Calamary Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠊⠁⠀⠀⠀⠀⠈⠙⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⠉⠉⠀⠀⢨⡙⠦⠀⠀⣄⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣤⠖⡡⠀⠀⣠⣷⣜⣫⠴⠶⠶⠋⠉⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢊⣉⣤⠞⣠⢀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢂⠀⢀⣔⡭⢶⢹⡿⢿⡇⣼⣇⢺⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢠⠋⢋⣴⣷⢸⠁⡼⢣⣿⣿⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣶⠷⠋⠁⣸⣔⣤⢸⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢠⠞⡹⣯⡍⡜⠉⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⡴⢻⣿⣿⡎⠘⣧⣠⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡝⠉⠀⡴⢻⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠀⠐⢼⣃⠜⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣧⠀⠀⢸⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡈⠀⠀⠀⢱⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠈⠁⠀⠀⣠⠏⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣟⡅⣀⣀⣠⡤⠤⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣶⠿⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢀
⠀⠀⠀⠀⣠⣀⡧⠀⠀⠀⠀⠒⠒⠒⠚⠛⠀⠀⠀⠀⠰⣤⣴⣄⣀⣾⠇⢀⣤⣾⣤⠤⢄⠤
⠀⠀⢠⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣼⣿⣿⣿⣿⢧⣤⠄⠀⠀⠁
⠀⠀⠀⠉⠓⠶⠆⠤⠄⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⢠⣾⣿⣅⡀⢹⠿⣿⣟⡷⠦⠄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠛⠋⠙⠛⠙⢻⣮⢻⠿⢷⣶⣴⣤⡰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢠⡇
⠀⠀⢀⣔⣀⣠⡤⠤⠐⠐⠂⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⣾⣿⣦⣀⣰⣿⡿⠀⠀⣠⣴⡾⣿⡶⠶⡒⣒⢓⡒⡲⠤⢄⡀
⢀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣁⠁⢹⣿⠿⢛⣷⣿⣿⣟⣫⠈⠀⠀⡀⠀⠀⠃⠒⠐
⠁⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠮⠘⠽⣛⣛⣻⣿⣟⣛⠛⠛⠟⠋⠀⠀⠂
⠀⠀⠉⠛⢋⠳⠶⠦⠤⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣄⡀⠀⠐⠾⠿⣿⣿⣟⡿⣿⣷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⢫⣽⢳⡾⢿⣶⣌⡻⢿⣿⣶⣤⣄⣀⣀⠀⣀⠀⠀⢀⣔⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢣⣿⣧⠈⢳⡙⠛⢿⣿⣟⣼⣷⢂⣂⠱⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢽⡆⠈⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣩⣙⢻⡟⣫⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠈⠐⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⡆⠱⠀⠀⠀⠀⠀⠀⠀⣀⢰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣾⠏⡸⣴⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡏⠀⣿⠀⣤⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠠⡄⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣇⢸⡟⣰⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠘⠰⢫⠵⠓⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠰⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠃⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠈⢻⡄⠀⠀⠀⢄
⠀⠀⢀⠄⡠⠆⠀⠀⠀⠀⠀⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠳⢄⠀⠀⠈⢙⡒⠶⢤⠄
⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⣦⠏⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢲⡘⣦⣍⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⣾⠟⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣸⡼⣷⡌⠿⣶⣤⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠀⠙⠿⠅⢀⠙⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡇⣿⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣰⠏⢸⡟⠀⢉⢿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⠀⣾⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢰⠋⡴⢟⣥⣀⡀⠀⠀⠀⠀⠀⢀⣀⡈⠨⠛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡜⠀⠀⢈⠕⠉⠀⠀⠙⠀⠀⠀⠀⠀⠨⣝⢿⣦⣐⠺⣿⣆⣠⠞⠉
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡉⢻⣷⡌⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡴⠃⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣈⡛⠶⢬⡓⠌⠉⢂⡀
⡄⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠦⡀⠀⠀⠈
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣏⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣘⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠁⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⢠⣴⡶⢆⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⠀⠀⠀⠱
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠉⠳⡐⡄⠀⠀⠀⠀⠐⡇⡀⠀⠀⠀⣧⠀⠀⠀⠀⡶
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢹⠘⡄⢄⠀⡄⠀⢳⡀⠀⠀⠀⠸⣄⠀⠀⠀⣿⡄
⠀⠀⢸⠃⠀⣶⣶⣶⣶⣶⣶⣶⡇⢱⣾⣶⣷⣶⣶⣇⠰⣶⣶⣶⣿⣷⣶⣶⣿⢱⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⡆⢇⠸⡜⢷⠄⠈⢧⠀⠀⠀⣽⣄⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣼⣄⠀⣿⠀⡀⠀⠀⠀⠀⠀⢹⡌⣄⢣⠀⠳⡔⢮⣧⠀⣀⣾⡏⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢠⣿⡏⢿⠀⣿⠀⠁⣄⣀⣀⡀⠀⠈⢳⡌⢆⠱⡀⢸⣦⡘⢧⣹⣼⢶⠶⢖⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡾⡿⡙⠀⠀⣿⠀⠀⠀⠉⠛⠢⠤⣥⣿⡿⢄⠣⡙⣦⡉⢷⡀⠹⣿⠃⠎⠁⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢱⣧⣇⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠛⠳⠸⣿⣿⣄⠹⣆⢹⡰⡄⠨⠉⢷⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⢡⠖⢰⢾⣷⣶⣌⡙⢻⠣⠈⠀⠁⢁⠀⠀⢨⡇⠀⠑⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠃⢰⡧⠓⠉⠪⢟⣿⣌⣒⣤⡀⠀⠀⢣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠨⠀⠀⠀⠀⠈⢯⣿⡋⢏⠹⣆⠰⣆⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⠟⠀⠀⡀⠀⠀⠀⠀⢸⣿⡿⣸⣦⣿⠹⠀⠙⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⠏⣉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠶⠘⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠀⢦⠀⠀⠀⠀⠀⠈⠉⠈⠓⢠⠛
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠊⠀⠀⠀⠈⢷⡵⡀
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⠞⠁⠀⠀⠀⠀⠀⠀⠙⡐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡀⠀⢶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠆⢄⡀⠀⠀⠀⠀⠀⠉⢛⢀⣞⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⣀⠀⠀⠻⣡⣿⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡙⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠙⠏⠛⠛⠻⠉⠉⠀⠉⠢⡄⠀⠀⠀⠀⠀⢠⣴⣿⣯⣭⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⣛⣭⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⣿⠿⠟⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣠⣾⠟⢋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣠⡿⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣾⣿⠟⠛⠉⠉⠉⠉⠙⠛⠿⣷⣦⣄⣀⡀⠀⠀⢀⣠⣴⠟⠁⢀⣾⠟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠟⠛⠋⠁⠀⢠⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⢿⣿⣿⣿⡇
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠙⠛⠋
⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⣿⣶⣦⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⢀⣠⠶⠛⠉⠉⠀⠀⠈⠉⠛⣶⣶⣤⣄⡀
⠀⠀⠙⢿⣿⣶⣤⣀⣀⠀⠀⣰⣿⡛⠉⣁⣀⣉⣭⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⡿⣧⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⠿⠛⣹⡿⠉⠉⢈⣀⣽⣿⡛⡶⠟⠋⠀⣤⣿⣿⣿⣿⣿⡰⠿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⢠⡿⠉⠀⣰⡟⣡⡴⠿⢛⣿⡿⠏⠀⠀⠀⠀⣼⡟⣿⣿⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⢸⠁⠀⣰⣟⡾⠃⠀⠀⣾⡿⠁⠀⠀⠀⠀⢰⢿⣽⣿⣿⣿⡼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⢸⢀⡴⠋⡜⠀⠀⢀⣾⡟⠂⠀⠀⠀⠀⢠⣸⣿⠿⣿⣿⡿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠐⠚⠉⠀⠀⠁⠀⢀⣾⠏⠁⠀⠀⣀⣤⣾⣿⡟⠁⠸⣿⣿⣳⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⢀⣴⣶⠿⠋⢁⣾⠁⠀⢈⣛⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣼⠟⠋⠀⠀⣠⠞⢁⣠⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢀⠠⠖⠉⠀⠀⢠⡟⠁⠀⠠⠔⢚⣡⡶⠟⠋⠡⣿⠇⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⡰⠛⠁⠀⠀⢠⣼⠏⠀⠀⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠼⠤⠠⠤⠴⠖⠋⠁⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢊⢁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣥⡴⠿⠛⠁⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠁⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠃⠀⠠⠀⢀⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢀⠀⢠⣾⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢿⣄⠀⠀⠀⠀⠀⣀⣶⣶⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠈⢙⣦⣶⣠⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠀⠀⠀⠀⡠⠤⣹⡿⠛⠙⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣠⣤⣴⠊⣠⠔⠀⠺⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣡⣴⣿⡿⠛⣡⡞⢡⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣖⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠒⢠⣶⣶⡿⢛⡩⢋⣴⣿⡿⢁⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⣿⣿⠿⡿⢡⡞⠋⡡⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠃⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉
⠀⠀⠀⠀⠀⠋⣙⡛⢥⣼⠭⢴⡴⢡⡿⠷⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠟⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠁⠹⢠⠋⠀⠀⣠⠔⢋⠄⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⢄⡴⠚⠁⠀⠀⠀⠀⠐⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠆⠀⠀⠀⠀⠰⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠀⠀⣾⠀⠀⠀⠀⠀⠀⣇⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⢿⠀⠀⠀⠀⠀⢀⡿⠀⢀⡀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⠀⠀⠀⠀⠀⠀⡗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠣⠐⠄⠀⠀⠠⠂⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⡄⠀⠀⠁⠇⠀⠀⠘⠈⠀⠀⠰⠂⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠀⠀⠀⠐⠁⠀⡠⠀⠀⠀⠀⠀⠀⢄⠀⠈⠂⠀⠀⠀⡀⠀⢰⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢀⡀⠀⠂⠀⠇⠸⠀⠐⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠒⠂⠀⣀⠔⠊⠑⠢⣀⠀⠐⠒⢈⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠉⠁⢄
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀⠀⠀⡠⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠓⠈⠚⠋⠀⢀⢰⡄⠈⢳⣞⣁⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠤⠤⠀⠶⠤⣤⣤⠴⠋⠉⠹⣿⣾⣯⠃⠀⢫⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠁⣀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡤⠖⠈⠀⠀⠀⠐⡂⠐⠢⠤⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠠⡀
⠀⠀⠀⠀⢦⡁⠀⠀⠀⣀⠀⠀⠏⢴⡆⣄⡀⠀⠈⠝⠓⠲⠬⠵⠤⡀⠀⠀⠀⠀⢀⠠⣀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠈⠓⠂⠊⠉⠓⠛⠉⠐⠊⠉⠙⢦⢀⡐⣬⡙⢷⡿⣶⡒⣖⠫⢶⢄⡐⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇⣿⢿⡜⠗⡌⢧⠹⠷⢦⣔⣽⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢿⣿⡄⠶⢾⡖⠠⣀⠀⠀⣿
⠀⠀⠘⢋⡙⠒⠢⠤⢄⡤⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⢸⣄⣆⠈⣮⠛⢵⣾⣿⣗⠒⠋
⠀⠀⠀⠀⠉⡇⠀⠀⠀⠈⠉⠓⠤⣈⠉⠀⠀⠀⠀⠀⢀⡙⠿⠷⣿⢤⡈⠉⠑⢜⡆
⠀⠀⠀⠀⠀⠱⡀⢰⢦⡀⠀⠀⠀⠀⠙⠦⣄⠀⠀⢠⡧⠂⠀⠀⢜⠢⠽⡆⠀⠀⢙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠑⢄⣄⠈⠑⠀⠀⣀⡔⠒⠛⠐⢀⠘⢄⠀⠀⠀⠀⠳⣀⠇⠀⠀⠘⢄⠀⠈⠑⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠙⢄⢃⡀⠈⡀⠀⠑⢄⠀⠀⠀⠋⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠦⠄⠀⠀⠶⣶⣄⣬⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠢⢄⡀⠀⠀⠀⠀⠀⡸⢿⡟⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⡴⠃⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣽⣯⣽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣭⣭⣽

⠀⠀⢀⣠⣤⣀⣀⣀⣀
⠀⠀⢿⣝⣗⢯⣉⠉⠁⠀⠋⣹
⠀⠀⠘⡌⠻⣇⠈⠛⢲⣤⣰⡇
⠀⠀⠀⢱⠀⠈⢳⡐⣦⡌⠀⠉⠓⢦⣄
⠀⠀⠀⢸⡄⠀⢈⠿⡍⠀⠀⠀⢄⡀⠈⠙⢦⣄
⠀⠀⠀⠈⢧⠞⠁⠀⠘⢦⡀⠀⠀⠉⠀⠀⠀⠈⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢤⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⠀⠀⡹⠆⡸⠘⢷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣃⣩⠾⣋⣁⠑⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⡰⠮⢃⠀⠀⠀⢀⣈⠀⠀⢀⣀⣀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠄⠀⠐⠆⠀⡉⠑⠒⠀⠉⡙⢿⣿⣿⡢⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣶⣄⠀⠳⣴⣭⠀⠨⣑⠀⡐⠑⢶⡙⠾⠶⣎⠡⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠜⢶⢢⣄⠈⠙⠳⢄⠈⢗⠪⢷⣶⣠⡐⢠⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⢦⠛⣦⣄⠂⠑⣄⠑⢄⡙⠌⠣⢶⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠳⡬⢆⢱⣄⠈⠅⠚⠉⠷⠦⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣹⡆⠙⢕⠨⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣌⠙⢯⣶⠂⠑⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠉⠓⠀⠈⠐⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⢒⡶⠋⢳
⠀⠀⠀⠀⡴⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠒⠉⠉⠁⠀⠀⣠⠔⠉⠀⠀⡎
⠀⠀⠀⢸⡇⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⢰⡇
⠀⠀⠀⣿⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⡞⡇
⠀⠀⠀⠧⣳⣄⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡃
⠀⠀⠀⠀⠉⠻⠷⠦⣄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣓⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⢀⣶⣭⡉⠳⣞⣁⠜⠋⢸⡆⢘⠄⠀⠀⠀⠀⢠⠔⠊⠉⠉⠣⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠈⢉⡴⢻⠀⢸⠁⠀⢀⠞⠀⣸⠀⠀⠀⠀⢠⠃⢠⣾⣿⣦⠀⢈⡎⠳⢄⡀⠀⠀⣠⠔⠋
⠀⠀⢀⡎⡴⠋⢀⡏⠀⢠⠋⠀⠀⡇⠀⠀⠀⠀⠘⣆⠈⠿⡿⠏⠀⢠⡇⠀⠀⠉⡳⢏
⠀⠀⢰⡟⠀⠀⢼⠁⠀⣹⠀⠀⠀⠸⣄⠀⣀⣀⡠⠼⠶⣠⣤⣤⠬⠚⠀⠀⣀⠴⠁⣸
⠀⠀⢸⡇⠀⠀⠸⣦⣄⣹⣧⣀⣠⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡥⠤⠖⠁
⠀⠀⠘⣧⠀⠀⠀⠈⠙⠙⠛⠉⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⡠⠴⠤⢤⡀
⠀⠀⢀⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⡄⠀⠀⠀⣠⢎⠖⠛⠢⡀⠈⢢
⠀⣼⣭⡀⠙⢿⠓⠖⠒⠒⠒⠒⠒⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⠀⢱⣀⡀⠀⠀⢸⣓⣛⣋⡵⠋⠀⠀⢰⡇⠀⠈⡆
⠈⠁⢹⣿⠀⢸⡀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣀⣤⡴⠋⣻⡄⠀⠀⠀⢸⠺⣷⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠈⢿⡄⣰⠃
⠀⠀⠀⡟⠀⠀⠱⠦⣄⣠⠴⠋⠀⠀⠀⢀⣴⡟⠓⠋⠀⢠⣿⠃⠀⠀⢠⡏⠀⡼⠀⠀⡼⠀⠀⣀⣀⣀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⢹⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣇⠻⠦⣀⠴⠛⠁⠀⣀⣴⣻⠾⠋⠀⡠⠞⠓⠋⠉⢁⣠⡤⢽⡄
⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠉⠁⠀⠀⠈⠙⠒⠒⠒⠒⠚⠯⣀⣀⣀⡤⠔⠋⠙⠒⠒⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠖⢛⣿⡿⠿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⢀⣤⡶⠛⠉⠀⢀⣠⡶⠂⠀⠀⠀⠀⢀⡴⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡴⠞⠋⠁⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⢀⡴⠛⠀⣾⠃
⠀⠀⠀⠀⠀⢀⣴⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠸⣇⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡉⠙⠛⠶⠶⣦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣴⣟⠋⠁⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣤⣄⣀⠉⠻⣦⣤⡴⠞⣋⣥⣀⠙⣧⡀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣭⣻⣾⠋⠁⠀⠰⣯⣀⣽⠂⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⢁⣠⣤⣀⣹⠇⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠻⣆⠀⠀⠀⠀⠀⣼⠃
⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠁⣰⠏⠁⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠙⢧⣀⣀⣀⣼⠏
⣾⡉⠛⢦⣄⡀⠀⢀⣰⡇⢀⡿⠀⠀⣀⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢦⡄⠻⣆⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉
⠈⠻⢦⣄⡉⠙⠛⠋⢉⣠⡾⠃⣠⡞⠋⣀⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠾⠃⣠⡿⠁
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⢰⡟⠀⣾⠋⢁⣼⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⢠⡿⠁⣠⠿⠷⣤⣄⣀⠀⠀⢀⣠⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣿⠁⢸⡏⠀⢠⡟⠉⣿⢻⡟⠋⣿⠃
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣤⠟⠁⣸⢿⡄⠘⢷⣄⠘⣧⠀⣿⡘⣧⠀⢿⡀
⠀⠀⠀⠀⠀⣿⠉⠙⠛⠛⠉⢁⣠⡾⠃⠀⠹⣦⡀⠙⣦⠹⣆⠈⣷⡹⣆⠈⢷⡀
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⢻⡄⢸⡇⢹⣆⠘⣷⠹⣦⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣸⠇⠀⢻⡄⠘⣧⠘⣧⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⢁⣴⠏⠀⠀⠀⣿⠀⢻⡄⠘⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣀⣤⡶⠟⠁⠀⠀⠀⢀⡿⠀⣼⠃⢰⡏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⣠⡴⠟⢁⣴⠏⠀⠘⠳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡴⠟⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠉⠛⠶⢤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠈⠻⢯⣍⡛⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢷⠀⠀⠀⠘⠛⠿⣭⡉⠉⠛⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡟⢿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠸⡇⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⣴⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣿⡄⠀⠀⠀⠙⠳⣄⡀⠀⠀⣠⣤⣤⣽⣿⢳⡀⠀⠀⠀⡾⠧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠉⢳⣼⣯⡞⠛⠯⠉⠈⠻⣄⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣼⣷⠀⠘⡷⢽⡄⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣽⣞⢠⣀⢠⡇⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢧⢻⣾⣿⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣄⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡼⢹⣿⣿⡏⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢀⣴⠟⠁⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠋⠁⠀⠀⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠇⠿⠉⠁


⡿⣿⢿⢷⡾⡾⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣷⣾⣶⣿⣶⡷⡶⣶⣶⡶⠶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⡀⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢿⠋⢴⣮⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⠁⣤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⡅⠀⠀⠀⣠⠞⢡⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡇⠠⣤⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⢋⢟⡁⡀⠢⣄⠀⢀⣴⡖⣶⣶⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⣶⠛⢳⣾⡇⣶⠛⣷⡾⣷⣿⡿⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢷⡀⣀⢉⣹⣯⣿⣯⣿⣿⡟⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠈⢷⡀⠀⠀⢉⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⣿⣷⣯⣄⠙⢶⣄⠀⠉⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⡎⣴⠅⠀⠀⠙⣿⣿⣿⣷⣦⣍⣳⣶⡁
⠀⠀⠀⠀⠀⠀⠀⢧⠙⣄⡀⠀⣤⣼⣿⣿⣿⣿⣿⣿⡈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡻⣷⣬⣿⠟⢙⣿⣿⣿⣿⣿⣆⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣿⣠⠎⠙⣿⣿⣿⣿⣣⣆⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡵⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠅⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡛⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠄⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢆⣾⠇⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢫⢯⡇⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠋⡼⢰⣾⡞⣃⢉⢹⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣶⣳⣰⢸⡘⡆⡇⣿⡧⣌⢢⣿⡿⡇⢀⢠⢠⠀⠀⠀⠂⠀⠂⠓⠀⠁
⠀⠀⠀⠀⠀⢴⡶⣶⣿⣿⣽⠖⡴⠻⢹⡼⢳⣧⡇⢿⢹⣬⣿⣿⣇⣧⠎⠑⠓⠷⣤⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠑⢮⡻⣿⣿⣷⣶⣾⣾⣶⣯⣾⣾⣿⣿⣿⡟⡜⠀⠀⠀⠀⣽⣿⠀⣈⠻⠉⠁⣶⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⡻⢿⣿⡏⠓⠪⣝⢿⣿⣿⡿⢟⠞⠀⠀⠀⠀⠀⠞⣻⣦⠉⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠑⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠰⠋⠡


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣟⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⠙⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⣀⠤⠔⠒⠊⠙⣏
⠀⠀⠀⠀⠀⠀⠀⢰⡡⠤⠒⠊⠁⢣⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢈⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⣀⣀⠀⣧⣞⡂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣯⣖⡀⢱⠙⠺⡖⠙⡖⠒⠒⠒⠒⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⠭⠔⠃⠠⡄⢼⢽⠁⠀⠈⠛⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡲⠄⠀⠀⠈⠉⠁⡤⢄⡙⠫⣅⠒⠻⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⢾⠁⠀⢠⡀⠀⢸⡀⢱⣄⠈⠳⡢⢽⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡱⠁⡸⢠⢻⢸⢳⠀⢸⠘⢦⡹⡑⢄⠈⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢠⢣⠃⢸⡎⠀⡇⠸⡆⠀⠙⠪⣦⡳⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⠁⠀⠇⡇⠸⡀⠀⠀⠈⠁⢸⠂⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠘⠙⢄⠛⢹⠔⣄⠀⠀⢏⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠩⠗⣦⠈⡖⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠃⠀⠀⡀⠀⠀⠀⠤⠤⠤⠤⠔⠶⠿⠆⠀⠀⠀⠀⠀⠀⢠⡄⢀⣀⣀⠀⠀⣼⣿⠃⠀⠀⣀⣠⡇⣀⣀⣀⣀⡀
⠀⢀⣴⠷⠶⠚⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣶⣾⣿⣇⣤⣤⣾⠟⠟⠛⠋⠁⠒⠒⡀⠩⠃⠂
⢖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣆⡄⡿⡿⡶⢿⣿⡿⠾⣧⣤⡤⠂
⠀⠙⠳⢶⢤⣤⣀⣀⡀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⡄⠀⡀⢀⠀⣀⣤⣶⣿⣟⠉⠀⠩⣽⣿⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠁⠀⠀⠈⠉⠈⠉⠀⠓⠂⠶⠲⡶⣶⣴⣤⠆⠀⠀⠘⢀⠃⣿⣿⣿⡿⣻⣶⣤⣶⣬⣟⢿⣿⣿⣍⣉⡉⡁⠀⠀⠀⠀⣀⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠉⠉⠀⠈⢫⣿⡇⠙⡝⠻⢿⣿⣟⣰⣷⢒⡈⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢿⡀⠉⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢲⣾⠁⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣻⢫⢀⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢋⡇⢠⢿⠼⡈⡃⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡶⡍⡄⡇⢿⢰⢸⣸⣀⠣⣝⣾⣿⠄⠀⠄⢀⠀⠀⠀⠄⠀⠄⠣⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣀⢤⣤⣴⣷⣿⡽⣍⡿⡇⣇⡿⣌⢸⠸⡏⢏⣱⣿⣿⢷⢃⠔⢴⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠁⠫⣝⢿⣿⣷⣾⣤⣤⣯⣤⣽⣻⣦⣷⣾⣿⣿⡿⡜⠁⠀⠀⠀⣶⣿⠀⠐⢶⠒⠂⣠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣿⣿⡿⠿⢽⡻⣿⣿⣿⣿⣿⢟⡝⠀⠀⠀⠀⠀⡹⣿⡄⠟⠀⢤⣄⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠛⠋⠀⠀⠈⠒⠽⠛⠫⠕⠊⠀⠀⠀⠀⠀⠀⠀⠛⠉⠐⠀⠀⠀⢤⠄⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣠⠤⣀⡀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠘⢦⣄⠉⠛⠫⢍⡉⠉⠉⠉⠩⣦
⠀⠀⠀⠀⠀⠸⣷⣷⣄⠀⠀⠀⠀⠀⢀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⣿⣿⡷⣝⢦⡀⠀⠀⠀⠙⠲⣾⡄
⠀⠀⠀⠀⠀⠀⢹⣿⣇⠈⠣⡙⢦⡀⠀⠀⠀⠀⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠘⡏⢿⣄⠀⠙⢦⣝⠳⣄⠀⠀⠀⠀⠀⠉⢷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢭⣑⣦⣀⣿⣷⣝⠳⣄⡀⠀⠀⠀⠀⢹⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⢮⡻⣦⣀⣀⠀⡀⠋⠀⠉⠳⡆⠀⢀⡠⠔⣪⡽⠟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣟⡫⠺⣿⣄⠀⠀⠀⣛⡚⠛⠶⠾⣥⠤⠤⠶⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢥⣸⠷⡍⠛⠯⢽⣿⠮⣳⡛⠋⢉⣳⣌⡢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢿⣿⣷⡶⢬⡳⣽⣗⣲⠗⠛⠻⠍⠒⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣦⡻⣏⠻⡶⣍⡲⢭⡷⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡾⠈⡇⣹⡇⢱⢳⠙⣆⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢼⡀⢰⠇⡇⡇⢫⡏⠀⢹⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⢦⡳⣽⡶⢽⠓⠘⣇⣓⣫⠭⠽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡼⠻⣎⣓⣦⣌⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠴⢉⢖⡿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣫⡾⠩⢀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⣫⢼⠶⡏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣖⣂⣯⣴⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠋⠜⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠂⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣦⣤⡀⠀⠀⠈⣯⡞⠄⠀⡽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⣿⣦⡀⠀⢻⠒⣃⣄⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠸⣿⡧⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢿⣉⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢸⣦⠼⡙⣀⠀⠀⠀⣠⣴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣼⣟⣿⠃⠀⣼⣿⠖⣫⡉⣀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣶⣿⣿⣿⠃⠀⠖⣪⣽⡷⠦⢎⣉⡘⣿⣿⡀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⣿⣧⠚⣚⠤⣾⣿⠨⠤⡈⢁⡙⢿⣿⣶⣿⠋⠉⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠼⢇⣩⣭⡟⠁⢠⣷⠛⢉⢭⢴⡏⢻⡶⠂⣌⠉⢃⢨⣿⣯⣿⡷⣄⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡼⠾⣉⣤⣽⣃⣴⣿⡿⠛⡁⠂⣾⠇⢸⡦⠴⣀⠋⠛⣿⣿⠈⢳⣍⡁⠒⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣸⢿⡷⠾⣹⣭⣿⣿⡽⠻⢗⠪⠠⣥⣿⠀⣸⡤⠥⠋⠓⠚⣿⣿⡄⢈⡧⠄⢊⢃⢸⡇
⠀⠀⠀⠀⠀⠀⣰⡟⢸⠶⠺⣱⢤⢿⡟⠀⡷⠶⢊⢄⣨⣿⠀⣿⣄⣠⠂⠒⠒⣿⣿⣷⣼⠷⠂⢀⣉⠸⣇
⠀⠀⠀⠀⠀⢰⢹⠇⢸⡶⠚⢋⡶⠛⢷⣰⠶⠴⠉⡀⣀⣿⣸⣏⡀⠀⠐⠦⠄⡆⢿⣿⡟⠓⠂⠠⠤⠀⢿⡄
⠀⠀⠀⠀⠀⢨⡈⣇⠈⣿⡶⢋⠊⡭⣉⣿⠤⠤⡢⡀⠀⣿⡟⠁⢀⠀⢆⣀⢠⡅⣿⣟⢉⡈⠀⠀⠶⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⢊⠈⠳⢼⣿⣷⠏⠩⠐⢭⠀⠀⠄⢉⣽⠟⠋⠉⠁⡄⠀⢀⡙⡰⡏⠁⠀⠀⠐⠒⠃⠀⢰⠣⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣻⣻⡟⣿⣿⣟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣧⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣶⣶⣤⣤⣤⢤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⡻⣗⡯⢞⣽⣾⣿⠿⢋⣴⢿⣻⢿⣿⣿⡷⠶⠷⠶⢬⡆
⠀⠀⠀⠀⠀⢾⡀⣹⣿⣯⢞⣵⡧⢞⡿⣻⡟⣴⡟⡱⢛⣵⢉⣀⢀⣀⡀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣯⠟⠴⠟⣥⣿⣾⠋⣼⢡⡞⣯⡀⠿⠟⢈⡗⠀⠀⠀⢤⡀⢣
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⡠⠒⠊⠀⠙⣿⣷⣗⣿⣹⢰⣿⣙⢶⠖⣿⡄⠘⢶⣄⠀⠹⣄⢣
⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠐⠂⠤⢹⣿⣿⣿⣿⡿⠀⣞⣵⢇⣇⢿⣄⠈⠻⣷⣄⠘⣆⡃⣤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠉⠉⠘⠋⡞⣍⢧⢻⢷⣤⣈⠙⠳⣝⠛⢮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⠎⢯⡻⢿⣛⠲⣜⣾⡛⢻⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠦⠙⢷⡀


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

⣶⠿⣍⡙⠳⠶⠖⠒⣒⡶⢤
⢹⡳⣿⣌⠳⢦⣄⡀⠀⢠⡞
⠀⢇⠈⠻⣄⠀⢀⠹⠗⠺⢤⣀
⠀⢸⡄⠀⠘⣧⡸⡷⠀⠀⠀⠈⠙⠢⣄⡀
⠀⠸⡇⠀⣀⠼⢷⡀⠀⠀⠑⠦⡄⠀⠈⠹⠦⣄
⠀⠀⠣⠞⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠠⣄⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣄⡀⠀⠀⠀⠹⠀⡿⠘⣷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢉⣡⢾⣋⠁⠲⠀⠐⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡌⢽⡝⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠠⡄⠀⠙⠲⠤⠀⠙⠚⢿⡦⡷⢶⠌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣤⠀⠈⢮⣑⡢⠄⢐⠢⢄⠁⢈⠪⣫⡳⣥⣌⣒⣢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢳⡓⣄⠂⠙⠿⣆⡀⠉⠲⣄⠢⣄⣈⠊⠍⡉⠙⢆⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⢄⠗⣤⣀⠀⢁⠢⡀⠳⡌⠚⢿⠭⡆⢈⠑⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠑⣎⠹⡟⢦⡀⠈⢤⡈⢀⢬⣁⠀⠛⠓⠄⠉⡒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⣶⢛⡄⢳⣄⠈⢂⠈⠁⠒⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣧⠾⡀⠑⢍⡒⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠛⢽⣎⠀⠉⣲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠓⠀⠈⠀⠻⣦
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠀⠀⠈⣙⡢⠀⠀⠀⡞⠁⠈⢳⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠃⠀⠀⡕⠀⠀⠀⣀⠀⠒⠂⠀⠠⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⢀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⢁⠀⠀⠀⠀⠋⠇⢀⣠⠔⠁
⠀⠀⠀⠀⢦⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⡄⠐⠒⠒⠁⢀⡔⠀⠀⢀⠼⠋
⠀⠀⠀⠀⠀⠑⠦⣀⠀⡐⣧⡌⠑⠂⠦⠄⠚⠛⣲⠤⠤⠀⠁⢀⡠⠰⠉
⠀⠀⠀⠀⡀⠤⠀⠀⢙⡗⠐⠚⠓⠂⢄⣀⣀⣀⡄⠀⢀⣴⣞⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠨⠉⠛⠀⢰⡿⠋
⠀⠀⠀⠐⢀⠀⠀⠀⠀⠂⠉⠠⠠⠆⠉⠀⢰⡇⠀⢾⣡⠔
⠀⠀⠀⠀⠀⠀⢰⠖⠀⠁⠁⠀⢀⠐⠈⠉⡝⢱⣄⠙⠥⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⢨⠝⠁⠀⠀⠀⠁⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠣⡀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠑⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠲⠲⠒⡐⢢⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠉⠘⢼⡋⣾⡏⣿⡖⣦⣤⣀
⠀⠀⠀⢀⡀⠀⢀⠤⠠⢄⡔⠁⠀⠀⠀⠀⠀⠀⣠⣸⠻⢡⣟⠱⢿⠂⡽⢃⣬⣿⢲⣦⢄⡀
⠀⠀⠀⢦⠽⡚⠡⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⢻⠰⣂⠟⣣⣷⠘⣅⣿⣡⣝⠎⡿⢜⡟⣗⣶⡤⣤⣀⣀⡀
⠀⠀⠀⠀⣉⠽⠶⠂⠀⠀⠐⠚⠸⠀⠀⠀⠀⠈⠻⡚⠃⢉⢁⠙⠺⠁⠫⢭⢈⣵⠰⠞⣜⣵⡿⠻⣃⡌⣮⠏⠹
⠀⠀⠠⠾⠓⡖⡰⢚⡲⠖⣠⠶⠂⠀⣀⠤⠒⠀⠒⠛⠿⠯⣮⣧⠐⣤⡝⢟⡋⢁⠠⡄⠐⣯⠤⠤⣙⣃⣈⠕⠁
⠀⠀⠀⠀⠀⡗⢰⠗⣽⣋⠤⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁⠀⠀⠙⠿⠻⠟
⠀⠀⠀⠀⠀⠁⠀⢸⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠙⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⢀⡠⠔⠊⠁⠀⠀⠀⠈⠐⠠⣀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡔⠂⢀⣰⣦⠀⠀⠀⠠⠒⠉⣩⣿⡍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢘⠀⠀⣾⣿⣿⡇⠀⠀⡅⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠢⢀⣘⡿⠟⠐⢄⠄⠐⠤⢀⡹⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠊⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡊⠁⠀⠀⠀⡰⠁⠉⠁⠖⠒⠖⠈⢋⠀⠀⠣⡀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⢀⡤⣊⢁⡀⠀⠀⠀⠀⣠⠞⠀⠀⠀⡘⠀⠀⢀⠀⠈⢆⠀⠀⠈⠢⡀⠀⠠⠑⣢⡀
⠀⠀⠀⠀⢠⠊⠶⡄⠀⠀⢀⡠⠐⠘⠀⠀⠀⠀⢀⠃⢤⠀⠘⡀⠀⠈⠣⡀⠀⠀⠙⢄⠀⠀⢁⢈⣦
⠀⠀⠀⢀⠃⠘⠀⠀⡠⠊⠁⠀⠀⡇⠀⠰⠀⠀⡌⠇⠀⡄⠂⢁⠀⠀⠀⠹⡄⠀⡃⠘⡢⢄⠈⠀⠄⢣
⠀⠀⠀⢸⠀⠁⢠⠊⠀⠀⠀⠀⣰⠁⠘⠀⡠⠊⠀⡌⠀⠀⠀⢸⡆⠀⠀⠀⢠⠈⠁⠤⢁⠀⠡⠀⠀⠋⠆
⠀⠀⠀⢸⠀⢀⠆⠀⠀⠀⠀⠠⠁⢀⠔⠉⠀⠀⡰⠀⠆⠀⢀⠆⠸⠀⢀⠀⢸⠀⠘⠃⡈⠀⠀⢣⠀⠀⠰⡀
⠀⠀⠀⠀⠆⡈⠀⠀⠀⠀⠀⢸⢠⠊⠀⠀⠀⡜⡈⠀⢀⡔⠃⠀⢸⢠⠊⠀⡈⠀⠀⢠⠃⠀⠀⠀⠑⠢⢄⡱⡀
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠰⠀⢀⠔⠉⠀⠀⠀⠘⠁⠀⢀⠃⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣘⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣾⣶⣷⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⢷⠿⢿⣿⢿⣿⣿⢿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢨⠍⠉⢋⡭⡩⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠪⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠠⡊⡇⠀⠀⠀⡢⠈
⠀⡀⠂⠀⠀⢈⠐⡀⠈
⡆⠀⠀⢀⠰⡧⠊
⡇⢀⣶⣬⠀⣄
⡇⣿⣿⣿⣿⣿⣷⣄
⠃⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣄⣀⡀
⠀⠸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣶⣤⣄⣀
⠀⠀⠙⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣟⣿⣛⡵⣫⡽⣻⣿⣿⣿⣷⣶⣦⣤⣤⣀⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣾⣿⣞⢥⡾⣫⡴⢛⣽⣿⣿⣿⡿⠛⣿⢿⣿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢋⣔⣧⣾⣫⣶⣻⣿⡿⠁⠈⠛⠎⠹⠚⠋⠹⢏⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢄⣀⠈⠑⠦⣑⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⣭⣽⣾⡎⡧⣵⣠⣶⣼⢿⣿⣖⣾⣿⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣛⢿⠯⠙⡓⠿⠿⠿⠳⠙⠛⠛⠛⠻⣿⣝⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠨⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠁⠈⠑⠂⢄⠀⠀⡄⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⠀⠑⠄⠈⠀⣀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠒⠀⠀⠀⠀⠀⠐⠒⠒⠨⠄⢀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠡⡀⠈⢂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠐⡀⠀⢂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠁⠀⠲⢀⠀⢢⠀⠀⠀⠀⣢⡬⢤⢒⠚⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠂⠱⠤⠠⠶⣷⣿⠞⠈⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠃⡀⠀⠀⠀⠀⢀⠠⠐⠁⠀⡀⠄⠂⠀⠀⠑⠒⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁
⠀⠀⢠⠒⠀⠐⠂⠉⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⠐⠠⢀⣀⣀⠤⠀⠀⠀⠀⢰⡻⠷⣾⣥⠆⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠂⠉
⠀⠀⠀⠑⠂⠀⠀⢂⠠⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠚⠋⠉⠀⠀⠀⣠⠀⠀⢀⠩⠛⠋⠁⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⢀⠔⠁⡀⠠⠀⠒⠒⡰⠒⠁⠀⠀⣀⠀⠀⣤⠄⠒⣩⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠔⠀⠀⡠⠀⠁⠀⠀⡔⠀⢀⠊⢀⠀⠀⢠⠐⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠂⠀⡠⠊⠀⠀⠀⠀⡜⠀⢀⠃⠀⠈⠄⠀⠸⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⢀⠤⠊⠀⠀⠀⠀⢀⠌⠀⢀⠃⠀⠀⠀⠐⠀⠀⠓⠠⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠈⠁⠀⠀⠀⠀⢀⠠⠊⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠈⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠢⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡤⠄⠀⢀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⠊⢉⢠⡄⣀⠔⠁⠀⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡶⠿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⣤⢴⡾⣿⠶⠚⠛⠶⣶⣤⣄⣀⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡴⢋⠔⠁⠀⣰⠤⠿⠛⠛⠛⠛⠛⠓⠒⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠟⠡⠃⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠠⣊⠔⠁
⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠘⣄⠉⠓⠶⢶⣒⠒⠒⠒⠒⠶⡢⡄
⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠈⠁⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣯⡳⣄⠀⠀⠀⠈⠒⢤⣠⣳
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠙⢮⡳⣄⠀⠀⠀⠀⠈⠛⢧⣀
⠀⠀⠀⠀⠀⠀⠈⡟⣿⡄⠀⠹⣮⡻⣦⡀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢳⡈⠳⢤⡀⠈⡳⣦⡙⢦⣀⠀⠀⠀⠀⠈⠛⢽⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠶⠾⠿⠿⢦⡙⢷⣄⠀⠀⠀⠀⠀⢣⠿⠤⣄⡀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢷⣦⣤⢀⣤⠀⠀⠀⠀⢳⣀⣀⡤⠒⣉⡴⠞⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠵⠋⣿⡦⡄⠀⣀⢨⣍⣉⣉⣛⡳⢶⡒⣛⣛⣓⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⣦⡟⢧⣈⡙⠲⠾⣟⠳⣽⡉⠁⡨⠽⣷⣝⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⣿⣿⣟⡒⢦⡱⢽⣝⡯⠟⠉⠙⠎⠙⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡿⣌⢿⣌⢻⣲⣌⡓⢿⡿⠷⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⠇⢹⠀⣿⡆⡇⡇⠙⡆⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡃⠀⣾⢸⢡⡇⣧⡇⠀⢻⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠳⣜⢦⣷⠬⡽⠆⠸⣆⠓⣚⣭⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡟⢷⣙⠲⢤⣉⠋⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠈⠉⠉⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠚⠁⢠⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⢀⣀⣤⠴⢻⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠤⠒⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⠀⢀⡞⢠⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⠶⠋⣰⣾⡟⠂⠛⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⠏⣁⣠⣿⣿⡿⢁⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣿⣯⣁⣴⣿⣿⣿⡿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠷⠶⣌⣹⣿⣿⣿⡿⠋⠀⡌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⣤⣀⣀⣸⣿⣿⣔⣾⣼⣯⣿⠛⠉⠀⢀⡼⠃⣰⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢁⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣤⠀⠀⠀⢼⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⢀⣴⠟⠉⠀⣀⣤⣶⣿⣿⣿⡿⢹⡿⠀⠀⠀⣁⣠⣤⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠤⠶⠛⠁⣰⡶⠿⠛⢉⣿⣿⠻⢟⣡⡿⠃⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠤⠄⠀⣠⡾⠛⠁⠀⢠⣾⠟⣵⣾⡏⠋⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡴⠞⠉⠀⣀⣤⡶⠟⠉⣴⡿⠋⠀⠀⠀⠀⠀⠀⢄⣠⡟
⠀⠀⠀⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⣰⠋⠉⠀⢀⣠⣾⣿⠀⠀⠀⠀⠀⢀⠀⠐⠛⠋
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠛⠉⠁⠈⣿⡀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⠝
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⡒⠈⠁⠀⠀⣀⠀⠈⠉
⠀⠀⠀⠀⣀⣴⣁⣠⠤⠴⠶⠤⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠁⠐⠚⡑⠂⠉⠉⠱⠿⢮⣤⠤⠔⠒
⠀⠀⠀⠻⠶⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠤⢀⠀⠀⠀⠒⠒⠶⠒⠂⠀⠀⠐⠶⣆⠠⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠙⠒⠶⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢧⣾⣇⡽⢲⣦⠬⢀⣀⣄⡡⠤⠤⠖⠦⠼⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡈⠛⠒⠦⢀⣒⣀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣄⣀



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⢛⠛⣛⡿⠖⠛⢋⣉⡤⠄⢖⣊⣳⡂⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢸⠘⠷⠶⠖⠛⠉⠁⠀⣀⣀⣤⣬⣽⣦⠘⣄⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⠛⠛⠻⠷⢖⡤⡒⠋⠉⢉⣒⣂⣠⣬⣧⠘⣦⣤⣄⣬⡍⢻⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣈⣛⣛⣛⠻⠿⠿⠿⠿⣛⣛⣛⣫⣭⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠁⠘⠲⠤⣤⣤⣀⣤⡔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⣧⠈⣉⡉⢁⠀⢀⡀⣀⣀⣀⣀⠤⠴⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⢿⡀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢀⣠⣼⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣦⣤⣤⣄⣀⠀⢀⣠⣤⠤⠀⠀⠤⠤⠤⣤⣤⣤⣤⣴⣾⣍⣀⣀⣻⡀⠉⠉⠉⠉⠉⡼⠋⠉⠈⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⡿⠛⠁⠀⢠⡰⣄⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⡍⠉⠛⠛⠛⠲⡾⠷⠶⢤⣤⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠋⠁⠀⠀⠀⠀⠀⠱⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣇⣤⡶⠶⠟⣾⠓⠚⠓⠲⢦⡀⠀⠈⠉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠳⣄⠀⠀⢀⣤⠶⠚⣩⣶⡾⠛⠁⠀⠀⠁⠶⠞⠃⠀⠀⠀⢹⣦⣤⠞⠁⢸
⠀⠀⠀⠀⠀⢠⣶⡛⠋⠙⣇⠀⠉⠉⠛⠛⠛⠷⠶⢶⣤⣤⣤⣤⠼⡧⡙⡂⠜⣋⡤⠖⢿⣿⡟⢀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠙⠛⠛⠾⠿⠿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣤⣤⣷⣽⣿⠞⢉⣤⣴⠋⣹⡇⠼⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⣈⠉⠉⠉⠛⠛⠛⠛⠻⠿⠶⠾⣷⣶⣾⣍⣷⡀⣀⣀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠂⣰⢂⡿⠂⠀⠀⠀⠀⠀⡔⠒⠲⠦⣄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡴⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⡷⠟⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⡜⢀⠀⠈⠣⣄⣀⣀⣀⣀⡀⢀⣀⣴⠏⠀⣴⠃⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣙⣒⣒⣂⠀⠀⠀⠀⠈⠉⠉⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠶⠶⠞⠛⠉⠀⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠤⠀⣀⠀⣰⡧⠴⡗⠚⣻⣁⣸⣦⡤⠖
⠀⠀⠀⠀⠀⠀⠤⠴⣿⣚⡽⠛⠁⢸⠀⢠⡿⡆⢸⠀⢰⡇⢰⡇⢈⡽⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣟⣁⡤⢤⡤⢼⠁⢸⠃⢻⣼⠀⢸⡇⠀⠛⠋⢠⠀⠀⢀⠀⠀⢀⡼⣣⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠉⣇⡤⠖⠋⠀⠻⠴⠺⠀⠀⠛⣤⠀⢠⡄⣷⠖⣾⡴⣦⠞⠀⢀⣞⢞⡵⠊
⠀⠀⠀⠀⠀⢀⡤⠾⡏⠀⠀⠀⠀⠀⢠⣀⣿⣠⠄⡟⠿⠿⢹⡏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣦⢶⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢀⣀⣤⣾⡜⠳⣻⠿⠂⠧⠖⠂⢀⣀⢀⣀⣤⣴⠶⣖⣉⣉⣉⠉⠒⢬⡁⠁
⠀⠀⠀⠀⠀⠀⠀⣷⣲⣾⡧⠛⠉⡏⠟⠈⠋⠀⠀⣀⡠⠊⠁⠀⠫⣴⢣⣀⠷⠈⡧⢄⠈⢳⠀⠀⠈⠳⢄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⡰⠂⡏⠀⠸⠀⠀⠀⠁⢀⣠⣴⡖⠉⡱⠁⠀⠀⠀⠁⠙⢗⣭⠷⣴⡳⠌⡇⢸⠯⡉⢳⡀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠑⠞⠁⠀⠀⣀⡤⠖⠋⠁⡟⠋⡻⢤⡃⠀⡔⠒⠂⠉⢂⡜⠁⠂⠀⠙⣞⣠⠷⣄⡹⢸⡣⢚⣶⠤⡈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⡀⢀⡀⠄⠠⡈⠒⠌⠒⢦⣶⣆⡀⡌⠀⠀⠀⣀⣀⠈⢏⡲⠗⠧⣞⠔⣱⠋⡰⣁⠠⢠⠈⠲⡀
⠀⠀⠀⠀⠀⠀⣼⠡⣴⢤⠐⠢⣀⠢⡕⠂⢁⠠⠐⡧⠠⠠⡈⠛⢶⡃⠀⡎⠀⠀⠈⣤⠋⠀⠀⠀⠈⢾⠃⢜⠔⢁⠔⡦⢀⡦⢿
⠀⠀⠀⠀⠀⠀⡟⣆⠀⠸⡇⠦⠀⠂⠒⣈⠠⡄⠰⣄⠢⠀⣴⣦⣶⡌⠑⠧⣶⡄⢐⠁⢠⠄⠐⠒⢢⠈⢟⠳⣪⡭⠞⠋⠁⠀⡼
⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡃⠘⠙⠣⠉⢮⢹⣈⠃⢈⣀⠴⢯⡁⡠⠛⠉⠙⢪⡑⠧⡀⢢⢠⢰⣄⣤⠤⠚⠋⡁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠳⣍⡀⡳⡜⠛⠛⡿⠉⠀⠀⠀⡸⢁⡴⠒⢢⠀⣇⣀⣨⠽⠚⠋⠁⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠉⠳⢤⣀⢸⠁⢠⠊⠑⡄⣇⣸⣠⡤⠜⠒⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠒⣚⠋⠉⠁⠀⠀⠒⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠁⠁⢀⣀⡤⠴⠒⠋⠁⠀⢀⠀⣠⡀⣴⣠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠙⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⢠⠟⣷⠁⠿⠘⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⡀⠀⠀⠀⡀
⣿⣯⢭⣟⡛⣛⣛⠛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⣠⠎⠉⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢆⠀⠶⠚⠉⠉⠉⠳⢆
⠀⠀⠼⠀⠀⠀⢀⣀⣠⡶⠷⠤⠤⢀⢀⣀⠀⠀⠀⠀⡇⠀⠀⣻⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⢲⣄⡀⠀⣾⡛⡟⠀⠀⣀⠀⠀⢻⡀⠀⢘⠉⠻⡛⢷⣾⠿⠇⠀⠸⠿⢷⡄⠀⠀⢧
⠀⠀⠀⠉⠻⢦⠀⠉⠻⣄⢸⣏⣷⠀⠈⡇⠀⢹⡄⠀⢙⠃⠀⢳⡆⠀⠀⠀⠀⢹⠀⠀⠘
⠀⠀⠀⣀⠶⠴⠀⠀⠀⠈⡟⢧⡀⠁⣴⠃⢀⣀⡄⠀⠰⠀⠀⠈⡇⠀⠀⠀⠀⠘
⠀⣼⠁⠀⠀⠀⠀⠀⠀⣠⡇⠀⣡⠀⠉⣇⠀⠉⠀⠀⢀⠀⠀⠀⡇⠀⢂⣀⡀⠚⠀⠀⢠⡀
⠀⣧⠀⠀⠀⠀⠀⣀⣴⠞⠻⠿⣿⠀⠀⢸⣦⣀⣤⣦⣾⡄⠀⣠⣧⡀⠀⠀⠀⠀⣀⣠⡟⠁
⠀⠙⠿⠿⠿⠿⠿⠏⠁⢀⣶⠟⢹⣀⣴⡟⠉⠉⠉⠀⠈⠿⠿⠟⢻⣿⣿⠿⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢠⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡄⠀⠀⠀⠀⡀
⡀⠀⠀⠂⠀⠀⠀⣴⣿⠾⠋⢡⡿⠀⠀⠀⠈⡟⠲⢤⣄⠀⠀⠀⢠⢸⣿⣷
⠁⠀⡀⠀⠀⠀⢰⡏⠷⠶⠶⠟⠀⠀⠀⠀⠀⢧⠀⠀⠉⢻⣶⡄⢠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⢰⣷⠀⠀⠈⠻⠶⠿⠛⢁⢄⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠄
⠈⠈⠀⠀⡀⠀⢸⣿⡄⢀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⢦⣬⣽⣿⡟⠃
⠀⠀⠀⠀⠀⡀⠀⠹⣿⣿⣦⣆⡀⣿⣷⠀⡀⠀⠀⠀⣼⣷⣾⣿⣿⠏
⠀⠃⢀⠀⠠⠐⠠⠄⠈⠻⠿⣿⣷⣮⣉⣾⣧⣿⣷⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡄⠀⠀⠀⠀⢈
⠀⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⢀⣸⣿⣿⣿⠉⣻⣯⣽⡿⢿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣔⡠⠀⠂
⢀⣼⡾⣦⡄⠠⣀⠀⠘⠀⠀⠀⣿⢹⡏⣿⠀⣹⡇⢸⡇⢸⠃⠀⠀⠀⠀⡀⢠⣿⢿⣿⣷⡄
⢹⢿⠃⠀⠹⣦⠀⠀⠀⠀⢀⣼⠃⣿⢸⣿⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠠⠁⣸⠃⠀⢸⣿⣿⠰
⢻⣿⣆⠀⠀⠘⣧⣤⣤⣴⠟⠁⣠⡗⢸⡇⠀⣼⡇⠀⣷⠘⣷⡀⠀⠀⢀⣴⠇⠀⠀⢨⣿⣿⢀
⠀⢿⣾⣷⣤⠀⠀⠈⠉⠀⢠⣰⠟⢀⣿⠇⠀⣿⣇⠀⢻⣧⡈⠳⠾⠷⠟⠁⠀⠀⠀⣿⣾⠇⠚
⠀⢡⣿⣿⣿⣿⣾⣶⣦⣷⡾⠉⢀⣾⡿⠀⠘⣿⣷⠀⠈⢿⣿⣦⣤⣤⡀⣤⣠⣴⣿⣿⠇⡈⠰
⢰⣿⣿⡁⠈⠀⠉⠉⠉⠁⢀⣴⣿⣿⠇⠀⣾⣿⣿⣧⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⡁⠀⢀
⠈⢻⣯⣷⣮⣁⣤⣤⣄⣤⣿⣿⡿⠃⠀⠀⣿⠇⢿⣿⣧⣄⠀⠀⠈⠛⢿⣶⣦⠄⠠⠉⠀⠈
⠀⠀⠉⠿⠿⠿⠿⠿⢿⣯⣿⠏⠀⠀⠀⠈⣿⠂⠀⠙⢿⣿⣿⣦⣶⣤⣾⣟⣿⡇⠀⠀⠠
⠀⠂⠐⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⣄⣸⡿⠂⠀⠀⠀⠈⠉⠛⢻⣿⣿⠿⠛⢁⠀⠑⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣷⣤⣶⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨
⠁⠀⠀⠏⠀⠀⠀⠈⠀⠙⠿⠿⠿⠿⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠃⢠⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠴⣾⠋⣽⣹⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠖⢋⣩⠖⠁⠀⠀⣀⠀⣾⣰⡇⡜⣿⢸⣇⠞⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⣠⠖⡋⠁⣧⠴⠟⠒⠛⣻⠆⢰⡷⡟⡿⠑⠟⠀⠏⠀⡁⠀⢰⠇⣰⠇⠀⢀⣠
⠀⠀⠀⠀⣴⡯⠖⠋⠀⠀⣧⠀⠀⣠⠞⠁⠈⠙⠚⢠⠀⢀⢠⠀⣤⢸⣷⢛⣾⠞⢹⠀⠀⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠚⠁⠀⠀⠀⠀⠀⣸⠀⠿⠻⠞⣿⣼⠙⠋⣿⠀⠘⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠀⠀⠀⣠⢤⡖⠀⠀⣿⣠⡴⠀⢸⡇⠛
⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠋⠁⠀⠀⠀⢀⣀⡠⢤⠔⠶⣒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠛⠉⠁⢢⡗⠀⠒⢠⠙⢆⠈⢲⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠊⠁⠀⠀⣠⡄⡰⠒⠾⢭⡢⢤⡊⢀⣠⠤⠃⡠⠗⠒⠐⢸⠀⡰⢀⡬⠔⢊⣉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣄⠎⠲⠃⠈⠁⠀⠀⣀⠓⠂⠉⠒⢤⣠⠊⢀⡀⠴⣒⠡⠶⠵⢍⠀⢎⢹⣂⠇⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠃⡄⠀⠀⠀⠀⠀⠀⠤⠏⠁⣨⡤⠒⠂⣏⢙⠤⣠⠊⢠⠂⡏⠌⡲⠑⣤⣈⡤⠖⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠐⠀⢀⣀⣶⣲⠃⠀⠀⡇⢀⣀⣰⣾⠄⠑⢩⠛⠲⣝⣓⣨⠴⠚⠉⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠉⠳⢤⣀⡔⡉⠀⠀⠀⣱⠼⠾⣔⠋⠀⠀⠈⢣⣀⣠⠷⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠙⠧⣄⣀⡞⠠⠀⠀⠈⣧⣠⠴⠒⠉⠁⠀⠀⠀⠈⠁⠀⢀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠈⠉⢛⣒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣈⣁⣀⡤⠴⠚⠉⠁⠀⠀⠀⣀⡴⡴⠖⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠉⠛⠛⠋⠉⠉⠳⣄⠀⠀⣴⠏⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣉⣤⠶
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠋⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⢁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠟⠉
⠀⠀⠀⢀⣠⣤⢶⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⣰⠟⣰⡟⠉⠙⠛⢶⡄⠀⠀⠀⠀⠀⢀⣠⡶⠛⣉⣤⠾⠋⠁
⠀⢀⡴⠛⣁⣤⠾⣗⠶⠀⠀⣤⠶⠄⠀⠀⠀⠀⠿⠀⠀⢀⡾⢋⣼⠋⠀⠀⠀⠀⠀⡿⠳⣦⣀⣴⠞⢋⣡⡴⠛⠉
⣰⡏⣠⡾⢯⡜⠓⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡿⠁⠀⠀⠀⣀⠀⢘⣻⡶⠟⣉⣴⠞⠋⠁
⣿⠀⣿⣹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠏⠀⠀⠀⠀⣀⣼⠷⢋⣥⡶⢻⡏⢸⡇
⢻⣦⡟⠷⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠞⣩⡴⠞⠋⠁⠀⢸⡇⢸⡇
⠈⣿⣿⣗⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⠶⠛⠉⠀⠀⠀⠀⠀⢈⣹⣿⠁
⠀⠘⣿⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠃
⠀⠀⠘⢷⡝⠶⠍⠛⠻⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠀⣼⠏
⠀⠀⠀⠈⠻⣾⠛⠦⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠙⠷⣝⡛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡂⠈⠀⠀⡈⠀⠠⠀⠀⢀⠀⢀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠠⠠⠄⠀⠂⢀⠀⡀⠀⠀⠈⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢠⠔⠁⠀⠀⠀⠀⠀⠀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢐⠜⠁
⠀⠀⠀⠀⠀⣠⠁⢰⠉⠄⠀⠐⠃⠀⠐⠋⠀⠈⠁⠀⠀⠉⠀⠒⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠘⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢙⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢾⣱⣾⣿⢰⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⣬⡀⠀⠀⠈⢻⠛⣼⢻⣿⢼⣿⣱⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⢛⠁⠀⠀⠀⢠⣿⢸⣿⣿⠸⣫⡩⢾⡿⣻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣴⠊⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⡾⠇⣾⣿⣿⣿⣾⡿⡌⣶⣿⣷⡿⢻⠟⣿⣿⣿⣿⣿⢋⠀⡁⠺
⠀⠀⠀⠀⠀⠀⢠⣶⠏⢠⠂⠀⡀⠀⡄⠀⠀⠀⢈⡀⠀⢀⠃⠀⠀⠀⠀⠀⢹⣷⣧⣿⣿⣿⣾⣿⣶⣿⣿⣿⠟⠁⠌⠀⡰⠃
⠀⠀⠀⠀⠀⣠⡾⠋⣰⣃⣠⠞⢁⠀⠀⢀⠀⠀⣀⣠⣖⣁⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡿⠿⢟⣛⠭⡀⠈⢀⡸⠊
⠀⠀⠀⠀⠐⠯⠁⠾⣿⠟⢁⠐⠁⢀⣾⠋⠀⠈⠀⠀⠀⠀⠉⠉⠓⠒⠒⠀⠘⠲⠒⠒⠒⠒⠒⠋⠁⠀⠀⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⡆⠀⠀⠚⢿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠖⠂⠐⠒⠒⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠹⢐⠘⠭⠉⠛⠷⢄⠀⠀⠀⢀⡖⠉⠁⠙⢯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠊⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⢤⠀⠀⢸⠁⠀⠀⠀⣟⠂⠀⠀⠀⠀⠀⢀⣀⣐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠒⡄⠜
⠀⠀⠀⠀⢠⠀⠀⡠⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⠏⠀⠀⠀⠀⣔⠖⠀⠀⠀⠀⠀⣈⣆⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠸⡀⠈⠀⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⢁⡔⠀⠀⠀⠀⠐⢥⢿⠀⣄⣠⠔⠋
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠐⠤⠤⠶⠋⠀⢀⡤⠀⠀⠂⠀⣸⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠈⣥⠐⠲⣖⣀⠀⠀⠀⢀⢿⣥⣄⡀⠀⠀⢀⡴⠛⠁⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⣦⡹⠶⢆⡀⠉⠉⠛⠉⠉⠉⠡⠴⠛⠛⠋⠁⠀⢀⣠⠖⠡⠃
⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢘⡻⠁⠐⠛⠓⠚⠤⣄⣀⡀⣀⣀⡄⠀⠀⢀⡴⣾⣏⠁
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠉⠝⠛⠩⠿⠁⠀⣰⣿⡟⠃⠀⢀
⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⣈⡷⠄⠀⠀⣀⡠⠶⢮⣁⢤⡆⠀⢀⣿⠂⠀⣀⠔⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠈⡁⢀⡄⠐⠊⠙⠊⣁⢀⡀⣾⡇⠀⢘⣿⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢁⡾⠗⠈⠁⠀⠀⠀⠀⣀⠖⠉⠁⢠⠏⢸⣆⠀⠉⠤⢀⡀⢀⣀⣀⠀⠀⡔⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⢸⠀⢛⠋⡗⠀⠀⠀⠁⠈⠓⠛⠏⠜⡌⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡆⠸⣅⠀⠀⠀⠀⠀⠀⠀⢰⠆⠈⡰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢱⡀⠘⢦⡀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠑⢤⡀⠈⠁

⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⡠⠀⠀⠀⠀⠀⡄⣐⣰⣂⡀
⠀⠀⠀⣤⣿⣿⣿⣿⣤⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⠬⣿⣿⣿⡎⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⣽⣿⣿⣿⡧⠀⠀⠀⠐⣾⣿⣿⣿⡒
⠀⠀⠀⢠⠿⢿⡿⢯⠀⠀⠀⠀⠀⠹⠿⠟⠃⠀⠀⠀⠀⠈⠽⠿⠿⠓⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠐⢚⠿⡿⢟⠓⠀⠀⠀⠈⠝⢿⠿⠛⠌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣄⣂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⡄⣂⡐⢀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⢀⢹⣿⣿⣿⡧⠄⠀⠀⠀⠠⣿⣿⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⢒⢾⣿⣿⢀⡒
⠀⠀⠀⠻⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠚⡻⢿⠿⡓⠂⠀⠀⠀⠀⠋⠛⠑⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠁⠆⡉⢁⠲⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢤⣰⣦⡆⡀⠀⠀⠀⡀⢦⣴⣤⠆⡀⠀⠀⠀⡀⢆⣶⣠⢄⠀⠀⠀⢀⡄⣴⣇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣅⡂⠄
⠀⠀⠀⣽⣿⣿⣿⣿⡥⠀⠀⠠⣽⣿⣿⣿⣿⠥⠀⠀⢠⢽⣿⣿⣿⡯⡄⠀⠀⣀⣻⠁⠀⠙⡟⠆⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠅⣾⣿⣿⣿⡎⠄
⠀⠀⠀⠚⣻⢿⣿⡟⠂⠀⠀⠀⠊⣻⢿⢿⡛⠂⠀⠀⠀⠊⡻⠿⢿⡓⠂⠀⠀⠈⣙⣷⢤⡞⠻⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠂⠝⠿⠿⠟⡔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠠⡰⠘⠰⢢⠀⠀⠀⠀⢀⣠⣤⣆⡀⠀⠀⠀⠀⣠⣢⣖⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣷⣶⣄⠀⠀⠀⢀⠰⣀⣆⡐⢀
⠀⠀⠠⠅⢰⣿⣷⡄⠩⠀⠀⠀⢺⡏⠀⠈⣿⡂⠀⠀⢸⣹⠁⠀⠈⣳⡅⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠌⣿⣿⣿⣿⡅
⠀⠀⠀⢫⢌⠙⢋⠠⠑⠀⠀⠀⠙⠷⡦⣶⠟⠀⠀⠀⠘⢭⡷⢤⡴⡿⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠀⠀⠀⠐⢙⠿⠿⢟⠐
⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣾⣽⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⢀⠤⠔⠒⠒⠢⢄⡀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣀⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⡀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠔⠒⠢⠤⠋⠙⣦⣀
⠀⡠⠔⠋⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠁⠑⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠜⡠⠔⠒⠒⠠⠄⣶⠤⣑⠂⣄
⠸⣀⠀⠀⢠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠃⠀⠨⠀⠀⠀⡠⡔⠋⠀⠀⠂⠈⡹⠯⠶⡄⡀
⠀⠈⠑⢢⢄⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠂⢡⠁⠀⡄⠀⠂⢇⡔⠉⠀⠀⠀⢋⠤⠒⠉⠠⠄⠀⢹⣌⡑⠢⣄
⠀⠀⠀⢸⠀⠉⠒⠤⡈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⠤⠀⠀⠘⠢⡀⠀⠄⢀⣠⣦⡲⠀⡀⠂⠁⠀⠈⢀⡀⠄⠊⠁⣠⢹⠀⠀⠉⠂⢄
⠀⠀⠀⠈⠢⢄⡀⠀⠀⠑⠢⢌⠑⠢⢀⠀⠀⠀⠀⠀⢀⠤⠒⡋⠀⣰⠥⠴⢦⣤⣌⡂⢁⠈⠢⢄⢩⣴⡶⢶⠵⣄⠑⢀⣞⡉⠀⠂⠀⠀⠁⠀⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠉⠒⠄⡉⠒⠀⠒⠊⠀⡰⠧⢭⣚⡥⢤⣥⣇⣀⣼⠚⠉⠉⠂⠆⠀⠀⢰⠁⠀⠀⠙⠉⠁⠙⢢⣀⣀⠀⠀⣀⢇⡠⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠈⠑⠠⢀⠀⠀⠑⢤⢾⡁⠀⠀⠀⠀⠉⠛⢦⠀⢀⠀⢠⣄⠠⡀⢀⠠⠴⡁⠀⠀⠀⠈⠂⠈⡉⠄⠊⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠉⠒⢄⡀⠉⠃⠀⠀⠀⠀⢀⡀⠜⣀⣀⢠⣌⡨⠏⣘⠁⡀⢠⠈⠁⠀⢀⡠⠒⠉⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠁⠀⡎⠀⢀⠀⠀⢙⡄⠃⠀⠓⠁⣀⠤⠊⠁⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠁⠢⢄⡀⠀⠃⠐⠀⠀⠀⠈⠃⢀⡠⠔⠈⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠈⠐⠤⣀⠀⠀⣀⠤⠂⠁⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⠁⠀⠀⣀⠤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣄⣠⣶⣶⠆⢐⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⠿⠟⠛⢛⣩⠥⠂⣠⠋⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠟⠛⠉⠩⠔⡀⠤⠀⠀⠀⠀⠀⢀⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠞⠋⠉⠀⠀⡀⠀⠠⠶⠇⠐⠂⠀⠀⢀⣠⡒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⣀⡠⠶⠾⠁⠀⠀⠐⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⡔⢠⣄⣥⣽⠠⢚⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⣐⡿⠋⡀⠁⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⣭⣽⣲⢾⣳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⢀⣀⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠶⠒⠃⠀⠀⠀⠀⠀⣠⣶⠋⢁⣉⠀⠘⠻⣦⡩⡤⠀⠀⠀⠀⢀⢠⣀⣤⣾⠟⠀⠛⠛⠟⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠛⠉⣀⢠⡤⢀⡀⢀⣀⣀⠼⠉⠹⣄⣀⠐⣒⠈⣷⣼⣷⣀⣀⢦⣤⣼⣿⣿⠿⠋⠁
⠀⠀⠀⢰⠇⠀⢀⡶⠛⠁⠀⠠⢔⣫⣖⣰⣶⣶⣦⣬⣤⠀⠀⠀⠀⠀⣩⢻⣏⠀⡿⣿⡿⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠐⠤⢛⣒⣀⣨⣴⣾⠿⠿⠛⠛⠛⠛⢉⣁⣠⠉⠂⠀⠀⠂⠹⠬⠃⡼⡿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠹⠋⢁⣠⡤⣠⣶⣾⠿⠚⢋⡁⣀⡤⠘⡁⢀⡠⠖⠓⠈
⠀⠀⠀⠀⠀⢀⠀⠥⣚⡽⠟⣡⣾⠟⢋⣠⡦⠴⠞⠋⣀⣰⡦⠗⠋
⠀⠀⠀⠀⠔⠕⠻⠞⣭⣶⡾⢋⡠⠂⣤⡶⣶⣶⢾⣿⠟⠋
⠀⠀⠀⠄⠀⠔⠂⢈⡾⠋⡰⠀⢠⠟⢁⣾⠟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠋⣪⡎⠀⠀⠙⣴⡿⠋⠀⡿⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⣰⡏⢀⣠⡶⠗⠨⠀⠀⢰⣧⣤⠤⠤⠶⣯⢥⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠁⠀⠀⠀⠀⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⠆⠘⠁⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⡀⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡶⠰⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢄
⠀⢊⠀⢀⠀⠀⠀⡈⠀⡄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠰⠁⢉⠁⠒⡆⠀⠀⠀⠀⠀⢀⠂⠂⠀⠈⠢⡀⠡⠀⠀⠸⢤⠈⠂⠁
⡇⡇⠀⠋⠀⠀⡐⢀⠎⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⡀⢄⠀⠀⢀⠠⠂⡀⠀⠀⠀⠀⠘⣄⠑⠄⣀⣀⠠⠂⡀
⠡⡈⠀⠀⠐⠀⠠⠃⠀⠀⠀⠀⠀⠈⠢⡀⠈⠉⠁⢠⡆⠀⢀⠁⠀⠀⡀⠀⠰⡄⡀⠁⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⠀⠊
⠀⠀⠀⠒⠂⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⢠⠆⠀⡜⠀⠐⣄⠠⡀⠀⠐⠤⠤⠄⠀⠀⠠⠌⢀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠔⠁⠀⠈⠒⠒⠀⠐⠒⠀⢀⠀⠠⠀⠐⣄⠈⠳⣌⠢⠀⠀⠑⠄⠀⠀⠀⠀⡈⠈⠠⡀⠢
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠰⡀⢃⠀⠰⢀⠈⠳⣄⠘⢶⠠⡄⢀⠀⡀⢀⠈⠐⢷
⠀⠀⠀⠀⢀⠄⢀⠠⠀⡆⠀⠀⢀⠠⠂⠁⠀⠀⠀⢀⡠⠀⠐⠈⠄⠀⠀⠁⠢⠈⢧⠈⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⣸
⠀⠀⠀⠀⢂⠨⠀⠜⡠⠃⠀⠀⠂⠀⠠⠂⠀⠀⠉⠁⠀⠀⠀⡀⢘⠀⠀⠀⠀⠁⠈⡡⠀⠀⠀⠉⠹⠆⠀⠀⣷⠀⠈⢄
⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⢄⠀⠀⠁⠐⠀⠀⠀⢀⡅⠀⡒⠃⢃⠠⡐⠠⠄⠀⠊⢀⠵⠀⠀⢂⠀⢮⡍⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠱⡄⠀⠁⢃⠚⣁⠔⠀⡀⠀⠀⠀⠠⠀⡐⠀⠰⠈⠀⠈⠐⠀⠀⠂⠁⠀⠐⠀⠀⠑⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠸⡀⠡⠀⠀⠀⡀⠔⠀⠀⠀⠀⡉⠠⠁⠀⠀⠱⡀⡀⠀⠀⠠⠤⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠒⠆⠀⢀⠀⠈⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡀⠀⠌⡀⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠋⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠉⠐⠁
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠄⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣶⢶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⢒⠒⣒⣒⣒⣒⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠠⠤⠴⠒⠒⣚⢒⢒⣐⣐⡇⠀⠠⠤⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠂⠠⠬⠭⠭⠭⠭⠍⠉⣹⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⣴⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⣀⠀⣒⣀⠁⡝⠻⣿⠦⣝⢛⡠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡢⠂⣂⡏⣼⡎⢶⢑⠂⣸⣃⠈⠅⠉⠻⣽⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡑⡐⢳⣬⣵⠋⠀⠅⣠⣈⡑⠄⡙⠳⠄⠈⠛⠲⠕⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣛⢃⠀⢆⠠⠈⡏⣥⢠⣯⢫⣯⡲⣅⠱⣦⡒⠶⣌⡀⠵⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⢠⢙⠋⡘⣧⡾⠶⢭⠟⠙⢮⣕⠂⠙⠪⠚⡟⢳⣤⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣧⡟⠙⢉⠂⢆⠀⠀⠈⠛⠢⠀⠀⠈⠲⡡⣭⡙⣥⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⣤⠈⢢⠀⠀⠀⠀⠀⢀⡀⠀⠈⠈⠛⢿⣧⡈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡡⠄⠠⢂⠀⠀⡀⡰⣄⡳⣳⡀⠀⢤⠈⢿⣧⠀⠠⢉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣄⣧⣳⣽⣿⣧⣻⢢⠈⣇⢈⢫⣟⠓⢶⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣰⠂⠀⢌⡹⢟⣷⡄⠀⠈⠈⡟⡍⠑⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⢉⠹⣿⣿⢰⠸⡇⠐⣏⠀⠑⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⢠⠠⠈⣻⣹⠐⣿⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎⠠⠀⠉⠽⢯⣼⣷⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⡀⢈⡟⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⡀⡰⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠄⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠂⠀⢀⠀⠀⠀⠁⠘⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣮⣦⣤⣀⣀⣀⡀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣯⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣾⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⣿⣿⣿⣿⠟⢉⣉⣈⣹⡿⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⣿⣿⣿⣤⣿⡇⢺⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡄⠘⣿⣿⠁⢠⣾⣿⠿⢋⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⣿⣿⣿⠀⣿⡇⢻⡇⢸⡇⢸⢿⡧⢾⡏⠴⣦⣽⣧⠈⣶⣾⣿⡿⠁⢰⣿⣿⡄⠘⣿⠀⠸⣟⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣿⠇⣿⡃⢸⡇⠘⡇⠀⠊⠁⢸⡟⠳⠖⢸⣷⠀⠿⢿⡿⢧⣰⠿⠟⠛⠻⠀⠘⡧⣀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⢿⣿⠿⠋⠁⠂⠀⠐⠒⠁⠈⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠶⠋⣠⢞⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⣋⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠋⣠⡶⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠉⣤⢞⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠷⣄⡀⡀⠀⠀⠀⣀⡴⠞⢁⡴⢚⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣀⣉⣛⣛⣛⣋⣉⡤⠶⣋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⠉⠉⠉⠉⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢸⣿⡀⢸⣦⡀⣿⡏⠀⣾⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠹⣶⣦⣿⣷⣤⣿⣿⣿⣷⣼⣿⣧⣾⡟⠀⣤⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣼⣿⡿⠟⠛⠋⠉⠉⠙⠛⠿⣿⣿⣧⣾⣷⣀⣴⣾⠟⠁
⠀⠀⠀⠒⠶⢶⣤⣤⣀⠀⠙⠾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⡿⠀⢀⣀⣀⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣩⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⠤
⠀⠀⠒⠛⠛⠛⠛⠛⠛⢛⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡛⠛⠛⠻⠿⠷⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠓⠂
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⢸⣿⠟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠻⢿⣦⣄
⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠋⢁⣴⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⢦⠀⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢻⡟⠀⣿⡿⣿⣿⠻⣿⡿⣿⣧⠈⢻⣷⡀⠀⠀⠀⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠈⠀⣸⣿⠁⠉⡏⠀⣿⣇⠀⠘⠂⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⡄

⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣿⣶⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⡶⠒⢶⣶⠆⠀⠄
⠀⠀⠀⠼⣿⣿⣿⣿⣿⣯⣾⣿⢟⣝⣿⣾⡟⡽⣿⣿⣿⣿⠷⠿⠓⠙⠲⢦⢁
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣾⣷⣯⢞⣿⡿⣿⡟⡒⡢⢸⢠⣄⠀⠻⣄
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣟⣭⣿⣿⢞⠵⣣⣸⡀⢻⣆⢀⠩⣠⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⠯⠿⢯⡜⡭⠿⣷⣄⠙⢦⡀⠱⠖⠚⠀⠛⡫⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠻⢿⡿⠿⠟⠋⠁⠀⠀⠀⠉⠓⠾⣓⣶⠷⠢⡙⠎⠢⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⢳⣡⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⣿⣟⣛⣛⣛⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⠿⣿⣿⣿⡿⠿⠶⢄⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⢿⣻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣴⡿⢛⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣠⡾⠋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣴⡾⠟⠛⠛⠛⠛⠿⣶⣤⣀⡀⠀⠀⠀⣀⣴⠏⢀⣾⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⢠⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⢻⣿⣿⡟
⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣤⣼⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⣤⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⡤⠖⠛⠉⠉⠉⠐⢶⣤⣤⣀
⠀⠀⠻⣿⣶⣤⣄⣀⣠⣾⣟⣉⣠⣤⣭⣟⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷
⠀⠀⠀⠀⠉⣙⣿⢿⡿⠽⠿⠻⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⢏⣭⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⠀⠀⠀⢀⡾⠋⢀⡿⣁⣤⠶⣾⡿⠃⠉⠀⢀⡾⣿⣿⣿⣟⠈⠁⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢸⠁⢀⣞⡟⠉⠀⣼⡟⠀⠀⠀⠀⡾⣽⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⢸⠠⠋⠘⠀⠀⣼⠟⠀⠀⠀⢀⣤⣿⢟⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠈⠀⠀⠀⢀⣼⠏⠀⢀⣰⡾⠟⣿⠁⠨⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡾⠛⠁⢀⡼⠃⣠⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠄⠊⠁⠀⡴⠋⠀⠀⠐⣩⠴⠛⠉⣼⠏⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠠⠊⠁⠀⣠⡼⠋⠀⠈⠻⣿⣶⣤⣀⣀⣀⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣞⠿⠛⠿⣯⡉⠙⢳⣀⣀⣀⡀⠀⠀⠀⢸
⢠⢂⣁⡀⡀⠤⣦⡠⣄⣁⣀⣤⣀⣄⣄⣀⣀⣀⣀⣀⡀⠀⢐⡶⠿⢶⣾⣧⡔⣓⣀⣠⣤⣤⣿⣷⣾⣟⠉⠈⠻⣄⠀⠀⢸
⠀⠈⢹⣿⣿⣷⣿⣿⠿⡍⠛⠛⠛⠻⠟⠿⠿⠿⠟⢿⣿⠿⡏⣨⣤⣾⡟⡇⠨⣭⣩⣭⣝⣿⣷⣾⣿⣶⣀⠀⠀⢹⡆⠀⢸
⠀⠀⠑⢾⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⢶⣴⣍⠛⠛⠿⠯⣍⣩⡽⠋⠙⢷⠀⠘⠁⠀⢸
⠀⠀⠀⠈⠂⠈⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣿⡷⠝⠛⠁⠀⠀⠀⠈⢧⣄⣀⣀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠠⠀⠂⢄⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢀⠠⠂⠁⠀⢀⡠⠖⠃⠂⢄⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⡀⡀⣤⣦⣀⠀⡤⠒⠁⠀⠀⢀⠠⠚⠁⠂⠄⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⡄⣤⣤⢤⣀⠈⢁⡬⡝⣦⣤⣤⡀⠂⠁⠀⠀⢀⠠⠊⠉⠑⠀⡀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⢠⠔⠋⠁⠀⠀⢀⣤⣤⣤⣀⠈⠁⡬⡜⢶⣶⢧⣅⠈⠁⡀⡥⡤⢄⡀⠊⠀⠀⠀⢀⣠⡞⠉⣹⡤⠠⡀⠀⠀⠉⠓⢤
⠀⠀⠀⢸⠀⠀⠀⠀⠰⠋⠉⠛⢉⣽⣧⣄⣡⡄⠀⠁⠀⢈⢀⣺⠉⠀⠀⠀⠈⡆⠀⣠⡞⠅⣹⠭⢾⠿⢀⣴⠷⠉⠁⠀⠀⠸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠋⠁⡌⠗⠚⠲⢤⠋⠀⠈⢱⠒⠀⠨⠤⣕⢤⣌⣩⣞⣧⢀⣼⠗⠋⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠂⠀⠀⢀⡀⠇⣀⡄⠘⠠⢀⠀⠀⢢⠤⠙⢩⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠆⠀⠈⠉⠁⡠⢒⣂⠳⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠁⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠠⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠘⢃⣀⣉⠀⠰⠇⠀⠀⠀⠀⠀⠀⣄⠹⣇⠹⠀⠀⡜⢀⡀
⠀⠀⠀⠀⠀⡀⣄⣴⠟⢯⡓⣄⠀⠀⠀⠀⠀⠀⠙⠁⡄⠀⡀⠀⡀⠀⠀⠶⠂⠀⠀⠀⠲⠀⠁⢈⣤⣤⣄⠐⣡⡴⡆
⠀⠀⠀⠀⠀⢀⠸⡧⣸⣅⣼⣇⠀⠀⠀⠀⠀⠛⠃⠰⠀⠢⣀⣀⡡⠄⠁⠠⡤⠀⠀⠨⠭⠄⠀⣿⣿⣿⣿⡇⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠛⠏⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠶⠒⣡⠌⠛⠛⠋⠀⢌⡙⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤⠀⠲⠄⠀⠀⠀⠀⠀⠀⠺⠃⠀⡆⢰⠀⠘⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠲⠄⠸⡄⠀⢠⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢃⣀⠃⢠⠆
⠀⠀⠀⠐⠶⣄⠢⠄⠐⠈⡔⢀⣤⡄⠀⠀⠀⠀⠀⢠⠿⣟⣛⡛⠿⣷⡀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣦⡀⠤
⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠠⠄⠀⢤⠄⠀⠀⠀⠀⢿⣜⢾⣜⣟⡶⣿⠁⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡇⠤⠄
⠀⠀⠀⠙⠋⠁⠔⡀⠄⣀⠢⠘⠲⠄⠀⠀⠀⠀⠀⠈⠮⣯⣿⣿⡵⠃⠀⠀⠀⠁⠀⠀⠐⠂⡘⠿⣿⣿⣯⠟⠡⢄
⠀⠀⠀⠀⠚⠁⡸⠁⠀⠘⡄⠐⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⢀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠀⣠⠆
⠀⠀⠀⠀⢠⣀⢻⠢⡸⠣⠞⣏⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣤⣀⣹⠟⠀⠀⠀⠀⠑⠧⢤⣤⣤⠀⠀⠀⠀⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠍⠫⣝⢦
⠀⠀⠀⠀⠈⣲⠄⠀⠀⠀⠀⠀⠺⣍⣀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢆⢞⣻⣾⣿
⠀⠀⠀⠒⠛⣡⣟⣀⠀⠀⠀⠀⣏⠈⠁⠀⠀⠀⠀⠀⠈⠢⣈⣋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠧⣂⠥⣕⣵⠏
⠀⠀⠀⠀⠘⠉⠀⡶⠉⣦⠲⡏⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠄⠀⠀⠀⠀⠑⠀⠆⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠠⠐⠀⠁⠔⡠⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠁⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠒⠂⠄⢰⠀⠀⠀⠀⠊⠀⠀⠒⡀⠐⠂⠂⠐⠀⠀⠄⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⠃⠈⠀⠈⠂⠀⠀⠒⠈⠀⠀⠀⡠⠋
⠀⢀⠈⢠⣎⠀⠒⠋⡀⠀⠀⣀⠀⢀⣀⠠⠮⢅⣀⡀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠬⠀⠀⠀⢀⣀⠤⠒⡀⠀⣀⠠⠊⠁
⠰⠀⠀⠃⣰⠂⠠⠈⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠀⠉⠉⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠂⢠⠀⠁⠀⠀⠘⠀⠑⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢀⠀⠁⠀⠁⠀⠀⠐⠆⢈⠁⢠⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣟⣴⣹⣿⢰⣦⢤⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠔⣉⡒⠄⠀⠈⠙⣿⠟⣼⢟⣿⢸⣿⢃⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡘⠷⠃⡀⠀⠀⡀⢈⣆⢷⡞⣿⢸⢏⣞⣡⣿⡿⣹⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⡤⠪⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⢀⠀⠀⠀⣾⠇⣾⣯⣿⢰⣼⣿⡌⢫⣽⣿⣉⣈⣨⡍⣿⣻⣿⣿⣿⣿⠁⠘⠀⡇
⠀⠀⢀⣤⠆⢀⠁⠀⢀⠁⢠⠀⠀⠀⢀⠎⠠⠀⢸⠉⠉⠉⠉⠙⠛⢻⣏⣾⢸⣿⣿⣏⣵⣿⣥⣿⣿⣿⣿⠟⡑⠂⠀⣲⠁
⠀⢠⣿⠏⢀⠎⢀⣠⠂⠀⠏⠀⠀⠔⠁⠔⢡⠄⠎⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠁⠀⠠⣄⠖⠁
⣴⠿⠁⣴⣧⡶⠋⣁⡔⠀⣀⡴⠄⠠⠤⠒⠓⠒⠦⠤⢄⣈⣀⡒⠀⠠⠈⠙⠛⠛⣛⣛⣋⡭⠥⠒⠉⣇⡡⠴⠒⠁
⠙⠀⠘⠙⢿⠀⡜⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠁⠸⡘⠄⠆⠀⠊⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠂
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣿⣿⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣆⠀⠀⢠⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⡄⠀⠀⣰⣿⡿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠈⠛⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠛⠁⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⣀⣠⣤⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣤⣤⣀⣀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣴⡿⠛⠋⠉⠛⢿⣷⡀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢠⣾⡿⠛⠉⠙⠛⢿⣦⡀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣾⠏⢀⠀⠀⠀⢀⣾⣿⠃⠀⠈⢿⠙⢻⣿⣿⣿⣿⡟⠋⡿⠁⠀⠘⣿⣷⡀⠀⠀⠀⡀⠹⣷⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠻⠷⠞⠀⠀⣠⣿⡿⠃⣠⣤⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣤⣄⠘⢿⣿⣄⠀⠀⠳⠾⠟⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⢸⡿⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⡏⠀⠁⠀⢿⡇⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠸⣿⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⣠⣿⠇⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⢿⣿⣿⣆⡀⠀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⠀⢀⣰⣿⣿⡿⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣄⣀⠈⠉⠉⠉⠉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⠉⠉⠉⠉⠁⢀⣠⣴⣿⣿⠟
⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣾⣿⣿⡿⢻⣿⣿⣷⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⢀⣀⣤⣤⣴⣤⣄
⠀⠀⠀⢾⡏⠁⠈⠉⠛⠻⢿⣷⣦⣤⣀⣀⡉⠉⠛⠛⣛⣉⣥⣶⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣶⣬⣉⣙⡛⠛⠉⢉⣀⣀⣤⣴⣾⡿⠟⠛⠉⠁⠀⢹⡷
⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡖⢩⡷⠂⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠐⡄⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣠⠤⠤⣀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠨⡤⠗⣀⡀⠠⠑⠦⣤⣀⣠⠞⠒⠒⢶⢤⡀⠀⠀⠀⠙⡗⠒⠒⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣲⠘⠻⣿⢌⡁⢜⣀⢀⠔⠋⢘⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠘⡄⣼⠃⠀⠉⢢
⠀⠀⠀⠀⠔⠒⢦⡇⡄⢱⣢⠀⣸⠀⠀⣠⠜⠁⠀⠀⠈⠢⢤⠆⠀⠀⠀⠘⡄⠀⠀⠀⢜⣿⡀⢏⡀⠀⢧
⠀⠀⠀⢸⠀⠒⠤⢧⡘⠘⠦⢖⠁⠤⠊⠁⠀⢀⣤⠤⠴⠚⢿⠀⠘⡀⣀⡺⠳⣄⠐⠀⠀⠙⠳⠤⠇⠀⡹⠉⠓
⠀⠀⠀⠈⠣⣑⠄⠀⠙⠶⢤⣀⣤⣠⠤⠔⢚⡝⠁⠀⠀⢀⡸⠷⠛⠉⠉⠀⠀⠈⠓⠤⣀⣀⡀⡀⣀⡴⡟⡠⠔
⣀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠑⠽
⠀⠀⢀⡴⢋⡥⣄⡉⠑⠒⠒⠒⠒⠊⢁⠠⠀⢀⡤⠚⠁
⠀⠑⠒⠈⠀⠀⠀⠉⠓⠲⢤⣤⣀⣀⡤⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠈⠀⠛⠉⠛⠙⠋⠉⠀⠈⠓⣄⠀⠀⠀⠀⠀⣠⣾⣿⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠟⣛⣭⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴⣾⠿⠛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣾⠟⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⣼⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⠿⣶⣦⣤⣤⣠⣤⣴⠾⠋⠀⣠⡿⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿
⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣰⣿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⢿⣿⣿⠏
⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠁
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣄⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⣘⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣠⡤⠶⠶⠒⠶⠤⢤⣀⡀
⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠙⠻⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⡀
⠀⠀⠀⠙⠿⣿⣿⣶⣶⣦⣴⣿⢳⣶⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣉⣽⡿⣿⡿⠱⠛⠛⠛⣽⣿⢟⣯⠿⠛⠛⣽⣿⣿⣿⣿⢋⣴⠄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿
⠀⠀⠀⠀⢀⣼⠋⠁⢰⡿⢁⣠⡴⢶⣾⡟⠃⠈⠀⠀⢀⣿⣻⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣸⠃⠀⢠⢿⡵⠋⠁⢀⣾⠿⠀⠀⠀⠀⠀⣼⢳⣿⣿⣿⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣿⠀⣰⠋⡞⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⠘⣧⣿⣿⣿⣿⠪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠠⢄⠊⠁⠠⠀⠀⢀⣾⠋⠀⠀⠀⢀⣰⣶⣿⠟⠡⣿⣿⡿⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⣤⣼⠿⠛⢹⡏⠀⠐⠿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⠿⠋⠀⠀⣠⠏⢀⣄⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⣰⠟⠁⢀⡀⠴⠊⣡⡶⠟⠉⣹⡏⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⣰⠟⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⢎⠀⢠⡤⠴⠞⠉⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⠶⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠙⠛⠦⣄⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢱⡀⠀⠀⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣿
⠀⠀⠀⠻⠿⠛⠛⠀⠀⠀⠀⣇⠀⠀⠀⢺⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⢦⣉⠓⠒⠶⠶⢒⡿⠋⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠈⠙⠒⠒⠋⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠖⠒⠒⠒⠲⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢉⡁⢀⡶⢀⡴⠀⢠⠞⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣱⠂⣰⠋⢠⠏⠀⡞⠀⢠⡏⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⢁⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⡤⠖⠛⣏⠁⠈⣇⠀⠀⠸⡍⠉⠹⡗⠦⣄⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠞⠉⠀⠀⠀⠸⡆⠀⢸⡄⠀⠀⢻⠀⠀⢻⠀⡌⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⣧⠀⠀⠘⡇⠀⠸⡇⠙⠸⡆⠈⢧⠀⠀⠀⠀⠀⣠⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡄⠀⠀⢿⠀⠀⣧⠀⠀⣷⠀⠈⣇⠀⢀⣠⠞⢁⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣶⣿⠳⡄⠀⠀⠀⠀⠀⠀⣷⠀⠈⡇⠀⠀⢸⡀⠀⢹⠀⠀⢸⠀⠀⢹⠖⣫⡤⠖⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠻⣿⡴⠃⠀⠀⠀⠀⠀⠀⢹⠀⠀⣷⠀⠀⠸⡇⠀⢸⡄⠀⢸⡆⠀⢸⡆⠐⣒⣛⣉⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣦⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⢸⡀⠀⢻⠀⠀⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠨⢭⣍⣉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡉⠁⠈⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠋⠓⠶⢤⣈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⡇⠀⢸⡇⠀⢸⠇⢠⡏⠀⠀⠀⠀⠈⠙⠦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣀⠀⡇⠀⢸⡇⠀⣸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠐⠦⠄⠀⢸⡇⠀⣾⠀⠛⢰⡇⠀⣸⣥⠖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣙⠓⠶⠤⠼⠤⢤⠿⠤⠴⠞⠛⢋⡁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣀⣆⠀⠳⠄⠙⠦⠀⠙⠂⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠑⠒⠂⠉⠙⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠒⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⢀⠶⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠈⢻⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡀⠀⢀⢀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⣻⣞⣭⣙⡿⣦⣄⠀⠹⣽⣗⢆⠀⠀⠀⠀⠀⠠⣄⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠁⠀⠀⠀⡰
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠋⠉⠉⠈⠉⠛⠲⣽⣷⣄⢱⢟⣿⡇⠀⢀⡴⣯⣟⡿⠋⠉⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠄⠶⠒⠲⠀⠈⢷⣿⡚⣟⣿⣿⣠⣬⣿⡟⠋⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣄⣸⣿⠁⠀⣠⡸⠉⢠⢤⣶⡶⠗⠉⠉⠛⢧⣿⣿⣿⣿⣿⣷⢃⣤⣤⡶⠶⣏⣹⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⣾⠟⠉⢝⣄⡈⠙⡻⣾⣿⣟⣳⣮⡶⠊⠟⣷⠿⠀⠈⠙⣷⣦⠀⢻⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠻⣿⣷⣆⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⡿
⠀⢀⡟⠁⠀⠀⠀⠉⠙⠛⠉⠀⠈⠈⠁⠀⢀⣼⣸⡧⠁⠀⠠⣶⣿⡿⠚⣿⣿⡟⠿⢋⣓⣓⡶⣦⣄⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣀⡼⠃
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡽⠋⠀⠀⣺⡿⠹⠋⢠⣾⣿⣷⣾⡿⠛⠛⢛⣿⣿⣿⣧⣄⠀⠀⠻⣿⣷⣤⢄⣀⣤⣶⡶⠊⡅
⠀⢨⠀⠀⠀⡤⣾⠿⠿⢷⣦⣀⣀⣂⡁⠄⠚⠁⠀⣠⡀⠉⠁⠀⠀⠋⣼⡿⣻⣿⠀⠀⠀⢸⣿⠟⠌⢿⣿⣇⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⣸⠁
⠀⠘⡄⠀⢸⣿⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠄⠋⠀⠀⠀⠀⠀⢰⣿⠿⣉⠏⠀⠀⠀⠈⣿⡻⡞⠈⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠁⠀⠘⣿⡀⠀⠀⠀⠀⢠⠃⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠤⢴⣿⣿⡉⠁⠀⠀⠀⠀⠀⢻⣾⣇⢀⣟⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇
⠀⠀⠀⠀⠐⠌⢻⣦⡀⠤⠔⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⡜⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣈⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠴⣺⠏
⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢷⣧⠄⠀⠀⠀⢀⣴⣘⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⡟⣗⠳⣶⢤⣀⣀⣠⣴⣫⡿⠃
⠀⠈⢂⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠈⢛⠌⠠⠀⣌⢯⣿⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡃⠀⠉⠙⠓⠛⠛⠋⠉
⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠷⢙⢭⡿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠂⠀⠀⠐⠀⠀⠂⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣹⣾⣮⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⣿⣿⣿⣿⣷⣻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⡞⣾⣿⣿⣿⣿⣷⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⣸⣿⣿⣿⣿⣿⣿⣯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣾⣿⣿⣿⣿⣾⣯⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢨⣟⡿⠿⠿⣟⢱⡤⠤⣤⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣴⣿⣿⣿⣿⢸⣿⢧⡙⠷⣦⣽⣆⣀⣠⡴⠟
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠋⣼⣿⣿⣿⢸⡟⠀⢹⣷⣦⣄⡙⠻⠷⣶⣶⣿⠿⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠿⡇⠀⣼⣿⣽⣿⡿⣸⣧⠀⠀⢻⣷⡈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⣼⡏⠀⠇⢰⣿⢹⡿⣿⣇⣿⣿⡇⠀⠘⣿⣧⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢻⡄⠀⠀⣸⡇⢸⣷⣿⣿⠇⢹⣿⠀⠀⣿⣿⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠈⠃⠀⠀⢹⣧⠈⣿⡿⠃⠀⢸⣿⠀⠀⣿⠇⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⢧⠀⠀⢸⣿⠀⠀⡿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠻⣿⡄⠀⠀⠀⠀⢿⠀⠀⠇⠀⠀⠀⠀⠀⣿⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠙⢿⣄⣀⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣶⣿⣿⣄⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠤⡤⢀⡀⠀⠀⠴⠶⢤⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠰⢤⡤⣀⣀⢀⠃⠒⠒⢦⢈⠗⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠘⢩⠏⡧⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠠⣵⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠃⠀⠀⣠⠞⠀⠑⢬⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠆⠀⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡀⠉⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⢀⣿⠗⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⣀⠀⠀⣠⠴⢥⣌⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣆⣀⡀⣸⠵⠓⠲⣄⣹⢾⠈⠉⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⠃⠀⠀⠀⡽⣽⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠨⢤⡍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠠⠀⠂⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣷⣿⣧⠀⣀⠀⢷⠃⠀⠀⠀⠀⡀⠄⠀⠉⡁⠀⢃⣬⡁⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠁⠀⠉⠀⠁⠀⠀⠀⢀⠈⠀⡄⠀⠀⢰⣦⡼⡿⠛⠉⠀⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢰⣶⣴⠿⠛⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠒⠠⠃⠒⠦⠿⠿⠿⠿⠛⢷⣝⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢰⣶⣭⣤⣦⢜⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣄⣤⣶⢲⡗⣏⡽⣻⡟⢿⡻⣿⣾⠦⡍⢻⣯⡙⡟⢻⣷⣤⣀⡁⠀⠀⠄⡀
⠀⠀⣤⡀⣰⣷⡀⠀⣀⢠⣔⣶⣿⠛⣿⡻⢇⢃⡿⣾⠇⣿⢷⣬⡙⣶⢾⣫⡟⠘⠖⠸⠁⠃⠃⢠⠈⠛⣯⣿⣷⣾⣤⣀⡀
⠀⢰⣿⣿⣿⣿⣿⣿⣻⡿⣿⣯⣏⣻⣠⣧⢟⡾⡇⢻⣧⡛⢷⣌⢷⡌⠳⣍⢻⣴⡀⠀⠀⢀⠁⡈⣸⠐⠻⣝⣭⣿⣿⣽⢻⣦⡀
⠀⠘⠻⠿⠛⢿⣿⣿⣯⣿⡿⣛⠍⠉⠡⠍⠘⠀⡇⣤⣝⠿⣠⣽⠀⣧⠀⣸⢧⣯⣽⠖⡠⡄⠐⡡⠋⠀⠀⠙⠳⢿⢿⠿⣕⡌⢻⡄⣆
⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⡧⢦⢧⡼⠧⢾⣿⢷⣿⢶⣤⣀⠀⠐⠀⠀⠄⢢⢂⢨⡻⡆⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣠⣴⡤⠈⠉⠉⠐⠂⠀⠐⠈⠯⠘⠛⠉⠀⠀⠈⠉⠒⠒⠠⡀⠚⡄⡟⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡎⠀⠑⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠤⠎⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⣉⣦⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⠶⠛⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⣠⡴⠞⠋⠉⠀⠀⢀⣀⣤⠶⡞⠋⢉⣹⠆
⠀⠀⠀⠀⠀⠀⢰⡶⢤⣤⣤⣄⠀⠀⣀⣤⠶⠛⣁⡤⠶⠛⠉⠀⠀⢀⣀⣤⠶⠚⠋⣁⣸⡤⠷⠛⠋⠁
⠀⠀⠀⢠⡾⢋⢻⢥⣂⣰⡄⢸⣷⣛⣩⡴⠖⠋⠉⠀⣀⣠⡤⠶⠛⠋⣁⣤⡴⠞⠋⠉
⠀⠀⣰⠏⣤⡍⢊⠀⣉⡙⠙⡄⢸⡏⠁⢀⣠⡤⠶⠛⢉⣡⣤⠶⠚⠋⠉
⠀⠈⢻⡆⢔⣩⠖⢢⡄⠰⣌⣡⡼⠷⠚⢋⣡⣤⠶⠚⠋⠁
⠀⠀⠈⣷⠰⢍⣡⡼⠶⠛⣉⣡⡴⠶⠛⠉⠁
⠀⠀⠀⠈⢻⣏⣥⣶⠾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠸⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣶⠄⣉⣤⣭⣥⣌⡁⢴⡞⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡌⢛⡷⠞⠛⠛⠻⢾⣟⢉⣾⣿⣿⣿
⠀⠀⠀⠀⠦⢀⣾⣿⣿⣿⣿⣿⣿⣆⠠⠆⠀⠀⠀⠀⣿⣿⣿⣿⣟⣻⠏⠀⠀⠀⠀⠀⠀⠙⣿⣻⣿⣿⣿
⠀⠀⠠⣴⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⡤⠀⠀⠀⣿⣿⣿⣛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠍⢛⣻⣿
⠀⠀⠀⠀⣤⠘⣿⣿⣿⣿⣿⣿⣿⡟⢠⡄⠀⠀⠀⠀⣿⣿⣿⣿⣟⣻⡄⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿
⠀⠀⠀⠀⢀⣴⡌⠛⠿⠿⠿⠟⠋⣴⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠇⢹⡦⠄⠀⣀⣠⣴⣟⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠀⠚⠀⢶⠆⠘⠃⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣯⣾⡏⢩⣿⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠈⠀⠀⠀⠀⠀⠀⡒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣷⣴⡁⠔⠐⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⢀⣼⢳⣒⡭⢛⡷⢺⣿⡟⢸⢿⠃⠀⠀⠀⠠⠐⠁⠀⠂⢀⡠⠄⠤⡀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⡴⣽⣺⣎⢻⣭⠏⠑⠤⣠⣇⠿⠿⠶⠤⠤⣀⠁⠀⡀⣄⡤⠊⠀⠀⠀⠐⡀⢠⠀⠈⡀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠐⠐⠉⠁⠀⠈⠓⠳⣽⡗⠣⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⣈⣧⡖⠉⠠⠁⠀⠀⡀⠐⠂⣁⡀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⡠⠒⠁⡀⠐⠀⠂⠀⢀⣄⢠⠬⡁⠂⢇⣀⠀⠀⠀⠀⠀⠠⣠⠊⣠⣤⣤⣈⠃⠤⡆⠁⠀⠀⠀⠀⠙⠀⠀⠇
⠀⠀⠀⠁⠀⠀⡄⠁⠀⠀⠈⠁⣾⠆⠀⢧⠘⠚⣀⠇⠀⢀⣀⠉⠂⢀⡀⠀⠀⠃⠀⠈⠀⠀⠉⠀⠀⠈⡄
⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠓⠊⠀⠀⠀⠈⠂⠰⣆⠀⠀⠀⠀⠀⠶⣛⠀⢠
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⡀⠀⠸⡱⠀⠀⠀⢀⠀⠀⠀⡤⠒⠒⠦⡀⠔⢢⠀⠀⠈⠢⣐⠲⠶⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠣⠞⡵⠀⡸⠈⠁⠀⠀⠀⠀⠀⠙⠈⣁⠄⠂⠁⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⠠⠴⠀⢉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠔⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡞⠀⠀⢀⡤⠀⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢠⣖⣁⡄⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠉⠀⠀⠀⣴⢠⣽⣷⠃⠀⣠⠞⠁⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣀⡠⠞⠁⠀⠀⢀⡤⠚⠁⠀⢀⡤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡠⢘⡿⣤⣤⠂⠀⠀⡴⠋⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣴⢋⠔⡩⡶⢶⠀⡾⠁⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⡏⡴⢀⡇⣿⠻⠃⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⢠⠟⡥⣯⣷⡜⠳⠄⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠔⠬⠒⢀⣼⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⡀⠈⣷⣄⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⣼⣿⣷⠀⣿⣿⣿⠃⠀⠀⣶⠀⠀⠀⠀⣀⣴⣶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣶⣦⣌⢿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⡏⢀⣠⣾⣿⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⢠⣄⣀⠀⢀⣀⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣇⣤⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣀⡈⢻⣿⣿⢟⣯⣶⣿⣿⣿⣿⣿⣷⣾⣝⠿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⡟⠉⠀⠀⢀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣽⣿⡿⣼⣿⣿⣶⣶⣦⣝⣿⣿⠿⢛⣛⠻⢿⣿⣎⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠿⣿⣿⣿⣧⣿⣿⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢸⣿⣿⣋⣉⣀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣟⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠛⠉⣩⣵⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠉⠁⠀⠀⣼⣿⣿⠿⠿⣻⣿⣮⣝⡻⢿⣿⣿⣿⣿⡿⢟⣫⣾⣿⣿⣿⡿⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⡏⠙⢿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⣿⣿⣿⡏⣿⣿⣿⡟⣿⣿⣇⠀⠈⠻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⣿⣿⠏⠀⣿⣿⣿⡇⠈⠻⣿⣄⡀⠀⠈⠛⠛⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠘⣿⠀⠀⢿⣿⣿⣧⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠉⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟