢀⠀⡄⣠⡾⢀⣠⣤⡤⠙⠿⠦⢀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠟⣫⣶⣶⣃⣂⡹⡇⠀⣿⡆⠃⣿⢃⣛⡛⠉⠶⣶⣦⠀⠘⠚⠛⣿⠛⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⢠⣵⠆⠀⠢⢙⠀⠠⠃⠛⠛⠿⡆⠀⠘⠛⠃⠀⢀⡾⠃⣠⣿⣴⡶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⢿⡟⠀⢀⣴⠈⠀⡂⠀⣠⡆⠀⢰⡄⠀⡄⠁⠀⠘⣶⣤⡀⠈⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⡇⠀⠁⠀⠸⣿⢠⡆⢡⣸⠟⠀⠀⠈⢣⣬⣀⠀⠀⣾⡇⠙⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢸⣿⠀⢡⠀⢠⣾⠴⣤⠌⣿⡅⠀⠟⢀⣴⠂⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠦⠙⠀⠀⠱⡿⠃⠀⠀⠀⠻⣧⠈⠀⠾⠃⢠⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⢰⣦⠀⡀⣠⣶⠞⠀⠀⠀⠀⠠⢸⡄⢂⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉⠀⠀⠙⠧⡀⠉⢁⣠⠀⠀⣦⣄⠀⠘⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⠀⠀⣠⣤⣤⣀⠀⢰⡿⠃⢀⣀⡈⠛⠛⡔⢀⣤⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠓⠀⠀⢀⡢⠀⠄⠙⠛⢻⣀⠂⢀⣠⡌⠉⣿⣧⠀⠀⠉⣩⡏⢁⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⠋⠀⠙⣻⡶⠐⣒⣦⣙⠂⡾⠟⠀⠀⠀⠁⠀⠀⡸⠋⠀⠾⣷⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⢀⡾⠟⠁⢸⠟⠋⠁⠈⡀⣰⡿⢋⡴⢁⣐⡀⠙⢷⣦⡀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⡶⠄⠖⠉⠀⣠⠾⢟⣋⡀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⡀⠊⠁⠘⢷⣮⠛⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣶⣶⣶⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹
⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⣸⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀
⢠⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣶⣾⣿⣿⠿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⡿⠁⡼⡀⠀⠀⠀⠶⣶⣶⣶⣿⣟⠉⢿⣿⣏⠁⡀⠉⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣦⡀
⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⡁⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⡿⠿⠟⠉⠙⢹⣷⣴⣄⣤⣄⡀
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⠉⠀⠀⠉⢻⣿⣿⣶⣤⣶⣾⣦⣶⣶⣿⣿⣿⠛⠉
⣤⣾⡞⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣽⠟⣷⣶⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⠋⠘⣿⡏⠙⢻⣿⣿⣿⣄⣠⢾⣿⣦⣴⡿⣿⣿⣿⣿⡿⠛⠿⣿⡻⣿⣿⡇⠀⠀⠀⠀⠰⣜⠆
⡏⡀⠀⡅⠀⠀⠀⠀⠀⠀⢸⠛⢳⣿⣷⣦⣬⣿⢤⣞⢻⣟⣹⣿⡷⣴⣿⣴⠿⣰⣽⣿⣋⣿⣤⡰⣴⣾⣹⠼⣟⠁⠀⠀⠀⠀⠘⣿⣆
⣂⠀⠐⡅⠀⠀⠀⠀⠀⠀⠈⣀⣤⣦⣿⡿⣟⡯⢾⠛⠿⢾⣿⣾⣄⠠⢝⣻⣯⣿⡿⠟⢫⣯⣻⡿⠟⣽⡿⠶⣿⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀
⡏⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢙⣿⡿⡿⠽⣿⠳⣦⣤⣀⣘⣻⣿⣿⣿⣿⡿⣿⣷⣰⣾⣿⠿⠩⣦⡴⢿⡾⡚⢻⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⢗⡉⢡⣂⣯⣴⣾⣽⡿⠿⠟⣻⣿⣿⣭⣍⣛⠟⠿⣷⣿⣖⣛⣿⣉⢹⣗⡏⢹⡷⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣾⣿⡇⠀⣤⠀⠀⠀⠐⢿⣷⡿⠷⠟⠫⣭⡟⠉⢤⣶⠖⠀⠻⠿⣿⣿⣿⣯⣤⡀⠀⠉⠉⣿⣿⣻⣿⣿⣵⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠈
⢰⣿⣿⢁⣾⣿⠀⠀⠀⠀⠘⠿⢿⣷⢶⣿⣿⣥⣤⣜⠋⣴⣶⣾⣿⣿⣿⣿⣯⣿⡿⠈⢻⠷⠛⠚⠈⢻⣼⣿⠿⠟⠂
⣾⣿⡿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠓⢿⣿⣯⡿⣧⣶⣿⣿⣿⣿⣿⠏⠉⠉⢀⣀⣀⣈⣁⣶⣶⣷⠿⢟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⣿⢿⣟⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣾⠯⢽⡿⢫⣷⣿⠟⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠀⠶⠀⠀⣿⠀⠛⢿⡿⣻⣿⠃⡘⣿⣿⠉⣿⣧⣶⣞⢋⣿⣿⣿⠀⠚⠋⠰⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠾⠆⠀⠠⠄⣿⠀⣠⣼⣿⣿⣿⣷⣇⢸⠈⢀⣿⣿⣿⣿⡟⠋⢸⣏⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⣙⠴⠿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⠓⠀⢸⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⢰⠁⠀⣾⣿⡇⠀⢸⣿⣿⣿⠻⣿⣿⡀⣿⣿⠟⠁⠈⠀⠀⢸⡇⠈⠉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣧⣿
⣿⣿⣿⣿⢠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⠀⢸⣿⣿⣿⠀⢽⣿⣿⡿⣧⣠⣀⡤⠀⠀⣸⠇⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣿⣿⣿⠀⢸⡏⠋⠀⣿⣿⣿⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠈⠛⠛⠻⠀⠘⠇⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⣴⣷⣶⡀⠀⠀⠀⢀⣾⢿⣿⣻⣿⣧⠀⠀⠀⢀⣴⣿⣟⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡤⠺⡃
⠀⢀⡀⢿⣿⣛⣿⡏⠀⠀⠀⢈⣿⣫⢖⡭⣚⣿⠂⠀⠀⣾⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠠⡓⢡⡄
⠀⠀⠐⠛⠠⠐⠛⠀⠀⠀⠀⠀⠻⢷⣿⣿⡿⠏⠀⠀⠀⠿⠿⠿⠿⠷⠶⠶⠶⠀⠀⠀⣀⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⡠⠤⠀⠀⠦⢤⡀
⠀⢀⣀⣴⣶⣦⣤⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡿⠷⣶⣶⣶⠟⠁
⢀⣿⡳⢾⡷⠦⣛⣿⣄⠀⠀⡠⠉⠛⠛⢛⠛⢛⠉⠀⠀⠈⠙⠛⡛⠛⠛⠋⠁⠀⠀⠀⡟⠀⠀⡿⠁
⠈⠛⠛⠿⠿⠟⠓⠛⠁⠀⠀⡤⠐⠃⠀⢉⡄⠀⠀⠀⠀⠀⠀⣸⡏⠁⠀⠀⠀⠀⠀⠀⠘⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠊⢀⠉⢕⠈⠀⠀⠀⠀⠀⠀⣾⣴⠇⠀⠀⠀⠀⠀⢠⣤⣤⡀⢴⣠⠀⠀⠀⠀⠀⣾⣿⡆⡀
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢀⢹⣿⢻⣾⠀⠀⠀⠀⠴⣿⣿⣿⡇⡿⠻⣆⠀⠀⠀⣸⣿⣿⡇⣳⣶⡀
⠀⠴⢝⣇⡟⣿⢸⡣⠀⠀⠀⠀⢸⡿⠂⠀⢸⡆⠀⠀⠀⠀⣿⡏⠉⣇⢇⠀⡹⠁⠀⢀⣿⣿⣿⢧⠋⠙⣷
⠀⠀⠈⠁⠘⠉⠀⠁⠀⠀⠀⠀⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⣼⣿⣿⣆⢀⠀⢄⠀⠀⠀⠀⠀⣼⣅⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣜⠂⡀
⠀⠾⠛⠋⠙⠿⠷⠥⠊⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠴⠿⣿⣿⠿⢿⡷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠂

⠀⠀⢶⣤⣀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⢀⣠⣴⠆
⠀⠀⠈⢿⣿⣷⣦⠀⢻⣿⣦⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢠⣾⣿⠃⢠⣶⣿⣿⠏
⠀⠀⠀⠀⠙⢿⣿⣷⡈⢻⣿⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢸⣿⠋⣰⣿⣿⠟⠁
⠀⠀⠀⠀⣀⣀⣀⣉⠛⢦⡙⡄⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⡜⣡⠞⢋⣁⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠿⠿⠿⠶⠮⠿⢦⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣤⠾⠯⠶⠾⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⣶⣤⣤⣽⠷⢦⣄⠀⠀⠀⠀⠀⢀⣤⠶⢿⣡⣤⣴⣶⣶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠚⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣴⣖⠒⠂⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠻⡗⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⠉⠑⠠⢀⠀⢣⠀⢠⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⠈⠢⣈⡇⠈⠳⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⣄⠀⢄
⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠤⠔⠛⠲⣄⠀⣎⠀⠀⠈⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠨⡀⠈⣆
⠀⠀⠀⠘⠁⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠻⣄⠀⠀⢀⠀⠀⠘⢄⢣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠰⡄⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠄⠀⠀⠠⠦⠠⠄⡀⠀⡀⠜⠛⠣⣧⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠠⡞⠀⠀⠀⠀⠀⠑⢤⣁⡎
⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⢀⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢀⠀⠀⠄⠠⠊⢁⠄⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⠀⠨⡀⣰⠖⠰⠚⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢸⣦⣐⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠐⢀⠀⠂⠀⢸⠛⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠉⠙⢻⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢨⠳⣰⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠂⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡇⠀⡀⠀⣀⠈⣴⠁⠀⠀⠀⠀⠀⠀⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠐⠀⠲⢤⡀⠀⠈⠠⠀⠃⠐⠠⠞⢁⠼⠁⠀⠀⠀⠀⠀⢀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⢀⣤⡆⠁⠰⠒⠒⠒⠁⢀⡹⠦⠄⢀⣁⢸⡟⠴⠏⠀⠀⠐⠀⠀⠀⠀⠀⠏⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠐⠔⠒⠛⠉⠀⢀⠴⣚⠿⣿⡷⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠁⡰⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣠⠇
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠳⡞⠁⢀
⠀⠀⠀⠀⠀⢧⠂⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸⠎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⢀⠌
⠀⠀⠀⠀⠀⡭⠂⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠱⢄⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⠀⠀⢘⠞⠉⠀⢀⣀⢤⠖
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠰⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠠⠀⠊⠀⠐⠀⠀⢠⠃
⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠻⢿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣑⡇⣠⠠⠖⠂⠠⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⠇⠈⠒⠤⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠿⠛⠓⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⢞⠸⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠃⠈⢣⠀⠄⠈⠄⢄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠘⠀⠀⠀⣸⠀⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠸⣇⠀⠀⠀⡴⠈⠀⠸⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⣀⣴⠎⢀⠊⠀⠘⡒⠴⠞⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⢀⣐⣠⠴⠚⢃⠘⠀⠞⠀⠀⠀⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠭⡽⠛⠀⠀⠀⡸⠚⠂⠈⡀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠊⠙⠉⠙⠃⠀⠎⠀⠀⡐⠀⠀⡇⠀⠀⠀⠘⠉⠁⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⢾⠁⠰⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠴⣆⠀⠀⠠⡀⠸⠀⠁⠀⢳⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠔⠁⠀⠙⠷⠦⠌⠀⠀⠃⠀⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⣺⣯⣛⣿⣫⣫⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⢰⣶⡄⢠⡀⠀⠀⠀⠀⠀⠈⠼⢻⡟
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣶⠀⠀⠻⠻⠆⠈⠃⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⠉⠁⣦⠀⠀⠀⠒⠀⠀⠀⠀⢢⡈⢠⣾⣧⠀⠀⠀⡼
⠀⠄⣶⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡐⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠛⢿⡿
⠀⠀⢻⠿⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠙⠓⢹⠁⢠⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢰⠀⣀⠀⠀⣦⣅⠀⠀⠀⠀⠀⠀⡇⢀⡈⡇⠀⢹⠆⠀⠀⠀⠰⠀⠸⡆⡀⡀⢸⣄⡀⠀⠀⠐⠁⡿⡇
⠀⢷⢸⣶⣿⠀⢀⣀⡮⠁⠀⠀⣠⣴⣶⣿⡿⢧⢹⡀⠛⢠⠁⠓⠀⣀⠄⠀⣇⢱⣁⢸⠀⠱⡄
⠀⢸⣿⠨⣿⠿⣯⣿⠀⠀⢀⠀⠈⢻⡄⠘⡇⠈⣏⡿⠀⡾⠀⠀⠀⠉⠁⠀⣿⠀⢿⣸⠀⡆⠹⡄⠀⠀⠀⣠⠁
⠀⢸⡼⣆⣷⣶⣿⣿⡖⠖⣿⣤⣦⡀⣿⣦⣷⠀⢹⣿⢀⡇⠀⢠⠀⢰⠀⠀⢻⡳⢾⣿⡀⣿⠀⢳⠀⠀⣾⠇
⠀⢸⡇⢻⠈⣷⡘⡛⢿⡷⢻⣿⣿⡇⢹⣿⣿⠀⠈⣿⣸⠇⢠⠁⢤⣯⡾⠁⣸⢳⣰⣿⡃⣧⢠⠈⡇⠀⡿
⠀⡖⣧⣿⣴⡇⣧⣸⡌⣇⣸⣟⣿⡇⢸⡿⢻⠀⠀⣿⣿⣠⣼⣽⣾⣭⡧⡔⢸⠀⣿⢸⢻⣿⢬⡀⣷⣿⡇⠘
⠀⡇⢻⠻⣷⣷⣾⣿⣿⣿⣿⣿⢸⡇⢸⡇⢸⡄⡆⢸⣿⡿⢻⢻⢇⡞⢠⠇⢸⣀⣿⣼⣿⢸⠀⠷⣾⣿⠇⠀⡇
⠀⡇⢸⡶⡟⣿⣿⣿⣿⣿⣿⣿⡄⡇⢸⣷⠸⠆⡇⡿⢿⣧⣾⣼⣼⠀⣸⡴⢺⠁⣿⣿⣿⣾⠀⣰⣽⣿⢻⠀⢁
⠀⣇⣿⡇⡇⣿⢻⣿⣿⢿⣿⣇⣷⣧⣿⣿⣤⣷⣧⠀⢸⢿⣿⣿⣿⣻⣯⡀⢸⠀⢿⣿⣿⣿⡋⢹⢸⣿⠈⡆⢸
⠀⣿⢻⣧⡇⣿⣾⣿⣧⣼⣽⡏⣿⣿⢻⡏⡟⡟⡋⡇⣸⢸⣿⣿⣿⣿⡇⠁⡟⢠⢸⣿⣿⠋⡇⢸⢸⣿⡆⡇⢸
⠀⡇⢸⣿⡿⢿⣟⣿⣿⢹⢹⡇⢿⣿⠀⠰⢷⡇⠁⣿⣿⠈⡿⡟⣽⣸⡤⠤⡇⢸⡏⣿⡿⠀⠀⢸⢸⣿⡇⡇⢸
⠀⡇⢸⣿⠁⣼⠉⣿⢸⢸⢸⡇⢸⣿⠀⡇⢸⡇⠀⣿⡿⠀⡇⡇⡟⢻⠛⢠⡇⢸⠁⣿⡇⠀⠀⢸⡟⡿⡇⠁⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠠⠀⠀⠤⠂⠠
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠈⠉⠀⠄⠈⠉⠘⠂⠘⠒⠂
⠀⠀⣾⠆⠀⠀⠠⠀⠀⠉⠀⠀⠂⢄⠙⠉⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢺⢹⢊
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠰⢀⠀⠄⢀⠀⠀⠀⠀⠀⢂⢄⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⣀⡀⡀⠂⠄⡁⠄⠆⠀⠀⢀⠤⠄⠰⢦⠵⠥⠄⠈⡬⣀⠨⢀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠃⠀⠐⠀⡀⠺⠟⠉⠀⠀⠾⠁⠀⠀⠁
⠀⢐⠭⢒⠄⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⠀⡀⠀⠂⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠤⠨⠐
⠀⠀⢀⠀⠀⠀⠀⠈⣀⠠⠀⠀⠀⠀⢁⠀⠀⡊⠀⠙⠀⠘⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠤⠄
⠀⠀⠋⠁⠀⠀⠀⢠⠀⠀⠀⢠⠀⠠⠁⢒⡒⣒⢂⠊⠀⡤⡌⠁⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠰⡖⠒⠒⡂⠈⠀⠀⡀⢀⠀⠼⠙⠛⠜⠤⠡⠛⠁⡀⠼⠋⠴⠦⠭⠧⠈⠁⠀⠀⠀⠀⢀⠉⡔⠀⢡
⠀⠀⡀⠆⠈⠣⠀⠘⠀⠁⠄⢨⢀⠀⢀⠀⡀⠆⡠⠀⠁⠀⣀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠂⠈⠀⠂⠠
⠀⠀⠀⣠⠤⢄⠀⢠⠰⠀⡄⠀⠀⠀⠈⠀⠈⠫⡁⠈⠀⠀⠌⠷⠀⠀⢀⠘⠀⠀⠀⠂⠃⠄⠀⠰⠀⠈⠉
⠀⠀⠀⠐⠤⠜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⡸⠃⠈⠈⠀⠀⠁⠀⠀⡀⠀⠀⠴
⠀⠀⠀⠀⡿⡀⠰⠀⠀⢠⠀⠀⠀⡠⠂⠀⠁⡰⠁⠁⡀⡄⠰⠀⢀⠄⠀⡀⠈⡕⣄⠀⠀⠀⠀⠀⠀⡀⠐⠲
⠀⠀⠀⠐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⠃⢁⢀⠌⠤⣀⡀⢀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆⠀⠀⣸⡿⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢠⡟⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⡞⠀⠀⠀⡏⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣄⠀⡆⠀⢀⡞⠀⠀⣤⠀⡇⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⡇⠀⣸⠁⢠⣾⣿⠀⣿⠀⠀⠸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⢳⠀⡏⠀⢻⣿⠟⠀⢹⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⢀⣾⡄⠀⠘⣾⡇⠀⢀⣤⣤⣴⠈⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠀⠀⣾⣿⣿⠀⠀⢸⡇⠂⣾⣿⣿⠏⠀⠸⣾⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⡿⠃⠀⠀⠘⣷⠊⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡆⠀⠲⣄⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢲⣤⡀⠘⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠀⠀⠀⠀⠑⢬⣆⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣿⣿⣧⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠻⠿⠀⡇⠀⢀⣤⣤⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⡄⠀⢉⠲⣌⢷⠀⠀⠀⠀⠀⣿⣦⠀⢷⠀⠀⠀⢳⠃⠀⠼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠁⠀⠀⠉⠚⢿⣧⠀⠀⠀⢰⣿⣿⡇⠸⡆⠀⠀⣼⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠸⣿⠿⢁⠀⣷⠀⢠⡟⠀⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣤⣾⡆⣿⠀⡾⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⢹⡄⠇⣾⣿⣿⠃⣿⡼⠃⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⠀⠀⠀⣼⣿⣿⡆⠀⢿⡤⠉⠉⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡄⠀⠹⣿⣿⠃⠀⢸⡇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠢⣄⠈⠁⠀⠀⠈⡇⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⢠⡇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⢹⡀⠀⣸⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⡀⠈⡇⢠⡏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⣤⣧⡿⠀⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡤⢀⡖⠢⡄⠨⠎⡥⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠐⢈⠁
⠀⠀⠀⠀⠀⣀⡤⠈⢤⡈⠆⢀⢀⠔⢃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠠⠌⡀⠀⡖⠀⢀⠊
⠀⠀⠀⠀⠈⠓⠶⠀⡠⠼⡿⢯⠤⠐⠉⠁⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢙⣶⣦⠔⠃
⠀⠀⠀⠀⠘⠀⠂⠏⡀⡞⢹⠘⠇⢬⡙⠅⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡽⠿⡏⠓⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠁⠌⢄⠓⠄⣁⠀⠀⠀⠀⠀⢀⡰⠶⣀⠉⠈⠉⢳⠀⠀⠀⠀⠀⠰⠚⠁⠀⢘⠃⠀⠄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠈⡆⢂⡴⠁⠐⢶⠀⠀⠀⠀⠀⠀⠀⣨⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠙⠢⣴⢛⣏⣐⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡀⢨⡴⠋⢏⠡⠈⠉⢩⡁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠔⠄⠄⡤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠁⠈⠢⡀⣠⠞⠁
⠀⠀⠀⠀⠀⢋⠁⠂⠀⠈⡀⠀⠠⠃⢀⠀⡄⠀⠀⠀⠈⠲⠢⠤⠂⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⣀⠀⠒⠄⣀⡀
⠀⠀⠠⣤⠐⠚⠀⠀⠈⡆⠑⡊⣠⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠉⠘⡄⠈⠄⠀⠜⢠⠆⠀⠰
⠀⠀⠀⠀⠉⠒⢀⠒⠂⠴⠾⢟⠀⠒⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠙⠂⠄⡘⡀⢸⡎⢠⠂⡀⠤⠇⠀⢠
⠀⠀⠀⠀⢠⠁⠀⠀⠀⢰⠰⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠒⠒⡒⠦⢉⣾⣴⡋⠡⠤⢄⠐⠈⠁
⠀⠀⠀⠀⠈⠉⢹⠀⣠⠜⠀⠢⣀⡊⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠄⡤⠂⢉⠕⠋⠋⠘⣍⠲⢤⠤⠌⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⣠⠁⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠎⠀⡙⠂⡌⠈⠳⣄⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⣗⡊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣀⡰⢆⠀⡸⢄⠀⢡⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⢙⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⡀⠀⠀⠈⠑⢄⡈⠚⢀⣄⡀⠖⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠀⠤⠖⢣⡄⢾⡃⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⠐⣢⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢀⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠰⢋⣋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⡀
⠀⠀⢧⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⠀⠀⠐⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠉⠃⣤
⠀⠀⢄⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣟⣲⡿⠿⠟⠻⣷⣦⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐
⣆⠀⠤⠀⠀⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠙⠃⢀⣄⡀⠀⠀⠙⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⣷⠙⠒⣆⢀⠃⠀⢰⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠞⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠆
⠻⣀⠀⠀⠈⠀⠀⢸⡅⢰⠀⠀⠀⢀⠀⠀⠀⠽⣾⣷⠁⠀⠀⠀⠀⢀⡠⠀⠀⠐⠀⠡⠀⢀⠀⠀⠀⠠⠀⠀⠒⠎⠈⢀⡀
⡀⡷⠶⡀⠀⠀⠀⢸⡇⢀⠐⠄⠀⠀⠀⠀⠀⠀⢹⣗⢁⠔⡏⢀⠀⠘⠀⠀⣀⠀⠀⠰⣤⡟⠄⠀⠀⠀⠒⢄⠘⠠⠰⠈⠁
⠀⢀⣤⡘⠀⠓⠀⢨⡧⣼⡄⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⢘⡀⢈⡤⠀⠀⡘⢁⡄⠉⠀⢴⡐⠀⠀⠀⠀⠀⠈⠳⢆⡀⠀⠘
⠀⠞⠁⢹⡀⠈⠀⢶⠀⣹⢷⡠⠆⠀⠀⠀⠀⣄⠀⡄⠀⠈⠠⠸⣄⠿⠓⠥⢀⡅⠸⡌⠿⠁⠀⢢⡀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⠀⠠⣌⢣⢖⡃⢺⢆⡋⢼⢷⣄⠀⠀⠘⢸⡏⠘⢥⡀⡀⠑⠐⠀⠀⠁⠒⢀⢙⣇⡈⠀⠀⢀⠀⢘⠐⡀⢰⠂⠐⠄⠀⠁
⠉⢡⢀⠀⠐⣨⣤⣾⣄⠴⢠⠷⠈⣅⠈⣠⣺⣀⠀⢀⠈⢳⡮⢤⠆⠀⠀⠀⠈⢛⣿⠋⠚⠀⠀⠚⠀⣍⡱⠤⠁⠀⠀⢀
⡀⠸⣋⠉⠙⢾⠄⢼⡅⠠⠌⡛⠀⠈⣠⣋⡽⠁⡰⠄⠈⠁⠃⣼⠀⢀⠐⣥⡄⣐⠿⠵⢊⡄⠺⠿⠀⠟⠠⢤⢠⡀⢀⣈⠱
⢶⠔⣿⡗⣀⣛⡛⢿⡷⠂⠀⢱⠈⣦⣤⣾⣷⣴⣥⣄⠀⠀⣠⡿⣪⠭⢰⡦⠇⠰⠀⠖⢺⢑⡃⠀⠀⢀⠀⢈⡛⢐⡍⠏⣴
⡤⢼⡟⡔⠛⢙⡻⠊⠁⠀⣠⡄⢸⣅⣯⡿⠟⣽⠋⠐⠤⠀⠐⣿⡷⠂⠘⡿⠿⡥⠑⢀⠖⠊⠙⠰⢆⡹⡽⣇⡀⢎⡧⣄
⠁⢴⣿⣠⣦⠀⣠⡔⣻⣿⠶⣲⢻⣃⠈⣔⡞⢹⣂⣠⡖⢠⣤⣏⡗⡁⡀⠃⠷⠐⠠⠈⡃⠸⢺⠈⠻⡽⢣⣱⡾⡞⣞⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠶⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡡⠀⠀⠲⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⢀⡀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡒⠚⠁⠈⠁⠀⠀⠀⠀⠀⣩⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠀⢚⠑⢿⣜⠓⠘⠃⠁⠀⢀⡄
⠀⠀⠀⠀⢀⣀⣠⠴⠞⠓⠋⠉⠉⠉⠁⠉⠙⠳⢦⣤⡀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⢀⣭⠀⠀⠉⠁⠘⠓⠀⠀⠉⠁
⠀⠀⠠⠞⠉⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢃⡀⠒⣂⠀⠀⠀⠀⠀⠛⢳⠆⠀⠉⠉⠐⠒⠍⢭⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡴⢶⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠀⡠⠀⠀⠀⠀⣠⣤⣄⡄⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⡠⠿⣧⠁
⠀⠀⠀⠀⠨⠔⣏⣿⠋⠛⠀⠀⠀⢀⣤⣰⣦⠀⠀⠀⠀⠑⠤⢤⠦⠉⠀⠀⠀⢿⣿⡟⠁⠀⠀⢾⠿⠣⠀⠀⠀⠀⠀⠀⠀⢸⣯⠰⡀
⠀⠀⠀⠀⠀⠀⠈⣿⢀⠀⠀⠀⠀⢿⣿⢿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠈⣭⡆⠴
⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠘⠿⡿⣿⣻⠃⠀⠀⠀⠹⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠐⠛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⣶⠀⢨⠷⠞⠀⠀⠐⢸⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣆⣶⣞⠇⠀⠀⡀⢣⢀⣄⠠⡀⠀⠀⠱⠀⠀⠀⠀⠀⠊⠁⢀⠁⠀⠀⠀⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⠋⠉⠁⠀⠀⠀⡀⠀⣙⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⢴⢨⡀⠀⠀⠀⣀⠀⠀⠀⣄⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠰⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠰⠆⢤⡄⠀⠀⠺⠿⠂⠀⡠⣪⡄⡚⠁⠀⠀⠀⠄⠀⠀⠀⢀⣤⣤⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠤⢘⣃⣤⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡿⢱⣆⠀⠀⠠⠀⠀⠀⠀⠀⠈⢸⠟⠀⠀⠈⠛⡓⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠸⣷⠀⡇⣽⠀⠀⢸⡆⠀⠀⣴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠀⡀⠀⢠⢰⣟⣿⡇⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⢀⠀⠀⠀⢀⣿⣼⣷⣴⣷⣾⣴⡔⣹⡇⢴⣧⢿⣾⡖⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣿⡇⡣⠀⣼⣼⣿⣿⣿⡃⠀⠀⠐⣢⣤⣼⣇⣸⣧⣼⡆⠀⠤⠬⢿⣿⡟⠉⢻⣿⣿⡇⣚⢻⣽⣿⣧⡿⢡⡛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⣿⣿⣿⣧⣨⡁⢻⣿⣿⡿⢿⠁⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⡿⠀⠀⠀⠙⣯⣥⢿⣾⣏⣺⣿⢕⣯⡄⠸⣷
⠀⠀⠀⠀⠀⠀⣀⣼⣾⣿⣿⣿⣿⣿⣫⡿⠀⠈⣿⣿⠇⠸⣀⡆⠀⠀⡌⠀⣻⣿⣿⠏⠁⠀⠛⡛⠓⣾⠃⠀⡀⡀⠐⠛⣥⡾⢻⣍⢹⣏⣴⠿⣿⠤⠿
⠀⠀⠀⢀⣷⣿⣿⡟⣿⣿⣿⣯⢿⡏⣼⠇⠀⠀⢹⡟⠄⠀⣿⡼⣷⡿⠄⠀⠂⣿⣿⣀⠀⠀⠈⠉⣠⠼⠃⠁⠀⠈⠒⠠⣿⣇⢈⣿⣿⡏⢿⣿⡉⡷⠄
⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⠿⠓⠛⠓⠏⠀⠀⠀⢸⠇⢀⡀⠘⣷⣽⢓⣀⣄⠠⠝⠿⠛⠳⠾⣿⢶⡇⠀⠀⢠⣠⣤⣀⣀⡜⢻⡿⣷⡿⡈⢼⣿⠳⢟
⠀⠀⠼⠿⠛⠉⣉⠁⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠋⠉⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠛⠉⠙⠗⠞⠃⠛⢂⠈⢠⣹⠆⠀⠃
⠀⠀⠀⠀⠀⠈⠽⠀⠂⠤⣤⣤⣧⠠⢠⣤⣤⡀⣀⠀⠤⠤⢀⣢⣄⣀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠶⠎⢉⣺⡟⣂⣉⣽⣷⣄⣀⣉⣱⡖⠀⠀⠀⠀⠀⠠⢶⣶⠤⢴⣈⡉⠷⣄⠀⠈⢻⡆
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠐⠺⠶⠶⠦⠶⠴⠶⠒⠛⠀⠠⠾⠷⠒⠒⠋⠉
⠀⠈⠀⠈⠁⢦⣴⣾⣿⣁⣀⣄⠀⣷⡄⠀⠀⣴⡄⠀⠀⠀⣆⠀⡀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣷⣷⡄⠹⣿⣤⣧⢾⡏⣧⣷⢠⢼⣷⡀⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣾⣿⡿⠿⠛⢿⣾⣷⣿⡇⠀⢁⠀⡆⡄⠀⡀⣼⣿⣿⠀⣆⣿⡆⠀⠀⢀⢸⡄⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠐⡻⢿⣿⡟⣿⠿⢿⣭⣥⠀⢘⠂⣻⢻⣧⣷⣿⣿⣿⡄⢸⢸⡇⠀⠀⠈⡄⣿⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠛⠁⠀⠒⠒⠀⠓⠄⠊⠀⡥⠜⠛⢛⠻⣿⣿⡗⡚⠉⢉⡠⠄⢠⣧⣿⡿⠴⠏⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠘⣿⠛⠏⠑⢿⠛⢛⢛⡻⢿⣧⣀⣀⣉⣭⡷⢶⣖⣚⣛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠙⠁⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡼⡓⢿⢷⣶⣴⣢⡄⠀⣠⣄⢠⣴⣶⣿⣿⣧⡄⠀⠐⠒⠶⠓⠲⠶⠶⠒⠲⠤⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡬⢝⠀⢁⠰⣼⣿⣿⣿⣯⣽⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠲⠘⠻⢿⠿⠿⡟⠛⣫⣁⢹⠷⢆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠉⢙⠓⠞⢦⣤⡛⣐⠃⡨⠁⣿⣦⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠿⢘⠳⠖⢾⠿⠛⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⠤⠄⠲⠦⢄⠀⠀⠀⠀⢨⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢀⡀⠤⠀⠈⠉⣀⡀⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣠⣤⣀⠀⠺⣁⠀⠀⠀⠀⠀⠀⢀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣿⣦⣀⠀⠀⠀⠀⠰⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠀⠂⠀⠐⠃⠉⠀⠤⢤⠾⠛⠋⢉⣡⣶⣶⡼⠿⠆⠀⢀⣤⡤⠐⠚⠂⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠰⠶⠶⠀⠀⢀⡔⠋⡴⠋⠉⠁⠈⠀⠀⠀⣴⠛⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠶⠄⠀⠀⠀⠀⠀⢀⡄⠁⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠑⠓⢤⡀⠀⠀⠀⠀⠀⠴⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠠⡌⢢⠀⠀⠀⡸⠄⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣷⠀⠀⠿⢢⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠳⣄⡙⣇⢀⣶⠋⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠉⠛⢿⠇⠀⠀⠀⠀⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢷⡀⠈⠃⠀⠈⢧⡀⠀⠀⠀⣿⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣲⣿⡀⠀⢀⣀⣼⡁⢄⠀⠀⠉⡄⠀⢱⠄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⣄⣀⠀⡉⠛⣄⠓⢄⠀⠘⢦⣼⠀⠀⠀⠀⠈⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠐⠲⢞⠿⠛⠋⠛⢉⣤⣤⡬⠛⠋⠓⠞⠓⢤⡄⢻⣧⡀⠄⠀⠀⠐⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠐⣠⠤⠔⡊⠀⢀⡴⠛⣡⠜⠁⠀⠀⠀⠀⠀⠁⢢⣴⢦⣍⡑⠚⢦⣀⠀⠀⠛⢦⣑⣤⡀⠀⠀⠀⢀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠒⠒⠁⠀⠀⠁⢀⣘⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠒⠂⠩⠶⢤⣀⣀⠉⠀⠻⠷⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠒⠒⠂⠀⣶⣶⠞⠛⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡐⢿⠋⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⣬⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⡆
⠀⠀⠀⠀⠀⠈⠛⠉⣉⠉⠙⠷⠶⢤⣀⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠙⠷⣤⣹⣆⠈⠀⠀⠀⢲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠠⠌⠙⢿⣇⠀⠀⠀⠈⢄⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢢⡀⠀⠀⠱⠀⠀⠃⡀⠀⠀⢤⣄⡀⢠⡀⢠⣄⣀⣀⣀⣄⡀⠀⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢀⠈⠑⠀⢰⡀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠉⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠀⠚⠛⠒⠚⠻⣦⣤⣤⡄⠀⠀⠀⠀⠒⠂⠉⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠈⠁⠀⠀⠀⠀⢀⡀⠶⣴⠛⡟⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⢿⡀
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⡰⠞⠻⠋⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⠟⡏⠀⠀⠀⠀⠀⢠⣾⠄⠠⠒⠚⠉⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠈⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠐⡎⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢪⡟⠀⠀⢻⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣯
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠘⠀⢀⠎⠀⠀⠀⠈⢣⠙⡄⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠁⠀⠀⠀⠀⠀⢠⡷⠊⠀⠀⠀⠀⠀⠀⠀⠙⠶⢄⣱⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣀⣠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⡼⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡼⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡔⠁⢤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠢⡀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢣⡎⠀⠀⠀⠀⢀⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⣧⠷⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣼⠇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣁⣀⣠⡴⠾⠛⠋⠙⠻⣦⣀⣤⠴⠾⠛⠛⠋⠀⠀⠉⠉⠲⢄⡀⠀⠀⠈
⠀⠲⣤⣀⡀⣀⣠⣿⣧⣴⡾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⣤⣾⣿⠛⠉⠁⣰⠋
⣾⣿⠿⠶⠾⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣄⠆⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⢰⠆⠠⠆⢰⠀⠀⠀⠸⢦⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⠀⠀⠀⠀⣿
⠀⠀⠀⠰⡀⢸⠀⠘⡆⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡇⠀⠀⠀⢱⠀⠀⠀⠀⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⢉
⠀⠀⠀⢸⡇⠀⢠⠀⠸⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣶⡀⠈⠗
⠀⠀⠀⢸⠇⠀⠈⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠉⡀⠀⢿
⠀⠀⠀⠀⡇⠀⠀⣧⠀⢠⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡀⠜⠀⠀⠀⠀⠀⠐⢿⠀⠺⠆
⠀⠀⠀⠀⡗⠀⠀⠸⡀⠀⠗⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠐⢷⠀⠀⠀⠀⠰⡆⢠⣄
⠀⠀⠀⠀⢷⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⢿⠀⠈
⠀⠀⠀⠀⣾⠀⠀⠀⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡀⠀⢷⡀⠀⣴⠀⠀⠀⠺⠃
⠀⠀⠀⠀⢹⠀⠀⠀⢻⡀⠀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣤⠀⠈⢱⣄⠙⢏⠀⠙⣷
⠀⠀⠀⠀⢸⡄⠀⠀⠘⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⣯⠀⠻⡆⠀⢩⣇
⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⢘⠄⠐⣟⢶⣄⣹⡀
⠀⠀⠀⠠⠾⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⠹⡇⠨⣦⠹⡼⣇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢳⣄⠻⡁⢽⡖⠓⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣴⠣⡀⢱⡄⠙⢀
⠀⠀⠀⠀⢙⣀⣠⠞⠃⠀⠀⠀⠀⠀⠀⣤⡀⡔⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠻⠀⠁
⠀⠀⠀⠆⠈⣿⣿⣾⣫⠖⢠⡄⠀⣤⠀⢿⣿⢇⣼⢀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀
⠀⠀⠀⠀⣾⣽⣿⡿⠟⠓⠂⠀⠀⠀⠠⢾⣿⣧⣟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣸⡀
⠀⠀⠀⠉⠁⠶⠀⠁⠀⠆⠀⠀⠀⠀⠀⢺⢩⠿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠘⠁⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⠀⠠⠁⠀⠀⠀⠀⠀⠈⠐⢶⣶⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢄⣦⡀⠀⡴⠀⠀⠀⠐⡆⢴⣋⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡼⢷⣿⣷⡋⠠⠀⠀⠐⠂⣳⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠃⠀⠀⣴⠴⣏⣿⡌⢳⡄⠀⠀⠀⠞⠙⡛⠠⣤⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⣀⠀⢠⡄⠀⠀⠀⠿⠃⠈⠉⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡠⣀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠔⠀⠀⣀⠀⠀⢡⠉⠀⠋⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠀⠀⠙⠁⠀⠀⠀⠀⠀⠑⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊